Optical Properties of Solar Absorber Materials and Structures (Topics in Applied Physics, 142) 9811634912, 9789811634918

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Topics in Applied Physics 142

Liang-Yao Chen   Editor

Optical Properties of Solar Absorber Materials and Structures

Topics in Applied Physics Volume 142

Series Editors Young Pak Lee, Physics, Hanyang University, Seoul, Korea (Republic of) David J. Lockwood, Metrology Research Center, National Research Council of Canada, Ottawa, ON, Canada Paolo M. Ossi, NEMAS - WIBIDI Lab, Politecnico di Milano, Milano, Italy Kaoru Yamanouchi, Department of Chemistry, The University of Tokyo, Tokyo, Japan

Topics in Applied Physics is a well-established series of review books, each of which presents a comprehensive survey of a selected topic within the domain of applied physics. Since 1973 it has served a broad readership across academia and industry, providing both newcomers and seasoned scholars easy but comprehensive access to the state of the art of a number of diverse research topics. Edited and written by leading international scientists, each volume contains highquality review contributions, extending from an introduction to the subject right up to the frontiers of contemporary research. Topics in Applied Physics strives to provide its readership with a diverse and interdisciplinary collection of some of the most current topics across the full spectrum of applied physics research, including but not limited to: • • • • • • • • • • •

Quantum computation and information Photonics, optoelectronics and device physics Nanoscale science and technology Ultrafast physics Microscopy and advanced imaging Biomaterials and biophysics Liquids and soft matter Materials for energy Geophysics Computational physics and numerical methods Interdisciplinary physics and engineering

We welcome any suggestions for topics coming from the community of applied physicists, no matter what the field, and encourage prospective book editors to approach us with ideas. Potential authors who wish to submit a book proposal should contact Zach Evenson, Publishing Editor: [email protected] Topics in Applied Physics is included in Web of Science (2019 Impact Factor: 0.633), and is indexed by Scopus.

More information about this series at http://www.springer.com/series/560

Liang-Yao Chen Editor

Optical Properties of Solar Absorber Materials and Structures

Editor Liang-Yao Chen Department of Optical Science and Engineering Fudan University Shanghai, China

ISSN 0303-4216 ISSN 1437-0859 (electronic) Topics in Applied Physics ISBN 978-981-16-3491-8 ISBN 978-981-16-3492-5 (eBook) https://doi.org/10.1007/978-981-16-3492-5 © Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Energy supply and environmental conservation are certainly among the most challenging problems that we and future generations will be faced with. Solar energy, as a renewable and plentiful energy resource on our planet, can provide an eventual solution for the energy demands of our society. There are mainly two solar energy utilization methods: solar-to-electric conversion and solar-to-thermal conversion. Solar-to-electric conversion has been widely studied around the world. Nevertheless, according to the detailed balance limit theory, the efficiency limit will be about 30% for a single-junction solar cell with about 70% of the incident sunlight wasted to degenerate the performance of the solar cell. In comparison, solar thermal conversion is the simplest and most direct method of harnessing solar energy, which can absorb more than 95% of the incident solar radiation. Solar thermal utilization was developed slowly until the significant breakthrough brought in the 1950s by Tabor who proposed the concept of solar selective absorber, which can absorb the sunlight more efficiently and suppress the infrared radiation in the long-wavelength range, and opened a new area of high performance of solar absorbers. After decades of efforts from scientists and engineers working around the world, different materials and structures have been proposed to serve as the high efficient solar selective absorbers. Many works are published to describe and review the structures, mechanisms, and applications of different solar absorbers. However, there is still an urgent need for a book to provide a fundamental understanding of optical properties of solar absorber materials and structures, beginning from the most fundamental Maxwell theory, the optical constants and optical properties of different materials, to the structure design, fabrication, and measurements. This group of people who have been working together through international cooperation to conduct researches in the field of solid-state optics, thin optical films, solar absorbers, and instrumentation for many years, therefore, try to write the book based on research experience and knowledge background. There are 13 chapters in this book. In Chap. 1, the introduction part of solar thermal conversion system is given. Section 2 discusses the conventional electromagnetic theory, while Sect. 3 focuses on the optical properties of solar materials. Optical characterization parameters for solar absorbers are outlined in Sect. 4. In Sects. 5–10, six typical solar selective absorbers v

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Preface

are discussed and summarized. The fabrication and measurement methods of solar absorbers are described in Sects. 11 and 12, respectively, while their applications are presented in Sect. 13. We hope that the book will serve as an important resource for the scientific community, new generations of researchers, and industry experts to stimulate the burgeoning development of solar absorbers and their applications that will benefit our human society supported by the green and sustainable energy resource in the long run of future. Shanghai, China

Liang-Yao Chen

Acknowledgements This book was supported by the National Natural Science Foundation of China (Nos. 61427815 and 61274054).

Contents

Optical Properties of Solar Absorber Materials and Structures . . . . . . . . Er-Tao Hu, Kai-Yan Zang, Jing-Ru Zhang, An-Qing Jiang, Hai-Bin Zhao, Yu-Xiang Zheng, Song-You Wang, Wei Wei, Osamu Yoshie, Young-Pak Lee, Jun-Peng Guo, David W. Lynch, and Liang-Yao Chen 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Conventional Electromagnetic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Maxwell’s Equations and the Dielectric Function . . . . . . . . . . . . . 2.2 Light Propagation in the Solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Reflection and Refraction of Light at the Interface . . . . . . . . . . . . 2.4 Optical Absorption of the Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Thermal Emittance of the Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Optical Properties of the Solar Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Photon-To-Electron Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Interband Transitions Based on Lorentz Model . . . . . . . . . . . . . . . 3.3 Free Electron Absorption Based on the Drude Model . . . . . . . . . . 3.4 Effective Medium Approximation Models . . . . . . . . . . . . . . . . . . . 3.5 Optical Constants of Metals and Dielectric Media . . . . . . . . . . . . . 3.6 The Extraction of Optical Constants of Refractive Index and Extinction Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Optical Characteristic of the Solar Absorbers . . . . . . . . . . . . . . . . . . . . . . . 4.1 Spectrally Weighted Broadband Solar Absorption . . . . . . . . . . . . . 4.2 Thermal Gain and Loss of the Infrared Absorption and Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Optical Evaluation of the Solar Absorbers . . . . . . . . . . . . . . . . . . . 5 Intrinsic Solar Selective Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Semiconductor–metal Tandems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Metal-Dielectric-Based Multilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Metal-Dielectric-Composited Cermets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Nano-Textured Surface Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2 13 13 17 21 27 30 32 32 33 35 36 38 40 45 45 46 48 50 53 56 66 76

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10 Photonic-Crystal-Based Metamaterials and Designs . . . . . . . . . . . . . . . . . 10.1 The Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Preparation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Recent Researches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Fabrication of Solar Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Electron Beam Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Sputtering Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Pulsed Laser Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Experimental Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Interferometric Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Principle of Integrating Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 Measurement of Reflectance and Absorbance . . . . . . . . . . . . . . . . 12.5 Measurement of the Thermal Emittance . . . . . . . . . . . . . . . . . . . . . 12.6 Radiation Energy Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.7 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Broad Applications of Solar Selective Absorbers . . . . . . . . . . . . . . . . . . . . 13.1 Temperature-Dependent Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Effect of Low and High Solar Concentrations . . . . . . . . . . . . . . . . 13.3 System Evaluation of the Solar-To-Thermal Conversion Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 Thermal Energy Extraction Apparatus . . . . . . . . . . . . . . . . . . . . . . . 13.5 Solar Thermophotovoltaics (STPV) and Solar Thermoelectric Generators (STEGs) . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84 84 90 91 93 99 100 102 106 109 109 113 114 116 123 128 134 134 135 137 138 139 147 150

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Contributors

Liang-Yao Chen Department of Optical Science and Engineering, Fudan University, Shanghai, China Jun-Peng Guo Department of Electrical and Computer Engineering, University of Alabama in Huntsville, Huntsville, AL, USA Er-Tao Hu Department of Optical Science and Engineering, Fudan University, Shanghai, China; College of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing, China An-Qing Jiang Graduate School of IPS, Waseda University, Fukuoka, Japan Young-Pak Lee Department of Optical Science and Engineering, Fudan University, Shanghai, China; Department of Physics, Hanyang University, Seoul, Korea David W. Lynch Department of Physics, Iowa State University, Iowa, USA Song-You Wang Department of Optical Science and Engineering, Fudan University, Shanghai, China Wei Wei College of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing, China Osamu Yoshie Graduate School of IPS, Waseda University, Fukuoka, Japan Kai-Yan Zang Department of Optical Science and Engineering, Fudan University, Shanghai, China Jing-Ru Zhang Department of Optical Science and Engineering, Fudan University, Shanghai, China Hai-Bin Zhao Department of Optical Science and Engineering, Fudan University, Shanghai, China Yu-Xiang Zheng Department of Optical Science and Engineering, Fudan University, Shanghai, China ix

Symbols and Abbreviations

AC A(D, ρ) Aj B B1 B2 C Cg Cm cmax c D D1 D2 Dθ Dl D DC d E E1 E1  E2 E1s E1s  E2s E1p E1p  E2p Ei

Alternating Current Integrating sphere constant Oscillator strength of the jth oscillator Magnetic flux density or magnetic induction Magnetic flux density or magnetic induction in media 1 Magnetic flux density or magnetic induction in media 2 Optical solar concentration ratio; capacitance Capacitance of air gap Capacitance of parallel plate sandwiching the dielectric film Maximum Courant number Light speed in vacuum Electric displacement vector Electric displacement vector in media 1 Electric displacement vector in media 2 Angular dispersion power Line dispersion power Diameter of the integrating sphere Direct current Penetration depth; thickness; distance between the parallel plate; grove space constant of the grating Electric field vector Electric field vector of the incident light in media 1 electric field vector of the reflective light in media 1 Electric field vector in media 2 Electric field vector of the incident light in s-polarization Electric field vector of the reflected light in s-polarization Electric field vector of the transmitted light in s-polarization Electric field vector of the incident light in p-polarization Electric field vector of the reflected light in p-polarization Electric field vector of the transmitted light in p-polarization Electric field vector of the incident light xi

xii

Er Et E loc E EW E0 En Es eλ f fj fa fA G H H1 H2 H 1s H 1s  H 2s H 1p H 1p  H 2p h H abs I Ii Ir It Is I bλ I0 Ip In i j j Je k k1 k1  k2 k˜

Symbols and Abbreviations

Electric field vector of the reflective light Electric field vector of the refractive light Local electric field Amplitude of electric field; brightness; irradiance of the thermal radiation or total power incident on the unit area of the object Illuminance measured by the detector Direct illumination Additional illumination Total illuminance Orthogonal unit vector Focal length of the focusing mirror Fraction of the jth constituent Volume fraction of material a Filling fraction of constituent A Reciprocal vector Magnetic field vector Magnetic field vector in media 1 Magnetic field vector in media 2 Magnetic field vector of the incident light in s-polarization Magnetic field vector of the reflected light in s-polarization Magnetic field vector of the transmitted light in s-polarization Magnetic field vector of the incident light in p-polarization Magnetic field vector of the reflected light in p-polarization Magnetic field vector of the transmitted light in p-polarization Planck constant; hour; height of metallic strip Sunlight energy incident on the solar absorber Time-average magnitude of the Poynting vector; light intensity Intensity of the incident light Intensity of the reflected light Intensity of the transmitted light Dolar intensity Planck’s blackbody radiation intensity Incident light intensity; sum of the intensities for non-interference light waves Intensity of the polarized light in the p direction Intensity of the polarized light in the n direction Incidence angle; Spectral distribution function Electric current density The jth oscillator Emission current density Wave vector or wave number Wave vector of the incident light Wave vector of the reflective light Wave vector of the refractive light Complex wave vector

Symbols and Abbreviations

K k k  kB L L sun (λ) L(λ) L b (λ, T ) L b (υ, Te ) L(λ,Te ) Lm Le l M M m m* n12 N Na Nb N1 Nr n n˜ n1 n2 ng P P Q qh qc qrad qconv r RF R R0 R(0, λ) R(λ)

xiii

Kelvin; reflected times Real part of k˜ or propagation constant Imaginary part of k˜ or attenuation constant Boltzmann constant Inductance; illuminance Standard solar radiation spectrum Spectral radiance of the spectrometer Spectral radiance of a black body per unit area, per unit solid angle and per unit wavelength Spectral radiance of a black body per unit area, per unit solid angle and per unit frequency Spectral radiance of a black body at ambient temperature Te Inductance of metallic strips Inductance excited by drift electrons Length of the loop Magnetization Number of measured ellipsometric parameters Mass of electron; Diffraction order Electron effective mass Normal unit vector pointing from medium 1 to medium 2 Number of electrons per unit volume; Total number of diffractive lines Number of electrons in material a Number of electrons in material b Complex refraction index of film 1 Complex refraction index of film r Refractive index; Diffraction order; number of high-speed electrons incident on the source material per unit time Complex refractive index Refractive index in media 1 Refractive index in media 2 Refractive index of the non-absorbing substrate Polarization Number of fitting parameters; output power of the black body Converted heat Heat flux Waste heat Radiative heat Convective heat losses Position vector Radio frequency Reflectance; lattice constant; radiated power or emittance power of the object unit area; resolution power Measured reflectance of the uncoated substrate Opitcal Reflectance of the absorber at normal incidence Response function of the spectrometer

xiv

R1 Rcalc Rf r rs rp (r, θ, ϕ) S S S(λ) S B (λ) S s (λ) T T Th T amb Te Tcalc T0 TC TH t ts tp U Vb (λ, T ) Vs (λ, T ) ν ν˜ W W’ w Y Z ZC ZL Z total ZT ZT α αa αb αs γ

Symbols and Abbreviations

Reflectance of the film on the substrate Calculated reflectance Reflectance of the reference sample Reflection coefficient Reflection coefficient of the s-polarized light Reflection coefficient of the p-polarized light Spherical coordinates Poynting vector Seebeck coefficient Background function Output response of the spectrometer Output response of the spectrometer Transmittance; temperature Temperature difference Temperature of solar absorber temperature Temperature of the environment around the solar absorber Ambient temperature Calculated transmittance Measured transmittance of the uncoated substrate Hot-side temperature Cold-side temperature Time; transmission coefficient Transmission coefficient of the s-polarized light Transmission coefficient of the p-polarized light Accelerating voltage Radiant energy of the black body at the temperature T Radiant energy of the sample at the temperature T Speed of the electromagnetic field Speed of the electromagnetic field in a complex form Power carried by the high-speed electrons Width of the m-th order of the diffracted beam Weighting factor; Width of metallic strip Optical admittance Impedance Impedance of capacitance Impedance of inductance Total impedance Thermoelectric figure of merit average thermoelectric figure of merit Absorbance; solar absorptance; polarizability Polarizability of material a Polarizability of mateiral b Absorbance of the sample Factor related to the screening and the shape of the inclusions; factor related to the effective cross-sectional area of the metal grating

Symbols and Abbreviations

δ δθ ε ε λ ελ ε˜ (ω) εs ε∞ ε1 ε2 εi εa εb  ε2  ε2 εA εB εBR εMG εambient εsubstrate ε˜ r εh εd ηabs ηC ηT E G θ θ1  θ1 θ2 θc κ κt λ λt λM λ1 λn μ υ ρ0 ρ

xv

Phase difference Angular width Thermal emittance of the solar absorptance; permittivity Spectral directional emittance Radiation emissivity or the specific emissivity Permittivity in a complex form Dtatic permittivity; emissivity of the sample Dielectric function at the infinitive high frequency limit Permittivity of media 1; real part of dielectric function Permittivity of media 2; imaginary part of dielectric function Dielectric functions of the film i Dielectric function of material a Dielectric function of material b; emissivity of the black body. Real part of dielectric function in media 2 Imaginary part of dielectric function in media 2 Dielectric function of material A Dielectric function of material B Average dielectric function of the composite in Bruggeman approximation Average dielectric function of the composite in Maxwell-Garnet approximation Dielectric functions of the ambient Dielectric functions of the substrate Relative permittivity in a complex form Dielectric function of the host material Permittivity of the dielectric film Solar-thermal conversion efficiency Carnot efficiency Thermal electric conversion efficiency Polar angle; diffraction angle Incident angle Reflected angle Refractive angle Critical angle Extinction coefficient Thermal conductivity Wavelength Transition wavelength Wavelength corresponding to maximum radiative power Shortest wavelength of the solar radiation Longest wavelength of the solar radiation Permeability Frequency Density of free electrons Electric charge density; ratio between the r p and r s ; reflectance

xvi

ρS ρs ρs ρi ρs (λ) ρ B (λ) ρsn σ σ SB τ χm χe φ ϕ ϕ0 ω ω0 ωp ωMR Γ Γp Δ L V λF  x y Ψ

Symbols and Abbreviations

Reflectance Diffuse reflectance Specular reflectance Reflectance of the inner wall coating Reflectivity of the solar sample Spectral reflectance of a reference standard Vertical emissivity Electric conductivity Stefan-Boltzmann constant Average life time of the electrons; life time or relaxation time of free electrons Magnetic susceptibility Electric susceptibility Azimuthal angle; phase of wave Work function Initial phase Angular frequency Resonant frequency Plasma frequency Magnetic resonance frequency Damping coefficient or Lorentz broadening constant Damping factor Ellipsometric parameters Optical path difference Voltage difference Free spectral range Period Period in x direction Period in y direction Ellipsometric parameters

Optical Properties of Solar Absorber Materials and Structures Er-Tao Hu, Kai-Yan Zang, Jing-Ru Zhang, An-Qing Jiang, Hai-Bin Zhao, Yu-Xiang Zheng, Song-You Wang, Wei Wei, Osamu Yoshie, Young-Pak Lee, Jun-Peng Guo, David W. Lynch, and Liang-Yao Chen

Abstract As the key approach to enhance the efficient application of solar energy, solar selective absorbers have been extensively investigated in the past years. With great efforts contributed by scientists and engineers all around the world, new materials and excellent structures were achieved in solid progress to stimulate applications in broad fields. In this book, we will present an overview of both theory and experimental methods to fulfill the high-efficiency solar absorber devices. It begins with a historical description of the study and development for the spectrally selective solar absorber materials and structures based on the optical principles and methods in past decades. The optical properties of metals and dielectric materials are addressed to provide the background on how to realize high performance of the solar absorber devices applied in the solar energy field. In the following sections, different types of materials and structures, including the experimental methods, are discussed for practical construction and fabrication of the solar absorber devices, aiming at maximally harvest the solar energy, at the same time to suppress the heat-emission loss effectively. The optical principles and methods used to evaluate the performance of E.-T. Hu · K.-Y. Zang · J.-R. Zhang · H.-B. Zhao · Y.-X. Zheng · S.-Y. Wang · Y.-P. Lee · L.-Y. Chen (B) Department of Optical Science and Engineering, Fudan University, Shanghai, China e-mail: [email protected] E.-T. Hu · W. Wei College of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China A.-Q. Jiang · O. Yoshie Graduate School of IPS, Waseda University, Fukuoka, Japan Y.-P. Lee Department of Physics, Hanyang University, Seoul, Korea J.-P. Guo Department of Electrical and Computer Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA D. W. Lynch Department of Physics, Iowa State University, Iowa, USA © Springer Nature Singapore Pte Ltd. 2021 L.-Y. Chen (ed.), Optical Properties of Solar Absorber Materials and Structures, Topics in Applied Physics 142, https://doi.org/10.1007/978-981-16-3492-5_1

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solar absorber devices with broad applications in different physical conditions are presented. The book will be suitable for graduate students in applied physics fields with valuables reference also for the researchers working actively in the solar energy fields.

1 Introduction Energy plays the most fundamental and essential part of roles in human society, in which nearly all of the achievements and activities made by human beings have to be sustained in terms of using energy. The energy demand is increasing rapidly, with the cursrent average global energy consumption about 15 TW and rising to 30 TW by 2050 [1]. The significant increasing of energy consumption has led to the excessive use of fossil fuels, resulting in the side-effect problems of air pollution and global warming to make serious deterioration of the natural environment condition. Efficient utilization of new and renewable energy resources, which is sustainable and environmental friendly as compared to tranditional energy resources, is increasingly being considered as a promising solution to the sustainable development of society for human beings [2]. Among the various renewable energy technologies, solar energy has emerged as the best choice because of the advantages such as great abundance, sustainability, and having benign effect on the environment, which can be produced on a larger scale at a comparatively lower cost than other renewable energy resources [2]. The average rate of solar radiation energy reaching the upper atmosphere of the earth is about 174 PW (1 PW = 1015 W), dwarfing other renewable or nonrenewable energy sources. Even if the solar radiation will be attenuated by both the atmosphere and clouds, there is still 51% (89 PW) of the total incoming solar radiation that can reach the land and oceans [3], which can satisfy the ever-increasing energy demand of human beings if the incident solar radiation can be fully utilized. The global solar resource distribution is shown in Fig. 1 [4]. Though solar energy available on the earth is of an enormous amount, it needs to be collected and stored efficiently due to its low density and intermittency. Solar radiation on the earth usually will be converted naturally into three forms of energy: electricity, chemical fuel, and heat [5]. (1)

For the solar-electric conversion (also called as photovoltaic: PV), it is based on the principle of converting the solar-induced photons into electricity by a photon absorption process in which the electron–hole pairs are generated in a solar cell. Si-wafer-based PV technology accounted for about 95% of the global solar cell production in 2017 [6], while its PV modules in usual applications convert only 12–18% of the incoming radiation into electricity, leading to more than 80% of solar radiation being converted to heat or reflected back [7]. This dissipated solar energy will deteriorate the performance of the solar cell due to overheating.

Optical Properties of Solar Absorber Materials and Structures

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Fig. 1 Global horizontal solar irradiation distribution [4]

(2)

(3)

For solar fuel conversion, the solar energy can yield chemical fuel via natural photosynthesis in green plants or artificial photosynthesis in human-engineered systems. For solar thermal conversion processes, heat can be generated by efficiently absorbing the incident solar photons from the solar radiation with wide applications such as solar water heating system [8], solar thermal electricity generation power station [9–11], and solar desalination [12–15].

Besides, solar thermoelectrics [16–18] and solar thermophotovoltaic [19–21] are also actively studied. The applications of solar thermal conversion process are shown in Fig. 2. One of the primary advantages of solar thermal conversion compared with other solar energy utilization technologies is that they can store thermal energy for later electricity generation [4, 9]. A typical solar thermal conversion system is presented in Fig. 3 [8]. In such solar thermal technologies, the sunlight incident on the absorber (H abs ) is converted into a heat flux (qh ) and delivered to the thermal system to produce the desired output (work, electricity, heat, cooling, etc.), accompanied by a waste heat (qc ) produced in the process. Radiative (qrad ) and convective (qconv ) heat losses at the surface will reduce the output energy of the system. This process is most efficient when the absorber strongly absorbs the most amount of the incident sunlight while losing ideally little heat in the way of application via convection and radiation process. The absorber surface with strong solar absorptance and low infrared emittance is called a spectrally selective absorber, which is the most critical factor to be concerned in the solar thermal conversion system. It has the function to separate two parts between the wavelengths containing most of the incoming solar energy and the wavelengths carrying most of the blackbody radiation for a device at the designed operating temperature [4, 22]. Surface temperature on the sun can be considered to be about 5500 °C, while any realistic terrestrial applications will work at much

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Fig. 2 Applications of solar thermal conversion process: a evacuated tube solar water heater, b flat plate solar collectors, c Parabolic dish concentrator, d Parabolic trough collector, e Central solar power plants, f Solar desalination, g Schematic diagram of solar thermoelectrics, h Solar thermophotovoltaic, and i Schematic diagram of solar thermophotovoltaic Fig. 3 A typical solar thermal energy conversion system [8]

Optical Properties of Solar Absorber Materials and Structures

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lower temperature conditions, resulting in a large gap between the regimes where high absorptivity and low emissivity are required, and making the design of solar selective absorber feasible in physics. The conversion efficiency of incident solar photons at the absorber is defined as ηabs [8, 9, 22]: ηabs = α −

4 ) qconv (Th − Tamb ) εσ S B (Th4 − Tamb − C Is C Is

(1.1)

where σSB is the Stefan-Boltzmann constant, T h is the absorber temperature, T amb is the environment temperature, C is the optical solar concentration, I s is the solar intensity (W/m−2 ), qconv is the convectional loss. α and ε represent the solar absorptance and thermal emittance, respectively, which can be formularized as:  ∞  2π  π/2 ’ ε (λ, φ, θ )Is (λ, φ, θ )cosθ sinθ dλdθ dφ (1.2) α = 0 0 ∞ 0 2π λ π/2 0 0 0 Is (λ, φ, θ )cosθ sinθ dλdθ dφ  ∞  2π  π/2 ’ ε (λ, φ, θ )Ibλ (λ, φ, θ )cosθ sinθ dλdθ dφ ε = 0 0 ∞ 0 2π λ π/2 (1.3) 0 0 0 Ibλ (λ, φ, θ )cosθ sinθ dλdθ dφ where λ is the wavelength of radiation, φ is the azimuthal angle, θ is the polar angle, ελ  is the spectral directional emittance at the operational temperature and I b is the Planck’s blackbody radiation intensity. If the solar absorber is encapsulated in a vacuum apparatus, the convectional loss qconv can be ignored, resulting in the disappearance of the last term in Eq. (1.1) [8, 9, 22]: ηabs = α −

  4 εσ Th4 − Tamb = α − wε C Is

(1.4)

σ T 4 −T 4 where w= ( hC Is amb ) is the weighting factor between the solar absorptance and thermal emittance which is dependent on the optical solar intensity CI s and working temperature T h as illustrated in Fig. 4. When w is close to 1, the solar absorptance and thermal emittance are equally important for absorber efficiency. While the value of w is much smaller than 1, the solar absorptance will become the critical parameter [8]. The ideal solar selective absorber should have a spectral radiation pattern like a step-function as shown in Fig. 5 [4, 8, 22], in which the emittance will have the values of 1 and 0 in the short- and long-wavelength regions, respectively, with a steep spectral transition between the two regimes. The transition wavelength λt is defined as the wavelength of the blackbody intensity exceeding the solar intensity,

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Fig. 4 The weighting factor as a function of surface temperature for different incident solar intensities

Fig. 5 The power density of the standard AM1.5 solar radiation spectrum by solid blue line, the reflectance spectrum of the ideal selective solar absorber by dashed black line, the reflectance spectrum of the real selective solar absorber by solid red line, the power densities of Planck’s blackbody radiation at different temperatures indicated by dashed pink, yellow, and green lines, respectively [11]

Optical Properties of Solar Absorber Materials and Structures

7

which is dependent on the absorber temperature T h and optical solar concentration C [8]. In the real situation, the transition region changes gradually [23–27], leading to the thermal emittance with a value higher than the ideal one in most application conditions. For solar absorbers, there are mainly two types of absorption mechanisms for the absorption of incident solar radiation: (a) intrinsic absorption and (b) interferenceenhanced absorption [7]. For intrinsic absorption, the extinction coefficient κ, presenting the wavelength-dependent imaginary part of the complex reflective index of the material, is a measure index of the energy absorbed by solar materials [4]. In terms of the interference-induced absorption, it depends on the refractive index n and thickness of the film as well as the substrate properties [7]. Hence, the optical constants of solar absorber materials should be specially considered to design the solar selective absorber. By combining both of the absorption mechanisms, different types of solar selective absorbers have been proposed. Based on their construction and working mechanism, solar selective absorbers can be mainly categorized into six types [4, 7, 11, 22, 28] as illustrated in Fig. 6. (1)

(2)

Intrinsic absorbers: An intrinsic absorber uses a single material with intrinsic spectral selectivity, which is mostly found in transition metals and semiconductors [4] including metallic W [29], MoO3 -doped Mo, Si doped with B, CaF2 , HfC, ZrB2 [30], SnO2 , In2 O3 , Eu2 O3 , ReO3 , V2 O5, and LaB6 [28]. The most intrinsic absorbing materials are structurally stable, but usually far from the ideal solar selectivity. Hence, intrinsic absorbers are always combined with other absorption designs to enhance the solar selectivity. Semiconductor-metal tandems: Semiconductor-metal tandems mainly consist of semiconductor on top of a metal layer. Semiconductor with band gaps from 0.5 to 1.5 eV, corresponding to absorption edges from about 2.5 to 0.8 μm, can absorb the short-wavelength solar radiation in the visible and near-infrared

Fig. 6 Schematic diagram of six typical solar selective absorbers

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regions and transmit the long-wavelength radiation. Then, the transmitted solar radiation will be reflected back by the underlying metal layer to restrain the emission from the heated substrate. The interested semiconductors include Si (1.1 eV), Ge (0.7 eV), and PbS (0.4 eV) [4, 22]. For semiconductor–metal tandem-based solar selective absorbers, the transition region of the reflectance spectra from the low to high value is very sharp because only the incident solar photons with energy larger than the band gap can be absorbed by the semiconductor, which will lower the thermal emittance of the solar absorber [31]. However, most of the semiconductor materials have high refractive indices, resulting in higher reflectance losses. Hence, an anti-reflection layer should be added [4]. On the other hand, due to the instability of semiconductors at high temperature [32], diffusion barrier or protection layers are required. Multilayer absorbers: Multilayer solar absorbers consist of alternating layers of antireflective, dielectrics, semi-transparent metal, and metal reflection layers as shown in Fig. 6c. Interference-induced absorption is dominant in this type of absorber. A particular range of solar radiation can experience enhanced absorption when the incident solar beams are multiple-reflected between the semi-transparent metal layer and metal reflection layer, which can be referred to as destructive interference effect [4]. The metal reflection layer is designed to reflect infrared radiation to reduce the heat loss from the heated substrate. For multilayer solar selective absorber, film thickness for each layer can be optimized based on the transfer matrix method [33, 34]. Nevertheless, optical constants for the constituted metal and dielectric film must be known in advance. Fortunately, optical constants of most metal and dielectric materials have been measured and summarized in the database [35]. Different dielectrics (Al2 O3 , SiO2 , AlN, CeO2 , Si3 N4 , MgF2, etc.) and metals (Al, Mo, Ag, Cu, Co, Fe, Pt, Cr, Ti, Ni, Au, etc.) have been numerically simulated to be used as IR-reflection, absorption, transparent dielectric layer in the multilayered metal/dielectric film structure [4, 36]. Due to the high fabrication cost in the past [4, 7], the multilayered technique developed slowly until recent years due to advanced progress of the physical vapor deposition (PVD) technologies as shown in Fig. 7 [37–40]. Various multilayer solar selective absorbers have been proposed such as SiO2 /Ti/SiO2 /Al [26], Alx Oy /Al/Alx Oy /Cu [41], SiO2 /Cr/SiO2 /Al [42], Cu/TiAlCrN/TiAlN/AlSiN [43], SS/TiAlN/TiAlSiN/Si3 N4 [44]. Transition metal nitride and oxynitride have been adopted to improve the thermal stability of the multilayered absorber, making it suitable for the middle- and high-temperature applications [45]. In addition, Mo interlayer [46] or Ta diffusion layer [47] was employed to overcome the thermal degradation issue in multilayer solar selective absorbers as well. Thin-film multilayer absorbers with the fabrication process compatible with PVD to have good high-temperature stability will have the potential for commercial applications [9, 39]. Cermet absorbers (metal-dielectric composites): A cermet is a metal-dielectric composite in which metal particles are embedded in the dielectric matrix of an

Optical Properties of Solar Absorber Materials and Structures

9

Fig. 7 PVD machine at an industrial scale that can fabricate multilayer films on large scale with substrates in different shapes (tubular, flat, and massive substrates) [38–40]

oxide, nitride or oxynitride. The cermet films are transparent in the thermal IR region, while they are strongly absorptive in the solar region because of interband transitions in the metal and small particle resonance [28]. A good selective surface with high solar absorptance and low thermal emittance can be achieved when the cermet layer is deposited on a highly reflective mirror. The solar selectivity can be optimized by properly controlling the constituents, metal volume fraction in the matrix, as well as particle size, shape, and orientation to tune optical constants of the metal-dielectric composites [48–50], which can affect strongly the ceramic

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Fig. 8 Schematic designs of three different cermet-based solar selective absorbers: (1) metal pigmented porous alumina solar absorbers, (2) graded cermet, and (3) double-cermet-layered film structure. [4, 28]

or metallic characteristics as expressed across the solar and IR spectra [51]. The cermet materials systems, including Cr2 O3 , Al2 O3 , AlN, and SiO2 as the ceramic matrix [9], and Cr, Ni, Mo, W, SS, Al, and some noble metals as metallic mirrors, have been investigated for the cermet-based solar selective absorbers [8, 37]. There are mainly three categories for cermet-based solar selective absorbers: (1) metal pigmented porous alumina solar absorbers, (2) graded cermet, and (3) double-cermet-layered film structure as presented in Fig. 8 [4, 28]. For the first category of the structures, it is usually obtained from the anodization of aluminum, which consists of a metal pigmented porous alumina layer on top of a compact barrier layer [52]. Ni, V, Cr, Co, Cu, Mo, Ag, and W, etc., are often used as the pigmented metals, with the rod-like particle in diameter of about 30– 50 nm and long about 300 nm [28]. Except for the rod-like metal particle, the self-assembly aluminum nanoparticles with a diameter of about 12 nm were also adopted to form a plasmonic solar absorber [12]. Due to the impedance mismatch with the AR coating, a single homogeneous cermet film usually show low solar selectivity itself. Hence, a graded cermet solar absorber with gradually decreased metal concentration from the bottom of the film to the top is proposed [53, 54]. Then, the refractive index increases with depth from the surface to the base of the film, resulting in a great improvement of the solar absorptance. In the fabrication of a graded cermet film, the deposition rate for metal inclusions should be continuously varied, which will greatly increase the fabrication cost and complexity [54]. A much easier solution is a double-cermetlayered film structure that consists of two layers in which a low metal volume fraction (LMVF) layer is deposited on a high metal volume fraction (HMVF) layer [55], resulting in an internally effective absorption of solar radiation by phase

Optical Properties of Solar Absorber Materials and Structures

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interference effect [4, 28]. This double-cermet-layered film structure is one of the hottest study direction in consideration of its high-temperature durability and high performance as well as being suitable for large-scale fabrication. Nevertheless, completely understanding the optical properties of the cermets is still a research issue due to the difficulty in predicting the exact performance of cermets by using the model alone [9, 50, 56]. Surface texturing: By properly texturing surfaces using dendritic, porous, granular or needle-like microstructures, it’s possible to produce high solar absorptance in the short wavelength region, either via multiple reflections inside the structures or by providing a more gradual gradient in refractive index, without increasing the absorption for longer wavelengths [9, 57–59]. The textured surfaces should appear rough for short-wavelength photons to absorb solar energy while appearing highly reflective and mirror-like to the thermal energy in the long-wavelength region. The desirable textured surface can be achieved with ion-beam treatments [60], ultrafast laser [61, 62], lithography [39] or other micro- and nano-manufacturing methods [22]. Random rough metal surface can even be obtained during deposition process merely by controlling the substrate temperature [63, 64] or material deposition rate [65, 66]. The textured surface absorbers have been demonstrated to have a high solar absorptance although their thermal emittance tends to be higher than that of cermet and multilayer absorbers [9, 67, 68]. In addition, it is quite insensitive to the effect of oxidation and thermal shocks, which can greatly increase its lifetime and is in favor of high-temperature applications [22, 37]. However, surface of the microstructure must be protected from damage caused by surface contact or abrasion. Photonic crystal-based designs: Photonic crystals (PhCs) allow unprecedented control of the photon density of states with of important applications in wide fields including selective solar absorbers. PhCs are made from light-scale periodic arrangements of two or more materials with distinct dielectric constants, which can give the desired bands and forbidden photonic states [9, 22]. PhCs with allowed states in the solar spectrum and forbidden states in the IR spectrum can be used as high-performance solar absorber. PhCs can not only offer unprecedented control over thermal emission as a function of wavelength, but they can also offer unique control over emission as a function of angle, opening up the possibility of only exchanging heat with the sun, to achieve a high-temperature operation even without optical concentration [22]. The main challenge for PhCs-based solar selective absorbers is the hightemperature stability. In PhCs-based solar selective absorbers, many surfaces exist, which can lead to delamination and many other thermal stability issues [69]. Hence, refractory metals such as W, Mo, Ta, etc., were the most popular metals to work with for high-temperature photonic crystals due to their high melting temperature. Different dimensional PhCs-based solar selective absorbers have been proposed [22]. In fact, the distinction between multilayer thin-film structures, textured surfaces,

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Fig. 9 Absorptance spectra for different solar selective designs: a ZrB2 intrinsic absorber [30], a PbS-based semiconductor–metal tandem [75], a six-layered SiO2 /Cr/SiO2 /Cr/SiO2 /Cu film coating [27], a AlN/W–AlN(LMVF)/W–AlN(HMVF)/Al cermet solar selective absorber [76], a nanopyramid nickel selective absorber [67], a tantalum photonic crystal coating [77]. A commercial cermet coating of Sunselect was presented for comparison [74]

and photonic crystals is not always clear since thin-film structures resemble onedimensional photonic crystals and structured surfaces can resemble two-dimensional photonic crystals [9]. Among the six typical solar selective absorbers, cermet absorbers have seen the most commercial success with the cermets coatings such as SS-AlN, TiNx Oy -Al, CrN-Cr2 O3 , Ni-NiO, Mo-SiO2 , Mo-Al2 O3 , etc. [4, 70–72]. In addition, photonic crystals and multilayer solar selective absorbers also present great promise for significant performance improvements in the future [9, 22, 45, 73]. Figure 9 shows the absorptance spectra of different solar selective designs, including the one with a commercial cermet coating [74]. Performance of various spectrally selective absorbers can be referred to in the reviews by Weinstein et al. [9]. For practical design, fabrication, and application of solar selective absorbers, not just one but several mechanisms are invoked to achieve better spectral selectivity, such as the cermet-based multilayer absorbers containing multilayer stacks and metal-dielectric composite coatings [46, 55, 70, 78, 79], semiconductor-based multilayer solar absorbers [80, 81], semiconductor nanowire arrays [31], periodic micro-structured multilayer absorbers [39, 82], surface roughened multilayer film structure [63, 65]. The cermet-based multilayer solar selective absorbers show the most promising feature for commercial applications in middle (100–400 °C) and high-temperature range (>400 °C) [28, 37]. For solar selective absorber, besides the photo-thermal conversion efficiency, special attention should be paid to its thermal stability in consideration of recent rapid development of concentrated solar power station [4]. According to the operational

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temperature, solar selective absorbers can be categorized into three types: (1) low temperature (100 °C), (2) middle temperature (100–400 °C), and (3) high temperature (>400 °C) [28]. There are numerous factors which will degrade the performance of solar selective absorbers at high-temperature condition including pollution-induced atmospheric corrosion, hydratization of the selective coating surface due to condensation of atmospheric moisture, interlayer diffusion, oxidation due to intensive thermal conditions, poor interlayer adhesion, chemical reactions, etc. [4, 7]. To prevent the solar absorbers from degradation or slow down the aging speed, refractory material, diffusion barrier layer, oxidation resistant layer or vacuum layer was introduced to enhance thermal stability of solar selective absorbers [47, 83, 84]. Many methods including electro-chemical plating, anodization, physical and chemical vapor deposition, and solution-based fabrication have been utilized to prepare solar selective absorbers [8, 37, 85–87]. Among them, PVD is the most widely used method because of the higher thermal stability of the film fabricated by PVD compared with other preparation methods, especially under the high-temperature condition [37]. Based on the above reviews of various types of solar selective absorbers, to enhance the photon-thermal conversion efficiency, it is very important for the optical properties such as the optical absorptance, emittance, and reflection of solar absorber structures to be well understood in the research and applications. Moreover, optical constants of refractive index and extinction coefficient of the constituting materials of solar selective absorber are very critical for the device structure design and modeling. Though many review works were proposed for the solar selective absorbers in past years [4, 7, 8, 22, 28, 37, 57], a comprehensive review is still absent on optical properties of solar absorber materials and structures. In this book, based on the conventional electromagnetic theory, optical properties and characteristics of solar materials and structures, different types solar selective absorbers, fabrication methods, and various applications were deeply reviewed with the hope for the book that will be helpful for the people who work both on the scientific research and technological development in the solar thermal conversion field.

2 Conventional Electromagnetic Theory 2.1 Maxwell’s Equations and the Dielectric Function Optical phenomena are connected with the interactions between electromagnetic radiation waves and matter. The interaction may be treated by the classical description or the quantum theory. Among them, the most important ones are Maxwell’s equations, which are suitable to be applied in both classical situations and some semiclassical approaches. Considering the classical models, for example the sunlight goes through a solar film, interactions related to the properties of the film materials and

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happened between the sunlight waves and the film structure can be well interpreted by Maxwell’s equations along with other appropriate equations [88, 89]. The theorem of Maxwell’s equations is based on several laws in nature, such as Gauss’s law related to the static electric field, and Faraday’s and Ampère’s laws related to the magnetic field. Gauss’s law indicates that the static electric fields always point from positive charges toward negative ones, and for any closed surface, the net outflow of the electric field through the surface is proportional to the charges enclosed inside. And the laws for magnetism are described as that the net outflow of the magnetic field through any closed surface is always zero due to the fact that the magnetic field is always generated by the magnetic dipoles. Faraday’s law is used to describe the electromagnetic induction, implying that the electromotive force on a loop equals to the decreasing rate of the magnetic flux through the surface enclosed by the loop. Ampère’s law shows that the integrated magnetic field around a closed loop is the same as the sum of the electric current passing through the loop. These laws reveal how the electric and magnetic field would change along with each other to make Maxwell’s equations be well-founded in application under some particular conditions. In isotropic media, Maxwell’s equations in Gaussian unit’s convention are as that ∇ ×H=

4π 1 ∂D j+ c c ∂t

∇ ×E =−

1 ∂B c ∂t

(2.1) (2.2)

∇ · D = 4πρ

(2.3)

∇ ·B=0

(2.4)

j = σE

(2.5)

D = E

(2.6)

B = μH

(2.7)

Here, the symbols E and H are the vectors of the electric and magnetic fields, D represents the electric displacement, B is called the magnetic flux density or magnetic induction, j is the electric current density, and ρ is the electric charge density. All the symbols in bold are vectors. Considering the seven equations, the first group of four Maxwell’s equations are presented in differential forms used to determine the fields for a given distribution of electric charges and currents. E and B are fundamental physical quantities, and the additional fields D and H need to be determined by relaying on other physical functions and quantities. The last three equations are the

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15

constitutive equations which describe the relationship of physical quantities in a given material and help to solve Maxwell’s equations. In those three constitutive equations, σ is the electric conductivity, ε is the permittivity, and μ is the permeability. For anisotropic media, these three quantities will be presented in a tensor form so that they can describe the properties of the material along different orientations. One of the key steps to solve Maxwell’s equations is to study and measure the functions of ε and μ. Under the vacuum condition, there is D=E

(2.8)

B=H

(2.9)

For other media, the electro-magnetic field will act on the charged particles and currents. As a result, there will be a static field pointing from the positive charges toward the negative ones, and microscopic magnetic dipole moments sorted to form a macroscopic one. The quantities of the polarization P and magnetization M are introduced to help solve the problem. First, we will discuss the magnetization. With the existence of external magnetic field, the dipoles in the microscopic level will be ranged. According to Ampère’s law, the magnetic field is always accompanied with an electric current. As a result, there would be a magnetizing current in accordance with the change of the magnetic field in the media. The quantity M is introduced to describe this change and is defined as the density of the induced magnetic dipole moments in the magnetic material. And the quantities B, H, M satisfy the relation H = B − 4φM

(2.10)

For a simplified linear mode, there is M = χm H

(2.11)

B = μH = (1 + 4π χm )H

(2.12)

and

where χ m is the magnetic susceptibility. The polarization of the material has the similar feature. The external electric field will cause the atomic nuclei and electrons to move in the opposite direction, which means that the inside micro-particles will form microscopic electric dipoles in the material. As a result, a macroscopic bound charge is formed and can be described by the polarization P, which is defined as the dipole moment per unit volume. In the case, if P is uniform, a macroscopic separation of charge will only appear at the surfaces. And if P is non-uniform, charges will be accumulated in the bulk.

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Likewise, the quantities D, E, P also have a relation as D = E + 4π P

(2.13)

For an isotropic material, there is P = χe E

(2.14)

  D = E + 4π P = 1 + 4π χ e E = ε E

(2.15)

and

where χ e is the electric susceptibility. One of the differences between the constitutive equations of the electric and magnetic fields is that in the optical region with very high frequencies, the permeability μ is very close to 1, while the permittivity ε is highly dependent on the frequency of the external field. Therefore, when dealing with the problem of interacting between the photons and dielectric material, the permittivity should be considered as a function of the optical frequency. The function is named as the dielectric function and ε becomes the form ε(ω). For the materials whose permittivity has a nonignorable variety with the frequency, the interaction should be studied individually at every single wavelength. Considering the monochromatic light at an angular frequency ω, both the electric field and the electric displacement will vary with amplitude D0 and E0 at the same frequency. The Eq. (2.15) has the form D0 e−iωt = (ω)E0 e−iωt

(2.16)

The time-dependent varying part at both sides of the equation can be canceled to make the equation be simplified as. D0 = ε(ω)E 0 or ε(ω) =

|D0 | |E0 |

(2.17)

However, for most materials in nature, the dielectric function has an imaginary part that cannot be neglected. It makes the function to be given in a complex form ∼

(ω) = ε1 (ω) + iε2 (ω)

(2.18)

where 1 (ω) and ε2 (ω) are the real and imaginary part of the permittivity. This imaginary part is related to the conductivity and absorption of the material. And additionally, it leaves a phase difference between the electric field and displacement as

Optical Properties of Solar Absorber Materials and Structures ∼

(ω) = ε1 (ω) + iε2 (ω) =

|D0 | iδ |D0 | e = (cosδ+isinδ) |E0 | |E0 |

17

(2.19)

where δ is the phase difference called loss angle. The response of a medium to the static electric field is usually described by the low-frequency limit of the permittivity which is ∼

s = lim (ω) ω→0

(2.20)

and is named as the static permittivity. At very high frequencies, the dielectric function reaches the infinitive high-frequency limit in assumption ∼

∞ = lim (ω) ω→∞

(2.21)

Both two limits physically have their intrinsic mechanisms to play significant roles in understanding the fundamental properties of materials. In the moderate-high optical frequency region, the dielectric function is usually treated by different models of particle interaction in approximations, such as the Drude and Lorentz models, which are deeply related to the mass internal charge particles how to response to the external electromagnetic field acted on the material.

2.2 Light Propagation in the Solid In this section, Maxwell’s equations will be used to derive the propagation of light inside media [88–91]. For a simplified situation, we study an isotropic medium with no optical loss, no internal charge source (ρ = 0) and currents (j = 0), Maxwell’s equations (2.1 ~ 4) become ∇ ×H=

1 ∂D c ∂t

∇ ×E=−

1 ∂B c ∂t

(2.22) (2.23)

∇ ·D=0

(2.24)

∇ ·B=0

(2.25)

Taking the curl of (2.23) and considering the constitutive Eqs. (2.6, 2.7), we obtain

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μ ∂H ∇ ×∇ ×E=∇ × − c ∂t

 =−

μ∂ με ∂ 2 E (∇ × H) = − 2 2 c ∂t c ∂t

(2.26)

Using the curl of the curl identity, there is ∇ × ∇ × E = −∇ 2 E

(2.27)

Together with (2.26), it can be get ∇2E −

με ∂ 2 E =0 c2 ∂t2

(2.28)

Similarly, for the magnetic field, it can be also obtained ∇2H −

με ∂ 2 H =0 c2 ∂t2

(2.29)

The Eqs. (2.28) and (2.29) are in differential forms for both of the electric and magnetic fields to be fit with the standard form of wave equations. That is, in vacuum and non-absorptive media, both electric and magnetic fields will propagate together in the waveform, called as the electromagnetic wave. According to the wave equation, the electromagnetic field propagates with a speed c υ=√ με

(2.30)

where c is the constant of the light speed in vacuum, which is approximately 2.998 × 108 m/s. The electromagnetic wave speed υ in media equals to c/n with the refractive index or refractivity n defined as n=

c √ = με υ

(2.31)

For common optical materials, the relative permeability is close to 1, and we then have n≈

√ ε

(2.32)

In addition, the value of υ here is actually the phase velocity of light. It represents the speed of a certain phase in the train of waves rather than the velocity of the energy transmission which is represented by the group velocity. In transparent or low-loss materials, the two velocities have the values being closer to each other. But in high dispersion materials, the values of these two velocities are quite different. In the next part of this section, we will discuss the solutions to the wave Eqs. (2.28, 2.29) for the common types of optical waves in the application.

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The simplest solution by solving the wave equation can be obtained under the assumption for a harmonic plane wave which is given as E = E 0 cos(k · r − ωt + ϕ0 )

(2.33)

H = H 0 cos(k · r − ωt + ϕ0 )

(2.34)

where k is the wave vector or wave number, r is the position vector of the light wave propagated in the space, and ω is the angular frequency of the light. It represents the light wave propagating along the k direction perpendicular to the electric field with an amplitude of |E0 | under the condition in which the vectors E, H, and k are orthogonal. The phase of wave is defined as φ(r, t) = k · r − ωt + ϕ0

(2.35)

The plane wave is to mean that at any time, the phases corresponding to the positions in a plane perpendicular to k are all the same. Among the different types of wave, the plane wave in assumption is most often applied to study the optical properties of multi-layered plane films. With the time t varying, the wave plane will vary along the k direction with the velocity υ in the material or especially with c in vacuum. The amplitude of vector k is k=

ω nω 2π = = λ υ c

(2.36)

The wavelength λ is also the periodical distance of the neighboring wave planes corresponding to the same phase. The wave equations are often mathematically expressed in a complex exponential form as E = E 0 ei(k·r−ωt+ϕ0 )

(2.37)

E = E 0 ei(k·r+ϕ0 ) e−iωt

(2.38)

or

where the space- and time-related parts part are divided. Another solution to solve the wave equations is to use a spherical wave assumption. When the light from a point source propagates in vacuum or an isotropic medium, the wavefront will always have a spherical shape featured by the spherical wave. Thus the wave Eq. (2.28) needs to be rewritten in spherical coordinates (r, θ, ϕ). First, the Laplace operator in spherical coordinates is

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∇2 =

1 ∂ ∂ 1 1 ∂ 2 ∂ ∂2 (r ) + (sinθ ) + 2 r 2 ∂r ∂r r 2 sinθ ∂θ ∂θ r 2 sin θ ∂φ 2

(2.39)

Due to the spherical symmetry, the amplitude of the field will not be the function of angles. By ignoring the angular part, thus, the Laplace operator for the spherical wave can be simplified as ∇2 E =

1 ∂2 1 ∂ 2∂E (r )= (r E) 2 r ∂r ∂r r ∂r 2

(2.40)

The wave equation has the form 1 ∂2 μ ∂ 2 E (r E) − =0 r ∂r 2 c2 ∂t 2

(2.41)

∂2 μ ∂ 2 (r E) (r E) − 2 =0 2 ∂r c ∂t 2

(2.42)

and

The general solution to Eq. (2.42) is r E(r, t) = E 1 (r − υt) + E 2 (r + υt)

(2.43)

E 2 (r + υt) E 1 (r − υt) + r r

(2.44)

or E(r, t) =

E 1 and E 2 are the general solutions to the one-dimensional wave equation, representing the outgoing and incoming spherical wave, respectively. In the complex exponential form, the outgoing spherical wave is expressed as E(r, t) =

A i(kr +ϕ0 ) − iωt e e r

(2.45)

Considering the light source under the linearized state condition, the outgoing wave is a cylindrical wave. In cylindrical coordinates, the wave equation is written as ∂2 E μ ∂ 2 E 1 ∂E − + =0 ∂r 2 r ∂r c2 ∂t 2

(2.46)

An outgoing cylindrical wave is expressed as A E(r, t) = √ ei(kr +ϕ0 ) e−iωt r

(2.47)

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21

These three types of optical waves mentioned in the section are assumed for the very ideal waves to help understanding the propagation of waves. There are more complicated forms of light waves such as the Gaussian beam quite usefully discussed for lasers and divergence light source. Readers are suggested to find related topics discussed in the books about contemporary optics. Moreover, the realistic light wave often will have a combination with different frequencies and polarizations in applications.

2.3 Reflection and Refraction of Light at the Interface To study the interaction between optical waves and media, it’s important to understand two basic optical phenomena, the light reflection and the refraction happened at the interface of the material in nature [33, 89]. At the boundary of two isotropic media without free charges and currents, the electric and magnetic fields satisfy the boundary conditions derived from Maxwell’s equations as n12 · ( D2 − D1 ) = 0

(2.48)

n12 × (E 2 − E 1 ) = 0

(2.49)

n12 · (B 2 − B 1 ) = 0

(2.50)

n12 × (H 2 − H 1 ) = 0

(2.51)

where n12 is the normal unit vector pointing from medium 1 to medium 2 at the interface. To simplify the problem, a monochromatic incident light is discussed, and the boundary of the media is considered to have an infinite surface. However, laws of reflection and refraction derived from such a simplified condition is still universally applicable and can be extended to different situations. When the incident light arrives at the boundary as shown in Fig. 10, possibly there will be two different beams of light generated at the incident point. One is the reflective light which will go back to the original medium 1, and the other is the refractive light which will go across the boundary into the other medium 2. According to boundary conditions, it is easy to prove that the incident, reflective, and refractive light beams will be in the same plane with the same frequency. Thus the electric field of the three beams of light can be written as. incident wave E i = E 1 exp[i(k1 · r − ωt)]

(2.52)

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E.-T. Hu et al.

Fig. 10 The reflection and refraction of monochromatic light at the boundary of medium 1 and 2

  reflective light Er = E 1 exp i k1 · r − ωt

(2.53)

refractive light E t = E 2 exp[i(k2 · r − ωt)]

(2.54)

Inserting the expressions of the light wave into the Eq. (2.48), we will get ε1 n12 · E 1 eik1y y + ε1 n12 · E 1 ’eik1y ’y = ε2 n12 · E 2 eik2y y

(2.55)

ε1 n12 · E 1 = ε2 n12 · E 2 ei(k2y −k1y )y − ε1 n12 · E 1 ’ei(k1y ’−k1y )y

(2.56)

and

To have the Eq. (2.54) stand for all y positions, it will be to satisfy k1y = k1y ’ = k2y

(2.57)

which means that the components of the wave vectors all will have the same values along the y direction, resulting in that k1 sinθ1 = k1 ’sinθ1 ’ = k2 sinθ2 Combining Eqs. (2.58) and (2.36), we will get

(2.58)

Optical Properties of Solar Absorber Materials and Structures

23

θ1 = θ1 ’

(2.59)

n 1 sinθ1 = n 2 sinθ2

(2.60)

Equation (2.59) is the law of reflection, revealing that the reflective angle is always the same as the incident angle. The Eq. (2.60) is the law of refraction, or called as Snell’s law, describing the relationship between the incident and refractive angle. Although the angles of reflection and refraction have been determined, the intensities of the generated light are still unknown and need to be derived from the Fresnel equations or Fresnel coefficients. Considering an oblique incidence with a random polarization, it is difficult to get a concise solution in terms of the boundary equations. However, the incident light can be divided into two components according to the orientations. One has an electrical field vector perpendicular to the plane of incidence, marked as E1s , and a magnetic field parallel to the plane. The wave is usually known as s-polarized or TE (transverse electric) wave. The other component is the opposite. Its electric field vector is parallel to the plane and called p-polarized or TM (transverse magnetic) wave. These two components will be treated according to the independent boundary conditions. For the s-polarized incidence as shown in Fig. 11, the boundary equations will become E 1s + E 1s ’ = E 2s

(2.61)

Fig. 11 The reflection and refraction of an s-polarized light at the boundary of medium 1 and 2

24

E.-T. Hu et al.

−H1s cosθ1 + H1s ’cosθ1 ’ = −H2s cosθ2

(2.62)

Together with the relationship between amplitude of E and H derived from Maxwell’s equations, Eq. (2.62) changes to that −n 1 E 1s cosθ1 + n 1 E 1s ’cosθ1 ’ = −n 2 E 2s cosθ2

(2.63)

The solution of the Eqs. (2.61) and (2.63) gives E 1s ’ =

n 1 cosθ1 − n 2 cosθ2 E 1s n 1 cosθ1 + n 2 cosθ2

(2.64)

E 2s =

2n 1 cosθ1 E 1s n 1 cosθ1 + n 2 cosθ2

(2.65)

The reflection and transmission coefficients are then defined by the ratio of reflected and transmitted electrical fields to the incident ones as that rs =

E 1s ’ n 1 cosθ1 − n 2 cosθ2 = E 1s n 1 cosθ1 + n 2 cosθ2

(2.66)

ts =

E 2s 2n 1 cosθ1 = E 1s n 1 cosθ1 + n 2 cosθ2

(2.67)

Likewise, for the p-polarized incidence light shown in Fig. 12, the boundary equations gives H1 p + H1 p ’ = H2p

(2.68)

E 1 p cosθ1 − E 1 p ’cosθ1 ’ = E 2p cosθ2

(2.69)

The p-polarized reflection and transmission coefficients can be derived as rp =

E1 p ’ n 2 cosθ1 − n 1 cosθ2 = E1 p n 2 cosθ1 + n 1 cosθ2

(2.70)

tp =

E 2p 2n 1 cosθ1 = E1 p n 2 cosθ1 + n 1 cosθ2

(2.71)

However, these coefficients describe only the change in amplitudes of the fields rather than the change in energy. In optics, the energy flow rate across the unit area is given by the Poynting vector which is S=

c E×H 4π

(2.72)

Optical Properties of Solar Absorber Materials and Structures

25

Fig. 12 The reflection and refraction of p-polarized light at the boundary of medum1 and 2

The direction of S is in accordance with the direction of energy flow. The intensity of a harmonic wave is defined as the time-average magnitude of the Poynting vector as I = (S) =

cn 2 c E × H ∗ = E ∝ n E 02 8π 8π 0

(2.73)

The reflectance R and the transmittance T is defined as the ratio of intensities, which measure the change in light energy. They are Ir = r2 Ii

(2.74)

It n2 cosθ2 2 = t Ii n1 cosθ1

(2.75)

R= T=

for both s-polarized and p-polarized incidence. There are two interesting phenomena arising from the light interaction with the media related to reflection and refraction. Firstly, it is the total reflection. It occurs when the light wave is trying to enter a medium from another medium with a relatively higher refractivity under the condition in which the incident angle is larger than a value, called as the critical angle. According to Snell’s law, therefore, for general situations, the refractive angle can be given as

26

E.-T. Hu et al.

θ2 = arcsin

n 1 sinθ1 n2

(2.76)

The equation stands only when n 1 sinθ1 ≤1 n2

(2.77)

Here, the equal sign corresponds to the critical angle as θc = arcsin

n2 n1

(2.78)

With n1 > n2 and θ 1 > θ c , the total reflection occurs and there will be an absence of refractive light. The incident light remains propagating in the original medium and no energy will be lost at the boundaries. It’s very important for the optical energy or information transmission in the material, such as that happened in the optical fiber. Considering the total reflection, there are also several side effects, known as the evanescent wave, Goos–Hänchen effect, and relative phase shift between two polarized waves, and so on, not to be discussed specifically here. The other interesting phenomenon occurs when the incident angle equals to a special angle named as the Brewster angle. When the incident and refractive angles meet the condition θ1 + θ2 =

π 2

(2.79)

Equations (2.70) and (2.71) can be calculated to satisfy that r p = 0 and t p = 1. As a result, there will be no reflection and a total transmission of the p-polarized light happened at the boundary. The special angle is the so-called Brewster’s angle. Thus for an un-polarized incident light with an incident angle equaling to the Brewster angle, the refractive light will be totally s-polarized, which is an efficient method to produce a linear polarized light. The Snell’s law and the Fresnel equations are two fundamental theorems describing the relationship of angles and amplitudes of light reflection and refraction occurred at the boundary of two media. However, in the design of solar absorbers, multiple reflections or refractions in multi-layered or nanostructured appliances will occur. Considering the multi-layered structures, it is important at the initial step to analyze the interferences due to multiple reflections occurred in the layered structure by determining the relationship between the incident and transmitted light at the interface of each layer. The calculation will be more complicated for light propagation in nanostructures. Computer-assisted calculation tools, such as the finite element method, can be recommended to deal with such kinds of problems in practical researches.

Optical Properties of Solar Absorber Materials and Structures

27

2.4 Optical Absorption of the Media In Sects. 2.2 and 2.3, most of our discussion is based on non-absorptive media. However, a lot of materials in nature are absorptive or opaque. In this section, we will discuss the situations of the materials that are optically absorptive in applications [33]. The absorption of light is actually an energy transfer from photons to the media in the light interaction process. The energy can be possibly absorbed by the atoms, phonons, and typically the electrons in the material. The mechanisms of absorption shown in conductors and dielectric materials are quite different. In conductors such as metals, the electromagnetic fields will do work on the free electrons and force them to move periodically back and forth with micro scattering of the direction varied by the electromagnetic field. In other materials, the amount of absorbed energy usually corresponds to the electron transitions happened over the gap between energy states. Thus the absorption properties differ greatly for the matters according to the type of the material characterized by the variety of electronic structures. First, we will derive the expression for an optical wave in the absorptive medium. According to the divergence of the curl identity and Maxwell’s equations (2.1, 2.3), there is   1 ∂D 4π j+ 0=∇ ·∇ × H =∇ · c c ∂t   1 4π ∂ρ 4π ∇ · j + ∂(∇ · D)/∂t = ∇· j+ (2.80) = c c c ∂t i.e., ∇ · j = −∂ρ/∂t

(2.81)

which represents the law of charge conservation. Combined with the constitutive equations (2.5, 2.6), there will be an equation describing the variation of the free charge in an absorptive medium as ∇ · j = ∇ · (σ E) =

4π σρ ∂ρ σ ∇·D= =− ε ε ∂t

(2.82)

The solution to Eq. (2.82) is ρ = ρ0 e−t/τ

(2.83)

where τ=

ε 4π σ

(2.84)

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E.-T. Hu et al.

In other words, the density of free electrons in absorptive medium will decrease exponentially with the very small value of τ, which presents the average lifetime suffering by the internal charge particle collision. As a result, the energy of the electromagnetic field will suffer a high loss to make the media opaque, especially in metals which has high absorptivity. The wave equations in absorptive media can be reduced by Maxwell’s equations as that ∇·E=0 ∇2 E −

με ∂ 2 E 4π μσ ∂ E − =0 c2 ∂t c2 ∂t 2

(2.85)

(2.86)

Considering a monochromatic plane wave satisfying E(r, t) = E(r)e−iωt

(2.87)

there is ∇2 E +

i4π μσ ω μεω2 E + E=0 c2 c2

(2.88)

The solution to the above equation is ∼

E = E 0 ei(k·r−ωt+ϕ0 )

(2.89)

with the complex wave vector defined by   4π σ μω2 k = 2 ε+i c ω

∼2

(2.90)

Similar to the real parameters in non-absorptive medium, a series of corresponding complex parameters are defined to describe the properties of an absorptive medium as ∼

ε= ε + i ∼

υ=

4π σ ω

c ∼

(2.91) (2.92)

με

∼

n=

c ∼ ∼ με= k ω

(2.93)

Optical Properties of Solar Absorber Materials and Structures ∼

k = k  + ik  =

ω ∼ 2π ∼ n= n c λ0

 1/2 ω 1 16π 2 σ 2 k = [ ( 1 + 2 2 + 1)] c 2 ε ω  1/2 ω 1 16π 2 σ 2 k  = [ ( 1 + 2 2 − 1)] c 2 ε ω 

29

(2.94)

(2.95)

(2.96)

Inserting the complex expression (2.94) into Eq. (2.89) and we will get   ∼ = E0 exp(−k · r) exp[i(k · r−ωt)] E = E0 exp i k ·r − ωt

(2.97)

The first part in the exponential component represents the attenuation of the amplitude, and k  is thus named as the attenuation constant. The second exponential component is related to the change of the phase with k  thus being the propagation constant. Considering the significant loss of light in an absorptive medium, the quantity of the penetration depth is used to measure the attenuation. The quantity is defined as the distance of transmission, after which the light is reduced to 1/e, as d=

1 k

(2.98)

For good conductors with a considerably large conductivity, the penetration depth is approximately  1 d =  ≈ k

2 ωμσ

(2.99)

For the metals with high optical absorption, the penetration depth is only several or dozens of nanometers, thus making these metals appear opaque. Inserting the expression (2.97) into Maxwell’s equations, we will get H=−

c   ic ∇ ×E= (k +ik ) × E ωμ ωμ

(2.100)

For good conductors, the magnetic field is approximately  H=c

π σ exp(i )k × E ωμ 4 

(2.101)

As a result, there is a phase lag of π/4 between the magnetic field and the electric field. In addition, the ratio of amplitude of the magnetic field to that of the electric

30

E.-T. Hu et al.

field is   H = c σ >> ε E ωμ μ

(2.102)

which means in metals, the magnetic field has a larger effect on the propagation of light than the electric field. Moreover, the reflection and refraction of light for the conductors are different from that of the non-absorptive materials. Due to the complex refractivity, the refraction angle shown in Snell’s law will turn to be a complex number also without its physical meaning in expression. There is room for this kind of phenomena to be studied more in the future.

2.5 Thermal Emittance of the Surface In the design of solar absorbers, it must pay attention to that solar devices not only absorb the optical energy, but also give out of the energy by thermal radiation [33]. At equilibrium, the energy of incident light equals the sum of optical energy corresponding to the reflection, absorption, and transmission of the light, and as well as to the thermal radiation. For most solar devices, they are thick and opaque, and the transmission can be ignored. Thus, one of the key ways to improve the efficiency of solar appliances is to lower the reflection and thermal radiation. Thermal radiation is the electromagnetic radiation generated by thermal motion of particles in all matters with temperatures above the absolute zero degree. The energy is emitted nearly by everything in nature and is one of the fundamental mechanisms of heat transfer. The spectrum of thermal radiation is broad and continuous, and mainly dependent on the temperature. The higher the temperature is, the larger the intensity of the radiation will be, with a blue shift of the spectrum distribution. Considering the thermal radiation and absorption, in a thermally insulated cavity, objects will reach the same temperature to achieve a thermodynamic equilibrium. To maintain the equilibrium, objects will radiate thermal energy as much as they absorb. It is presented by Kirchhoff’s law of thermal radiation as that in thermodynamic equilibrium, a body of arbitrary material emits and absorbs thermal electromagnetic radiation at every wavelength, and the ratio of its emissive power to its absorptivity is equal to a universal function only of radiative wavelength and temperature, rather than any physical property of the material. It can be inferred that a good absorber is also a good emitter, and vice versa. One of the classical models for thermal radiation is the blackbody radiation. A blackbody is an idealized object that absorbs all incident light regardless of frequency, intensity or incident angle. According to Kirchhoff’s law of thermal radiation, a black body in thermodynamic equilibrium will not only absorb all incoming light but also

Optical Properties of Solar Absorber Materials and Structures

31

radiate electromagnetic wave according to a unique law universal for all black bodies. Besides, the emissivity of a black body always equals to the absorptivity. According to Planck’s law, thermal radiation power of a black body per unit area of surface, per unit solid angle and per unit frequency υ is L b (υ, T ) =

2hυ 3 1 · hυ/k T 2 B c e −1

(2.103)

or per unit wavelength rather than frequency is L b (λ, T ) =

2hc2 1 · hc k T λ 5 λ e / B −1

(2.104)

Planck’s law is based on the quantized hypothesis on electromagnetic radiation, and is in accordance with the experimental results. Integrate Eq. (2.103) over all frequencies, and we will get the total power output of the black body described by the Stefan–Boltzmann Law as P = σSB AT4

(2.105)

where A is the radiating surface area, and σ SB is the Stefan–Boltzmann constant for black radiation defined as σSB =

2π 5 k 4B ≈ 5.67 × 10−8 W · m−2 · K−4 15c2 h3

(2.106)

The wavelength corresponding to maximum radiative power can be calculated by taking the derivative of Eq. (2.104) to be λM =

b T

(2.107)

where b is a constant of about 2.8978 × 10–3 m·K in approximation. The relationship is named as Wien’s displacement law. Kirchhoff’s law of thermal radiation establishes the fundamental relationship of absorption and thermal radiation of a certain body. Planck’s law gives a mathematical expression for the spectral density of blackbody radiation. Both laws will help to find the best design solution for the absorptive spectrum of a solar device with the feature as high as close to that of a black body at certain wavelengths. To achieve a higher photon-to-heat conversion efficiency, it is equally important to cut off the absorption of the infrared light as to raise the absorption in the visible region for two reasons. First, the absorbed infrared light won’t be efficiently utilized or converted into the expected form of energy due to that the energy of a single photon at the corresponding wavelength is too low to exceed the threshold for conversion. This

32

E.-T. Hu et al.

part of absorbed energy will only cause increasing of the solar system temperature beyond the temperature limitation in design, which is very harmful to the efficiency. Besides, the energy of sunlight mainly concentrates in the ultraviolet, visible, and near-infrared range. Thus a less absorption in the infrared region has little effect on the utilization of solar energy. The second reason is that the thermal radiation of a solar device is proportional to the absorption at the same wavelength. According to Wien’s displacement law, for a device operating at 800 K, the wavelength corresponding to maximum radiative power is calculated to be 3.62 μm which is in the middle infrared region. A reduced absorption in the appropriate wavelength range, especially in the infrared region, will help decrease unwanted energy loss due to the thermal radiation. In conclusion, an ideal solar device with high efficiency should be able to absorb solar light highly in its best and wanted wavelength region, at the same time to reflect most of other light to suppress effectively the thermal emission especially in the infrared region.

3 Optical Properties of the Solar Materials 3.1 Photon-To-Electron Conversions Photon-to-electron conversion, as one of the most important ways for solar energy utilization, is based on the principle of converting photons into electricity directly by a photon absorption process in which the electron–hole pairs are generated in a solar cell. In this process, only the photon with energy larger than the bandgap of the semiconductor can be absorbed and excites one electron–hole pair. Then the built-in electric field at the p–n junction interface of a solar cell separates the electron–hole pairs and drives electrons in one direction and holes in the opposite direction, creating a potential difference at the external electrodes. The photons with energy larger than the bandgap of the semiconductor material in the solar cell will lose the excess energy which will be converted to heat in the photon-to-electron conversion process. For photons with energy lower than the bandgap, it will not be absorbed but transmits through the solar materials. Based on the detailed balance limit theory, Shockley and Queisser predicted the efficiency limit of 30% for a single-junction solar cell [92]. As so far [6], based on the modern Si-wafer technology, the recorded lab cell efficiency is about 26.7% and 22.3% for the single-crystal and polycrystal Si wafer, respectively. Based on the advanced thin-film technology, the highest lab efficiency is about 22.9% and 21.0% for CuInGaSe (CIGS) and CdTe solar cells, respectively. The commercial efficiency of silicon wafer-based modules is about 17%, while it is about 16% for the CdTe module. With respect to market applications, the Si cell device based on the PV wafer technology accounts for about 95% of the total cell production. Shockley and Qusisser’s analysis was based on four assumptions: (1) a single p–n junction, (2) one electron–hole pair excited per incoming photon, (3) thermal

Optical Properties of Solar Absorber Materials and Structures

33

relaxation of the electron–hole pair energy in excess of the bandgap, and (4) illumination with unconcentrated sunlight. Hence, the Shockley–Queisser efficiency limit can be overcome by breaking through one or more of its premises. Multijunction solar cell, intermediate band solar cell, spectrum-splitting solar cell and other thirdgeneration cells are being intensively studied worldwide by dramatically increasing the efficiency and at the same time lowering the material and fabrication cost. In consideration of less than 20% conversion efficiency of the commercial solar cell, more than 80% of the incident sunlight cannot be extracted to be converted into useful electricity. This part of energy will be lost as heat, raising the temperature of the solar cell, degenerating its photon-to-electron efficiency. In general, for silicon PV cell, a temperature rise of 1 °C compared to standard test conditions of 25 °C, will reduce the efficiency by about 0.25–0.8% depending on its composition of the solar cell [7]. The heat can also be considered as useful energy for thermal applications by combining both the photovoltaic solar cell and thermal collector [93]. As discussed above, only the photons with energy higher than the bandgap can be absorbed by the solar cell. However, the sun has electromagnetive radiation over a wide wavelength range, which will lead to unavoidable energy loss more than 80%. In terms of the solar-to-thermal conversion process, in comparison, more than 95% of the incident sunlight can be absorbed by the solar selective absorber.

3.2 Interband Transitions Based on Lorentz Model For solar absorber structure, usually metal, dielectric and metal-dielectric composite was used as the constituted material. To design the solar absorber with suitable spectral properties, optical constants of the constituted materials must be measured to know in advance. Actually, optical dispersion models have been demonstrated to be valid in the prediction of the optical constants for most of the solar materials. Hence, in the following parts, the Lorentz and Drude models with the effective medium theory will be reviewed. For photons incident on a solar material, due to the interaction between the photons and matters, incident photons can be absorbed either by interband transition or by intraband transition depending on the magnitude of the energy carried by the photons to the material, as well as depending on energy band structure of the material. In this section, we will give a brief description of interband transitions happened in the situation in which the energy carried by the photons has the value higher than the bandgap of the material in nature. The transition of the electrons from the valence band to the conduction band under the excitation of incident photons is referred to as the interband transition, which can be divided into direct and indirect interband transition. In general, interband transition happens in the ultraviolet and visible wavelength range because the energy of the incident photons should be larger than the bandgap of the semiconductor. With respect to the interband transitions, the dielectric functions can be derived based on quantum mechanism, mathematically which often is not easy to get the

34

E.-T. Hu et al.

Fig. 13 Classical oscillator model of the bound electrons moving around an atom

solution in a straightforward way. In fact, the Lorentz model [88], developed from a classical model in physics, can be employed to characterize the dielectric functions of the body responding to the external electromagnetic field through the electron interband transition process. In the Lorentz model, it treated electric polarization as a negatively charged electron bounded to a positively charged atomic nucleus with a spring as depicted in Fig. 13. Furthermore, under the effect of electric field of the light, electron vibrates in a viscous fluid, while the position of the atomic nucleus which is much heavier than the orbital electrons moving around, is fixed. According to Newton’s second law, the equation can be established: m

dx d2x = −eE 0 e−iωt − mω02 x − m 2 dt dt

(3.1)

where m and e are the mass and charge of the electron, respectively. On the right side of Eq. (3.1), the first term represents the electrostatic force. The second term shows the restored force according to Hook’s law with ω0 as the resonant frequency of the spring. The last term is the viscous force with  as the proportional constant, termed as the damping coefficient, or as the Lorentz broadening constant in other ways. By solving Eq. (3.1), we get x(ω) = −

1 eE 0 e−iωt 2 m ω0 − ω2 − iω

(3.2)

If the number of electrons per unit volume is given by N, the dielectric polarization − → P P can be expressed as P = −Nex(ω), by inserting it into ε = 1 + 4π − → , the dielectric E functions can be obtained as follows: ε =1+

1 4π N e2 m ω02 − ω2 − iω

(3.3)

In actual data analysis, the dielectric function can be expressed by counting electromagnetic contributions from different oscillators to obtain that:

Optical Properties of Solar Absorber Materials and Structures

ε =1+

 ω2j j=1

Aj − ω2 − i j ω

35

(3.4)

Here, j denotes the jth oscillator and Aj represents the oscillator strength of the jth oscillator. Though the expression as shown above was reduced from the classical model in physics, the result is quite in accordance with that derived from the model of quantum mechanics. Once the complex dielectric functions ε = ε1 + iε2 were obtained, according to ˜ n + iκ), the refractive index n and extinction coefficient the relation of ε = n˜ 2 (n= κ can be determined: ε1 = (n 2 − κ 2 )

(3.5)

ε2 = 2nκ

(3.6)

n=

κ=



  ε2 + ε2 + ε  1 1 2 2 

  ε2 + ε2 − ε  1 1 2 2

(3.7)

(3.8)

3.3 Free Electron Absorption Based on the Drude Model For metals and doped semiconductors, electrons are not bounded and can move freely in the body, suffering from the internal collision of electrons to each other, including interactions between the electrons and the positively-charged atomic nucleus. Those electrons in high concentration can absorb the energy of the photons in the intraband transition process. In comparison to Lorentz model which depicts the dielectric functions suitable for interband transition, the Drude model was applied to characterize the dielectric functions by free-electron absorption. With respect to the Drude model, the dielectric function can be derived in the way similar to that of the Lorentz model, but by ignoring the restoring force shown in Eq. (3.1) due to the free motion feature of electrons in metals. That is, free electrons are only influenced and driven by the electric field of light accompanied with the internal microscattering by some complicated mechanisms to make the energy loss in certain magnitude. The dielectric functions for free electron absorption can be obtained:

36

E.-T. Hu et al.

ε = ε∞ −

ω2p

(3.9)

ω2 + iω p

where ε∞ represents the dielectric functions performed in the

ultra high frequency 2

N region, ωp depicts the plasma frequency given by ω p = 4πe . In the case of m∗ semiconductors, ωp is located in the infrared region, while for metals, ωp happens in the visible and UV regions. In the Drude model, Γ p represents the damping factor, which is the reciprocal of τ (called as life time or relaxation time of free electrons). In general, the longer the free-electron relaxation time, the stronger of metallic character. Thus, the dispersive optical constants change with the wavelength can be predicted by studying the feature of the optical parameter of Γ p .

3.4 Effective Medium Approximation Models In solar absorber structures, for convenience, composites consisting of two or more materials are always adopted. By properly tuning the composition of the constituent materials, the required optical constants of the composite can be achieved. Then, the issue becomes how best to perform the calculation in average for the media consisting of multiple composites having two or more sets of optical functions independently. The effective medium approximation (EMA) theory can be applied to model the optical constants of the composite. When an external ac electric field is applied to a spherical dielectric, electric polarization will happen. The local field in the center of the sphere can be expressed as [88]: E loc = E +

4π P 3

(3.10)

where P is the electric polarization. By setting N e that is the number of electrons driven by the electric field, and α that is the polarizability proportional to the dielectric polarization, we get P = N e αE loc . By substituting Eq. (3.10) into P = N e αE loc yields   4π Ne α 1− P = Ne αE 3 Then, according to = 1 + Mossotti relation:

4π P , E

(3.11)

we can get the well-known formula of Clausius–

4π N e α ε−1 = ε+2 3

(3.12)

Optical Properties of Solar Absorber Materials and Structures

37

When the above spherical dielectric is composed of two composites a and b, we get ε−1 4π = (Na αa + Nb αb ) ε+2 3

(3.13)

From Eqs. (3.12) and (3.13), three common EMA theories can be obtained and jointly expressed as [94]:  ε j − εh ε − εh = fj ε + γ εh ε j + γ εh j

(3.14)

where ε is the dielectric function of the effective medium, εh is the dielectric function of the host material of the inclusion, f j is the fraction of the jth constituent, and γ is a factor related to the screening and the shape of the inclusions (γ = 2 for three-dimensional spherical dielectric). (1)

Lorentz-Lorenz model ε−1 εa − 1 εa − 1 = fa + (1 − f a ) ε+2 εa + 2 εa + 2

(2)

In this model, εa and εb represent the dielectric constants of the composite a and b, respectively, while f a and (1-f a ) are the volume fraction for each composite. The ambient surrounding the spherical dielectric is vacuum or air, implying εh = 1 in Eq. (3.14). It is the earliest EMA theory, which is based on the Clausius-–Mossotti relation. It assumes the individual constituents are mixed on the atomic scale. Nevertheless, real materials tend to be mixed on a much larger scale. This limited its practical applications in real mixed materials. Maxwell-Garnett (MG) model εb − εa ε − εa = (1 − f a ) ε + 2εa εb + 2εa

(3)

(3.15)

(3.16)

This model assumes a structure in which the composite a is surrounded by the composite b, meaning εh = εa . It is the most realistic EMA theory when the fraction of inclusions is significantly less than the fraction of host material. It was properly valid for the volume fraction less than 0.3. The MG model is very useful for cermets or certain types of nanocrystals embedded in hosts well below the percolation threshold. Bruggeman model

fa

εa − ε εb − ε + (1 − f ) =0 εa + 2ε ε a b + 2ε

(3.17)

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E.-T. Hu et al.

The model assumes ε = εh , where the host material is just to have the EMA dielectric function. It is often suitable in application for the part of volume fraction over 0.3. The model has been successfully used to depict the dielectric function of the surface roughness layer containing voids up to about 50%. The model can be extended easily to describe a material consisting of multiple composites.

3.5 Optical Constants of Metals and Dielectric Media For metals, the optical constants commonly can be represented by the Drude model under the condition in which the free electrons intra transmitted in the conduction band will dominate the photonic energy absorption process when the photon energy is lower than the fundamental energy gap of the metal. In comparison of the cases in the solar spectral region, the dielectric media often will be formed in the amorphous state to have the feature of optical constants that can be well described by the Cauchy or the Sellmeier model. Optical constants referring to the complex refractive index n˜ (n˜ = n +iκ) with the real n and imaginary part κ are shown in Fig. 14 for some kinds

Fig. 14 Optical constants of several commonly used metal and dielectric media in solar absorbers

Optical Properties of Solar Absorber Materials and Structures

39

of metal and dielectric materials, respectively [35, 95–98]. As mentioned above, both of the Drude and Cauchy (or Sellmeier) models can principly be reduced from the Lorentz oscillator model. For the dielectric media with nearly transparent optical properties, the photon energy loss due to the electron collision in the body can be neglected, resulting  = 0 in Eq. (3.4). In consideration taking only one oscillator and substituting ω = 2πc/λ into Eq. (3.4), we can get the Sellmeier model: n=

√

 ε=

1+

Bn λ2 λ2 − Cn2

(3.18)

Notice that extinction coefficient κ = 0 when  = 0 in the Sellmeier model. By series expansion of Eq. (3.18) with 1/λ2 as the independent variable, the Cauchy model can be obtained: n=A+

C B + 4 + ··· λ2 λ

(3.19)

Normally, only the first three terms of the expansion in the refractive index are considered in the characterization of the optical constant of dielectric media. The optical constants of several metal and dielectric media commonly used in solar absorbers are given in Fig. 14 to show the spectral feature in agreement with the Drude and Cauchy models in practical applications [35, 95–98]. In solar absorbers, the transition metals such as Cr, Ti are always used as the light absorption layer [26, 42]. It is mainly because the d atomic orbitals of transition metals are not fully filled by the d electrons, which can absorb the incident photons over a wide wavelength range due to electron intraband transition in the d orbitals. In comparison, the d orbitals for the noble metals such as Au, Ag, and Cu are fully filled with d- electrons. Thus, the d-electrons will be not attributed to intraband transitions but will be attributed to interband transitions by absorbing the photons with the energy higher than the energy bandgap between the s and d bands of the noble metals that are often used as the metal reflection layer to reduce thermal emittance of solar absorbers [99]. To maintain a high absorptance over a wide wavelength range for the solar absorber, the imaginary part of dielectric functions for the absorption material should be as flat as possible. Figure 15 presented the dielectric functions for Cr, Ti, Au, Ag, and Cu. As can be seen, the imaginary part of dielectric functions for transition metals are obviously less fluctuated than those of the noble metals. To pursue the better optical performance of the solar absorbers, thus, the dielectric function of the alloyed materials can be modified to absorb more of the incident sunlight in practice [100].

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Fig. 15 a Real part and b imaginary part of dielectric functions for the transition metals (Cr, Ti) and noble metals (Au, Ag, and Cu)

3.6 The Extraction of Optical Constants of Refractive Index and Extinction Coefficient In the design of solar absorber structures, optical constants of the solar absorber materials must be measured to know in advance. At present, there are commonly two kinds of methods to characterize the optical constants of different materials. (1)

Reflection and transmission measurements [101]

For unpolarized light incident under the near-normal angle condition, reflectance and transmittance data related to n, κ, d, and λ can be derived from: Rcalc (n, κ, d, λ) = R + Tcalc (n, κ, d, λ) =

T 2 R0 1 − R0 R1

T T0 1 − R0 R1

(3.20) (3.21)

where R0 and T 0 are the reflectance and transmittance measured for the uncoated surface of the substrate, respectively. R1 is the reflectance of the film put on the substrate. R and T are the measured results from the spectrophotometer. R0 , T 0 and R1 can be expressed as follows: R0 = (

1 − ng 2 ) 1 + ng

T0 = 1 − R0

(3.22) (3.23)

Optical Properties of Solar Absorber Materials and Structures

R1 =

M1 coshα − M2 sinhβ − M3 cosβ − M4 sinβ G 1 coshα + G 2 sinhβ − G 3 cosβ + G 4 sinβ

41

(3.24)

α = 4π κd/λ, β = 4π nd/λ

(3.25)

   M1 = n 2 + κ 2 + 1 n 2 + κ 2 + n 2g − 4n 2 n g

(3.26)

    M2 = 2n[n g n 2 + κ 2 + 1 − n 2 + κ 2 + n 2g ]

(3.27)

   M3 = n 2 + κ 2 − 1 n 2 + κ 2 − n 2g + 4n 2 n g

(3.28)

    M4 = 2k[n g n 2 + κ 2 − 1 − n 2 + κ 2 − n 2g ]

(3.29)

   G 1 = n 2 + κ 2 + 1 n 2 + κ 2 + n 2g + 4n 2 n g

(3.30)

    G 2 = 2n[n g n 2 + κ 2 + 1 + n 2 + κ 2 + n 2g ]

(3.31)

   G 3 = n 2 + κ 2 − 1 n 2 + κ 2 − n 2g − 4n 2 n g

(3.32)

    G 4 = 2κ[n g n 2 + κ 2 − 1 + n 2 + κ 2 − n 2g ]

(3.33)

where n and κ are the refractive index and extinction coefficient of the reflecting material, ng is the refractive index of the non-absorbing substrate. The optical constants can be obtained after the fitting and iteration processes between the calculated and measured reflectance and transmittance data. (2)

Spectroscopic ellipsometry

Spectroscopic ellipsometry is the most commonly used method to obtain the film thickness and optical constants of materials. It measures the change of the polarized state of the light reflected by the sample to obtain the optical properties of the sample material after a careful modeling and data reduction process. The name “ellipsometry” comes from the phenomena in which the polarized electrical field of light often will be elliptically rotated in the space upon light reflection. Compared to reflection and transmission methods that measure the absolute intensity values of the reflected and transmitted light, as shown in Fig. 16, the spectroscopic ellipsometry has a much higher measurement precision because it detects the relative changes of amplitude and phase in the polarized state of the incident and reflected light [88]. Spectroscopic ellipsometry measures the two values  and  that express the amplitude ratio and phase difference between p- and s-polarizations, respectively.  and  known as ellipsometric parameters, are defined as:

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Fig. 16 Measurement principle of ellipsometry

ρ = tanei =

rp rs

(3.34)

where r p and r s represent the amplitude reflection coefficient for p and s polarized light, respectively. For a simple sample structure as depicted in Fig. 17a, according to the Snell’s law and Fresnel equations, Eq. (3.34) can be rewritten as follows:

ρ = tanei =

rp = rs

sin 2 θ − cosθ sin 2 θ + cosθ

 

ε εambient

− sin 2 θ

ε

− sin 2 θ

εambient

 

(3.35)

where θ is the incident angle, ε is the complex dielectric functions of the sample, εambient is the dielectric functions of the ambient. Then, the dielectric function for a simple homogenous surface or a pseudodielectric function for a complex film structure containing the surface can be written in terms of the ellipsometric variable ρ as follows [88, 102]:

Fig. 17 Reflection at a bare substrate and b film on the top of the substrate

Optical Properties of Solar Absorber Materials and Structures

1−ρ 2 ε= sin 2 θ 1 + tan 2 θ ( ) 1+ρ

∼

43

(3.36)

For a complicated system such as the film with surface as shown in Fig. 17b, the ellipsometric parameters are not only correlated with the incident angle, dielectric functions of the sample and the ambient, but also affected profoundly by the dielectric functions of the substrate and optical properties of each layer. For multilayered film sample, the ellipsometric parameters can be expressed as: tanei = ρ(θ, εambient , εsubstrate , ε1 , d1 , ε2 , d2 , . . . , εi , di )

(3.37)

To accurately extract useful optical properties of the films including surfaces from the ellipsometric parameters, the optical objective which consists of the substrate, films, and ambient to be investigated needs to be approximated, called as the optical modeling of the sample system. In terms of a correct optical model with physically meaningful parameters will be helpful to determine the optical constants of the material with less error by the ellipsometric measurement in high precision. Figure 18 shows the commonly used optical models which can deal with most of the materials or multi-layered films without nano structures [88, 102]. For the materials and films with nano structures, some new modeling approaches will be required in the study. After the construction of optical models, suitable optical dispersion models to characterize the optical constants of each constituted layer should be applied. Then, a linear regression analysis is performed to minimize the fitting errors between the calculated and measured ellipsometric parameters. The fitting error function is

Fig. 18 Optical models used in data analysis of spectroscopic ellipsometry

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Fig. 19 Flowchart of the data reduction process performed in spectroscopic ellipsometry [88]

defined by the root mean square error (RMSE):  RMSE =

 M  1 2 2 (taniex − tanical ) + (cosiex − cosical ) i=1 M − P −1 (3.38)

where the superscripts “ex” and “cal” refer to the experimental and calculated ellipsometric parameters, respectively. M and P represent the number of measurement points and analytical parameters, respectively. After the data fitting process, the

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45

optical constants of the sample can be extracted rather effectively. Figure 19 shows the data reduction flowchart in spectroscopic ellipsometry [88]. As a non-destructive, contactless, surface-sensitive optical measurement method, spectroscopic ellipsometry has been applied extensively over the past 50 years, not only for the optical characterization of bulk materials and thin films, but also for in situ real-time measurement of multilayered film structures, interfaces, and composites, during the sample fabrication and data processing. Nevertheless, as an indirect measurement technique, construction, and selection of optical and dispersion model and fitting process are required in the data analysis of spectroscopic ellipsometry. Hence, accumulated knowledge and experience will be helpful and play a significant role to obtain right results in the data analysis and processing of ellipsometric experiment in the study.

4 Optical Characteristic of the Solar Absorbers Solar selective absorber plays an important role in the solar technology field to harvest as much as the solar energy with relatively low cost and long working life time. Ideal solar selective absorber should have high light absorption in the solar radiation wavelength region and low infrared re-radiation in the long-wavelength range, which can be characterized by solar absorptance α and thermal emittance ε. Both of the parameters are correlated with the absorption or reflectance spectra of the solar selective absorber. Hence, in the design of solar selective absorber, the strategical objective is to find a suitable absorption or reflectance spectrum pattern by properly choosing the film structure, thickness, and the constituted materials.

4.1 Spectrally Weighted Broadband Solar Absorption The sun radiates nonuniformly in the wavelength range from 250 to 2500 nm, with energy mainly concentrated in the ultraviolet, visible, and near-infrared region. In comparison, blackbody radiates the electromagnetic energy at the same time in the long-wavelength range [4, 8, 9, 22, 28]. This type of spectral features of absorptance and emittance required for the solar selective absorber makes it possible for people to design the device in many proper ways in the study based on the optical principle and feasible technologies. Under the ideal condition, the solar selective absorber should have the zero reflectance and transmittance of light in the visible and near-infrared wavelength range, and close to 100% reflectance in the long-wavelength range, to have a step-like spectra function as shown in Fig. 20. The cutoff wavelength depends on the designed operating temperature of the device since Planck’s blackbody radiation scales inversely with temperature [34]. For the ideal solar selective absorber, solar light can be absorbed completely due to its 100% absorption of spectral properties designed in the certain and expected wavelength region. However, for the

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Fig. 20 The standard AM 1.5 solar radiation spectrum in solid red line, Planck’s blackbody radiation at 373 K in dashed bule line, the ideal solar selective absorbing spectrum in dashed black line, and the typic solar absorbing spectrum in solid green line [4]

actual solar selective absorber, the solar absorptance should be weighted by the solar radiation spectrum, which can be expressed as [4, 34]:  λn α=

λ1

[1 − R(0, λ)]dλ  λn λ1 L sun (λ)dλ

(4.1)

To realize high-efficient solar absorption, the solar absorber should have high light absorptance in the spectral region covering the entire solar radiation. Nevertheless, the higher solar absorptance will make the solar absorption spectrum be expanded to the long-wavelength region, resulting in overlap more with the spectra of Planck’s blackbody radiation, especially at the higher temperature, implying a higher infrared thermal radiation loss.

4.2 Thermal Gain and Loss of the Infrared Absorption and Reflection According to Kirchhoff’s Law, the absorptance of a light absorber is equal to its emittance under the thermal equilibrium state. To reduce the thermal emittance due to the temperature rising of the absorber when cumulatively heated by absorbing sunlight, a metal reflection layer always was used to increase its reflectance in the long-wavelength range. The opaque metal reflection layer also has the advantage to make the optical transmittance be zero of the absorber body. According to the law of energy conservation, hence, the absorptance α and emittance ε at the wavelength λ can be described as:

Optical Properties of Solar Absorber Materials and Structures

a(λ) = e(λ) = 1 − T (λ) − R(λ) = 1 − R(λ) = A(λ)

47

(4.2)

Here, T (λ), R(λ), and A(λ) is the transmittance, reflectance and absorptance of the absorber at wavelength λ. Thermal emittance of the solar selective absorber can be obtained by [4, 34, 42, 103]: ∞

[1 − R(λ)]L b (λ, T )dλ ∞ 0 L b (λ, T )dλ −1  c  c1 2 −1 L b (λ, T ) = 5 exp λ λT

ε(θ, T ) =

0

(4.3) (4.4)

where L b (λ, T ) is the Planck blackbody radiation spectrum at temperature T. c1 and c2 , (c1 = 3.7405 × 108 W·μm4 ·m−2 and c2 = 1.43879 × 104 μm·K), are Planck’s first and second radiation constants, respectively. Figure 21 shows Planck’s blackbody radiation spectrum at different temperatures. As can be seen, the spectral power of radiation increases dramatically with the increasing of temperature. Moreover, the peak wavelength of blackbody radiation spectrum shifts to the short wavelength range with the increase of temperature, which will lead to more overlap between the solar absorption spectrum of solar selective absorber and the blackbody radiation spectrum. Therefore, thermal radiative losses of the absorbers will increase with the temperature proportionally in fourth power of temperature. Fig. 21 Planck’s blackbody radiation spectrum at different temperatures

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Fig. 22 Plane wave incidents on a film system (the subscript represents the layer number, while m means the substrate)

4.3 Optical Evaluation of the Solar Absorbers In terms of Eqs. (4.1)–(4.3), reflectance spectra of the solar absorber are always adopted to obtain its solar absorptance and thermal emittance. According to the transfer matrix method used in the film device design, for a single layer with film thickness of d 1 and incident angle of φ1 , its characteristic matrix can be expressed as [33]:

B C



=

cosφ1 ηi1 sinφ1 iη1 sinφ1 cosφ1



1 η2

(4.5)

where, φ1 =

2π N1 d1 cosθ1 λ

η1 = N1 cosθ1 for s-polarized light (TE wave) N1 for p-polarized light (TM wave). η2 = cosθ 1 N1 = n 1 + iκ1 Then the optical admittance of the single layer can be obtained by Y = C/B. The characteristic matrix of a film system can be obtained:

B C

  q  cosφr ηir sinφr 1 = η iη sinφ cosφ m r r r r =1 

(4.6)

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49

where φr =

2π Nr dr cosθr λ

ηr = Nr cosθr for s-polarized light (TE wave), Nr for p-polarized light (TM wave). ηr = cosθ r Then, the optical admittance of the entire film system can be obtained. Reflectance of the film system is derived by:  R=

η0 − Y η0 + Y



η0 − Y η0 + Y

∗ (4.7)

where * represents complex conjugate and η0 = 1. After that, we can theoretically obtain the solar absorptance and thermal emittance for various optical thin film systems, which can be used to design and optimize the optical properties of the multilayered solar selective absorber. For the experimental characterization, the reflectance spectrum of a solar absorber can be measured by the UV–Vis-infrared spectrophotometer over the wide solar radiation spectra range. The incident angle-dependent reflectance spectra can also be measured to obtain the angle tolerance of different solar selective absorbers. Figure 23 shows the reflectance spectra of a nano-Cr film-based six-layer solar selective absorber at different incident angles [27]. As can be seen, with the increase of incident angle, reflectance of both of the p and s-polarized light increase, though they exhibit different behaviors.

Fig. 23 Incident angle-dependent reflectance spectra of solar selective absorber under a p and b s-polarized light [27]

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Fig. 24 Effects of annealing duration and temperature on the reflectance spectra of the Inconel625/MoSi2 -Si3 N4 (FF = 50%) (50 nm)/MoSi2 -Si3 N4 (FF = 10%) (50 nm) /Al2 O3 (66 nm) and Inconel-625/MoSi2 -Si3 N4 (FF = 60%) (50 nm)/MoSi2 -Si3 N4 (FF = 10%) (50 nm) /Si3 N4 (20 nm)/Al2 O3 (40 nm) sample [104]

The reflectance spectra are also employed to characterize the thermal stability of the solar selective absorber. Figure 24 shows the effects of annealing duration and temperature on the reflectance spectra of the Inconel-625/MoSi2 -Si3 N4 (FF = 50%) (50 nm)/MoSi2 -Si3 N4 (FF = 10%) (50 nm)/Al2 O3 (66 nm) and Inconel-625/MoSi2 Si3 N4 (FF = 60%) (50 nm)/MoSi2 -Si3 N4 (FF = 10%) (50 nm)/Si3 N4 (20 nm)/Al2 O3 (40 nm) sample [104]. As can be seen from Fig. 5a, for the fixed annealing temperature at 600 K, the intensity of reflectance shows a small increase when the annealing time increases from 15 to 415 h. This led to an increase in PC value to about 0.015 (Performance Criterion = α − 0.5ε, while α and ε are the change in the absorptance and emittance, respectively [104]). Figure 5b shows the influences of annealing temperature on the reflectance spectra of the sample by fixing the annealing time at 15 h. By increasing the annealing temperature, the reflectance spectra show a variation, especially for the temperature of 700 °C. The increase in temperature will deteriorate the solar absorptance from 0.92 to about 0.90 affected mainly by the variation of optical properties of the individual layer materials working under the higher temperature condition, while the influence on the thermal emittance seems to be small and can be neglected.

5 Intrinsic Solar Selective Materials The intrinsic solar selective materials are homogeneous materials in which spectral selectivity is an intrinsic property of the materials. In general, they are structurally stable and easy to fabricate, but their natural optical absorption property appearing in the solar radiation spectral region is typically far from the desired specification suitable for solar absorber applications, offering poor optical spectral selectivity [4,

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51

Fig. 25 Reflectance of an ideal solar selective absorber compared to that of a metal and a heavily doped semiconductor [22]

9, 22, 28]. Therefore, there is no natural materials to exhibit intrinsically ideal solarselective properties that can matche to the specification satisfied by the industry standard, except from some roughly approximate selective properties. The intrinsic solar absorbing materials mostly are found to have the optical features of transition metals and semiconductors. For transition metals, the d atomic orbitals are not completely filled with electrons, after combining with oxygen, nitrogen, oxynitrides or others, their internal orbital energy gaps are appropriate to absorb the photons of visible light, which makes them potentially be the candidates suitable for solar selective materials [4]. In comparison, for semiconductors, only the incident photons with the energy higher than the bandgap of the semiconductor materials can be absorbed to selectively make the intrinsic optical absorption happen. Nevertheless, the bandgap has the value that is usually not high enough to serve as the cutoff wavelength for the solar selective applications [22]. Metallic W [29], MoO3 -doped Mo [105], Si-, B- doped CaF2 [106], Si [31], ZrB2 [30], HfC [107], SnO2 [107], In2 O3 [106], Eu2 O3 [108], ReO3 [108], V2 O5 [108], LaB6 [28], graphite [109], reduced graphene oxide [110], and carbon nanotube [111] have been proposed to be used as solar selective materials. The chemically vapordeposited (CVD) ZrB2 exhibited a plasmon frequency that roughly matches the ideal cutoff wavelength [30]. By combining with the Si3 N4 AR layer, the ZrB2 absorber showed a solar absorptance of 0.93 and an emittance of 0.09 at 375 K. It can also work stably in air to the temperature of 800 K. Carbon nanotubes (CNTs) dispersed in an alumina-silica matrix on Al substrate has been prepared to have a very high solar absorptance of 0.985 [111]. However, due to the low spectral selectivity, its thermal emittance has a large value reaching up to 0.9 at 100 °C, causing always huge energy loss not suitable for practical applications. A black paint named Pyromark 2500 also has been applied in high-temperature collectors, which can survive after thousands

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Fig. 26 a Measured absorptivity spectra for the silicon-nanowire-based solar absorber and silicon wafer. Insets are the optical photographs of silicon wafer (left) and silicon-nanowire sample (right). b SEM images of silicon-nanowire-based solar selective absorber before and after annealing at 1373 K for 1 h. c Absorptivity of silicon-nanowire-based solar selective absorber before and after 1 h’s annealing treatment at 1373 K [31]

of heating and cooling cycles at the temperature of 600–1000 °C [112]. It exhibits a solar absorptance of 0.96. However, its thermal emittance is as high as 0.8 at 800 °C, which will limit its applications as well. Wang et al. fabricated a silicon-nanowire-arrays-based solar selective absorber by combining lithography and reactive ion etching [31]. The absorber exhibits an extremely sharp transition cut-off with a spectral transition region of about 200 nm as illustrated in Fig. 26a. The absorption efficiency measured for the device in the spectral range above the bandgap is about 97%, while it drops to about 15% in the spectral range below the bandgap. The sharp absorption cut-off between the high and low optical absorptance will be highly favored for the spectral selectivity of solar selective absorber. The structure of the silicon-nanowire-based solar selective absorber keeps nearly unchanged after annealed at 1373 K for 1 h as depicted in Fig. 26b. Moreover, the absorption spectra before and after high-temperature annealing are almost unchanged as well with results presented in Fig. 26c. Recently, a reduced graphene oxide-based spectrally selective absorber (rGO) has been fabricated successfully, which possesses a solar absorptance of 0.92 with a recorded low thermal emittance of 0.04 at 100 °C for the carbon-based materials as presented in Fig. 27 [110]. The GO suspension is made on the polished Al substrate

Fig. 27 a The absorptance spectra of the Al/rGO/ARC solar selective absorber. b In-situ thermal emittance of the rGO-based solar selective absorber, Al substrate, and the black-body paint (inset is IR photos of the samples at a heating temperature of about 100 °C) [110]

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and then is coated and hydrated in tetraethoxysilane (TEOS) solution successively to form the Al/GO/TEOS multilayer structure. The sample is then heat-treated at 300 °C for 30 min to change GO to the rGO film. The TEOS gel will transform to silica nanoparticles layer, which will serve as the anti-reflection layer to reduce the reflection loss. By adjusting the film thickness of the rGO layer, the cutoff wavelength of rGO solar selective absorber can be tuned to range from 1.1 to 3.2 μm. The rGO based solar selective absorber also shows a high-temperature tolerance at 800 °C for 96 h. In general, intrinsic solar selective materials are not the ideal candidates used in solar selective absorbers. Performance can always be improved by combining intrinsically solar selective materials with more advanced selective absorber designs, such as multilayer thin film stacks or cermets. So in practice, intrinsic materials are not typically used alone.

6 Semiconductor–metal Tandems Semiconductor materials are generally transparent in the spectral region where photons with the energy below the bandgap of the material are not absorbed, but will turn to be opaque beyond the region where photons with the energy higher than the bandgap can be strongly absorbed. If a semiconductor is placed on top of the reflective metal to form a semiconductor–metal tandem, the solar radiation in the short wavelength (higher energy) region will be absorbed by the semiconductor, while the solar radiation in the long-wavelength (low energy) region will transmit through the semiconductor layer and get reflected by the underlying metal layer, providing low thermal emittance with desired spectral selectivity for the semiconductor–metal-tandem absorber [9, 22]. Semiconductors with forbidden bang gaps ranging from about 0.5 eV (2.5 μm of wavelength) to 1.5 eV (0.8 μm of wavelength) are supposed to be suitable for solar absorbing applications. Those semiconductor materials have the proper energy gap (E g ), like silicon (E g = 1.1 eV), germanium (E g = 0.7 eV), lead sulfide (E g = 0.4 eV), and so on [4, 9, 22, 28, 57]. However, semiconductors typically have a high refractive index in the solar radiation region, resulting in higher detrimental reflectance losses. Hence, high porosity and antireflection coatings on the top surface of semiconductors usually will be required to reduce the high reflection effect in applications. Donnadieu et al. designed a solar absorber device consisting of a silicon/germanium tandem absorber on a silver reflector [113]. The device has a fourdielectric-layer structure with refractive indices varying from 1.43 to 2.79 acting as the antireflection layer. The optimized solar absorptance is 0.89 by numerical simulations with the thermal emittance of 0.0389 and 0.0545 at each temperature of 300 K and 600 K, respectively. Okuyama et al. fabricated the amorphous silicon on the aluminum reflector with an antireflection layer consisting of SiO2 and TiO2 [114]. A solar absorptance of 0.79–0.81 with the thermal emittance of 0.12–0.14 at 400 °C is

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Fig. 28 a Schematics of the Ge/Ag solar selective absorber with front- and back-side coatings to optimize the device performance working under the unconcentrated sunlight and temperature of 400 K conditions. b Thermal emittance spectra of the designed Ge-based solar selective absorber. c The film structure of the Si-based solar selective absorber [115]

demonstrated for the amorphous silicon-based solar selective absorber [114]. Chatterjee and Pal prepared a lead sulfide-based solar absorber by thermal evaporation technique. A solar absorptance of 0.95–0.97 with the thermal emittance of 0.21–0.27 at 375 K is obtained for the sample [75]. Bermel et al. numerically optimized two sets of solar selective absorbers aiming at the two different operating conditions [115]. First, a germanium absorber and silver reflector with the optimized front- and back-side coatings are designed to work at the unconcentrated AM1.5 sunlight and temperature of 400 K conditions as presented in Fig. 28a. The optimized emittance spectra is shown in Fig. 28b. The light absorptance of the designed film structure is very high in the short wavelength region but decreases rapidly with a wavelength over 2 μm. A solar absorptance of 0.907 with the thermal emittance of 0.016 at 400 K is achieved for the germanium-based solar absorber. For concentrated sunlight (C = 100) at the absorber temperature of 1000 K, silicon is chosen due to its appropriate bandgap. The film structure of the designed siliconbased solar selective absorber is illustrated in Fig. 28c. At this condition, the solar absorptance and thermal emittance for the designed solar selective absorber are 0.868 and 0.073, respectively. In 2017, Tian et al. fabricated semiconductor–metal tandem solar selective absorbers based on commercially available Si wafer [116]. The selective absorber consists of a standard 300 μm, double side polished Si wafer, sandwiched by a 300 nm-thick silver layer and 215 nm Si3 N4 antireflection layer as shown in Fig. 29a. The device shows a high absorption selectivity at a temperature as high as 490 °C. Under solar concentration of 50 Suns and temperature of 490 °C, the solar absorber shows a solar absorptance of 0.7022 with the thermal emittance of 0.4877, yielding a photo-thermal conversion efficiency of about 0.5148. The silicon-based solar selective absorber is demonstrated to be mechanically and thermally stable at a higher temperature of 535 °C. However, thermal re-radiation increases dramatically for the

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55

Fig. 29 a Measured and simulated emissivity of the solar selective absorber with and without front Si3 N4 antireflection coating at room temperature. b The simulated emissivity of the Si-based solar selective absorber with different Si thicknesses [116]

Si-based absorber at elevated temperatures due to the increased free carrier absorption and lattice absorption of Si. By thinning the Si wafer to the thickness of 5 or 10 μm, the problem can be mitigated to produce a thermal transfer efficiency of about 60–70% at the solar concentrations of 20–100 Suns. An amorphous Ge-Ag-based selective solar absorber was proposed by Thomas et al. as shown in Fig. 30a [80]. Ge is chosen due to its favorable energy bandgap while CaF2 is used as the antireflection layer because of its low refractive index of about 1.4 and transparency in the infrared region up to the wavelength of 20 μm. Figure 30b gives the reflectance spectra of the sample measured before and after sample-exposing under the Sun for 4 cycles and under an AM 1.5G solar simulator for 2 cycles. The sharp drop of the optical absorption to about 76% can be observed

Fig. 30 a Cross-sectional TEM images for the fabricated Ge-based solar selective absorber. b Reflectance spectra of the sample measured before and after cycling exposure under the Sun and AM 1.5G solar simulator [80]

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at the energy bandgap position with a low thermal emittance of about 5% at the thermal wavelengths. By using the absorber, a peak temperature of 225 °C is obtained under the unconcentrated solar thermal system, while the optimization of the system shows the stagnated working temperature can exceed 300 °C. The results indicate the potential of eliminating the need for solar concentrators for mid-temperature solar applications [80]. For the semiconductor–metal tandem solar selective absorbers, due to the electron–hole pair generation and free carrier emission at high temperatures intrinsically happened by the material, it is still challenging to achieve low thermal emittance of the device [9, 116]. Moreover, the semiconductor materials are always not stable at high temperatures, hence a diffusion barrier could be required as a buffer to reduce the high-temperature diffusion effect [4, 57].

7 Metal-Dielectric-Based Multilayers A multilayer solar selective absorber consists of alternate layers of dielectrics and semi-transparent metals as illustrated in Fig. 31 [4, 9, 11, 22, 26–28, 42, 57, 103]. The bottom metal layer serves as the reflection layer to reflect the infrared radiation mainly from the heated substrate, which will reduce the thermal emittance of the solar absorber. It also assures the light transmittance of the absorber to be negligible. The absorption of incident solar light is greatly enhanced due to the intrinsic absorption of the semi-transparent metal layer when they are repeatedly reflected between the semi-transparent metal layer and the reflective metal layer, which is known as the destructive interference effect [4, 9, 42]. The film thickness of the semi-transparent layer will range from several nanometers to about twenty nanometers depending on the optical constants of the thin metal layer [34, 57, 117]. Moreover, more layers adding to the system can widen the high-absorption spectral band [9, 27, 34]. In solar selective absorbers, metals such as Al, Cu, Mo, W, Fe, Cr, stainless steel, nickel, nimonic have been used as the infrared reflection layer [45, 79, 118, 119]. For the light absorption layer, materials such as Cr, Ti, Pt, Zr, Al, nitride, silicide, and

Fig. 31 Schematic film structure of the metal-dielectric-based multilayer solar selective absorber [4]

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silicon–nitride compound have been chosen [26, 41, 42, 47, 119–121]. Dielectrics including SiO2 , Cr2 O3 , TiO2 , AlN, Si3 N4 , MgO, Alx Oy , nitride, and oxynitride have been adopted to serve as the protection layer [23, 26, 44, 120, 122–125]. By properly choosing the metal and dielectric materials, layer numbers, and film thickness of each layer, high-efficient solar selective absorbers can be achieved. Computer aid design methods have been well developed to figure out the optimal design for the multilayer-based solar selective absorber. Based on the optical constants obtained from the tabulated data for different dielectric and metal materials in literature [35], the reflectance and transmittance spectra for the multilayer film structure can be numerically simulated based on the transfer matrix method [33]. Consequently, the solar absorptance, thermal emittance, and solar thermal conversion efficiency can be given. By combining with the design method such as the semiempirical method [26, 42, 126], traversing method [127], or the admittance locus method [128, 129], the solar absorptance of the multilayer solar selective absorber in the primary solar radiation spectra like in the wavelength range of 300–1200 nm can be maximized [27, 103]. In a recent work [130], deep Q learning method have also been implemented to design multilayer solar selective absorber by optimizing the light absorptance in the wavelength range from 300 to 1400 nm. For metal-dielectric multilayer solar selective absorber, its spectral selectivity is associated with the Fabry–Perot resonance and anti-reflection effects [131]. Hence, its film structure can be designed semi-empirically. A four-layered solar selective absorber with the film structure of SiO2 (105 nm)/Ti (15 nm)/SiO2 (95 nm)/Al (100 nm) was proposed by Li et al., which showed an average optical absorptivity over 95% in the wavelength range of 450–1000 nm at normal incidence [26]. The film structure also exhibits a good optical absorption property up to an incident angle of 60°. Zhou et al. further investigated the influences of different transition metals, reflective metal layers, dielectric materials on the optical absorptance of a four-layered solar selective absorber [42]. The film structure of SiO2 (90 nm)/Cr (10 nm)/SiO2 (80 nm)/Al (≥100 nm) was proposed with the average optical absorptance higher than 95% in the 400–1200 nm wavelength range. Admittance-matching method, as an optical interference film design technique that has been extensively used in the modeling and design of filters, is also adopted to design the solar selective absorbers [128, 129]. For planar film structure, its optical admittance can be properly obtained by using the optical transfer matrix method. When the optical admittance of the multilayer film structure equals the incident medium (1 + 0i for the air), there will be no reflected light at the medium/film interface. For the design of solar selective absorber, the admittance-matching condition must be maintained over a wide wavelength range to cover the main solar radiation spectra region. In addition, the equivalent extinction coefficient of the multilayer film structure should be large enough to absorb the incident light. With the admittancematching method, Chen et al. designed a Mo-based solar selective absorber with the film structure as SiO2 (64.32 nm)/Nb2 O5 (30.21 nm)/Mo (7.16 nm)/Nb2 O5 (37.53 nm)/Mo (150 nm). The admittance loci at 550 nm for the designed solar selective absorber were depicted in Fig. 32a. As can be seen that, by adding the layers of Mo, Nb2 O5, and SiO2 , the admittance changes from 1.52 to 1.15–0.06i,

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Fig. 32 a Admittance loci at 550 nm of the designed solar selective absorber by Chen et al. b The reflectance spectra for the designed Mo-based five-layered solar selective absorber [128]

approaching the value of 1 for air. The reflectance spectra were presented in Fig. 32b. The reflectance is quite low in the wavelength range of 500 to 900 nm due to admittance matching between the proposed solar selective absorber and air in this wavelength range. The solar selective absorber with advanced features should harvest the incident solar energy as much as possible and at the same time suppress effectively the infrared radiation due to the heating of the solar absorber. Since most solar selective absorbers are designed atop of metal reflection layer or metal substrate, the low thermal emittance often can be satisfied due to the high reflectivity in the long-wavelength range. Hence, fitting the target reflectance value of 0% in the main solar radiation wavelength range can be employed to design solar selective absorber [27, 34, 103, 132]. Liu et al. [103] and Hu et al. [27] designed a Ti and Cr-based six-layered solar selective absorber, respectively, by varying the film thickness of each layer to fit the reflectance of 0% in the wavelength range from 250 to 1200 nm. The global-modified Levenberg–Marquardt method was employed to minimize the difference between the designed target and simulated result at each wavelength [27]. The designed solar selective absorber can obtain a solar absorptance of about 95.5% with thermal emittance of about 0.09–0.1. By adding more of layers, the wavelength range of the target function can also be extended to overlap more with the solar radiation photon region [34, 132]. Other optimization methods such as the needle optimization method [132], deep Q-learning method [130] were also used to design solar selective absorber. Besides the parameter of solar absorptance, the merit function of F(T ) = αsolar × [1−εthermal (T )] was also proposed as the optimization objective to design metaldielectric multilayer stacks because of its independence of geometry and operation [82, 133]. In the merit function, αsolar is the fraction of solar radiation absorbed by the multilayer stack at normal incidence, while εthermal (T ) is the integrated emissivity over both the azimuthal angle and wavelength at temperature T. By using the needle optimization method, the solar selective absorbers based on Mo-MgF2 -TiO2 and W-MgF2 -TiO2 planar aperiodic multilayer structures were designed, respectively,

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Fig. 33 The optimized hemispherical absorptivity spectra for the aperiodic multilayer metaldielectric solar selective absorber with the operation temperature fixed at 720 K. a Mo, TiO2, and MgF2 and b W, TiO2 , and MgF2 [133]

with the operation temperature fixed at 720 K [133]. The results were presented in Fig. 33a, b. By increasing the layer numbers, the solar absorptance and the merit F for both solar absorbers are dramatically increased, while the thermal emissivity has only a marginal increase. For the 11 layers of Mo or W-based solar selective absorbers, the solar absorptance was about 0.94–0.95 and the merit function F was about 0.88–0.89. The thermal emissivity was about 0.06 for both of the 11-layered solar selective absorbers. For the solar selective absorber, its solar photothermal conversion efficiency will be more valuable to be optimized than just considering only its solar absorptance. The particle-swarm optimization method [131], genetic algorithm [117, 134] have been proposed to directly optimize the solar photo-thermal conversion efficiency of the solar selective absorber. By using the particle swarm optimization algorithm to maximize the solar-topower conversion efficiency, Wang et al. designed a sub-micro-thick selective fivelayered solar thermal absorber made of tungsten, SiO2 , and Si3 N4 [131]. The multilayer solar selective absorber is constituted of SiO2 /Si3 N4 /W/SiO2 /W from top to bottom. The film thickness of each layer was optimized for the solar radiation intensity of 50 Suns and absorber temperature at 100, 400, 600, and 800 °C, respectively. Figure 34a shows the optimized absorptance spectra of the five-layered film structure at the normal incident condition. The high optical absorptance in the visible to near-infrared wavelength range with low absorptance in the long-wavelength range indicates the good solar selectivity of the designed solar selective absorber. The evolution of solar power conversion efficiency with the iteration numbers is illustrated in Fig. 34b. The maximum solar-to-power conversion efficiency is 18.1%, 50.6%, 57.3%, and 54.8%, respectively at the corresponded temperature of 100 °C, 400 °C, 600 °C, and 800 °C. Genetic algorithm, mimicking the natural process of biological evolution, has been also used to design the multilayer solar selective absorber [117, 134]. Sakurai

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Fig. 34 a Simulated absorptance spectra of the optimized multilayered solar selective absorber at the normal incidence. b Calculated maximum solar-to-power efficiency after the optimization under different temperatures [131]

et al. used the genetic algorithm method to study the multilayered W-SiO2 cermetbased solar selective absorber [134]. The layer number, film thickness, and metal volume fractions are optimized to maximize the photo-thermal conversion efficiency. Wang et al. [117] also used the genetic algorithm to design multilayer solar selective absorber by using the measured optical constants for the ultrathin thin Cr absorption layer rather than the tabulated data in literature [35]. The solar photothermal conversion efficiency is defined as the evolution function. The large discrepancy between the optimized results by using the measured optical constants and the data from the literature for the ultrathin Cr absorption demonstrates the significance of using the practical optical constants for the ultrathin metal film, especially with film thickness smaller than its electron mean free path [117]. The influences of temperatures and solar concentrations are also particularly investigated in the work. For the fabrication of solar selective absorbers, though wet chemical methods such as electrodeposition, electro-less deposition, anodization, sol-gel, and other solutionbased methods have been reported for fabrication of the solar selective absorber, due to the lower chemical and thermal stability caused by the wet chemical methods with consideration of the environmental pollution in the fabrication process, physical vapor deposition method has been the mainstream technology for the fabrication of solar selective absorbers [8, 37]. Li et al. fabricated a typical four-layered solar selective absorber with the film structure of SiO2 (105 nm)/Ti (15 nm)/SiO2 (95 nm)/Al (≥100 nm) with the magnetron sputtering method [26]. The sample shows a high solar absorption of greater than 95% in the 400–1000 nm wavelength region. The sample can also hold its high optical absorption characteristic even with the incident angle increasing up to 60°. Other metals of Cr, Zr, Pt, Al, W are also employed to be used as the absorption layer [11, 41, 42, 120, 125, 132, 135]. With the typical four-layered film structure, the nano-Cr-film-based solar selective absorber can obtain a higher solar absorption of 95% in the 400–1200 nm wavelength. By adding the layer numbers, the wavelength

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range with high optical absorptance can be extended to overlap more with the solar radiation spectrum and obtain a higher solar absorptance [27, 34, 81, 103, 132]. For the typical multilayer solar selective absorbers, the semi-transparent absorption metal layer with film thickness from several nanometers to about twenty nanometers may chemically react with its adjacent layer to deteriorate the thermal stability of the solar selective absorber under high temperature. To improve the thermal stability of solar selective absorbers, nitrides, and oxynitrides were usually adopted [136, 137]. Barshilia et al. fabricated TiAlN/TiAlON/Si3 N4 tandem absorbers on copper substrate by a reactive direct current magnetron sputtering system and obtain a solar absorptance of 0.958 and an emittance of 0.07 (82 °C) [45]. In the absorber, TiAlN is the main absorption layer, while the Si3 N4 and TiAlON act as the antireflection layer and semi-absorber layer, respectively. The film structure is depicted in Fig. 35a and the film thickness for TiAlN, TiAlON and Si3 N4 are 42, 24, and 34 nm, respectively. The sample can work stably at 625 °C in air for 2 h and 525 °C for 50 h. They further proposed the other multilayered film structures such as: Cu/Ti/AlTiN/AlTiON/AlTiO, stainless steel (SS)/Ti/AlTiN/AlTiON/AlTiO, SS/W/TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO, SS/W/WAlN/WAlON/Al2 O3 [138–140]. The Cu/Ti/AlTiN/AlTiON/AlTiO-based solar selective absorber exhibited a solar absorptance of 0.933 and thermal emittance of 0.07 (82 °C). For the sample deposited on the SS substrates, the solar absorptance is 0.930 with the thermal emittance of about 0.16–0.17 to work stably in air and vacuum up to 350 and 450 °C, respectively, under cyclic heating for more than 1000 h. The reflectance spectra of the absorber after heat treatment at 450 °C in vacuum for different durations are presented in Fig. 35b. For the SS/W/TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandem absorber, high solar absorptance of 0.961 with the low thermal emittance of 0.07 (82 °C) is achieved. The absorber shows high thermal stability up to 325 °C in air for 400 h and up to 650 °C in vacuum for 100 h as illustrated in Fig. 35c, d. The SS/W/WAlN/WAlON/Al2 O3 -based solar absorber shows an absorptance of 0.958 with the thermal emittance of 0.08 at 82 °C [140]. Its thermal stability is carefully investigated by heating the sample in the temperature range of 300–550 °C for 2 h by several steps. The reflectance spectra with the absorptance and thermal emittance are recorded after the cooling of the absorber. The variation trends of absorptance and emittance as a function of temperature are presented in Fig. 35e. The reflectance spectra of the as-deposited and heat-treated samples in air for 2 h are shown in Fig. 35f. Results prove that the sample can work stably in air up to 450 °C. Many of other multilayered solar selective absorbers based on nitrides, oxynitrides were also studied such as: Cu/Ti0.5 Al0.5 N/Ti0.25 Al0.75 N/AlN [141], Al/Ti0.5 Al0.5 N/Ti0.25 Al0.75 N/AlN [122], Cu/TiAlSiN/TiAlSiON/SiO2 [142], Cu/Ti/AlN/Ti/AlN [25], Cu/AlN/Ti/AlN/Ti/AlN [25], SS–(Fe3 O4 )/Mo/TiZrN/TiZrON/SiON [143], Al/NbTiSiN/NbTiSiON/SiO2 [144], Cu/Zr0.2 AlN0.8 /ZrN/AlN/ZrN/AlN/Al34 O62 N4 [73], Cu/TiNx Oy /TiO2 /Si3 N4 /SiO2 [145]. The other strategy to improve the thermal stability of multilayered solar selective absorber is introducing the barrier layer between the metallic reflection layer and the covering layer to suppress the outward atom diffusion from the bottom metal because

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Fig. 35 a Cross-sectional TEM image of TiAlN/TiAlON/Si3 N4 tandom absorber [45]. b Reflectance spectra of the SS/Ti/AlTiN/AlTiON/AlTiO tandom absorber after heat treatment at 450 °C in vacuum [138]. c and d Reflectance spectra of the SS/W/TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO tandom absorber. Heat treatment is done in air at 325 °C and in vacuum at 600 °C, respectively [139]. e Temperature dependent solar absorptance and thermal emittance of the SS/W/WAlN/WAlON/Al2 O3 tandom solar absorber [140]. f Reflectance spectra of the as-deposited and heat-treated SS/W/WAlN/WAlON/Al2 O3 tandom solar absorber in air for 2 h [140]

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of the high mobility of atoms in some metals at elevated temperatures [46, 47, 83, 84, 146, 147]. Different metallic materials such as Ta [47], Mo [46], and Al [84] have been adopted to serve as the diffusion barrier layer in solar selective absorber to improve its thermal stability. Selvakumar et al. fabricated a Cu/HfOx /Mo/HfO2 solar selective absorber by a magnetron sputtering system [46]. Initially, the sample is only thermally stable up to 400 °C for 2 h in air. To improve its thermal stability, a thin Mo interlayer with a thickness of 40 nm is added to form the multilayer film structure as Cu/Mo/HfOx /Mo/HfO2 . The new sample shows to have higher thermal stability to work stably in air up to 500 °C for 2 h. Nuru et al. proposed a multilayer solar selective absorber of Cu/Ta/Alx Oy /Pt/Alx Oy by e-beam evaporation method [47]. The sample is found to be thermally stable up to 700 °C in air for 2 h. In comparison, the Cu/Alx Oy /Pt/Alx Oy absorber can only work stably in air up to 500 °C and degraded at higher temperatures [148]. In the above-mentioned works, the metallic barriers were deposited by the sputtering or e-beam evaporation method. In fact, the atomic layer deposition (ALD) technology has been widely used to fabricate barrier layer against copper diffusion in the microelectronic industry [149] because films deposited by ALD exhibit a dense, conformal, uniform, non-columnar, and defect-free film structure as compared to that deposited by other vacuum deposition methods [150]. Kotilainen et al. investigated the thermal stability of copper substrate used in solar thermal absorbers with and without HfO2 barrier films deposited by ALD at the temperature of 200–400 °C [83]. Results show that a 50 nm thick HfO2 can prevent Cu oxidation and diffusion happened at the interface after 2 h’ heat treatment in air at 300 °C, resulting in low thermal emittance retained after heat treatment. Wu et al. fabricated a six-layered Cu (>100.0 nm)/Al2 O3 (59.8 nm)/Cr (17.8 nm)/SiO2 (66.3 nm)/Cr (4.4 nm)/SiO2 (83.0 nm) solar selective absorber [147]. The magnetron sputtering method is used to prepare Cu, SiO2 , and Cr layers, while ALD method is adopted to deposit Al2 O3 layer. Compared to the sample with all film layers deposited by magnetron sputtering, the ALD-Al2 O3 sample works stably at 500 °C for 72 h. Figure 36a, b show the reflectance spectra of the ALD-Al2 O3 sample and the sputtered sample after annealing at 500 °C for different durations. As can be seen that, after the initial 2 h’ heat treatment, the reflectance spectra of ALD-Al2 O3 sample keeps nearly unchanged, while for the sputtered sample, the reflectance decreases gradually in the long-wavelength range with annealing time. XPS depth profiles for the annealed sputtered sample and ALD sample are depicted in Fig. 36c, d. As clearly shown that for the sputtered sample, Cu atoms have diffused through the SiO2 layer and into the space region of the Cr layer. In comparison, Cu diffusion is effectively suppressed by the ALD-Al2 O3 layer inserted into the ALD-sample. For the ideal solar selective absorber, its absorptance spectra should have the feature like a step-function profile with a very sharp cutoff wavelength [8, 22, 31]. The sharp cut-off between the high solar absorption band and the low infrared emission band is critical for efficient solar energy conversion. In most of the proposed solar selective absorbers, however, the cut-off wavelength region is always quite wide, ranging from 1.08 μm to about 9.36 μm, which is very detrimental to high efficient

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Fig. 36 a Reflectance spectra of the ALD sample after heat treatment at 500 °C for different times. b Reflectance spectra of the sputtered sample at the temperature of 500 °C. c and d XPS depth profiles for the annealed samples fabricated by the conventional sputtering and special ALD methods, respectively [147]

solar thermal conversion [31]. To overcome the problems, Thomas et al. proposed a semiconductor-based multilayered film structure for solar thermal purposes [80]. Semiconductors can strongly absorb those incident photons with the energy above the bandgap, while very little absorption for the photons with sub-bandgap energies, resulting in a quite narrow bandwidth for the transition from absorbing to nonabsorbing. The film structure was illustrated in Fig. 37a. Amorphous Ge is selected due to its favorable bandgap energy. Reflectance spectra of the sample are presented in Fig. 37b. As can be seen that, the transition region from low to high reflectance is about 0.5 μm. The solar selective absorber achieved a measured absorptance of 76% at solar wavelength and a low thermal emittance of approximately 5% at thermal wavelengths. The stagnation temperature of the surface under solar insolation was tested with the results shown in Fig. 37c. The peak temperature can achieve 225 °C, comparable to that obtained with state-of-the-art selective surfaces. By appropriately adjusting the layer number and film thickness of the multilayer solar selective absorbers, it can show a colorful appearance, which is very interesting for applications of architecture integration and military camouflage [25, 145, 151,

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Fig. 37 a Schematic of multilayer film structure consisting of Ag, CaF2 , Cr, and amorphous Ge. b Measured reflectance spectra of the sample before and after the sun exposure. c Sample surface temperature over the day under solar insolation [80]

152]. Wu et al. designed and fabricated five-colored solar selective absorbers with Ti and AlN multilayer film structures [25]. Figure 38a shows one of the solar selective absorbers with the film structure as Cu (120 nm)/Ti (24 nm)/AlN (52 nm)/Ti (25 nm)/AlN (83 nm). The sample shows the purple color with a solar absorptance of 0.94 and thermal emittance of 0.05. The color coordinates of the five samples in the CIE tristimulus chromaticity diagram are presented in Fig. 38b. Five colors of black, purple, yellowish green, yellowish orange, and red were produced. Chen et al. presented a monolithic integration of colored solar absorber array with different colors on a single substrate based on a multilayered structure of Cu/TiNx Oy /TiO2 /Si3 N4 /SiO2 [152]. By controlling the film thickness of the SiO2 , the colored solar selective absorber array is produced as shown in Fig. 38c–d. The measured reflection spectra of the 16 elements in the colored solar selective absorber array were presented in Fig. 38e. All the absorbers can absorb more than 92% of the solar radiation with the thermal emissivity ranging between 3.3% and 5.5%. The chromaticity coordinates of the colored solar selective absorber array are illustrated in Fig. 38f, indicating the wide color gamut of the proposed solar selective absorber. With respect to the advantages of design flexibility, fabrication, and high performance of the solar device, multilayer solar selective absorbers have been extensively investigated in the past decades, demonstrating certainly the potential of application in the middle to high-temperature solar thermal conversion system. Table 1 reviews and summarizes the typical examples of multilayer solar selective absorbers.

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Fig. 38 a Reflectance spectra of the sample with the film structure of Cu (120 nm)/Ti (24 nm)/AlN (52 nm)/Ti (25 nm)/AlN (83 nm) [25]. b Chromaticity diagram of the colored solar selective absorber with Ti and AlN multilayer film structure [25]. c Schematic diagram of monolithic integrated colored solar selective absorber array with different thickness of SiO2 [152]. d Image of the fabricated colored solar selective absorber array. e Measured reflectance spectra of each element in the colored solar selective absorber array. f Chromaticity coordinates for each element of the colored solar selective absorber array [152]

8 Metal-Dielectric-Composited Cermets Metal-dielectric-composited cermets mainly consist of nanoscale metal particles embedded in dielectric matrix, which can absorb well the sun radiation in the visible and near-infrared region due to interband absorption in the cermet layers and the small particle resonance [4, 37]. Generally, a single homogeneous cermet film does not show extremely high solar selectivity itself because of the impedance mismatch

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Table 1 Multilayer solar selective absorbers Material and film structure

Solar Thermal absorptance α emittance ε

Thermal stability

Al/ SiO2 /Ti/SiO2 [26]

0.95

0.063 (327 °C)

–

Cu/TiAlN/TiAlON/Si3 N4 [45]

0.958

0.07 (82 °C)

2 h at 625 °C in air, 50 h at 525 °C in air

Cu/NbAlN/NbAlON/Si3 N4 [23]

0.956

0.07 (82 °C)

116 hat 450 °C in air

Cu/TiAlN/AlON [153]

0.931–0.942

0.05–0.06 (82 °C)

100 h at 400 °C in air

Cu/Alx Oy /Al/Alx Oy , Mo/Alx Oy /Al/Alx Oy [41]

0.95–0.97

0.05–0.08 (82 °C)

400 °C in air (Cu), 450 °C in air and 800 °C in vacuum (Mo)

Cu/HfOx /Mo/HfO2 , Cu/Mo/HfOx /Mo/HfO2 , SS/HfOx /Mo/HfO2 [46]

0.905–0.923 (Cu), 0.902–0.917 (SS)

0.07–0.09 (Cu, 82 °C), 0.15–0.15 (SS, 82 °C)

2 h at 400 °C in air (Cu), 2 h at 500 °C in air (Cu/Mo), 2 h at 500 °C in vacuum (SS/Mo)

Cu/Ti0.5 Al0.5 N/Ti0.25 Al0.75 N/AlN [141]

0.945

0.04 (82 °C)

–

Cu/Alx Oy /Pt/Alx Oy [24, 124]

0.94

0.06 (82 °C)

–

Cu/TiAlSiN/TiAlSiNO/SiO2 [142]

0.96

0.05 (100 °C) 278 °C in air

SS/HfMoN(H)/HfMoN(L)/HfON/Al2 O3 [123]

0.94–0.95

0.13–0.14 (82 °C)

34 h at 475 °C in air, 450 h at 600 °C and 100 h at 650 °C in vacuum (continued)

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Table 1 (continued) Material and film structure

Solar Thermal absorptance α emittance ε

Thermal stability

Al/SiO2 /Cr/SiO2 [42]

0.95

0.058 (327 °C)

6 h at 600 °C in vacuum

Al/Ti0.5 Al0.5 N/Ti0.25 Al0.75 N/AlN [122]

0.926–0.945

0.04–0.06 (82 °C)

192 h at 500 °C in air

Cu/Ti/AlN/Ti/AlN, Cu/AlN/Ti/AlN/Ti/AlN [25]

0.82–0.94

0.05–0.27 (80 °C)

–

SS/Ti/AlTiN/AlTiON/AlTiO, SS/Cr/AlTiN/AlTiON/AlTiO [138]

0.93

0.16–0.17 (82 °C)

1000 h at 350 °C in air and 450 °C in vacuum

Cu/TiNx Oy /TiO2 /Si3 N4 /SiO2 [145, 152, 154]

0.975

0.043 (100 °C)

–

Cu/SiO2 /Ti/SiO2 /Ti/SiO2 [103]

0.955

0.136 (427 °C)

6 h at 450 °C in vacuum

SS-(Fe3 O4 )/Mo/TiZrN/TiZrON/SiON [143]

0.95

0.08 (80 °C)

300 h at 500 °C in vacuum

Cu/Alx Oy /Pt/Alx Oy [148]

0.951

0.09 (82 °C)

2 h at 500 °C in air, 24 h at 450 °C in air

Cu/Ta/Alx Oy /Pt/Alx Oy [47]

0.932

0.1 (82 °C)

2 h at 700 °C in air, 24 h at 550 °C in air

Cu/TiAlCrN/TiAlN/AlSiN, SS/TiAlCrN/TiAlN/AlSiN [43]

0.91

0.07

4 h at 500 °C in air

SS/Mo/TiAlN/TiAlON/Si3 N4 [155]

0.946

0.052 (127 °C)

–

Cu/TiN/TiSiN/SiN, SS/TiN/TiSiN/SiN [156]

0.95

0.04 (70 °C)

2 h at 700 °C in vacuum, 300 h at 200 °C in air (continued)

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Table 1 (continued) Material and film structure

Solar Thermal absorptance α emittance ε

Thermal stability

SS/TiAlN/TiAlSiN/Si3 N4 [44]

0.938

0.099 (75 °C) 300 h at 272 °C in air

Pt/Al2 O3 /Pt/Al2 O3 /Pt/Al2 O3 /Pt/Al2 O3 [132]

0.93

0.43 (650 °C) 100 h at 650 °C in air

SS/TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO [139, 157]

0.961

0.07 (82 °C)

400 h at 325 °C in air, 100 h at 650 °C in vacuum

SS/Zr/MgO/Zr/MgO [120]

0.92

0.09 (82 °C)

2 h at 400 °C in vacuum

SS/W/AlSiNx /AlSiOy Nx /SiO2 [158]

0.94

0.08 (400 °C) 2500 h at 400 °C in air, 850 h at 580 °C in vacuum

SS/Al/NbTiSiN/NbTiSiON/SiO2 [144]

0.931–0.91

0.13 (400 °C) 100 h at 550 °C in vacuum, 2 h at 500 °C in air

SS/Al/NbMoN/NbMoON/SiO2 [159, 160]

0.948

0.05 (80 °C)

500 h at 400 °C in vacuum

SS/W/WAlN/WAlON/Al2 O3 [140]

0.958

0.08 (82 °C)

2 h at 500 °C in air

SS/TiC/Al2 O3 [161]

0.92

0.13 (82 °C)

2 h at 650 °C in vacuum

Cu/SiO2 /Cr/SiO2 /Cr/SiO2 [27]

0.958

0.104 (327 °C)

12 h at 400 °C in vacuum

Cu/Zr0.2 Al0.8 N/ZrN/AlN/ZrN/AlN/Al34 O62 N4 [73] 0.942

0.12 (100 °C) –

SS/Mo/ZrSiN/ZrSiON/SiO2 [162]

0.06 (25 °C)

0.94

500 h at 500 °C in vacuum (continued)

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Table 1 (continued) Material and film structure

Solar Thermal absorptance α emittance ε

Thermal stability

SS/TiAlNx /TiAlNy /Al2 O3 [163]

0.93

0.22 (550 °C) –

Cu/TiNO_H/TiNO_L/TiO2 /SiO2 [164]

0.956

0.095 (400 °C)

–

W/WSiAlNx /WSiAlOy Nx /SiAlOx [165]

0.96

0.105 (400 °C)

400 h at 450 °C in air, 300 h at 600 °C in vacuum

Cu/SiO2 /Ti/SiO2 /Ti/SiO2 /Ti/SiO2 [34]

0.983

0.12 (127 °C) 72 h at 400 °C in vacuum

SS/Cr2 O3 /Cr/Cr2 O3 [125, 166]

0.89

0.25 (100 °C) –

Cu/Zr0.3 Al0.7 N/Zr0.2 Al0.8 N/Al34 O60 N6 [167]

0.953

0.079 (400 °C)

192 h at 400 °C in vacuum

W/SiO2 /W/Si3 N4 /SiO2 [131]

0.95

< 0.1

1 h at 600 °C in air

SS/black chrome/ITO/SiO2 [168]

0.9

0.4

120 h at 900 °C in air

SS/Cr/AlCrN/AlCrNO/AlCrO [169]

0.9

0.15 (20 °C)

2 h at 500 °C in air

SS/CrAlSiN/W/CrAlSiN/CrAlSiON/SiAlO [121]

0.965

0.12 (400 °C) 150 h at 600 °C in vacuum

Mo/Nb2 O5 /Mo/Nb2 O5 /SiO2 [128]

0.97

0.13–0.2 – (400–800 °C)

SS/Cr/AlCrN/AlCrON/AlCrN/AlCrON/AlCrO [170]

0.90

0.15 (500 °C) 1000 h at 500 °C in air

TiN/TiNO/ZrO2 /SiO2 [171]

0.922

0.17 (727 °C) 150 h at 727 °C in Ar

Cu/ALD-Al2 O3 /Cr/SiO2 /Cr/SiO2 [147]

0.954

0.196 (500 °C)

72 h at 500 °C in vacuum

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Fig. 39 a Schematic of the cermet-based solar selective absorber structures. a single compositegraded cermet layer, b double-cermet-layer structure composed of low and high volume fraction of metal particles in layers [22]

between the cermet and the AR coating. A graded cermet with the metal concentration gradually decreased from the bottom to top of the layer can be the candidate as shown in Fig. 39a [22]. A second approach is for the device to contain double cermet layers with typical structure from surface to substrate consisting of an AR layer, a low metal-volume fraction homogeneous cermet layer, a high metal-volume fraction homogeneous cermet layer and a metallic infrared reflection layer at the bottom as illustrated in Fig. 39b [4, 22, 57], which is very similar in concept to the structure of multilayer solar selective absorbers [57]. Through fundamental analysis and computer modeling, the double-cermet-layer structure has a potentially higher photothermal conversion efficiency than a single cermet-graded layer structure. Moreover, it is easier to deposit the double-cermet-layer solar selective absorber than to fabricate the single-cermet-graded selective surfaces [28]. The metal-dielectric-composited-cermet solar selective absorbers have a high design flexibility because the solar selectivity can be optimized by varying metal and dielectric constituent elements, nanoparticle coating materials and thickness, as well as nanoparticle concentration, shape, size, and orientation [22]. Different metals such as Pt [172], W [48, 76, 79], Ti [51], Stainless-steel (SS) [70], Mo [173, 174], Ni [175], Cr [175], Co [22], Al [176], and dielectrics such as SiO2 [51, 173], Al2 O3 [127, 172], MgO, AlN [70, 76], Cr2 O3 [177], AlON [176, 178], nitride [136], have been used as the cermet constituents [8]. For the optimal structure design of the cermet solar selective absorber, an appropriate optical dispersion model should be chosen to characterize the optical constants of the metal-dielectric composite. Effective medium approximation (EMA) has been widely used to describe the dispersion of the optical constants of metal-dielectric composites [175, 179]. Two well-known EMAs are the Bruggeman model and Maxwell-Garnet model [172, 175]. For the Bruggeman approximation, it is expressed as [172]: fA

εA − εB R εB − ε B R + (1 − f A ) =0 B R ε A + 2ε ε B + 2ε B R

(8.1)

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where f A is the filling fraction of constituent A and 1–f A for constituent B, ε is the dielectric function for either A or B, and εBR is the average Bruggeman dielectric function of the composite. The Maxwell-Garnet model is given by [172]: εMG = εB

ε A + 2ε B + 2 f A (ε A − ε B ) ε A + 2ε B − f A (ε A − ε B )

(8.2)

For composite corresponding to a matrix with isolated and poorly interacting inclusion, the Maxwell–Garnett model is often used. While there is some degree of interconnection between components and the role of matrix and inclusions cannot be clearly defined, the Bruggeman expression appears to be more appropriate [179]. In general, Bruggeman model was used for metal volume fraction of above 0.3, while Maxwell–Garnett model was used for volume fraction less than 0.3 [172, 174]. Sometimes, the standard EMA theory may fail to describe the effect behavior of a complex mixture because of its simple mixing formula in approximation, like Ag-SiO2 [179], W-Al2 O3 [48]. Then, parametric formulas like Lorentz multiple oscillator model [179], Kramers–Kronig consistent B-spline function [48], can be used to describe the effective optical constants of a metal-dielectric composite. Babar et al. fabricated a series of W-Al2 O3 nanocomposite films by precisely varying the W cycle percentage from 0 to 100% in Al2 O3 during atomic layer deposition (ALD) [48]. Spectroscopic ellipsometry is used to investigate the optical constants of the ALD W-Al2 O3 nanocomposite films. They use the Bruggeman EMA for the nanocomposite films with Al2 O3 as the matrix and W as the inclusion. Al2 O3 is modeled by a Cauchy dispersion model and W-Al2 O3 is modeled using a Bspline formula. For W% < 40, the ALD composite is accurately described by the EMA model. However, EMA fails with W% ≥ 50, because the composite is no longer composed of well-dispersed nanoparticles in an amorphous matrix. They use a Kramers–Kronig consistent B-spline function to extract the optical constants for W-Al2 O3 nanocomposite films with W% ≥ 50. The obtained optical constants for WAl2 O3 are presented in Fig. 40a, b. By using the obtained optical constants, the solar thermal conversion efficiency is calculated and suggests that the films with the 30– 50% concentration of W will have favorable optical properties to serve as selective solar absorbing materials[48]. Hu et al. investigate the optical constants of Ti-SiO2 nanocomposite thin films [51]. The Ti-SiO2 composite thin films are prepared by co-sputtering Ti and SiO2 simultaneously with controlling the sputtering power for Ti varied from 0 to 100 W. The optical constants of the composites are fitted with the modified harmonic oscillator approximation model, rather than the EMA model, because of the interaction of Ti and SiO2 . With the increasing concentration of Ti in the composite, values of both n and k are improved with the results shown in Fig. 40c, d [51]. With the advantages of accurate characterization of the optical constants of the cermet layer and high design flexibility, a large variety of cermet-based solar selective absorbers have been designed and fabricated [8, 136, 137]. Qi-Chu Zhang proposed W-AlN, SS-AlN, Al-AlON cermet solar absorber with the typical double cermet layer

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Fig. 40 a Refractive index and (b) extinction coefficient of the ALD W-Al2 O3 nanocomposite films [48]. c Refractive index and d extinction coefficient of the Ti-SiO2 nanocomposite thin films [51]

film structures [70, 76, 176]. Solar absorptance of 0.92–0.96 and thermal emittance 0.03–0.05 at room temperature are achieved for the sample to have good thermal stability after annealing at 500 °C in vacuum for 1 h. The reflectance spectra for the Al/W-AlN (HMVF)/W-AlN (LMVF)/AlN sample are shown in Fig. 41a [76]. Esposito et al. fabricated a Mo/Mo-SiO2 (FF = 0.5)/Mo-SiO2 (FF = 0.3)/SiO2 -based double cermet layer solar selective absorber [173]. The measured reflectance spectra are presented in Fig. 41b. A very low thermal emittance value of 0.13 at 580 °C and an appreciable solar absorptance value of 0.94 are realized for the sample [173]. Chester et al. particularly studied and optimized the cermet solar thermal conversion film structure with different cermet layer numbers as illustrated in Fig. 41c [175]. The Bruggeman approximation model is used to characterize the effective dielectric constants of the cermet layer over the entire range of physical metal volume fractions and solar thermal transfer efficiency is evaluated as the figure of merit to optimize the multilayer cermet film structure. Results indicated that the four-layer silica-tungsten cermet solar selective absorbers can achieve thermal transfer efficiencies of 84.3% at 400 K, and 75.59% at 1000 K. However, the benefit of adding more than four cermet layers seems to be not enhanced very much [175]. To improve the thermal stability of the cermet solar selective absorber, refractory metal or compound with high melting point and nitride ceramic matrixes are

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Fig. 41 a Reflectance spectra of the Al/W-AlN (HMVF)/W-AlN (LMVF)/AlN sample [76]. b Measured reflectance spectra of the Mo/Mo-SiO2 /Mo-SiO2 /SiO2 sample [173]. c Film structure of multilayer cermet solar selective absorber [175]

always adopted to make the film structure, interface structure and optical stability not change much at elevated temperatures [8, 136, 137]. Wang et al. developed a solar selective absorber with the film structure of SS/W/Al2 O3 /WTi-Al2 O3 (HMVF)/WAl2 O3 (LMVF)/Al2 O3 , which has a very high thermal stability even after annealing at 600 °C for 840 h in vacuum condition [127]. In comparison, the sample with the film structure of SS/W/Al2 O3 /W-Al2 O3 (HMVF)/W-Al2 O3 (LMVF)/Al2 O3 will deteriorate rapidly after annealing at 600 °C for 10 h. The results are presented in Fig. 42a, b, respectively. The TEM images of the annealed W-Al2 O3 and WTi-Al2 O3 samples are shown in Fig. 42c, d. As can be seen that, after heat treatment, the WTiAl2 O3 -based sample shows to have sharp interfaces among different layers, while the interface between the two cermet layers has become blurred for the W-Al2 O3 -based sample. The conclusion made by the authors to indicate that the segregation of solute Ti atoms with their partial oxidation to form local protective layer may suppress the outward diffusion of W and random agglomeration of the WTi nanoparticles [127]. The insight of the mechanism is quite different from the conventional one.

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Fig. 42 Measured reflectance spectra for the a W-Al2 O3 and b WTi-Al2 O3 based solar selective absorber under different annealing conditions. TEM images of the annealed c W-Al2 O3 (630 h at 600 °C in vacuum) and d WTi-Al2 O3 sample (840 h at 600 °C in vacuum) [127]

Up to date, cermet solar selective absorbers with different constituent metal and dielectric materials have been extensively studied and reviewed [4, 37, 136, 137]. The cermet solar selective absorbers based on Cr2 O3 , Al2 O3 , AlN, SiO2, and other materials and their spectral characteristics have been reviewed by Cao et al. [8]. Selvakumar et al. reviewed the graded cermets, single layer cermets, and double-layer cermets for high-temperature solar selective absorbers [37]. Besides the typical double cermets solar selective absorber, more absorbing and dielectric layers, including the barrier layer and adhesion can be added to enhance the spectral performance and thermal stability of solar selective absorbers, which is referred to as multilayer cermets. Cermets such as SS-AlN, CrN-Cr2 O3 , Mo-SiO2 , W-Al2 O3 , Mo-AlN have been successfully commercialization for mid- and high-temperature applications [4]. There still will be room to improve the absorption properties of the cermet-based solar selective absorber by tuning the optical constants of the materials with structure optimization to flatten more of the spectral pattern with extremely low reflectance value in the main solar radiation region to enhance effectively the solar-to-heat conversion efficiency in the future.

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9 Nano-Textured Surface Structures Structuring a surface with feature sizes comparable to the wavelengths of incident solar radiation can be useful in tailoring the optical properties of solar absorbers. Short-wavelength photons can be easily trapped in the nano-textured surface either via multiple reflections inside the nanostructure or by providing a more gradual gradient in refractive index, while photons with wavelength larger than the dendrite spacing see a mirror-like surface with a high reflectance, resulting in the high solar absorptance and low thermal emittance as presented in Fig. 43 [4, 9, 22, 28]. Grooves, needle-like, dendrite, and porous textured surface have been designed and fabricated to enhance solar absorptance [4, 28]. The solar absorptance for material with intrinsic absorption can be further enhanced by properly texturing its surface. Zhu et al. fabricated hydrogenated amorphous silicon (a-Si) nanowire and nanocones using a chlorine-based reactive ion etching process with the assembled silica nanoparticles as the etch mask [180]. The light absorptance of a-Si nanocones can be greatly enhanced over a wide range of incident angles and wavelengths. Figure 44a shows the SEM images of the a-Si nanocones with a length of 600 nm, tip diameter of 20 nm, base diameter of 300 nm for each nanocone. The measured optical absorptance of the a-Si nanocone sample was maintained higher than 93% in 400–650 nm at normal incidence, much higher than the nanowire sample as illustrated in Fig. 44b. The light absorption enhancement is explained due to the nearly perfect impedance matching between a-Si and air through a gradual reduction of the effective refractive index [180]. Gittleman et al. used reactive sputter etching to texture the surface of Si wafers, with the surface structure in the form of pillars whose diameters and internal micro space are small as compare to the useful solar wavelengths with heights comparable to or higher than those wavelengths [181]. The overall solar absorptance was about 0.85 while the solar absorptance is found to be 0.99 for wavelengths below 1.0 μm. Sai et al. numerically investigated the spectral properties of two-dimensional (2D) tungsten surface with the rectangular cavity, pyramid, and cylindrical cavity, respectively [182]. Results indicate that the gratings with rectangular cavities have good spectral selectivity for high-temperature application with solar absorptance over 0.85 Fig. 43 Schematic diagram of the nano-textured surface [9]

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Fig. 44 a SEM images for the a-Si nanocones. b Absorption spectra for the a-Si thin film, a-Si nanowire, and a-Si nanocones [180]

and thermal emittance of 0.075 at 800 K. W gratings with pyramid arrays have a high solar absorptance over 0.92. The 2D W surface is fabricated with submicron holes on W substrates by the fast atom beam (FAB) etching technique with the highly ordered porous alumina masks. Two different samples are fabricated with the SEM images as shown in Fig. 45a and b. The measured diffuse reflectance spectra are presented in Fig. 45c in comparison to the flat W. The solar absorptance is 0.76 and 0.82 for sample A and B with the thermal emittance of 0.0764 and 0.0904 at 800 K, respectively. The sample also shows high thermal stability after heating at 1170 K for five hours in the vacuum condition as illustrated in Fig. 45d. Rephaeli and Fan also designed a tungsten nanopyramid absorber with a period of 250 nm and a height of 500 nm [183]. The predicted absorptance in the solar spectrum is about 0.965 with a thermal emittance of 0.198 at 727 °C. Ungaro et al. further designed a black tungsten absorber with the pseudo-random cone-based surface with Gaussian-based distributions for width, height, and placement with a very high solar absorptance of 0.99 reported [184]. Ultrafast laser processing has been used to fabricate textured surfaces [61, 62, 185]. Lyengar et al. fabricated titanium textured surfaces by ultrafast laser treatment [62]. Figure 46a shows the SEM image of the titanium textured surface. As can be seen, it shows a conical microstructure. The total reflection and scattering of the titanium sample in the wavelengths from 0.4 to 1.6 under the incident angles of 10, 30, and 50° are presented in Fig. 46b. The absorption of the textured surface is greater than 96% over a broad spectral and angular range. Figure 46c shows the angular dependent total reflection, including scattering for the textured titanium surface, indicating the small angular dependence for all the wavelengths. The optical properties of the textured metal surface are not affected after annealing at 500 °C in air. Fan et al. fabricated micro/nanostructure Cu surface by picosecond laser radiation [61]. Porous coral-like structures fabricated on the Cu surface shows a high absorptivity of over 90% in 250–2500 nm as illustrated in Fig. 46d.

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Fig. 45 SEM images of the 2D W surface with submicron holes: a inter-pore distance = 0.5 μm, pore diameter = 0.45 μm, depth = 0.3 μm and b inter-pore distance = 0.5 μm, pore diameter = 0.35 μm, depth = 0.25 μm. c Measured diffuse reflectance spectra of the 2D W surface with submicron holes in accompany with the flat W surface. d Reflectance spectra of the sample before and after heating at 1170 K for 5 h in vacuum condition [182]

Chi et al. fabricated a large-scale silicon-dioxide-covered rough tantalum solar selective absorber [186]. Figure 47 shows the fabrication processes and SEM images of some fabricated structures. First, a Ta thin film was sputtered on a Si substrate. Then polystyrene nanospheres (PS NPs) are self-assembled on the Ta surface. Afterward, the sample is etched by oxygen plasma to reduce the sizes of the PS NPs followed by deposition of another Ta thin film. Finally, the PS NPs are removed and a SiO2 thin film is sputtered on the textured Ta surface. The absorptance spectra of the fabricated nanostructured solar selective absorber in accompany with the spectra for the black paint and planar absorber are presented in Fig. 48a, b. As can be seen, the black paint has the highest absorptance of 0.94 in the solar radiation region, while the absorptance for the nanostructure absorber and planar one is 0.84 and 0.78, respectively. In the long-wavelength range, the optical absorptance for black paint is higher than 0.8, but absorptance of the nanostructured and planar sample drop quickly to the value less than 0.3. The suppressed absorption in the long-wavelength range of the proposed nanostructured sample will be beneficial for heat accumulation as illustrated from

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Fig. 46 a SEM image of the titanium textured surface [62]. b Total reflection including scattering of titanium textured surface under incident angles of 10, 30, and 50° [62]. c Angular dependence of total reflection, including scattering for the textured surface at different wavelengths [62]. d Reflectance spectra of micro/nanostructure Cu surface (the insert is the photograph of polished Cu (left) and blackened Cu (right)) [61]

Fig. 47 Schematic fabrication processes and SEM images of some fabricated structures [186]

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Fig. 48 Absorption spectra for the nanostructured solar selective absorber, planar sample, and black paint in a 0.4–2 μm and b 2–16 μm. c Stable temperature of the fabricated nanostructured sample, planar one, and black paint under 1 and 7-sun solar illumination [186]

the stable temperature under solar insolation for different solar absorbers as shown in Fig. 48c. The highest temperature for the nanostructured sample is 196.3 °C under 7-sun solar illumination in air conditions, much higher than those achieved by the black paint and planar sample. Li et al. developed a nickel nanopyramid nanostructured solar selective absorber by a template stripping method [67]. Figure 49 shows the fabrication process. First, a thin silicon nitride layer is deposited on Si wafer and nanohole arrays are patterned onto the silicon nitride layer by laser interference lithography. Then, the sample is etched by KOH, resulting in inverted nanopyramids on the silicon wafer. After the etching, the silicon nitride layer was removed with hydrofluoric acid etching. The resulted Si wafer was used as the template for rapid replication of the nanopyramids on Ni. The nanostructured sample shows solar absorptivity of 95% and thermal

Fig. 49 Fabrication processes for Ni nanopyramid solar selective absorber [67]

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emissivity of 10%. The sample maintains its high selective absorption in a wide range of incident angles of ± 50°. The Ni nanopyramid arrays are thermally stable after annealing at 800 °C in a vacuum for 5 h. Besides the solar selective absorbers-based texturing surface of intrinsic absorption materials such as metals and semiconductors, more complex film structures with surface nanostructure were also adopted for high efficient solar selective absorbers [39, 65, 82, 187–189]. Sergeant et al. theoretically investigated the solar selective surfaces consisting of sub-wavelength V-groove gratings coated with aperiodic metal-dielectric stacks [82]. The absorptance spectra for the aperiodic metaldielectric multilayers coated Mo or W V-groove gratings are shown in Fig. 50a, b. As can be seen, the performance of uncoated metallic V-groove gratings can be improved by coating the gratings with an optimized metal-dielectric multilayer stack. Nishimura et al. fabricated a high-performance multilayer solar selective absorber based on Al infrared reflector with optimized surface roughness [64]. The roughened surface of the Al film is prepared by a two-step deposition process. A high solar absorptance of 0.92 with a low normal thermal emittance of 0.06 at 373 K is obtained. Hu et al. also fabricated a surface-roughened metal-dielectric solar selective absorber based on Cu reflector with rough surface, which is fabricated by just increasing the deposition power of the Cu film [65]. The solar absorptance of the roughened sample is about 94%, 2% higher than that of the smooth sample. Bichotte

Fig. 50 Absorptance spectra of the aperiodic metal-dielectric multilayers coated a Mo and b W Vgroove gratings at normal incidence [82]. c Schematic diagram of the 1D microstructured absorbing multilayers. d Measured reflectance for the flat and textured absorber at normal incidence [39]

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et al. proposed one-dimensional (1D) microstructured absorbing multilayers for high efficient solar thermal conversion [39]. As illustrated in Fig. 50c, the multilayer film structure of Al/TiAlN/TiAlN/Al2 O3 is deposited on the 1D sub-wavelength gratings. The gratings are fabricated using two-beam interference lithography. Figure 50d gives the reflectance spectra for the microstructured and planar periodic solar selective absorber. Compared to the flat solar selective absorber, the microtexturation increases the absorption from 95% to 96.6%, while the total hemispherical emissivity at 300 °C has an acceptable level increase only from 10.0% to 10.9%. Li et al. fabricated plasmonic metamaterial absorbers (PMAs) by using the metal– insulator-metal sandwich structure, with triangular nanodisks on a dielectric-coated tantalum reflector as illustrated in Fig. 51a [190]. The proposed Ti/Al2 O3/Ta PMAs are fabricated using the standard e-beam lithography and lift-off method. Figure 51b shows the SEM image for the fabricated PMA with edge-length for the equilateral triangular Ti meta-atoms of 270 nm. The absorptance spectra for the PMA sample are shown in Fig. 51c. The solar absorptance of the proposed sample was 91.3%, while the thermal emittance is as low as 24.2% at 1000 K. Thermal stability of the samples is also tested by annealing the sample at 1000 K for five hours in an encapsulated quartz tube under an argon atmosphere. To prevent the samples from surface reactions or nanodisk morphology degradation at high temperatures, the conformal Al2 O3 film is deposited on top of the PMA samples. Figure 51d gives the absorptance spectra

Fig. 51 a Schematic of the Ti/Al2 O3 /Ta PMAs. b SEM images of the PMA with edge-length of 270 nm. The scale bar is 1 μm. c Absorptance spectra of the PMA sample. d Absorptance spectra of the PMA sample before and after heat treatment at 1000 K for five hours [190]

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of the PMA samples before and after heat treatment. The absorptance spectra before and after annealing were nearly unchanged, indicating the high stability of the PMAs up to 1000 K. Solar selective absorbers with textured or nanostructured surfaces can greatly enhance the design flexibility, which has aroused special interest in the past decades of years [187]. The other advantage of textured surface is its quite insensitive to the effect of oxidation and heat shocks that may have catastrophic influence on the traditional solar absorbers [4, 37]. It should be noted that textured surface must be well protected to avoid surface contact or abrasion that may result in lethal damage to the textured surface.

Fig. 52 SEM images of 2D single crystalline W grating by EBL technology. a Top view. b Oblique view [198]

Fig. 53 Fabrication of pyramid arrays as a solar selective absorber by IL method [67]

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10 Photonic-Crystal-Based Metamaterials and Designs Photonic crystals (PhCs) are periodic arrangement of macroscopic media with differing dielectric constants. With photonic band gaps, photonic crystals could be designed and constructed to prevent light from propagating in certain directions with specified frequencies [191]. Photonic crystals have a unique advantage for selectivity of solar selective absorbers. In particular, metallic photonic crystals have been shown to possess large bandgaps [69]. Photonic crystals with high absorption at the solar radiation region and forbidden states at the IR emittance region perform a great role as high-efficiency solar selective absorbers. Usually, photonic crystals are combined with multilayered structures, and two-dimensional photonic crystals successfully demonstrate selectivity enhancement over multilayers.

10.1 The Simulation Methods 1.

Transfer matrix method (TMM)

TMM is one kind of analytic method. According to the continuous boundary conditions of magnetic and electric fields, iterative equations of electric and magnetic fields are deduced from Maxwell equations to analyze the propagation properties and dispersion relations. TMM is usually applied to solve one-dimensional (1D) and two-dimensional (2D) problems. Pendry also proposed that TMM could be directly used to solve three-dimensional (3D) problems [192]. Due to complex boundary conditions of 2D and 3D PhCs, the algorithms of TMM are much more complex than other methods. Therefore, TMM is more suitable for 1D PhCs, especially for people to study and solve the problem of dispersion and nonlinear medium. 2.

Plane wave expansion method (PWE)

PWE method is one kind of effective spectral method applied to normal PhCs, despite of the disadvantages of low convergence speed and large scales of plane wave expansion numbers [193]. Fourier expansion is made to the dielectric constants of PhCs in reciprocal vector space, and the incident wave vectors are expanded at the same time. Then, eigen equations of electric or magnetic fields are degenerated from Maxwell equations. Finally, after solving the equations, the eigenvalues along the boundary of the first irreducible Brillouin zones are obtained. Even if there is a scale of periodic units in PhCs, the calculated results by the PWE method are still precise. Basic ideas of PWE method are listed below. The example is based on the PhCs with dielectric spheres (the radius is r, and the dielectric constant is εa ) orderly arranged in host material (the dielectric constant isεb ). Assumed that the PhCs are composed of linear, isotropy medium and the electric or magnetic fields are simple harmonic models. Therefore,

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H(r, t) = H(r)ex p(−iωt)

(10.1)

E(r, t) = E(r)ex p(−iωt)

(10.2)

Substituting the expressions above into Maxwell equations, then k · D = εε0 k · E = 0

(10.3)

k·B =0

(10.4)

where the electromagnetic waves are transverse. Then, ∇ × E(r) = iωμ0 H(r)

(10.5)

∇ × H(r) = −iωε0 ε(r)E(r)

(10.6)

Then, ∇ ×[

ω2 1 ∇ × H(r)] = 2 H(r) ε(r) c

(10.7)



Introducing operator L H {H(r)}, 

L H {H(r)} = ∇ × [

1 ∇ × H(r)] ε(r)

(10.8)

Hence, the equation above is rewritten into 

L H {H(r)} =

ω2 H(r) c2

(10.9)

Among the equations, ε(r) is the dielectric function, which r is periodic with lattice constantR, ε(r ) = ε(r + R) 1 ε(r)

(10.10)

is expanded into Fourier Series,  1 = ηG ex p(i G · r) ε(r) G

where the coefficient is expressed as

(10.11)

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ηG =

1 V0

˚

1 ex p(−i G · r)d r ε(r)

V0

(10.12)

For the assumed PhCs with periodically distributed dielectric spheres, also be expressed into the following formula: 1 1 1 1 = + ( − )S(r) ε(r) εb εa εb

1 ε(r)

could

(10.13)

where S(r) is defined as  S(r) =

1, |r| ≤ ra 0, |r| ≤ ra

(10.14)

Therefore, the coefficient ηG can be expressed as ηG =

1 1 1 1 δG0 + ( − ) εb V0 εa εb

˚ S(r)ex p(−i G · r)d r

(10.15)

V0

According to Bloch-Floquet theory, electromagnetic waves in periodic structures are expanded by a series of plane waves, and the magnetic field in PhCs is expressed into the following formula: H(r, t) = ex p(−iωt)

2  G

HG,λ eλ ex p(i(k + G) · r)

(10.16)

λ=1

where ω is the frequency and k the wave vector in the first Brillouin district; G is reciprocal vector; eλ (λ = 1, 2) is the orthogonal unit vector with (k + G). The following equation could be obtained as 



λ,λ MG,G  HG  ,λ =

G  ,λ

ω2 HG,λ c2

(10.17)

where MG,G  = |k + G| k + G  ηG,G  3.



e2 · e2 −e2 · e1 −e1 · e2 e1 · e1

(10.18)

Finite element method (FEM)

The finite element method is first proposed by Courant in 1940s to solve the problems of equilibrium and vibration. The method has been becoming one kind of major design tool for electromagnetic devices [194]. The commercial software COMSOL

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uses FEM to solve the problem of physical fields. Briefly speaking, the fields are divided into finite elements in FEM, and the interpolation function is applied to describe field variables. The unknown variables of every point in a unit could be described by the node of this unit with the boundary of other unit. Therefore, the calculation of the whole field is simplified to the calculation of field variables at finite nodes, which means the infinite-dimensional freedom is transformed into the limited one. Ritz variational method and Glalerkin’s method are considered to form the basis of the modern FEM. Ritz method is one kind of variational method with a variational expression (functional) describing the boundary-value problem. The minimum of this functional corresponds to the governing differential equation under the given boundary conditions. The approximate solution is then obtained by minimizing the functional with respect to variables that define a certain approximation to the solution. Glalerkin’s method belongs to one kind of weighted residual methods, and the solution to the equation is calculated by weighting the residual of the governing differential equation. In both two methods mentioned above, it is of great importance to find out the trial function approximate to the true solution. The trial function is composed of a series of basis functions defined in the whole domain. Due to the small scale of subdomains, the basis functions defined in the subdomain are also simple. 4.

Finite-difference time-domain method (FDTD)

Since Yee first proposed FDTD method in 1966 [195], the method is widely applied to electromagnetic radiation, antenna radiation, and bioelectromagnetics. FDTD was introduced into the research of PhCs from 1990s. PhCs with every shape could be simulated in FDTD. At the same time, the simulation with a large region of frequency is easily calculated at one time. But the high computation complexity of FDTD requires high-powered computers. Now FDTD method has been widely applied into the research of one-dimensional and two-dimensional photonic crystals. Relevant software or software packages are frequently used by designers of PhCs, like FDTD Solutions by Lumerical Solutions company and MEEP, a freely available software package developed at MIT. In Yee’s grids, each component of the electric field and magnetic field is intersected at the space value points. All the electric field components are then surrounded by magnetic field components, and all the magnetic field components are surrounded by electric field components at the same time. In this way, the propagation in time, in particular, uses a leap-frog scheme where the electric fields at time t are computed from those at timet − t, while the magnetic fields at time t − t/2 computed from those at time t + t/2 [196]. The spatial arrangement of the electromagnetic field is in line with the basic requirements of Maxwell equations. The original differential equation is transformed into a difference equation with spatial and time discretization, the solution of electromagnetic field is then gradually carried out on the time axis. The distribution of spatial electromagnetic field at different grid points and different time is obtained by time iteration gradually, which is based on the boundary conditions

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initial values and of electromagnetic problems. The transform processes of Maxwell equations in FDTD method were not included in this part. If interested, you could refer to reference [196]. It is of great importance to note that the solutions to Maxwell difference equations after discretization must be stable and convergent. The numerical dispersion in FDTD is expressed by 

1 ct



2 sin2

ωt 2



    1 1 2 k x t 2 k y t + sin sin x 2 2 y 2 2   k t 1 z (10.19) + sin2 z 2 2

=

where, ω represents the angular frequency of plane wave, and k x , k y , k z represent the three coordinate components of wave vectors. When t, x, y, z approaching zero, the equation is simplified as ω2 = k x2 + k 2y + k z2 c2

(10.20)

Equation (10.20) is same as the analytical dispersion relation in planar electromagnetic wave propagating in the homogeneous medium. Therefore, Eq. (10.20) is the limit equation of Eq. (10.19), indicating that the numerical dispersion is caused by the approximate difference quotient. If the space and time steps are small enough, the numerical dispersion would be decreased to the value required. However, the decrease of space and time steps would increase the number of grids and the time min , λmin is the loop. Usually, the maximal space step is expressed as max = λ20 minimum wavelength of electromagnetic in the calculation region. The numerical dispersion in FDTD method is inevitable, and the space step takes the value max , the calculated maximum error is about 0.3%. In order to ensure the stability of the derived difference equation, the selection of time and space steps is crucial and should be satisfied by Courant stability condition. 3D Courant stability condition is expressed by

t ≤ cmax

1 1 x 2

+

1 y 2

+

1 z 2

(10.21)

where cmax represents the maximum Courant number. If the uniform grids are taken,x = y = z = s, Eq. (10.21) could be simplified into t ≤

s √ cmax 3

(10.22)

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In 2D condition, z = 0, when x = y = s, the stability condition is then expressed by t ≤ c s√2 . In 1D condition, cmax t ≤ x. max Perfect matched layer (PML) for absorbing layers are used to simulate open boundaries. One PML is an artificial absorbing material design to eliminate reflections from the edge of the computational region. 5.

Finite-difference frequency-domain method (FDFD)

FDFD method is based on the same principle with FDTD method but is quite different in solving progress from the FDTD method. The FDFD method is one kind of frequency domain of finite difference method without the stability problem and Fourier transform as that in FDTD method. Especially, additional amendments are not required when dealing with the oblique incidence of periodic structures. In addition, the optical constants of dispersive materials could be directly applied into FDFD method, instead of fittings of optical constants in FDTD. In spite of these advantages, FDFD method is seldom used in 3D electromagnetic field models for the large matrix and low solving speed. FDFD method is then usually applied to 2D models. In short, the solving process of FDFD method is to set up difference equations on every node after spatial discretization, and one matrix equation then consists of all difference equations. The values of the corresponding field at nodes of discrete space are finally obtained by solving the matrix equation. 6.

Rigorous coupled-wave analysis (RCWA)

Rigorous coupled-wave analysis (RCWA) [197] is an efficient algorithm to reduce the matrix dimension and therefore calculation time. The correct implementation of the Fourier factorization is used to achieve a sufficient convergence of the diffraction efficiencies. The convergence efficiency of the algorithm has been enhanced gradually in recent decades. The process of RCWA is mainly divided into three steps. At the first step, the equations of electromagnetic field in the incidence and transmission are needed. At the next step, the optical constants and electromagnetic fields are then expanded based on Fourier series, and then substitute to Maxwell equations for the coupled-wave equations. Finally, according to tangential boundary continuity conditions of electromagnetic components, the coupled-wave equations are calculated. In terms of mathematics, RCWA is equal to solving an eigenvalue problem. By dividing the space components of the electromagnetic field, the eigenvalue is obtained by expanding structure-related spatial periodic parameters based on Fourier series. After limited truncation of infinite-ordered Fourier expansion, ordinary differential equations are then dispersed to be a linear system of equations. It is remarkable that the accuracy of the algorithm is determined by the finite of Fourier series. Essentially, no approximation is used in RCWA, so the method is rigorous as it is called. However, the calculating speed of RCWA is greatly depended on the convergence order.

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10.2 Preparation Methods In view of the existing photonic crystal fabrication technology, there are mainly following preparation methods: mechanical preparation method, lithography, chemical etching, X-ray lithography etching, etc. The mechanical preparation method is mainly applied to the PhCs working in microwave and millimeter-wave region. For PhCs working as solar selective absorbers, lithography technology is a preferred approach. Higher working frequency of PhCs, and more difficult of processing 2D or 3D structures. Modern lithography methods include e-beam lithography, atomic force microscopic lithography, ultraviolet lithography, X-ray lithography, mask manufacturing, laser interference lithography, etc. In the above-mentioned methods, e-beam lithography (EBL) and laser interference lithography (IL) are widely employed in solar selective absorbers, especially IL method. 1.

E-beam lithography (EBL)

The method of EBL is to get the structure by exposing photoresist with highenergy electron beam. With the resolution below 1 μm, EBL is one of the highestresolution lithography methods at present. Because the electron beam could be easily deflected by electromagnetic field, complex graphics could be written directly on the photoresist without masks. Thus, flexible is another advantage of EBL method. The microfabrication method of electron beam scanning exposure and fast atom beam etching to fabricate subwavelength gratings are sometimes used in metallic PhCs for solar selective absorbers. 2.

Laser interference lithography (IL)

IL technology is based on interference and diffraction characteristics of light, and the graphics are then recorded by photosensitive materials after regulation of light intensity distribution in the interference field. It is relatively inexpensive, fast, and precise while allowing exposure of relatively large sample sizes. Because the expensive optical projection systems are not required, and the exposure area is only limited to the area of aperture. Laser holographic lithography is one of the popular IL methods. Laser holographic lithography could be simplified as a two-step process. First, spatial periodic interference patterns are formed by the intersection of multiple laser beams. Then, photosensitive resin is exposed in holographic interference patterns. Laser holographic lithography has great advantages of larger etching area and one forming over other traditional methods. Thus, IL method is quite popular among solar selective PhCs. 3.

Other methods

There are also some lithography technologies applied in PhC-based solar selective absorbers, just like deep-ultraviolet lithography (DUV), sidewall lithography, and nanoimprinting. DUV is one kind of normal optical lithography technologies. UVsensitive photoresist is exposed by ultraviolet light on the material surface to pattern

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Fig. 54 Process sketch of sidewall lithography

Fig. 55 The process diagram of nanoimprinting

it, and the patterns are then transferred by following etching and coating. Finally, the substrate with designed patterns is obtained. Sidewall lithography is one kind of indirect nanofabrication methods, depositing film material on the sidewall of a supporting structure with a certain height to obtain thin gratings (Fig. 54). Nanoimprinting is one kind of technology transferring micro-nanostructures from template to substrate by mechanical methods. Nanoimprinting is usually a threestep process. First, the template should be processed by exposing electron beam on substrate. Then, the patterns are transferred to photoresist by pressure. Finally, the photoresist is solidified by ultraviolet light. Removing the template, and the highaccuracy sample is obtained by etching. Templates could be used over and over, which depresses the operating costs and shorten the processing cycles (Fig. 55).

10.3 Recent Researches Metallic PhCs are highly promising as solar selective absorbers since their large optical bandgaps and outstanding control over the photonic density of states [199]. Solar selective absorbers using PhC structures are discussed extensively in recent decades, especially for 2D PhC structures [82, 183, 199–206]. Different pattern

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designs such as cylinder [199, 205, 207], pyramid [67, 183], and square nanostructure [208] have been proposed to achieve high absorption in the solar region and low emittance in the IR region. These 2D PhCs for selective emitters and absorbers were usually fabricated using the above-mentioned electron-beam lithography (EBL) [198, 205, 206] or interference lithography (IL) [199–202, 209]. Deep-UV stepper lithography [210], deep reactive ion etching (DRIE) technique, [211] and nanoimprint lithography [212] are also applied to fabricate the metallic PhCs for solar selective absorbers. Solar selective absorbers using 3D PhC structures have also attracted great attention [213–215]. Although technologies like self-assembly may help to solve the difficulties in fabricating 3D metallic PhCs, 3D PhCs are still much more complex in experiment than 2D ones. Direct laser writing [216] and layer-by-layer fabrication [217] have been reported to fabricate 3D metallic PhCs. The researches on solar selective absorbers based on PhC structures include numerical simulations and experiments. The most popular simulation methods applied into solar energy absorption are FEM, FDTD and RCWA. Some researchers have compared the results between two kinds of simulation methods as mentioned above [203, 204, 218]. Thermal stability is one concentrated point of metallic PhC-based solar selective absorbers in recent years. One-dimensional metal dielectric stacks have demonstrated promising solar absorbing properties but are unstable at temperatures greater than approximately 600 °C [9]. For high-temperature application just like Solar thermal photovoltaic (STPV), thermal stability is of great importance. Thus, the most commonly studied materials for photonic crystals absorbers are refractory materials. Especially, refractory metals are advantageous due to their high melting points and low vapor pressure for solar energy absorption. As shown in Table 2 Tungsten and Tantalum have been most popular refractory metals used in PhC-based solar selective absorbers. The melting point of Tungsten is about 3410 °C. There are some shortcomings of Tungsten since it is difficult to weld, impeding successful system integration [69]. Tantalum has a high melting point (3290 K) and low vapor pressure, similar to Tungsten, but is much more weldable [9]. Table 2 Performance of various PhC-based solar selective absorbers Metal

Simulation

Experiment

Thermal stability

W with etching cylinder structure [209]

FDTD

IL

At least 1200 K

W with square-formed gratings [198]

RCWA

EBL

Up to 1400 K

Ta with etching cylinder structure [202]

FDTD

IL

910 °C

Ta with etching cylinder structure [203]

RCWA + FDTD

DRIE

900 °C

Prism-structured Ti [188]

FDTD

EBL

350 °C

Pt pucks [210]

/

DUVL

1328 K

Ru with hollow cylinder structure [218]

FDTD + RCWA

Lithography

1000 °C

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Except for thermal stability, absorptivity and emissivity are other crucial factors of metallic PhC-based solar selective absorbers. Sometimes, for higher absorptivity, 2D metallic crystals are simulated combing with metal-dielectric multilayers, and results are predicted to be high efficiency. Wu et al. designed a 2D structure on the metal-dielectric layers with a predicted average solar absorptivity of 96.4% over the wavelength range of 400–2000 nm [204]. The structure consisting of a tungsten nanoparticle array monolayer embedded in a SiO2 layer, which is arranged on the multilayered (W/SiO2 ) films was proposed to have high absorptivity above 99% from 435 to 1520 nm and a low emission between 20% beyond 2.3 μm [219]. A 2D Tantalum-based superlattice PhC consisting of octagonal and square cavities is calculated with the absorptivity of 96% [212]. Some researchers have discussed about the demand of wide-angle properties. One kind of metallic photonic crystal based on tungsten nanodisk was experimentally proved to have average absorptivity higher than 90% from 0.5 to 1.75 μm and less than 12.6% beyond 2.5 μm. The broadband solar selectivity remains invariable up to 40° [205].

10.4 Analysis Methods Since 2D PhC-based solar selective absorbers have attracted much attention, the analysis method introduction would be focused on 2D PhC. The tangential component of the wave vector of each diffracted waves is specified by the Bloch-Floquet condition [220]: k x,m = k x,inc +

2π m 2π n , k y,n = k y,inc + x y

(10.23)

where m and n are the diffraction orders in the x and y directions, and x and  y the period in the x and y directions, respectively. The reflected wave has amount of diffraction orders, corresponding to the incident angle satisfying the Bloch-Floquet condition. Thus, higher diffraction orders should be avoided to reduce reflectivity. It is quite linked to the periodicity of the structure. Different resonances could be excited in designed structure, contributing to the absorption enhancement [187]. In the following parts, several typical resonances will be introduced. 1.

Surface plasmon polariton (SPP) resonance

Surface plasmon polariton (SPP) resonance has attracted great attention in recent years. The strong coupling of external electromagnetic fields with surface plasma is called the SPP, resulting in a surface wave propagating along the interface and an evanescent wave in the normal direction. The SPP resonance usually occurs on the interface between two media, one medium usually is air, and the other metals. One medium is characterized by a dielectric function ε1 (ω), while the other one ε2 (ω) = ε2’ + iε2’’ . ε1 is assumed to be real. For TM wave, according to boundary relations of electromagnetic field, the following equations are satisfied:

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Hy1 = Hy2 , E x1 = E x2

(10.24)

The following equations are also satisfied in TM wave: ±k z E x − iβ E z = iωμ0 Hy

(10.25a)

−k z1 Hy1 = iωε0 ε1 E x1

(10.25b)

k z2 Hy2 = iωε0 ε2 E x2

(10.25c)

Substituting Eqs. (10.25b and 10.25c) into Eq. (10.24), then the following relationship is obtained ε1 k z1 =− k z2 ε2

(10.26)

It is clear that two media have opposite signs of permittivity. According to wave equation ∇ 2 E + k02 ε E = 0

(10.27)

The dispersion relation of SPP is then expressed by  β = k0

ε1 ε2 ω = ε1 + ε2 c



ε1 ε2 ε1 + ε2

(10.28)

where c is the speed of light in vacuum (Fig. 56). For a 1D grating with grooves are parallel to the y axis, only TM waves can excite SPPs. Because the electronic field is not continuous in the normal direction, surface electron accumulation occurs. While for TE waves, the electronic field is parallel to the interface without normal component and no electron accumulated on the surface. Fig. 56 Interface between two media 1 and 2 with dielectric function ε1 and ε2 .

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However, for 2D gratings, SPPs could be excited by both TE and TM waves, and SPPs could propagate along both x and y direction [220]. For a 2D grating, the tangential component of the wave vector could be expressed as the following formulation, according to Eq. (10.23),     2π m 2π n x + k y,inc + y = k x,inc + x y 

kII,mn



(10.29)

where kII,mn represents the component of wave vector in the x–y plane. As mentioned above, 2D grating surface structures are periodical in both x and y direction. For TM incident waves, assuming n = 0 when discussing SPPs in x direction and m = 0 when discussing SPPs in y direction. SPPs can be excited in x and y direction when satisfying dispersion relation, respectively [187]: ε1 ε2 2π m = k0 sinθ + ε1 + ε2 x     ω ε1 ε2 2π m 2 2 = (k0 sinθ ) + c ε1 + ε2 y ω c



(10.30)

(10.31)

SPPs may occur in the form of propagating along the interface or localized oscillation on nanostructures. In the position of interface between air and metal, the electric field enhancement would occur. The absorption peaks of SPP are usually sharper than other absorption peaks. An example of a 2D grating surface structures exploiting surface plasmon resonance at wavelength of 503 nm is presented in Fig. 57 [205].

Fig. 57 a The structure of 2D tungsten-based nanodisk array. b Absorptance of the absorber. c Field intensity and energy loss at the wavelength of 503, 671, and 1569 nm in the x–z plane, respectively [205]

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Micro-cavity Effect

Some studies have demonstrated the thermal radiation enhancement by the microcavity effect [221]. Cavity resonance could be excited in the cavity or groove on the grating surfaces. Micro-cavity resonance in a 2D photonic crystals with an aperture to the z direction is given by the relation λlmn = 

l Lx

2

+



2 m Ly

2

+



n 2L z

2

(10.32)

where L x , L y , L z are corresponding cavity dimensions. In addition, l, m, n are positive integer numbers. Micro-cavity effect occurs in both TM and TE polarizations. The depth of the cavity is usually amount to the wavelength of radiation. 3.

Magnetic polariton resonance

When a thin dielectric film is placed between two metal films or between metallic nanostructure and metal film, magnetic polariton resonance would be exited. Two examples are shown in Fig. 58. A magnetic polariton resonance is excited by the enhanced magnetic field in the thin dielectric film between two metal films. In fact, the Magnetic polaritons are excited because the time-varying magnetic field could induce the electric current at the surface of metals with opposite direction according to Lenz’s Law. Two metal layers must be located very close to each other in order to excite magnetic polariton resonance. This is quite different from exciting plasmonic resonance, which is supported at the surface of a single metal layer. The frequency of magnetic polariton resonance, especially the fundamental magnetic polariton resonance, is usually estimated by the inductor-capacitor (LC) model. Here we explain the equivalent LC model by some examples. The equivalent LC model is based on the definition of inductor and capacitor as it is called. The capacitor and inductor are expressed in the following form, respectively:

Fig. 58 Cross-sectional view of electromagnetic field at the magnetic polariton resonance wavelength from the FDTD simulation [188, 208]

Optical Properties of Solar Absorber Materials and Structures

C=

ε0 εr A1 μA2 εA = ,L = d d l

97

(10.33)

where A1 is the area of the parallel plate capacitors, and d the distance between them. A2 represents the area of the loop, and l the length of the loop. In a 1D grating or a metal-dielectric-metal structure like the structure in Fig. 59a, the location of resonance is in the FP-like gap or the dielectric film. The capacitor and inductor are respectively defined as [187]: Cg = L = Lm + Le =

c1 ε0 εd hl d h μ0 hd + 2l ε0 ω2p (δl)

(10.34) (10.35)

where ε0 is the permittivity of vacuum, and εd the permittivity of the air or the dielectric film. c1 is a correction factor, typically with a value between 0.2 and 0.3, representing the non-uniform charge distribution of the metal surface. Noted that l is the length of the metallic strip in the y direction, h and w are the height and width of the metallic strip, respectively. Here, L m is the inductance of two metallic strips with the distance ofd, and L e the inductance excited by drift electrons. ωp represents the plasma frequency of the chosen metal, and δ is the penetration depth, which is λ , where κ is the extinction coefficient of the metal. Ifh ≤ δ, calculated byδ = 4πκ then in the Eq. (10.35), δ takes the value ofh. According to the impedances of capacitance and inductance, which are expressed as ZC =

1 , Z L = jωL jωC

(10.36)

Fig. 59 a A 1D grating structure. b Equivalent LC circuit model for the prediction of the magnetic resonance of the fundamental mode

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Then the total impedance could be expressed as  −1   Z = 2Z L + 2Z C = 2 j ω(L m + L e ) − ωC g

(10.37)

The magnetic resonance occurs when Z = 0, so the magnetic resonance frequency of the fundamental mode could be expressed as 1 ωM R =  C g (L m + L e )

(10.38)

In the situation of gratings on the dielectric-metal structure, like the structures in Fig. 60, the solution of equivalent LC circuit model is similar to 1D gratings. The capacitance Cm by two parallel plates sandwiching the dielectric film with thickness d is expressed as [208] c1 ε0 εd wl d

Cm =

(10.39)

where εd is the dielectric function of the dielectric film. In addition, the capacitance C g from the contribution of the air gap between metal gratings is obtained by Cg =

ε0 hl −w

(10.40)

The inductance also consists of the inductance of two parallel metal films sandwiching with one dielectric film and the inductance from drift electrons, and inductance could be calculated as L = Lm + Le =

w μ0 wd + 2l ε0 εm ω2p γ hl

(10.41)

Fig. 60 a Schematic of a grating on dielectric-metal films. b Equivalent LC circuit model for the prediction of the magnetic resonance of the fundamental mode

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where γ represents one factor considering the effective cross-sectional area of the metal grating [222]. According to the LC circuit model in Fig. 60b, the total impedance can be obtained as Z total = jω[

1 Lm + Le −2 2 + (L m + L e )] 1 − ω2 C g (L m + L e ) ω Cm

(10.42)

The magnetic resonance occurs when Z total = 0. In this way, it is the magnetic resonance of fundamental mode which is independent of the length of metal gratings. The LC model can also be extended into higher modes of magnetic resonance.

11 Fabrication of Solar Absorbers Physical vapor deposition (PVD) and chemical vapor deposition (CVD) are the methods commonly used for preparing solar energy selective absorber devices. As implied by the name of terminology, physical processes will be characteristic in the PVD, while chemical reaction occurs in the CVD. A common PVD method is based on vacuum evaporation. Conventional vacuum evaporation is carried out in a high vacuum coating machine. The sample is prepared by evaporation of the source materials directly onto the substrate. The source materials are usually heated at a relatively fast evaporation rate by using an electrically heating wire or boat under power supply control and ultra-high vacuum conditions. Vacuum evaporation also includes hot-wall epitaxy and ion beam growth methods. Molecular beam epitaxy is a slow vacuum evaporation process under ultra-high vacuum. It can be used to grow epitaxial monolithic films. Another common PVD method is sputtering, including direct current sputtering, radio frequency sputteringe, magnetron sputtering, reactive sputtering, etc. Among them, reactive sputtering involves the chemical reaction that happened between different kinds of atoms, and can be used to grow a composite film. Recently developed laser fusion methods, which use laser pulses to evaporate atoms or molecules from the target to form a thin film on the substrate, are also a PVD method. CVD methods include conventional CVD and metalorganic chemical vapor deposition (MOCVD), which use a special organometallic compound to transfer the metal atoms through a chemical reaction process to form the thin metal film on the substrate. The non-vapor deposition method by oxidizing the single crystal thin film is advantageous for epitaxy and growth of the films, and mainly includes liquid phase epitaxy, solid-phase epitaxy, the IANGMIR-BODGT method, chemical solution coating method, etc. This chapter will focus on several PVD methods, including electron beam evaporation, sputtering, and pulsed laser deposition.

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11.1 Electron Beam Deposition In the electron beam deposition process [223–227], the atoms or molecules of the evaporating source materials are detached from the surface when it is heated under vacuum. This phenomenon is called thermal evaporation. The traditional heating method uses resistance wire, which is usually made of high melting point metal materials such as tungsten and molybdenum. The advantage of the resistance-heating thermal evaporation method is that the coating machine has a simple structure and is cheap and reliable to use. This method can be used for evaporation coating of materials with lower melting temperature, especially for mass production where film quality is not critical. The disadvantages of resistance-heating are the maximum temperature limited by the heating system, low evaporation rate, small evaporation area, uneven evaporation, easy splashing during heating, and possible contamination from the resistive material crucible and various support components. Electron beam evaporation (EBE) method can overcome the shortcomings of the resistance-heating thermal evaporation method and has become the main stream of heating methods for evaporation coating. The EBE method refers to a method in which a source material is placed in a water-cooled crucible, and is directly heated by an electron beam to vaporize the source material and condense on the substrate to produce thin films. The mechanism of electron beam generation is the effect of thermionic emission, i.e., when a large enough current passes through the filament, it reaches a very high temperature, and some of the internal electrons get enough energy to escape the surface of the filament. This is called thermal electron emission. The current density emitted is: Je = A0 T 2 e−ϕ/kB T

(11.1)

where J e is the emission current density (A/cm2 ), A0 is a constant, T is the absolute temperature of the filament, ϕ is the work function, and k B is the Boltzmann constant. The ejected electrons acquire their kinetic energy from an accelerating electric field. If the initial velocity of the emitted electrons is not considered, the kinetic energy of the accelerated electrons is given by: E=

1 2 mv = eU 2

(11.2)

where m is the mass of the electron, e its charge, U the accelerating voltage and v its velocity after being accelerated. v = 6 × 104 km/s can be calculated when U = 10 kV. It is noticed that the speed of electrons is about 20% of the speed of light, which is a very high speed. When high-speed electrons strike the source material in the crucible, the kinetic energy carried by electrons is converted into thermal energy, which causes the source material to reach a very high temperature. If the number of high-speed electrons incident on the source material per unit time is n, and the power carried is W = neU, the converted heat is:

Optical Properties of Solar Absorber Materials and Structures

Q = W t = neU t

101

(11.3)

Electrons are produced in electron guns, which come in many different configurations according to the classification of electron beam focusing methods, such as a ring gun, a straight gun (Pierce gun), and an e-gun, and the latter is most widely used. The schematic diagram of the e-gun is shown in Fig. 61. It consists of a tungsten cathode, a focusing electrode, a magnet, and a water-cooled copper (oxygen-free) crucible. The electron beam emitted from the filament is deflected 270° by the magnetic field, and is named after its trajectory is “e” shaped. The electron beam produced from the filament is accelerated by a bias voltage of several thousand volts and deflected 270° by a transverse magnetic field, and then bombarded on the source materials in the crucible to melt and evaporate. The e-gun overcomes the shortcomings of the direct gun type, avoids the contamination of evaporating materials to the filaments and as well as the contamination of the filaments to films under deposition, and is one of the electron guns, more widely used in current coating application. The egun type has the characteristics of large power (about 10 kW), which can evaporate high-melting materials, and the generated evaporating particles have high energy, and high adhesion of the film to the substrate with high quality of the film deposited on the substrate. However, the electron gun requires a higher vacuum, and needs to use a negative high voltage, the operation system is more complicated, difficult to maintain with relative high cost. The advantages of EBE are as follows: (1) It can directly heat the evaporation materials. Therefore, heat loss is reduced, and thermal efficiency is higher; (2) The high energy density generated by the electron beam is suitable for evaporation of the materials even with high melting point temperature over 3000 °C by high deposition rate; (3) The crucibles containing the evaporation materials are cold or water-cooled, which can avoid both of the reaction of the evaporation materials with the container materials and the evaporation of the container materials, thereby improving the purity

Fig. 61 Schematic diagram of e-shaped electron gun for vacuum evaporation

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of the films. The disadvantages of EBE are as follows: (1) The heating system is complicated; (2) The residual gas molecules in the vacuum chamber and the vapor of the partially evaporated material are ionized by the electron beam, which may affect the structure and physical properties of the films. This method can be used for the evaporation of high purity or high-melting point materials and has now become the mainstream of the heating methods used for vapor deposition of high-melting point films in high purity.

11.2 Sputtering Method Sputter coating method [223, 228–244] is also a common PVD method. During sputtering, a small amount of inert gas (such as argon) is introduced into the vacuum system and discharged to generate ions (Ar). The inert gas ions are accelerated by the bias voltage to obtain kinetic energy. High-energy ions carrying kinetic energy bombard the target (cathode) and transfer energy to the target atoms. The target atoms are detached from the target and deposited on the surface of the substrate when its energy is greater than the sublimation energy. While the ion beam bombards target to produce neutral atoms,—a large number of secondary electrons are also generated and accelerated by the electric field to move toward the substrate connected to the anode. During the movement, the cascade collision of electrons and gas molecules generates more ions which bombard the target to generate more secondary electrons and target atoms, so that the glow discharge continues. The application scope of sputtering coating technology has been greatly expanded after a long period of development and improvement. A variety of new methods such as radio frequency sputtering, magnetron sputtering, ion beam sputtering, and reactive sputtering have been gradually developed from the initial simple structure of two-pole DC sputtering or cathode sputtering. DC sputtering systems are generally only used for sputtering targets of good conductors; RF sputtering is suitable for sputtering any target such as insulators, conductors, semiconductors, etc. Magnetron sputtering changes the direction of motion of electrons by applying a magnetic field. And restraining and extending the trajectory of electrons, thereby, increase the ionization efficiency and sputtering deposition rate of electrons to the working gas. Magnetron sputtering has two main features: low deposition temperature and high deposition rate. 1. DC Sputtering The DC sputtering system is the first and simplest sputtering system, and its structure is shown in Fig. 62. The target is placed opposite to the substrate. The target and the substrate are connected to the cathode and the anode of the power source, respectively. During coating, the background vacuum in the vacuum chamber is about 10–3 ~ 10–4 Pa, and then a working gas such as argon (partial pressure 10–1 ~ 10 Pa) is introduced into the vacuum chamber. A glow discharge is generated between the two electrodes by applying a voltage of several thousand volts to the electrodes.

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Fig. 62 DC sputtering device and model of gas discharge system between two poles

A plasma is generated in the vacuum chamber in which positively charged argon ions are accelerated toward a target connected to the negative electrode of the power source. Argon ions gain kinetic energy and bombard the target during acceleration. Some neutral atoms near the surface of the target are impacted and fly out of the surface. Part of the sputtered target atoms are deposited on the substrate to form a thin film. DC sputtering has the advantages of simple structure, lower equipment cost, convenient operation, etc. It can sputter difficult-to-melt materials and prepare uniform films on large scale. However, this method has the disadvantages of low deposition rate and the ability to sputter only conductive materials. Hence, the simple DC sputtering system is only used in the laboratory and is rarely used in industry manufacturing. 2. Magnetron Sputtering The sputtering efficiency of the DC sputtering system is low because of the low electron ionization efficiency. The ionization efficiency of electrons can be improved

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Fig. 63 Structure of planar magnetron target

by applying a magnetic field. The magnetic field is applied in order to extend the movement path of electrons by changing the direction of movement of the electrons, thereby increasing the collision chance of electrons and gas molecules and improving the ionization efficiency. This is the basic principle of magnetron sputtering. There are many types of magnetron sputtering, a schematic diagram of the structure of a planar magnetron target is shown in Fig. 63. A set of permanent magnets is placed on the back side of the target, the magnet forming a non-uniform magnetic field on the surface of the target, with a portion of the magnetic lines of force parallel to the target surface. The electrons emitted from the target surface will be subjected to the Lorentz force of the magnetic field during the accelerated motion from the target surface by the electric field force. Under the action of electric field and magnetic field, the electron motion will drift to the direction indicated by E (electric field) × B (magnetic field), which is called E × B drift, and its motion trajectory is similar to the cycloid. If the magnetic field is ring-shaped, the electrons are constrained to make a circular motion in the plasma region of the target surface, and their motion paths are greatly increased, which increases the collision probability with the gas atoms, improves the ionization efficiency of the gas atoms, and thus improves the deposition rate and increases the adhesion of the film. At the same time, the working gas can work at a lower pressure because the ionization efficiency is improved, which reduces the impurity gas content (contamination) of the film layer and improve the film quality. High-energy electrons are prevented from strongly bombarding the substrate due to the constraints of the magnetic field, and the substrate temperature is lowered. 3. RF Sputtering In addition to the low sputtering efficiency, the DC sputtering system has the disadvantage in not being able to sputter an insulating material. This is because the positive ions bombarding the target surface are not neutralized when an insulating material target is used. They accumulate on the target surface, causing the target potential to rise so that the applied voltage is almost applied to the target. The voltage between

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the electrodes is lowered, the electric field is reduced, the acceleration and ionization of the ions are reduced, and finally the glow discharge is extinguished and the sputtering is stopped. Therefore, the DC sputtering device cannot be used for sputter deposition of insulating dielectric films. To solve the problem, RF sputtering method has been developed for sputtering insulating materials. In RF sputtering, a high-frequency AC power supply is used instead of a conventional DC power supply, as shown in Fig. 64. The dielectric target is placed on the surface of the cathode. After the high-frequency AC voltage is applied, the positive ions and the electrons can alternately bombard the target surface in one frequency cycle, thereby maintaining the gas discharge and achieving the sputtering of the dielectric material. When the target is in the positive half cycle, the electron moves toward the target. Because the electron mass is small and the mobility is large, the target and the electrode are quickly charged. In the negative half cycle, the mass of ion is larger than that of the electron, the mobility is small, and the movement of ions is much slower than electrons. Therefore, the electronically charged capacitor (target and electrode) discharges slowly, and electrons accumulate on the target, causing the surface to exhibit a negative bias, and the positive ions to bombard the target during the negative half cycle of the RF voltage, thereby achieving sputtering. RF sputtering is designed for sputtering insulated targets, but can also be used to sputter metal targets. Since the metal target cannot produce a self-biasing effect, a capacitor is required in series with the target to block the DC component. Due to the DC blocking capacitor, the metal target can also be self-biased and effectively sputtered under a negative bias most of the time in an alternating RF period.

Fig. 64 Schematic diagram of RF sputtering

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11.3 Pulsed Laser Deposition Pulsed laser deposition (PLD) [245–248] is a PVD technique where a high-power pulsed laser beam generated by the pulsed laser is focused onto the surface of a target of the material inside a vacuum chamber, causing high temperature and ablation in a very short time, and further resulting in high-temperature and high-pressure plasma to form a luster that looks like a feather, i.e., so-called plume. The plasma plume expands locally vertical to the surface of the target, to deposit a film on a substrate. PLD technology started in the 1960s, but it did not develop rapidly until the late 1980s. This technology has advantages in the preparation of superconductors, semiconductors, ferroelectrics, diamond or diamond-like carbon and some organic thin films, and has been used in the preparation of low-dimensional structural materials (nanoparticles, quantum dots, etc.). A schematic diagram of the PLD system is shown in Fig. 65. The system generally consists of a pulsed laser, an optical system, a deposition system, and ancillary equipment. The optical system includes a pupil scanner, a focusing lens, a laser window, etc. The deposition system is composed of a vacuum chamber, a vacuum pump, an inflation system, a target, a substrate heater, etc. The ancillary equipment is composed of a measurement and control device, a monitoring device, a motor cooling system, etc.(Fig. 66) The pulsed laser beam emitted by the pulsed laser is focused by a lens and projected onto the target. The surface temperature of the target material rises after absorbing the laser radiation. The heat is not quickly enough to be transferred into the interior of the material through heat conduction. This causes the temperature of the surface material and the material near the surface to rise quickly and causes rapid evaporation. The temperature of the vapor is usually very high, which is enough to cause a considerable number of atoms to be excited and ionized. A dense density of 1016 –1021 cm−3 and a temperature of 2 × 104 K will be formed in the range of about 1–10 μm on the surface of the target. The plasma, which absorbs the energy of the subsequent laser, causes its temperature to rise rapidly. The interaction between the laser and the target is complex. In essence, the effect of the laser on the target is different from evaporation, which is commonly referred to as ablation. This is the fundamental reason why PLD can keep the target film composition consistent. The pulsed laser beam emitted by the pulsed laser is focused by the lens and projected onto the target. The surface temperature of the target material rises after absorbing the laser radiation. The heat is not quickly enough to be transferred into the interior of the material through heat conduction. This causes the temperature of the surface material and the material near the surface to rise quickly and causes rapid evaporation. The temperature of the vapor is usually very high, which is enough to cause a considerable number of atoms to be excited and ionized. A dense density of 1016 –1021 cm−3 and a temperature of 2 × 104 K will be formed in the range of about 1–10 μm on the surface of the target. The plasma, which absorbs the energy of the subsequent laser, causes its temperature to rise rapidly. The interaction between the laser and the target is complex. In essence, the effect of the laser on the target

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Fig. 65 Schematic diagram of pulsed laser deposition system a optical system b photo of deposition system

is different from evaporation, which is commonly referred to as ablation. This is the fundamental reason why PLD can keep the target film composition consistent. The ablated particles from target are preferentially transported along the normal direction of the target. The speed of ablated particles is as high as 105 –106 cm/s and the density may reach 1018 –1021 cm−3 under typical conditions for the preparation of oxides. At the beginning, the high-speed and high-density ablation compresses

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Fig. 66 Schematic diagram of the working principle of the grating

the atmosphere gas at a high speed and forms a strong shock wave at a position of 1– 2 cm from the target. After the shock wave is formed, it is independently transmitted in a gas atmosphere. The front edge of the shock wave to the ablator is the region where the temperature, density, and pressure abrupt change are increased, and the thickness is about the order of micrometers, which is roughly equivalent to the mean free path of the gas molecules in a growing atmosphere. During the transmission, the thin layer of shock wave can reach tens of thousands of degrees of high temperature, and the ablation is close to the thin layer. As the spread continues, the shock will become weaker and weaker, eventually becoming a sound wave. In the sonic phase, the ablator essentially loses the speed of the directional movement and acts as a thermal diffusion under the action of gravity. After the ablated material is spatially transferred to the surface of the substrate, it is nucleated and grown on the substrate to form a thin film. Generally, it is necessary to apply a temperature of several hundred degrees to the substrate to improve the quality of the film. Compared with other coating technologies, PLD has the following features and advantages: (1) The composition of the deposited film can be consistent with that of the target. Therefore, the PLD can prepare a multi-component film containing a volatile element. (2) The textured film or epitaxial single-crystal film can be grown in situ at a lower temperature. PLD is suitable for the preparation of high-temperature superconducting, ferroelectric, piezoelectric, electro-optical, and other functional films with high quality. (3) A continuous ultra-fine film can be obtained to prepare high-quality nanofilms. (4) The growth rate is fast with high efficiency. (5) A variety of gases, including active and inert gases, and even their compounds can be introduced in situ during the growth process. (6) Due to the flexible position of the target, it is easy to realize the growth of the multilayer film and the superlattice film. The multilayer film formed by the in-situ deposition has an atomic-level clean interface. (7) The film in fabrication is less polluted.

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There are some inadequacies of the PLD coating method, such as: (1) It is not easy to prepare a large-area film. (2) There is micron-submicron-scale particle contamination on the surface of the film, and the uniformity of the prepared film is poor. (3) The composition of the target and film of some materials are not consistent. For multi-component compound films, if certain cations have a high vapor pressure, the stoichiometric growth of the film cannot be guaranteed at high temperatures.

12 Experimental Measurements Experimental measurements should be carried out to evaluate the optical properties and the performance of solar selective absorber devices. Absorptance and reflectance are the most important optical parameters of solar absorption device. In solar energy utilization, it is necessary to know the absorptance and reflectance of each film layer. Therefore, the fundamental measurements of those optical quantities are the key issues both in academic research and industry applications. The optical absorptance and reflectance of the materials are mainly measured by photometric spectrometers, including monochromatic spectrometers and interferometric spectrometers. An integrating sphere with a hollow sphere cavity is generally used in the measurement of reflectance. The inner wall of the sphere is especially coated to have a feature of nearly ideal and high diffuse reflection without selectivity.

12.1 Spectrometer The basic function of the spectrometer [249–262] is to separate or extend the composite light in space according to different wavelengths, and obtain the original information at each individual wavelength by using various photoelectric instrument accessories for subsequent processing and data analysis. A monochromatic spectrometer is a typical type of spectrometer consisting mainly of the entrance and exit slits, gratings, mirrors, and so on. Among them, the grating or other dispersive element like the prism is the key diffraction component split the light with different wavelength in the space. When the composite light enters the entrance slit of the monochromator, it is first proceeded to become a parallel light by an optical collimator, and then diffracted by the grating along the angular direction distributed in wavelengths. Each diffracted wavelength light with certain bandwidth then will be focused by the mirror onto the exit slit. The wavelength coming out of the exit slit can be accurately chosen or scanned in control of the computer. As an important optical device, the properties of the grating made by different ways of fabrication will directly affect the performance of the monochromator. Many types of gratings, including the scribed grating, replica grating, holographic grating, and so on, are applied. The scribed grating is mechanically scribed on the coated metal surface with a diamond knife. The replica grating is duplicated one of a mother

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grating. The holographic grating is lithographically patterned by laser interference fringes. The basic equation of the diffraction grating is. (sini − sinq) · d = m · λ

(12.1)

where i and λ is the incidence and diffraction angle of the light, respectively, m is the diffraction order of number with respect to the spectral line, d is the grove space constant of the grating, and λ is the wavelength of the diffracted light. In most spectral analysis systems where gratings are applied, the positions of the entrance and exit slit are fixed when light enters the system. With some form of mechanical control, the grating will rotate around the axis to make an image of the incident slit of quasi-monochromatic wavelength light precisely be out of the exit slit (Fig. 66). Important parameters of the grating monochromator: (1)

Angular dispersion power

Angular dispersion power refers to the distance of the diffraction angle generated by the diffracted light per unit wavelength difference. If the diffraction angle interval between two lines of a certain wavelength difference dλ is dθ, the angular dispersion power is defined as: dθ dλ

(12.2)

m dθ = dλ d · cosθ

(12.3)

Dθ = From Eq. (12.1), we can get Dθ =

Obviously, the angular dispersion is independent of the total number of grating lines, but proportional to the spectral order m and inversely proportional to the grating constant d. (2)

Line dispersion power

Line dispersion power Dl is the distance between the spectral lines of the unit wavelength difference separated by the focusing mirror on the focal plane. If the distance is d, which is distance between two lines with a certain wavelength difference dλ in the focal plane, i.e., dl = f dθ, then Dl =

m· f dI = dλ d · cosθ

(12.4)

where f is the focal length of the focusing mirror. For a monochromator, f is the distance from the concentrating concave mirror to the exit slit. From Eq. (12.4), the

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line dispersion ability Dl is proportional to order of the diffraction light and focal length. The higher the line density, the higher the angular and line dispersion power. (3)

Resolving power

Resolving power is the ability to resolve the minimum wavelength difference between two spectral lines, which is defined as R=

λ δλ

(12.5)

After the parallel light is diffracted by the grating, due to the limited width of the grating, the entrance slit image of light will not be well focused in the focal plane, except of a bright spot (diffraction pattern). The bright spot has a narrow angle θ on the center of the focusing mirror as θ =

λ W

(12.6)

W’ is the width of the m-th order of the diffracted beam, and its value is. W  = N · d · cosqm Usually, the angular width δθ at half-height of the two lines will be equal to θ, i.e., θ = δθ, when the two lines are just able to distinguish according to the famous “Rayleigh criterion”. From Eq. (12.1), we get δθ = mδλ/(dcosθm )

(12.7)

From Eqs. (12.5)–(12.7), we obtain R=

λ =m·N δλ

(12.8)

The above equation shows that the resolving power of the spectrometer by using the grating is proportional to the order m of diffraction and the total number N of grating grooves being illuminated, regardless of the grating constant. (4)

Free spectral range

The free spectral range is the wavelength range in which the lines do not overlap, and is denoted as λF . This means that the m-order line of λ + λF coincides with the (m + 1)-order line position of λ. According to the grating diffraction formula (12.1), we have m(λ + λ F ) = (m + 1)λ

(12.9)

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Therefore λ F =

λ m

(12.10)

λ in Eq. (12.10) actually refers to the lower limit of wavelength λm . Thus, the range of wavelength usually is λ < λm /m. Take the first-order of line as an example, λ < λm , the upper limit of wavelength is λM = m + λ = 2λm . The free spectral range is closely related to the grating constant d. Taking the first-order of diffraction spectrum at the normal incidence condition as an example, from Eq. (12.1), m = 1, θ has a maximum of π/2. Then λM = d, λm = d/2. (5)

Blaze wavelength

For conventional non-blazed gratings, most of the diffracted light is concentrated in a dispersion-free “zero-order spectrum” with a small portion of the energy dispersed in other levels of the spectrum. The zero-order spectrum does not work as a spectrometer and cannot be used for spectral analysis. The primary and secondary spectra with increasing dispersion are getting smaller and smaller. In order to reduce the intensity of the zero-order spectrum, and concentrate the radiant energy in the required wavelength range, the grating-direction-blazed method is adopted, that is, the grating indentation is carved into a certain shape, so that the small reflecting surface of each notch and the grating plane are fixed. The blazed angle is made as that the diffracted light intensity is shifted from the original zero-order light direction to the reflection direction determined by the shape of the score, and as a result, the spectrum of the reflected light along the blazed direction will have much strong intensity. Thus, the wavelength at which the radiation energy has maximum value is called the blaze wavelength (Fig. 67).

Fig. 67 Schematic diagram of C-T structure monochromator

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12.2 Interferometric Spectrometer One of the most common types of interferometric spectrometers is the Fourier transform spectrometer, a new spectrometer developed based on the Michelson interferometer. As shown in Fig. 68, assuming that a beam of monochromatic light passes through the beam splitter B and is split into two beams, which are reflected by M1 and M2 , respectively. They meet at a certain point in space and are coherently superimposed with the intensity I expressed as I = I0 (1 + cosδ) = I0 [1 + cos(

2π L)] λ

(12.11)

In the formula, I 0 is the sum of the intensities when the two light waves are not interfered, δ is the phase difference between the two light waves at the meeting point, λ is the wavelength of the light wave, and L is the optical path difference of the two light waves. Equation (12.11) indicates that the superposed light intensity I is a function of the phase difference δ or the optical path difference L of the two optical waves. For convenience, let L = x, and express the formula (12.11) as I (k, x) = I0 [1 + cos(kx)]

(12.12)

Now consider that the two light waves participating in the superposition come from the same point source with the spectral distribution function i, then the relative superimposed light intensity of the monochromatic light component with the wave number k can be expressed as Fig. 68 Schematic diagram of the Fourier transform spectrometer

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i(k, x) = i(k)[1 + cos(kx)]

(12.13)

By integrating all wavelengths in the above equation to get the total superimposed light intensity, which is given by. ∞

∞

I (x) = ∫ i(k, x)dk = ∫ i(k)[1 + cos(kx)]dk 0 ∞

0

∞

= ∫ i(k)dk + ∫ i(k) cos(kx)dk 0

1 = I (0) + 2 1 = I (0) + 2

0

1∞ eikx + e−ikx ∫ i(k) dk 2 0 2 1 ∞ ∫ i(k)eikx dk 2 −∞

(12.14)

Define W(x) as W (x) = 2I (x) − I (0) =

∞

i(k)eikx dk

(12.15)

−∞

The above equation shows that the spectral distribution function is actually the Fourier transform of W (x) = 2I(x)-I(0), which is 1 i(k) = √ 2π

∞

W (x)e−ikx d x

(12.16)

0

Fourier transform spectrometers have the advantages of high resolution, high signal-to-noise ratio, and wide operating band.

12.3 Principle of Integrating Sphere The integrating sphere has a hollow sphere cavity with a highly reflective inner surface [263–265]. It is primarily used to collect the light scattered or emitted from a sample placed in or outside the ball or emitted by the source itself. It can also be used to accurately measure the optical reflection and transmission properties of materials, as well as the radiance, brightness or chromaticity of the light source. The inner surface of the ideal integrating sphere is a complete geometric spherical surface with equal radii everywhere. The inner wall of the sphere is a neutral uniform diffusing surface with the same diffuse reflectance for incident light of various wavelengths. As shown in Fig. 69, the direct illuminance of the light source S at any point on the ball wall is E A , and the illuminance at the M point of the probe is set to E M . The diffuse radiant exitance produced by the area element dS at A is M = ρE A . According to Lambert’s law, the brightness of the dS surface is

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Fig. 69 Schematic diagram of the principle of the integrating sphere

L 0 = ρ E A /π

(12.17)

The second illumination at M produced by the diffusion of dS at A is

dE 2 =

L L · ds (AM/2)2 L · ds 2 ·cos θ ds = · = 2 2 2 r 4r 2 (AM) (AM)

(12.18)

Therefore

dE 2 =

ρEA · ds 4πr 2

(12.19)

The second illuminance generated by the diffusion of the entire spherical surface at M is E2 =

dE 2 =

ρ 4πr 2

E A ds =

ρφ 4πr 2

(12.20)

The third illumination at M produced by the diffusion of the entire sphere is: dE 3 = E3 =

dE 3 =

ρ E 2 ds 4πr 2

ρ E2 4πr 2

(12.21) ds = ρ E 2

(12.22)

In the same way, we get E4 = ρ E3 = ρ 2 E2

(12.23)

E5 = ρ E4 = ρ 2 E3 = ρ 3 E2

(12.24)

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Therefore, the total illumination at point M is E M = E 1 + E 2 + E 3 + · · · = E 1 + E 2 (1 + ρ + ρ 2 + . . . ) E M = E1 +

1 ρ φ = E1 + Eρ E2 = E1 + · 1−ρ 1 − ρ 4πr 2

(12.25) (12.26)

When blocking the light from the light source S and letting the light directly into the M point with a screen in front of the M point, we obtain E M = Eρ = φ=

φ ρ · 1 − ρ 4πr 2

1−ρ 4πr 2 E ρ ρ

(12.27) (12.28)

Therefore, the total luminous flux of the light source (apparatus) can be obtained by measuring the illuminance at the M point of the ball wall.

12.4 Measurement of Reflectance and Absorbance 1. Integrating Sphere for Absolute Measurement As distinguished between specular reflections and diffuse reflections of samples, the absolute method integrating sphere can be used to measure reflectance with great convenience [264–268]. The absolute method integrating sphere is shown in Fig. 70a. The structure of the ball is basically the same as the so-called comparison method,

Fig. 70 Schematic diagram of absolute method integrated sphere

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which will be introduced in the next part. The only difference is that a baffle T is placed in the ball to block the direct illuminance of the sensing element hole, implying that the direct illuminance generated by the reflected beam of the sample will not be received by detector D and only a few additional illuminances are received, namely, Es =

ρs F ρw · 4π R 2 1 − ρw

(12.29)

When the beam is projected onto the ball wall W, the illuminance measured by the detector D is E W = E 0 + E n , where the direct illumination E 0 and the additional illumination E n are E0 =

ρS F 4π R 2

(12.30)

and En = E0 ·

ρw ρw F ρw = · 1 − ρw 4π R 2 1 − ρw

(12.31)

respectively. The illuminance E W generated by the beam projected onto the ball wall W is E W = E0 + En =

ρw F 1 · 2 1−ρ 4π R w

(12.32)

Dividing the formula (12.29) and the formula (12.32), we get ρs =

Es Ew

(12.33)

Equation (12.33) is an expression for absolute reflectance measurement. The advantages of this method are that standard samples and identification of the type of sample are not needed. In addition, the sample under test is placed in the center of the ball, so that the sample acts as a baffle, and the absolute reflectance can also be measured. The optical path principle is shown in Fig. 70b. When the beam is projected onto the sample S, the illuminance perceived by the detector D is the same as that presented by Eq. (12.29). The sample S is subsequently removed, and the beam is projected onto the wall W, and the illuminance detected by D is the same as that presented by Eq. (12.32). Measuring the reflectance with this type of integrating sphere is also the same of Eq. (12.33).

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For opaque samples, the absorbance of the sample is based on the law of conservation of energy. αs = 1 − ρS

(12.34)

2. Integrating Sphere for Comparison Method of Measurement The comparison method integrating sphere is shown in Fig. 71. Sample S is mounted on the wall of the ball. The ball can rotate around the point O, causing the incident beam to be projected at the sample S and the ball wall W, respectively, and ensuring that the incident optical path is uniform. The standard of the comparison method can be the integrating sphere wall. The ball wall is an ideal diffuse reflection material, and the sample tested is not necessarily a diffuse reflection object. Therefore, different types of reflective samples should be treated separately when measuring the reflectance with a comparative method integrating sphere. (1)

The sample is an ideal diffuse reflector. As shown in Fig. 71, when the beam F is projected onto the diffuse reflection sample S, the direct illumination E 0 and additional illumination at any point on the wall of the ball are expressed by Eqs. (12.30) and (12.31), respectively. The total illuminance E s produced is   ρs F ρs F ρw 1 = Es = · 1+ · 2 2 1 − ρw 4π R 4π R 1 − ρw

(12.35)

When the incident beam F is irradiated onto the ball wall, the total illuminance produced is Ew =

Fig. 71 Schematic diagram of comparison method integrating sphere

ρw F 1 · 2 1−ρ 4π R w

(12.36)

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Then from Eqs. (12.35) and (12.36), we get ρs = ρw (2)

Es Ew

(12.37)

For the sample with ideal mirror-reflecting surface, the beam projected onto the surface of the sample will be reflected to the other point of the ball wall according to the law of reflection, while the other points in the ball wall will not obtain the direct illuminance of the beam F, only a few additional illuminances, whose value is

Es =

ρs F ρw · 2 1−ρ 4π R w

(12.38)

When the beam is projected onto the wall, Eqs. (12.38) and (12.36) are divided to obtain the expression of the reflectivity of the ideal mirror reflection sample, like Eq. (12.29) ρs = (3)

Es Ew

(12.39)

The sample which has both diffuse and specular reflections is the most common situation. Let the diffuse reflectance of the sample be ρs’ , and the specular reflectance of the sample be ρs’ ’, then the true reflectance of the sample will be ρs = ρ ’s + ρs’ ’. Similarly, the illuminance E s of the integrating sphere can be expressed as

’

E s = E ’s + E s’ = =

ρs’ F 1 ρ ’’ F ρw · + s 2· 2 1−ρ 4π R 4π R 1 − ρw w

 F 1  ’ ρs + ρs’’ ·ρ w · 2 1−ρ 4π R w

(12.40)

Dividing Eq. (12.40) by Eq. (12.36), we get Es ρ ’ + ρs’’ ·ρ w = s Ew ρw

(12.41)

Es · Ew

(12.42)

Then, ρs =

1 ρs’’ ρs

+

ρs’ ρs

·ρ w

=

Es ·k Ew

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k=

1 ρs’’ ρs

+

ρs’ ρs

(12.43)

·ρ w

In general, this percentage cannot be directly measured, and only a method in approximation can be used. The specular reflectance ρs’ ’ of the sample can be measured by an absolute specular reflectance measurement device. Let’s do the first approximation calculation, ignore the k value in Eq. (12.42), and calculate the sample reflectance ρs . Substituting the known ρs , ρs’ ’ and ρw into the Eq. (12.43), this yields the first approximation k. Then substituting k into Eq. (12.42), this gets ρs2 , as well as the second approximate synthesis coefficient k 2 . We can continue to do such steps one by one. The more times of approximation, the closer to the true value. However, more approximations are not necessary, and the k-value with two times approximation is sufficient. As mentioned above, for opaque samples, the absorbance of the sample is. αs = 1 − ρS

(12.44)

3. V-W-Shape Optical Path Measurement of Reflectivity of Samples The measurement of the reflectance of a regularly reflecting sample can be achieved with a simple optical path. A typical method, called the V-W type method, also called the Strong method, is shown in Fig. 72. It is configured of two measurement optical paths, as the V-shape and W-shape, respectively. The reference sample is first placed at position I, and the detector measures the reflected light intensity as I 1 . If the incident light intensity is I 0 , then we get. I1 R f I0

(12.45)

Fig. 72 Schematic diagram of measurement of reflectivity by V-W shaped optical path method

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The reference sample is placed at position II, and the sample to be tested is placed in position III. If the incident light intensity is still I 0 , the incident light enters the detector after two reflections by the surfaces of the sample and reference sample. The detector measures the light intensity I 2 , then we get. I2 R f R 2 I0

(12.46)

The reflectance can be obtained from the above two equations and given by. R = (I2 /I1 )1/2

(12.47)

The V-W optical path can also be extended to multiple reflections, as shown in Fig. 73. The reflectance of the reference sample is first measured, as shown in Fig. 73a, and the light beam enters the detector after being reflected K times by two identical reference samples H. The optical path for measuring the sample is shown in Fig. 73b. The light beam is reflected K times by the reference sample H and enters the detector after being reflected K + 1 times by the sample. Setting the incident light intensity of the optical paths (a) and (b) to I 0 , and the measured light intensity at the detector is I 1 and I 2 , respectively. Then Fig. 73 Schematic diagram of multiple reflections to measure reflectivity

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I1 = I0 R Kf

(12.48)

I2 = I0 R K +1 R Kf

(12.49)

where Rf is the reflectance of the reference sample. Reflectivity R is obtained from Eqs. (12.48) and (12.49), as given by 1

R = (I2 /I1 ) K +1

(12.50)

For high reflectance samples, the more the number of reflections, the higher the measurement accuracy. 4. Measurement Principle Based on Fourier Spectrometer (FT-IR) and Integrating Sphere Reflectometer On the basis of the measurement principle of the Fourier spectrometer and the integrating sphere reflectometer, the optical path design of the solar spectrum absorptance measurement device is shown in Fig. 74, and the part in dashed-line frame shows the optical path of the spectrometer. Fig. 74 Optical path diagram of solar spectrum absorptivity measuring system

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An elliptical metal mirror M1 is added to the optical path in the spectrometer for transmission measurement, so that the spectrometer optical path is conducted into the integrating sphere through the entrance hole to make the beam irradiate on the surface of the coated sample. The reflected light is diffusely multiple-reflected in the integrating sphere. In terms of the reflections by the coated sample and the integrating sphere, the output response in the spectrometer is S s (λ), as given by Ss (λ) = R(λ)A(D, ρ)ρs (λ)L(λ)

(12.51)

where A(D, ρ) is the integrating sphere constant, which is related to the diameter D of the integrating sphere and the reflectance ρi of the inner wall coating. R(λ) is the response function of the spectrometer (V·μm·m2 ·sr·W−1 ), and ρs (λ) is the reflectivity of the coated sample. L(λ) is the output spectral radiance of the spectrometer. The coated sample is replaced with a reference standard one of known spectral reflectance ρ B (λ), and the output response of the spectrometer is S B (λ), as given by SB (λ) = R(λ)A(D, ρ)ρB (λ)L(λ)

(12.52)

For opaque samples, the spectral absorbance of the coated sample is given by. α(λ) = 1 − ρS (λ)

(12.53)

From Eq. (12.51) and (12.53), we get α(λ) = 1 −

SS (λ)ρB (λ) SB (λ)

(12.54)

12.5 Measurement of the Thermal Emittance Object which radiates energy in the form of electromagnetic waves due to its own temperature or thermal motion is called thermal radiation. Thermal radiation has a continuous spectrum with a wide frequency distribution. The spectral distribution of radiation and the magnitude of radiant energy mainly depends on the temperature of the radiating surface. The radiation increases with the temperature. The wavelength distribution of the radiation also varies with temperature. It mainly radiates invisible infrared light at low temperature. When the temperature increases to 500 °C or higher, it emits visible light or even ultraviolet light. Although thermal radiation is one of the approaches for heat transfer, it is different from heat conduction or convection. It can transfer heat directly from one system to another without relying on media. Thermal radiation is the main way of long-distance heat transfer. For example, the heat of the sun is transmitted to the earth through space in the form of heat radiation. Thermal

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radiation is an intrinsic property of various substances. In this process, the radiating object radiates heat to the outside and absorbs heat from surrounding objects. When the temperature of the object is higher than the ambient temperature, the radiation is greater than the absorption; otherwise, the radiation is less than the absorption. When the object is at the same temperature as the surrounding environment, the radiated heat will be equal to the absorbed heat. The system reaches an equilibrium state. The thermal radiation in this case is called equilibrium thermal radiation. Thermal radiation research has important applications in many fields, including military, solar applications, metallurgy, etc. For example, the identification and thermal control of space targets, infrared guidance and stealth, resource detection, and disaster prediction are all related to the detection of thermal radiation. The emissivity (also called blackness coefficient, etc.) for the surface of the material is usually used to characterize the radiation power of the substance. The material emissivity is an important parameter for analyzing the properties of surface thermal radiation, radiant energy absorption, and radiation cooling. Accurate measurement of material emissivity is an indispensable part of thermal radiation research. Emissivity can be influenced by factors such as the nature of the material, its surface state, temperature, etc. Reflectance measurement, radiation measurement, and calorimetry are widely used methods for measuring emissivity. 1. Emissivity and Kirchhoff’s Law According to Kirchhoff’s law [269], an object is placed in the cavity in assumption, and it is thermally insulated from the cavity wall, as shown in Fig. 75. If the wall of the chamber maintains a constant temperature, the thermal radiation will fill the entire cavity, with some of the radiation absorbed by the object. At the same time, the object also emits radiation. When the rate of emissivity for the object is equal to that of radiation absorbed, the cavity will reach thermal equilibrium. Thus, the temperature of the object is the same as the temperature of the chamber wall. The irradiance of the thermal radiation in the cavity E means the total power incident on the unit area of the object. α represents the proportion of the incident power absorbed by the object. R represents the radiated power or emittance power of the object of unit area. Then in the case of thermal equilibrium, we get. R = aE Fig. 75 Schematic diagram for deriving Kirchhoff’s law [269]

(12.55)

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When the cavity contains multiple objects, it is assumed that these objects have different values of α, which are distinguished by subscripts 1, 2, …, respectively. When all the objects reach thermal equilibrium, then R1 = α 1 E, R2 = α 2 E, and so on. E can be written as: E=

R2 R1 = = ··· α1 α2

(12.56)

Therefore, for a given temperature, the ratio of the transmitted power to the absorbed power of all objects is the same and it is equal to the irradiance within the cavity, which is known as Kirchhoff’s law. Kirchhoff’s law applies not only to total radiation at all wavelengths, but also to any monochromatic radiation at a specific wavelength, then E(λ) =

R1λ R2λ = = ··· α1λ α2λ

(12.57)

According to this law, a good absorber is also a good emitter, and vice versa. In other words, an object with high absorption power has high emission power. If the object cannot emit radiation of a certain wavelength, it cannot absorb radiation of that wavelength. The fact above can be verified by simply smoking a black spot on the glass rod. If the rod is heated to white hot, the blackened spots are brighter than the rest of the rod. An ideal absorber is called a black body. For blackbody, α = 1. According to Kirchhoff’s law, the black body has the largest value of R, namely. Rmax = E

(12.58)

One may find that the black body is the most effective emitter of thermal radiation, with the emission power per unit area being equal to the irradiance in the cavity. Therefore, blackbody radiation is also referred to as cavity radiation. The actual black body radiator is only required to have a small aperture in a cavity surrounded by the heat insulating wall. If the wall of the chamber maintains a constant temperature, then the heat radiation from the aperture is essentially the same as that from an ideal black body. The significance of Kirchhoff’s law is to link the absorptive capacity of the object with the emitting ability, and to link the absorption and emission capabilities of various substances with those of the black body. In order to describe the radiation of non-blackbody, the radiation emissivity or the specific emissivity ελ is introduced and defined as ελ =

eλ Mλ = e0λ M0λ

(12.59)

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where ελ is a function of wavelength, temperature, and surface properties, with values between 0 and 1, for blackbody ελ =1. The thermal radiation of materials is different at different wavelengths and different directions. Therefore, according to the wavelength range, emissivity can be divided into spectral (or monochrome) and full-wavelength emissivity. According to the emission direction, it can be divided into directional, normal, and hemispherical emissivity. 2. Reflectance Measurement Method According to the law of energy conservation and Kirchhoff’s law, for the opaque sample, the sum of the reflectance ρ and the absorbance α is equal to 1, that is, ρ + α = 1. When radiant energy of known intensity is projected onto a surface of measured sample with zero transmittance, the reflectance of the sample can be obtained by a reflectometer and then emissivity will be determined. Thermal cavity reflectometers, integrating spheres (paraboloids, ellipsoids, etc.) reflectometers, specular reflectometers, and goniometers are commonly used reflectometers [270–272]. 3. Integrating Sphere Reflectometer The integrating sphere reflectometer is suitable for measuring the reflectance in the wavelength range of 0.25~2.5 μm at room temperature. The main part of the system contains an integrating sphere with a diffuse inner surface of high reflectivity. The working principle of the integrating sphere is introduced as follows. The tested sample is placed at the center of the sphere, and the incident light is projected from the entrance of the integrating sphere to the surface of the sample and reflected onto the inner surface of the integrating sphere. The light is uniformly distributed on the surface of the sphere after the first reflection. The detector receives radiant energy from the surface of a sphere through another orifice. Then the tested sample is replaced with a standard sample of known reflectance and the foregoing process is repeated. The ratio of the measured radiation energy of the two measurements is a reflectance coefficient. Therefore, the reflectance of the tested sample is the coefficient multiplied by the reflectance of the standard sample. Besides, another working mode can also be adopted, the incident beam is first irradiated on the spherical surface. Then the diffused radiation beam is projected onto the sample or the standard sample before the detector receives the reflected radiant energy of the sample through the orifice. If the sample or the integrating sphere is rotated about the axis, the directional reflectance can also be measured. Changing the inner wall coating of the integrating sphere can change the operating wavelength range. Wiley (1976) used a rough gold surface layer (reflectance up to 0.95) as the inner wall of the integrating sphere, extending the working wavelength to 2~20 μm. However, there are many sources of error in this method, including blackbody radiation model error, radiant energy measurement error, optical system error, standard sample reflectivity error, deviation of the sample to diffuse gray body, and the influence of stray radiation.

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4. Thermal Cavity Reflectometer In 1962, Dunkle et al. developed a thermal cavity reflectometer. The measurement range of wavelength is usually 1~15 μm with an error of 3–5%. The measurement accuracy highly depends on the sample temperature which must be much lower than the temperature of the chamber wall. Therefore, this method is not suitable for high-temperature measurement. It still has certain applications, however, since this method can measure the spectral and directional emissivity of the sample with simple equipment preparation for the sample in a short test period. 5. Laser Polarization Method In the 1990s, Nordince proposed a method for measuring the emissivity of rod-shaped samples by laser polarization method. The principle is to measure the intensity ratios of the two polarization directions of reflected light, which is related to the reflectivity of the tested material, namely. Ip = 1 + ρsn In

(12.60)

where I p is the intensity of the polarized light in the p direction; similarly, In is the intensity of the polarized light in the n direction;ρsn is the vertical emissivity of the sample. Cezairliyan et al. also used this method (Fig. 76) to measure the emissivity of several materials. The measurement accuracy is better than 95%, with measurement

Fig. 76 Schematic of emissivity measurement by laser polarization method

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time less than 0.3 s. But only the material emissivity of the smooth surface can be measured.

12.6 Radiation Energy Method The basic principle of the radiation energy method [273–280] is to measure the radiant power of the sample directly and calculate the surface emissivity value of the sample according to the Planck’s or Stefan–Boltzmann law with the definition of emissivity. Since the absolute measurement of radiation is still difficult to achieve high precision, the energy comparison method is usually applied. The same detector is used to measure the radiant power of the absolute black body and the sample at the same temperature. The ratio of the two is the emissivity value of the material. In recent years, the Fourier analysis spectrometer has been widely used for measurement. The advantage is that the measured spectral range is wide, about 2~28 μm, and the temperature range is from room temperature to 3000 °C. The black body and the sample are separately scanned by the spectrometer. The measurement results are Vb (λ, T ) and Vs (λ, T ), respectively. Assuming that the spectral response of the spectrometer is linear, then we get Vb (λ, T ) = R(λ)L b (λ) + S(λ)

(12.61)

Vs (λ, T ) = R(λ)L s (λ) + S(λ)

(12.62)

where Vb (λ, T ) is the output corresponding to the radiant energy of the black body at the temperature T and Vs (λ, T ) is the output corresponding to the radiant energy of the sample at the temperature T. R(λ) is the spectral response function of the spectrometer, and S(λ) is the background function of the spectrometer. L b (λ) and L s (λ) can be expressed as L b (λ) = εb · L b (λ, T) + (1 − εb ) · L(λ, Te )

(12.63)

L s (λ) = εs · L b (λ, T) + (1 − εs ) · L(λ, Te )

(12.64)

where L b (λ,T )is the spectral radiance of the black body at temperature T, and L(λ,Te ) is the spectral radiance resulting from the ambient temperature Te ; εb and εs are the emissivity of the black body and the sample, respectively, and εs then can be given by: εs =

Vs (λ, T ) − S(λ) [εb + t (λ, T, Te )] − t (λ, T, Te ) Vb (λ, T ) − S(λ)

(12.65)

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where t (λ, T, T e ) =

L(λ, Te ) L b (λ, T ) − L(λ, Te )

(12.66)

and S(λ) is a background function related to the instrument. In order to eliminate the influence of the background function of the spectrometer on the measurement results, the R(λ) and S(λ) of the spectrometer are generally calibrated by the double black body method or the multi-temperature method. When multi-temperature calibration is applied, we get Vb (λ, T1 ) = R(λ) · L b (λ, T1 ) + S(λ)

(12.67)

Vb (λ, T2 ) = R(λ) · L b (λ, T2 ) + S(λ)

(12.68)

then R(λ) = S(λ) = Vb (λ, T1 ) −

Vb (λ, T1 ) − Vb (λ, T2 ) L b (λ, T1 ) − L b (λ, T2 )

Vb (λ, T1 ) − Vb (λ, T2 ) · L b (λ, T1 ) L b (λ, T1 ) − L b (λ, T2 )

(12.69) (12.70)

1. Independent Black Body Method The independent blackbody method uses a standard blackbody furnace as the reference radiation source. The radiation parameters of sample and the blackbody are independently measured. When measuring the full-wavelength emissivity of a material, the detector needs to choose a non-spectral-selective thermopile or pyroelectric device. When measuring the spectral emissivity of a material, the photon detector should be chosen and equipped with a specific monochromatic filter. The advantage of the independent blackbody scheme is able to finely fabricate standard sources of radiation and accurately calculate their radiation characteristics. The disadvantage is that isothermal conditions are difficult to guarantee, especially for poorly conductive materials. In practical applications, people often use the whole black body method and the conversion blackbody method, as shown in Fig. 77, to measure the emissivity of the material, which means drilling holes in the sample or adding a reflector to make the material to be tested black or close to the black body. Thereby, the measurement of the material emissivity is performed. 2. Infrared Fourier Spectroscopy Since the 1990s, due to the development and wide application of infrared Fourier spectrometers, many measurement systems and devices for spectral emissivity of materials have been established based on this technology. The infrared Fourier spectrometer is mainly composed of a Michelson interferometer and a computer. The

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Fig. 77 Schematic diagram of two conversion blackbody methods

right emitted by the light source is modulated by the Michelson interferometer and becomes interference light, and then the various frequency optical signals after the irradiation of the sample are modulated by interference. For the interferogram function, the Fourier transform is performed by the computer to obtain spectral information of the sample in a wide wavelength range at one time. Therefore, the infrared Fourier spectrometer is a powerful instrument for measuring infrared emissions. In recent years, many groups around the world have carried out research work on the measurement of spectral emissivity of materials based on Fourier transform infrared spectroscopy. The most representative is the semi-ellipsoidal mirror reflectometer system, which was developed by Markham et al., as shown in Fig. 78. The system can simultaneously measure the spectral emissivity and temperature of the material, with a temperature measurement range of 50~2000 °C, a typical measurement accuracy of 95% in the spectral measurement range of 0.8~20 μm. The diameter of the sample is 10~40 mm, and the effective diameter of the measured part of the sample is 1~ 3 mm. To ensure the uniformity of the temperature of the sample during heating, the optimum thickness of the sample is 1~3 mm. In 2004, the National Institute of Standards and Technology (NIST) used a series of blackbody radiation sources to establish a new material spectral emissivity measurement system with a temperature range of 600 to 1400 K and a wavelength range of 1 to 20 μm, mainly for the measurement of opaque materials. The schematic diagram of the emissivity measurement system is shown in Fig. 79. The system consists of the following components: (1)

A series of reference blackbody radiation sources are mounted on the mobile platform, including two fixed-point and four temperature-changing black bodies. Each black body contains a standard platinum resistance thermometer (PRT) or standard thermocouple temperature sensor for controlling and monitoring temperature changes in the black body. Two fixed-point blackbody

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Fig. 78 Schematic diagram of a semi-ellipsoidal reflector reflectometer system

Fig. 79 Schematic of NIST infrared spectral emittance characterization facility

furnaces with replaceable crucibles (In, Sn, Zn, and Al, Ag, Cu, respectively) are used for absolute temperature determination. The filter-type radiometer

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(2) (3)

(4)

(5) (6) (7)

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is used for the transfer from the fixed-point blackbody to the temperaturechanging blackbody. The spectral emissivity of the blackbody is obtained by the Monte Carlo ray-tracing algorithm. The sample heater is mounted on a moving and rotating platform, which can be replaced according to the measurement conditions. Visible/near-infrared integrating sphere is mainly used for measuring the temperature of samples above 500 K. PRT for contact measurement is applied below 500 K. Optical system is used to image the center area of the sample or black body radiation source from 3 to 5 mm to the water-cooled field diaphragm, and then re-image the field to the Fourier transform infrared spectrometer or the filter radiometer. A sealing device is used for the entire optical path gas purge. The power supply, signal, purge gas (nitrogen or argon), and cooling water system are equipped. The system control and data processing through LabVIEW software programs of several computers are applied.

The specific measurement steps for the emissivity measurement of the solar device are as follows. In the first step, the reflectance of the hemispherical direction of the sample is measured by an integrating sphere reflectometer at a required temperature. The laser or broadband source is selected to be incident on the integrating sphere based on the estimates of temperature and emissivity for the sample. The reflectance of the sample can be obtained by comparison with a calibrated standard sample. Then the emissivity of the sample can be calculated according to Kirchhoff’s law at the selected wavelength. In the second step, the relative radiant energy of the sample and the black body at the same wavelength is measured by a filter-type radiometer. Through the above two steps of measurement, the temperature of the sample can be calculated. Finally, by using the FITR spectrometer to compare the spectral emissions of the sample and the reference blackbody, the spectral emissivity of the sample can be calculated. To evaluate the performance of the emissivity measurement system, NIST measured the normal spectral emissivity of two standard sample candidates, SiC and Pt-10Rh in the wavelength region of 2–20 μm and at 300~900 °C. In addition, the uncertainty is also evaluated in detail. The evaluation results show that the standard uncertainty of measurement of SiC and Pt-10Rh at 600 °C is 0.47% and 1.46%, respectively. In 2000, the National Metrology Institute of Japan (NMIJ) developed an emissivity measuring system based on a Fourier transform infrared spectrometer, as shown in Fig. 80. The emissivity measuring device uses a simple Michelson interferometer, and a photovoltaic MCT detector with good linearity and sensitivity. The measurement spectrum ranges from 1 to 12 μm, with the measurement time of a few seconds. And the temperature range is from −20 to 100 °C. To avoid the effects of carbon dioxide and water in the atmosphere, all optical equipment, specimens, and blackbody radiation sources operate under vacuum.

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In order to calibrate and compensate for drift, the measuring system is equipped with two high-quality blackbody radiation sources, one is a constant temperature blackbody furnace that uses liquid nitrogen refrigeration and temperature control as a “0” radiation reference source. The other is a variable temperature black body furnace with a temperature range of −20–100 °C. Both the sample and the variable temperature black body furnace are heated and temperature controlled by a mixed liquid of constant temperature water and ethylene glycol. The temperature of the constant temperature bath is measured by a PRT sensor. In order to evaluate the performance of the system, the source size effect of the spectrometer was measured. It was found that when the target diameter is larger than 20 mm, the source size effect is negligible. Another black body (placed at the sample exit) is used to test the linearity between the incident spectral radiation and the measured values. It was found that the nonlinearity error within 10 μm bandwidths was less than 0.5% at 100 °C. Compared with the measurements of similar instruments designed by Lohrengel, the consistency of the system was good at 8–12 μm. Next, the uncertainty of the measurement system was evaluated. The relative uncertainty of the measurement for high emissivity samples (emissivity close to 1) was found to be less than 1%. While for low emissivity samples (emission), the relative uncertainty of the measurement (with a rate of approximately 0.2) is less than 3%.

Fig. 80 Schematic of NIMJ FTIR spectrometer system

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12.7 Calorimetry The basic principle of the calorimetry method is introduced as follows [281–285]: A heat exchange system contains the tested sample and surrounding related objects. The heat transfer equation of the system related to the emissivity of the material can be derived according to the heat transfer theory. The heat exchange state of the system is obtained by measuring the temperature values of some points of the sample. Therefore, emissivity can be obtained. The calorimetry method is divided into a steady-state calorimetry method and a transient calorimetry method. 1.

Steady-state calorimetry

The commonly used steady-state calorimetry method is the filament-heating-based method. For example, Worthing’s steady-state heating method uses a filament for heating with a measurement accuracy of 98% and a temperature range of −50 to 1000 °C. However, the system has complicated sample preparation and long measurement time. Besides, only the full-wavelength hemispherical emissivity can be measured, while the spectrum or directional emissivity cannot be performed. 2.

Transient calorimetry

The transient calorimetry uses transient heating technology (such as laser, current, etc.) to make the temperature of the sample rise sharply. By measuring the parameters such as sample temperature and heating power, and combining the auxiliary equipment, the emissivity of the object is measured. In the 1970s, NIST’s pulsed heating transient calorimeter based on the integrating sphere reflectometer method achieve a fast measuring speed and an upper measurement limit of up to 4000 °C. It can measure multiple parameters accurately, but the measured object must be a conductor, which limits its application range.

13 Broad Applications of Solar Selective Absorbers In solar thermal conversion system, conversion efficiency is a very important figure of merit to evaluate its performance, which can be reduced from the viewpoint of thermodynamics. The overall system can be divided into two subsystems of the sunlight-to-heat conversion process of the receiver and heat to electricity conversion system. The solar-to-heat conversion efficiency of incident solar photons at the solar selective absorber is defined as: ηabs = α −

4 ) qconv (Th − Tamb ) εσ (Th4 − Tamb − C Is C Is

(13.1)

When the solar selective absorber is encapsulated in a vacuum, the convection loss qconv can be ignored, leading to [8, 9, 22, 162, 175]:

Optical Properties of Solar Absorber Materials and Structures

ηabs

  4 εσ Th4 − Tamb =α− C Is

135

(13.2)

The heat-to-electricity conversion efficiency in the heat engine subsystem is limited by the Carnot efficiencyηC : ηC = 1 −

Tamb Th

(13.3)

The total conversion efficiency is thus given by the product of the receiver efficiency and Carnot efficiency [9]: !

 "   4 εσ Th4 − Tamb Tamb η= α− 1− C Is Th

(13.4)

Maximize the total conversion efficiency can lower the levelized cost of energy (LCOE) for solar thermal conversion system. Here, we will mainly focus on the solar thermal conversion efficiency ηabs of the solar selective absorber.

13.1 Temperature-Dependent Efficiency For solar-to-heat conversion efficiencyηabs , it is obviously dependent on the solar concentration C and working temperature T h of the solar selective absorber. Moreover, thermal emittance, which can be calculated from blackbody-curve fitted reflectance spectra [28], was also related to T h . According to the principle of Planck’s blackbody radiation, with the increasing of temperature, blackbody radiation spectra will shift to the short wavelength region, which will overlap more with the absorption spectra of the solar selective absorber, resulting in the rise of thermal emittance [34]. The thermal emittance of some commonly available solar selective absorbers at different temperatures are summarized by Kennedy et al. and shown in Fig. 81 [7, 286]. As can be seen, thermal emittance apparently increases with temperature. Though thermal emittance can be calculated from the room temperature reflectance spectra by setting blackbody radiation at different temperatures [26, 134], it’s difficult to directly measure the thermal emittance due to the hemispherical thermal radiation at the half-space over the sample, especially at high temperature [116, 287, 288]. Integrated sphere [288] or angularly distributed optical fibers [163, 289] integrated with sample heater have been adopted to directly measure thermal radiation. It has also been demonstrated that the total hemispherical emittance is rather close to the near-normal emittance value with a relative deviation of 2–3%, indicating that near-normal reflectance measurements can be routinely implemented to estimate the total hemispherical thermal emittance [163, 290].

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Fig. 81 Temperature-dependent thermal emittance of some actual solar selective absorbers [7]

In the calculation of solar absorptance and thermal emittance based on roomtemperature reflectance spectra, it was assumed that optical properties of the absorber do not change at elevated temperature [288]. In fact, optical constants of constituting materials of solar selective absorber will change with the temperature [291]. Temperature-dependent optical properties of various materials including metal [292], oxide [293] and nitride [291, 294] have been investigated. TiN, as a refractory transition metal nitride, also shows temperature-dependent optical properties with refractive index n increasing with temperature and extinction coefficient κ decreasing with temperature as shown in Fig. 82 [295]. Its optical constants even have a relatively large change compared with the room temperature case when the operating temperature is high enough [294]. Nevertheless, several works demonstrate that thermal emittance for heated sample at high temperature can be reasonably estimated from room temperature reflectance measurements [163, 290]. It’s mainly because the tested highest temperature is only about 500 °C, which is much lower than the melting temperature

Fig. 82 Temperature-dependent dielectric functions of TiN films with thickness of 200 nm [291]

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of the constituted materials. For solar thermoelectric and thermophotovoltaic applications, to enhance the solar-to-electricity conversion efficiency, the solar absorber temperature may be higher than 1000 °C, in which, the temperature-dependent optical constants must be considered [16, 19].

13.2 Effect of Low and High Solar Concentrations From the expression of solar thermal conversion efficiency, it can be seen, ηabs varies inversely with solar concentration C. It is apparently that increase of solar concentration C can increase the solar-to-heat conversion efficiency. To increase the solar concentration C, four primary solar concentrators have been proposed, including parabolic trough collectors (PTCs), heliostat fields, parabolic dish reflectors, and linear Fresnel reflectors (LFRs) [9–11]. Among them, heliostat fields and parabolic dish reflectors can achieve concentration ratios of 1000×, while for PTCs and LFRs, the concentration ratios were lower than 100 × [7, 9]. This is because two-axis solar tracking system was used for PTCs and parabolic dish reflectors, while single-axis tracking system was employed in heliostat fields and LFRs. The solar-to-heat conversion efficiency ηabs for black absorber, evacuated enclosure, selective surface, and vacuum enclosed selective surface at different solar concentration ratios were calculated with temperature fixed at 500 °C and solar intensity at 600 W/m2 . The results are presented in Fig. 83 [9]. In the calculations, for black absorber, transmittance, absorptance, and emittance are all set to unity and the convective heat-transfer coefficient h is set to 20 W/(m2 ·K). It can absorb all incident light but has maximum losses. Transmittance and heat-transfer coefficient were set at 0.96 and 0 W/(m2 ·K) for evacuated enclosure, respectively. For solar selective surface, it has a reduced absorptance of 0.95 and a reduced emittance of 0.15. As Fig. 83 Solar-to-heat conversion efficiency for various absorbers at different solar concentrations [9]

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can be seen from the figure, at low concentration ratios (500×), the blackbody absorber is most efficient because the second term of ηabs can be ignored due to the high concentration ratio. Furthermore, vacuum enclosure can greatly improve the performance of solar selective absorber at low solar concentration ratio. Therefore, for single-axis solar tracking system with concentration ratios typically lower than 100×, evacuated spectrally selective surfaces will be preferred. However, at higher concentrations (>500×), solar absorber with the highest absorptance, like black absorber, should be chosen. Moreover, black absorber has better thermal stability than other systems. It’s worth noting that, in practice, solar concentration ratios also influence the temperature of absorption system. At low concentration (500 × ), the system would typically operate at higher temperatures [9].

13.3 System Evaluation of the Solar-To-Thermal Conversion Efficiency For solar selective absorber, solar absorptance and thermal emittance can partly characterize its performance. Intuitively, solar absorptance should be as high as possible, while thermal emittance should be as low as possible. However, the increase of solar absorptance was always accompanied by the extension of absorption spectrum to the long-wavelength region, which will overlay more with Planck’s blackbody radiation spectra, resulting in the rising in thermal emittance. Hence, it will be a balance between the solar absorptance and thermal emittance to maximize the solar-to-heat conversion efficiency in consideration of working conditions of solar concentration ratio and temperature. The solar absorptance and thermal emittance of Al2 O3 and SiO2 -based cermet spectrally selective absorbers were summarized by Cao et al. as presented in Fig. 84 [8]. It shows that larger solar absorptance is always accompanied by bigger thermal emittance. Moreover, it’s difficult to directly distinguish the best solar selective designs. With the improvement of computational ability and development in optical modeling [33, 296, 297], people are trying to numerically design solar selective absorbers by directly optimizing the solar-to-thermal conversion efficiency [134, 175] or solar-to-power conversion efficiency [131]. Transfer matrix method [33] has been adopted to characterize the spectral properties of one-dimensional multilayer thin films with optical constants of constituted pure material or metal-dielectric composite either obtained from database [35] or dispersion models [134, 175]. To optimize the exact film parameters, particle swarm optimization algorithm [131] genetic algorithm [134] or other global searching algorithm [175] has been used.

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Fig. 84 The solar absorptance and thermal emittance of Al2 O3 (metal inclusions: Ag, Co, Mo, Ni, Pt, and W) and SiO2 (metal inclusions: Cu, Ni, Au, and Mo)-based cermets [8]

Many review papers have been published to summarize solar absorptance and thermal emittance of different solar selective absorbers [4, 7, 8, 11, 22, 28, 37, 57, 136], but values for solar-to-thermal conversion efficiency are rarely provided [136]. Hence, to system evaluation of the performance of different solar selective absorbers, solar-to-heat conversion efficiencies of some recently published works are tabulated in Table 3. It’s worth noting that the solar-to-heat conversion efficiency for each solar selective absorber was calculated with the working temperature T h identical to the value that thermal emittance was obtained.

13.4 Thermal Energy Extraction Apparatus In a solar thermal energy conversion system, solar energy can be efficiently converted to heat by solar collectors with selective surface. The thermal energy can be extracted directly to heat water or harvested by heat transfer fluid (HTF) to drive heat engine to produce electricity [4]. Various types of solar collectors including concentrating and non-concentrating ones have been developed as illustrated in Fig. 85 [2, 9, 10, 37, 305]. 1. Non-Concentrating Collectors The non-concentrating solar collectors with solar concentration ratio of unity mainly consists of flat plate and evacuated tube collectors. They occupy a major share of solar energy market with wide applications such as heating waters for homes and indoor swimming pools due to their design and simplicity [2]. The flat plate collector (FPC) is most commonly consists of a transparent glass cover, an absorber plate, and an insulated box shown in Fig. 86 [2]. The glass cover can reduce the convection and radiative heat loss from the absorber. Based on the HTF, FPC can be divided into two categories including liquid and air types, respectively. For water as heat transfer liquid, the incident solar radiation passes through

α 0.95 0.953 0.983 0.956 0.93 0.927 0.94 0.942 0.958 0.92 0.942 0.966 0.963 0.941 0.958 0.948 0.931 0.93–95 0.961 0.93

Material

SiO2 /Si3 N4 /W/SiO2 /W

Cu/Zr0.3 Al0.7 N/Zr0.2 Al0.8 N/Al34 O60 N6

Cu/SiO2 /Ti/SiO2 /Ti/SiO2 /Ti/SiO2

Cu/TiNO_H/TiNO_L/TiO2 /SiO2

W/Al2 O3 /WTi-Al2 O3 _H/W-Al2 O3 _L/Al2 O3

SS/TiAlNx /N-rich TiAlNy /Al2 O3

SS/Mo/ZrSiN_H/ZrSiON_L/SiO2

Cu/Zr0.2 AlN0.8 /ZrN/AlN/ZrN/AlN/Al34 O62 N4

Cu/SiO2 /Cr/SiO2 /Cr/SiO2

SS/TiN/Al2 O3

LaAlO3 /W/TiN-SiO2 _H/TiN-SiO2 _L/SiO2

Periodic Al/TiAlN_L/TiAlN_H/Al2 O3

Cu/TiNx Oy /TiO2 /SiO2

SS/W/Ag/graded WN-AlN/AlN/SiO2

SS/W/WAlN/WAlON/Al2 O3

Al/NbMoN/NbMoON/SiO2

Al/NbTiSiN/NbTiSiON/SiO2

SS/W/Al2 O3 -W_H/Al2 O3 -W_L/SiO2 , SS/W/AlSiNx /AlSiOy Nx /SiO2

SS/W/TiAlC/TiAlCN/TiAlSiCN/TiAlSiCO/TiAlSiO

SS/Pt/Al2 O3 /Pt/Al2 O3 /Pt/Al2 O3 /Pt/Al2 O3

0.43@650 ºC

0.07@82 ºC

0.07–0.1@400 ºC

0.12@400 ºC

0.05@80 ºC

0.08@82 ºC

0.08@580 ºC

0.061@400 ºC

0.109@300 ºC

0.08 @ 82 ºC

0.11 @ 82 ºC

0.104 at 327 ºC

0.12 at 100 ºC

0.12 at 500 ºC

0.223 at 500 ºC

0.1 at 600 ºC

0.095 at 400 ºC

0.12 at 127 ºC

0.079 at 400 ºC

0.1 at 400 ºC

ε

650 ºC in air

325 ºC in air 650 ºC in vacuum

400 ºC in air 580 ºC in vacuum

550 ºC in vacuum

400 ºC in vacuum

500 ºC in air (2H)

580 ºC in vacuum

–

–

700 ºC in vacuum

500 ºC in vacuum

400 ºC in vacuum

–

500 ºC in vacuum

–

600 ºC in vacuum

–

400 ºC in vacuum

400 ºC in vacuum

600 ºC in air

Stability

Table 3 Solar-to-heat conversion efficiency of different solar selective absorbers as seen in recent literatures ηabs

0.565

0.960

~0.920

0.903

~0.948

0.957

0.892

0.949

0.953

0.941

0.919

0.943

0.940

0.891

0.835

0.862

0.934

0.981

0.935

0.927

Refrences

(continued)

[132]

[139]

[158]

[144]

[159]

[140]

[126]

[300]

[39]

[299]

[298]

[27]

[73]

[162]

[163]

[127]

[164]

[34]

[167]

[131]

140 E.-T. Hu et al.

0.94 0.95 0.923 0.939 0.95–0.97; 0.957 0.931–0.942 0.956 0.958

Cu/NbTiON_H/NbTiON_L/SiON

Cu/Mo/HfOx /Mo/HfO2

W/graded W-Al2 O3 /Al2 O3

Cu/Alx Oy /Al/Alx Oy ; Mo/Alx Oy /Al/Alx Oy

Cu/TiAlN/AlON

Cu/NbAlN/NbAlON/Si3 N4

Cu/TiAlN/TiAlON/Si3 N4

0.95

SS/HfMoN_H/HfMoN_L/HfON/Al2 O3

Cu/Alx Oy /Pt/Alx Oy

0.926–0.945

0.932

Cu/Ta/Alx Oy /Pt/Alx Oy

Al/Ti0.5 Al0.5 N/Ti0.25 Al0.75 N/AlN

0.946

SS/Mo/TiAlN/TiAlON/Si3 N4 0.955

0.975

Cu/TiNx Oy /TiO2 /Si3 N4 /SiO2

0.961

0.95

SS/Cu/TiN/TiSiN/SiN

Al/NiCrO_H/NiCrO_L/two AR layers

0.938

SS/TiAlN/TiAlSiN/Si3 N4

Cu/SiO2 /Ti/SiO2 /Ti/SiO2

α

Material

Table 3 (continued)

0.07@82 ºC

0.07@82 ºC

0.05–0.06@82 ºC

0.05–0.08@82 ºC; 0.06@82 ºC

0.102@400 ºC

0.09@82 ºC

0.07@80 ºC

0.06@82 ºC

0.14@82 ºC

0.04–0.06@ 82 ºC

0.022@100 ºC

0.136@427 ºC

0.1@127 ºC

0.052@127 ºC

0.043@100 ºC

0.04@70 ºC

0.099@75 ºC

ε Stability

525 ºC in air

450 ºC in air

400 ºC in air and 900 ºC in vacuum

400 ºC in air; 400 ºC in air and 800 ºC in vacuum

580 ºC in vacuum

500 ºC in air

500 ºC in vacuum

–

650 ºC in vacuum 475 ºC in air

400 ºC in air

–

450 ºC in vacuum

550 ºC in air

–

–

200 ºC in air 500 ºC in vacuum

272 ºC in air

ηabs

0.957

0.955

~0.936

~0.959; 0.956

0.915

0.922

0.939

0.949

~0.935

~0.961

0.918

0.930

0.945

0.974

~0.95

0.937

Refrences

[45]

[23] (continued)

[153]

[41]

[79]

[46]

[55]

[24, 124]

[123]

[122, 141]

[56]

[103]

[47]

[155]

[154]

[156]

[44]

Optical Properties of Solar Absorber Materials and Structures 141

0.93

SS/TiC/Al2 O3

SS/CrN_H/CrN_L/CrON/Al2 O3

0.89 0.95 0.95

SS/Zr/Mgo/Zr/MgO

SS/Cr2 O3 /Cr/Cr2 O3

SS/Mo/Mo-SiO2 _H/Mo-SiO2 _L/SiO2

SS(Fe3 O4 )/Mo/ TiZrN/TiZrON/SiON

ε

W/m2 ,

Stability

500 ºC in vacuum

600 ºC in vacuum

–

400 ºC in vacuum

278 ºC in air

350 ºC in air 400 ºC in vacuum

700 ºC in vacuum

400 ºC in air

650 ºC in vacuum

600 ºC in air

600 ºC in air

450 ºC in air 600 ºC in vacuum

T amb = 300 K

0.08@80 ºC

0.15@400 ºC

0.25@100 ºC

0.09@82 ºC

0.05@100 ºC

0.16@82 ºC

0.04@27 ºC

0.14@100 ºC

0.13@82 ºC

0.12@25 ºC

0.14@25 ºC

0.105@400 ºC

_H (high metal volume fraction), _L (low metal volume fraction). C = 50, I s = 960 T h equals the temperature that emittance was obtained

0.95 0.92

Cu/TiAlSiN/TiAlSiON/SiO2

0.88

0.92

Mo/AlCrON_H/AlCrNO_L/AlCrOx

0.930

0.921

SS/Cr/AlCrSiN/AlCrSiON/AlCrO

SS/Ti/AlTiN/AlTiON/AlTiO

0.958

SS/W/WSiAlN/WSiAlON/SiAlO

SS/Zr/ZrC-ZrN/ZrOx

α 0.96

Material

Table 3 (continued)

0.949

0.915

0.887

0.919

0.949

0.929

0.880

0.928

0.919

~0.921

~0.958

0.936

ηabs Refrences

[143]

[174, 304]

[166]

[120]

[142]

[138]

[303]

[302]

[161]

[301]

[119]

[165]

142 E.-T. Hu et al.

Optical Properties of Solar Absorber Materials and Structures

143

Fig. 85 Various solar collectors and HTF for concentrating collectors (ETC: evacuated tube collector; SAF: synthetic aromatic fluid; Other liquids: ionic liquids, fluids with metals, and liquid metals) [2, 10, 37]

Fig. 86 Exploded view of a FPC [2, 305]

the transparent glass and is absorbed by the selective surface on the absorber. Afterwards, the converted thermal energy is transferred to the tube array to heat water circulating inside the tubes. When air is used as HTF, the tubes are replaced by a back plate to form a gap between the absorber plate and back plate for the flow of air [10]. During the practical usage, dust settling on the glass cover will degrade the performance of FPC. Hence, several cleaning approaches have been proposed including water washing, compressed air blowing, tilting the collector, using of automatic wiper, covering super-hydrophilic nano-film, and electrostatic dust removal prevention method [10]. For evacuate tube collector (ETC), it consists of glass tube with anti-reflection coating for solar spectrum, heat pipe with a spectrally selective surface, and vacuum

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Fig. 87 Diagram of typical ETCs [2]

enclosure. Due to the circular structure, it can absorb both the diffuse and direct solar radiation, which can obtain a higher temperature compared with the FPC [2]. There are mainly two typical ETCs of direct flow and heat pipe ETC as illustrated in Fig. 87. The direct flow ETC has curved or flat copper loops in the evacuated tubes to circulate the liquid. It operates under similar principles as the conventional FPC with only difference in the vacuum insulation. In terms of heat pipe ETC, the vacuum-sealed heat pipe is filled with a small amount of a highly volatile liquid like ethanol, methanol, water with special additives, etc., which can easily expand or boil even at low temperatures. Once the solar flux falls on the absorber, the liquid inside the tube undergoes phase change to convert into vapor, which rises to the condenser where it releases the stored heat. The condensed liquid flows back to the bottom of heat pipe due to gravity, and the circulation continues [10]. 2. Concentrating Collectors Concentrating solar collectors (CSCs) usually have concave reflectors to intercept and focus the solar radiation to a much smaller receiving area, resulting in increased heat flux. Then, the heat engine can achieve a higher Carnot efficiency when working under a higher temperature. Because the intensity of solar radiation varies during the day as well as with seasons, a solar tracking system is needed for CSCs to maximum the absorbed solar energy. There are mainly four CSCs including parabolic trough collectors (PTCs), heliostat fields (solar power), parabolic dish reflectors, and linear Fresnel reflectors (LFRs) as presented in Fig. 88 [9–11]. (1)

Parabolic trough collectors

The PTCs consist of a parabolic reflecting surface and an absorber tube placed along the focal line. The incoming solar radiation can be concentrated to the focal line of the vacuum insulated absorber pipe to heat the HTFs. It has been demonstrated that single-axis tracking is more economically feasible compared to two-axis tracking

Optical Properties of Solar Absorber Materials and Structures

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Fig. 88 Schematic of the four solar concentration systems: a parabolic trough collector, b solar tower, c parabolic dish concentrator, and d linear Fresnel reflector [11, 306]

system for PTCs in consideration of the additional parts, control power requirement, and higher maintenance cost for two-axis tracking system [2]. The PTCs are usually employed for large-scale commercial power generation with temperature range of 300–400 °C. It can also be used for small scale such as industrial process heating, space heating, domestic heating, swimming pool heating with required temperature of 100–250 °C [10]. The PTC technology is very energy-efficient and cost-effective, especially for those areas where the beam solar irradiance is high. For concentrated solar thermal power installations, more than 71% market shares were occupied by PTCs due to its relatively mature technology compared to other technologies [3]. (2)

Solar power concentrator

The solar power concentrating system has a central tower surrounded by a large number of mirrors, for which each mirror is equipped with a two-axis sun tracking system. Each solar tracking mirror system, called a heliostat, reflects the incident solar radiation onto the absorber or receiver located right at the top of the central tower. This type of arrangement is employed in large-scale installations meant for power generation. It has been reported that a very high temperature up to 2000 °C can be generated for central solar power due to its high solar concentrations [307]. Though PTCs are still the mainstream technologies, solar power tower technology is the future system because it can achieve much higher thermodynamic efficiencies than PTCs due to the much higher solar concentration ratios [3]. (3)

Parabolic dish concentrator

Parabolic dish concentrators (PDCs) have an array of parabolic dish-shaped mirrors to focus solar energy onto a receiver located at the common focal point of the dish

146

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mirrors as shown in Fig. 88c. Heat transfer fluid contained in the receiver is then heated up to desirable working temperatures and pressures in order to generate electricity in a small engine attached to the receiver. To concentrate the incident radiation onto the focal point, a precise two-axis solar tracking system is required for PDCs. Thus far, among all the concentrated solar power systems, those with a parabolic dish have the highest thermal-electrical conversion efficiency (up to 30%) [2, 9]. It has the advantages of high optical efficiency, low start-up losses, and good modularity which can be easily scaled up to meet the power needs in remote area [3]. However, commercially available large parabolic dish collectors are costly because of the requirement of very high precision in its manufacturing and controlling of the two-axis solar tracking system as well as difficulties in their transportation [10]. (4)

Linear Fresnel reflector

For LFRs, a large number of segments of mirrors are attached in a row to concentrate the solar radiation collectively on an elevated single absorber pipe located at a space above the reflectors. This system is more cost-effective than the PTCs because mirror segments share the same absorber row. However, the main problem for LFR system is the shading and blocking of solar radiation by the neighboring reflectors, resulting in a lower concentration factor than that of PTCs [2]. Hence, the operation temperature of the working fluid is lower, producing a lower efficiency for the total system. The solar thermal power stations based on the technology of LFR are very few with the installed capacity much smaller than that of other technologies [3]. 3. Heat Transfer Fluid In solar thermal system, sunlight is focused on a solar receiver where it is absorbed and ultimately converted to thermal energy. The thermal energy is typically delivered to heat transfer fluid (HTF) through convection. The HTF needs to collect, transport, and exchange heat with the power cycle to produce electricity, which can be identified as another major component of a concentrating solar thermal power system. In addition, the gain heat from the receiver should be efficiently injected to the thermodynamic power cycle to run the turbine. This heat-transfer capability is related to the convection heat-transfer capability of the HTF, which includes a high thermal conductivity that enables efficient transfer of heat from the absorber and to the power block, a high density and specific heat capacity that enable high heat fluxes at reasonable mass flow rates, and a low viscosity that minimizes the required pumping power. On the other hand, HTFs are required to have low freezing points to avoid freezing at night and high operating temperature to increase the power cycle efficiency. Other factors such as long-term stability, toxicity, environmental danger, and cost should be considered as well [9]. Different types of HTFs have been developed including synthetic aromatic fluid, molten salt, pressured gases, and other new approaches using ionic liquids, nanoparticle-laden fluids, and liquid metals [308]. The operating temperature range for different classes of HTFs was summarized as presented in Fig. 89 [9, 309]. Synthetic oils are important HTFs for a majority of solar thermal plants since they can offer a relatively large operating temperature range. On the other hand, molten salts show the promise for higher efficiencies due to the possibility of operating

Optical Properties of Solar Absorber Materials and Structures

147

Fig. 89 Operating temperature range of different types of HTFs [9]

temperatures beyond 600 °C. However, its efficiency gains are limited by the higher melting point and higher pumping costs. To overcome the deficiencies of oils and molten salts, new approaches including ionic liquids, nanofluids and liquid metals are being actively studied. Nanofluids can even be designed to directly absorb solar light by eliminating the intermediate heat-transfer step in conversational solar collectors of absorption sunlight first and then transferring the converted energy to the HTF [7]. Additionally, gas-based HTFs using pressurized gases or steam were also investigated to reduce the cost of electricity production by decreasing the complexities associated with the handling of HTFs such as chemical stability, material compatibility issues, sealing, and safety.

13.5 Solar Thermophotovoltaics (STPV) and Solar Thermoelectric Generators (STEGs) In the above-mentioned concentrated solar thermal conversion systems, the absorbed heat was converted to electricity indirectly via a two-step process (Heat energy to mechanical energy and mechanical energy to electricity). In fact, the harvested heat energy can be converted to electricity through solid-state direct heat-to-electricity conversion technologies that do not require an intermediate conversion to mechanical energy. These direct heat-to-electricity conversion systems are often scalable, quiet, and reliable, allowing lower capital investment and maintenance costs compared with the conventional concentrated solar power plants [9, 310]. The most extensively explored technologies for direct solar heat-to-electricity conversion are solar thermophotovoltaics (STPV) [19, 20, 311] and solar thermoelectric generators (STEGs) [16, 17], though there are other technologies such as solar thermionic [312], ferroelectric [313], pyroelectric [314] generators. Below we will give a brief review on STPV and STEGs. 1. STPV A solar thermophotovoltaic (STPV) conversion system as shown in Fig. 90 is a modification of a traditional photovoltaic (PV) converter. In traditional PV cell, only

148

E.-T. Hu et al.

Fig. 90 Schematic of a STPV device

the incident solar photons with energy larger than the bandgap can be absorbed and contribute to the cell current, while photon energy in excess of the bandgap energy is dissipated via thermalization. This leads to a Shockley-Queissier efficiency limit of than 30% for a single junction solar cell [92]. Moreover, the dissipated heat will deteriorate the performance of the solar cell due to overheating. To exceed Shockley–Queisser’s limit, various technologies of multi-junction solar cells [315], hot-carrier cells [316], intermediate-band cells [317], spectrum splitting [318], and multiple electron–hole pair generation [319] have been developed. STPV is another completely different strategy to exceed Shockley–Queisser limit. In an STPV generator, the solar radiation is absorbed by a body which then re-emits the heat in the form of radiation toward the PV cell. Compared with the wavelengthindependent sunlight, the emitted radiation can be tailored with spectrally selective emitter, filter or reflective coating to suppress photons with energy below or well above the bandgap of PV cell. Only photons with energy just above the bandgap can incident on the PV cell. Hence, it works much more efficiently than a traditional PV cell. In fact, the absorber, emitter, and filter used in STPV can be considered as a spectrum reshaping tool, tailoring the wide solar spectrum into narrow band radiation to match well with the base PV cell [9]. Because of the re-emission process in a STPV, a high enough temperature of at least 1000 °C for the emitter is required even for the lowest bandgap semiconductor material (0.5 eV) [9]. It has been simulated that, when the emitter temperature can reach 2360 K, the efficiency for a single-junction TPV can be 54%, but only 44% when the emitter temperature is limited to 1300 K [115]. Hence, the thermal stability and reliability issue needs to be carefully managed. Rare-earth elements of erbium, thulium, ytterbium, samarium, or holmium and refractory materials of tungsten, molybdenum, or tantalum with sufficiently high melting point show high stability under high operating temperature, making them good candidates for selective emitters of TPV systems [20].

Optical Properties of Solar Absorber Materials and Structures

149

Though STPV systems are proposed for long time decades ago, the produced efficiency is just a few percent higher or less [310, 320]. A prototype of STPV was built by Datas et al. and a solar-to-electricity conversion efficiency of about 1% was achieved which was mainly limited by overheating of PV cell and natural selectivity of high-temperature emitters [321]. By integrated using a multiwalled carbon nanotube absorber and a one-dimensional Si/SiO2 photonic-crystal emitter, Lenert et al. demonstrated a 3.2% STPV conversion efficiency [311]. Rinnerbauer et al. used a monolithic two-dimensional tantalum photonic crystal with different periodicity for selective absorber and emitter, and solar-electricity conversion efficiency of 3.5% was obtained [77]. Based on Lenert’s work, they continued to add an optical filter on the PV cell, improving the solar-to-electricity conversion rate to 6.8% [19]. Future studies should continue to seek high-quality spectral control with cost-effective and scalable components to improve the performance of STPV. 2. STEGs Solar thermoelectric generators (STEGs) usually comprise a solar absorber, a thermoelectric generator (TEG), and a heat sink as schematically depicted in Fig. 91 [9, 17, 310]. Sunlight incidents on the solar absorber are captured by the selective surface and converted to heat. Then the absorbed heat is converted to electricity in the TEG via the Seebeck effect. The Seebeck effect is the generation of voltage in a material under a temperature gradient, which is due to majority carriers (electrons for n-type materials and holes for p-type materials) diffusing from the hot end to the cold end of the material [322]. In physics, it’s the coupling between carriers and phonons with the coupling capability depicted by Seebeck coefficient S = −V /T. For STEGs, it can be divided into two sub-systems: solar thermal conversion system and TEG. Hence, its efficiency is the product of solar receiver efficiency and TEG efficiency. The solar receiver efficiency has been discussed before as ηabs , while TEG efficiency ηTEG can be expressed as [17, 310]:

Fig. 91 Schematic diagram of a STEG

150

E.-T. Hu et al.



ηT E G

TC = 1− TH



! 

1 + ZT − 1

" (13.5)

1 + Z T + TC /TH −

where T C and T H are the TEG cold and hot-side temperatures. Z T is the average thermoelectric figure of merit over its working temperature, while ZT is defined as ZT = S 2 σ/κt with σ and κt representing the electrical conductivity and thermal conductivity, respectively. In Eq. (13.5), the first term is the Carnot efficiency, while the second term is a −

value less than one, which increases with Z T . Thermoelectric materials, including bismuth telluride, lead telluride, and silicon–germanium, always exhibit a ZT value below 1. Two different approaches have been developed to improve the ZT value including exploring new materials with complex crystalline structures and reducing the dimensions of the materials [322, 323]. A high ZT value of up to 2.4 at 300 K was reported for Bi2 Te3 /Sb2 Te3 superlattices by Venkatasubramanian et al. [324]. Subsequently, with the PbTe/PbTeSe quantum dot superlattices, a ZT value greater than 3.0 at 600 K was obtained [325]. Besides the low-dimensional material system, nanostructural bulk materials such as skutterudites, Ag-Pb-Sb–Te (or LAST), and half-Heusler alloys have been reported to have higher ZT values [322]. With the rapid progress in recent years, ZT value for bismuth telluride and bismuth telluride-based alloys has been improved to about 2.0, while it is up to about 1.4 for skutterudites [323]. The first experimental demonstration of a STEG was reported by Telkes in 1954, from which solar-to-electricity conversion efficiencies of 0.63% for the nonconcentrating and 3.35% for 50 × concentrating systems were obtained [326]. In 2011, a STEG system with conversion efficiency of 4.6% under one-sun radiation at an operating temperature of 200 °C was achieved by Kramer et al. by integrating an evacuated enclosure, a spectrally selective absorber, and thermal concentration rather than optical concentration [17]. Subsequently, by using segmented thermoelectric legs and adding optical concentration, a peak efficiency of 7.4% was obtained [16]. Based on a novel detailed balance model for STEGs, Baranowski et al. predicted that the STEG efficiency can reach 15.9% with today’s thermoelectric materials under the conditions of 100× solar concentration and a hot-side temperature of 1000 °C [327]. To improve the STEGs with comparable efficiencies to those of existing CSP, further investigations are needed with careful design on thermoelectric materials and STEG system.

References 1. G. Chen, J. Karni, Introduction: challenges and opportunities in solar-thermal technologies, in Annual Review of Heat Transfer (Begell House, Inc., 2012) 2. M. Imtiaz Hussain, C. Ménézo, J.-T. Kim, Advances in solar thermal harvesting technology based on surface solar absorption collectors: A review. Sol. Energy Mater. Sol. Cells 187, 123–139 (2018)

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Summary

As the key component of the solar thermal conversion system, solar selective absorbers have been extensively investigated for long time in past years. With the hard efforts of scientists and engineers working together around the world, new materials and excellent structures have been continually studied with advanced progress marching successfully toward applications. In the review of this book, we not only pay attention to the optical properties of materials and structures that play the significant role to enhance the efficiency of the solar-to-heat conversion, but also to varieties of technologies how to fabricate and measure the solar devices in applications. As the researchers working in this field, we truly hope the content and information provided in this book will help readers to understand the issues, that are partly solved but partly still remained to be studied. This will stimulate further the scientific research and technological development in the solar thermal field of the future. The introduction part on the solar thermal conversion system with the typical solar selective absorbers is given in Chap. 1. The conventional electromagnetic theory has been discussed in Sect. 2, including Maxwell’s equations to help understanding more fundamentally of the optical absorption and thermal emittance of the materials in applications. Section 3 is focusing on the optical properties of the solar materials, based mainly on the photon-to-electron conversion, Lorentz and Drude models, and effective medium approximation models, and so on. The typical optical constants that are characteristic of metals and dielectric media including their measurement techniques are presented. In Sect. 4, the optical evaluation and characterization for featured parameters of the material are outlined. In Sects. 5–10, six typical solar selective absorbers are summarized, including intrinsic solar selective materials, semiconductor-metal tandems, metal-dielectric-based multilayers, metal-dielectriccomposited cermets, nano-textured surface structures and photonic-crystal-based metamaterials and designs. In real situations, the material components and structures as regard to the six types of materials developed by different methods are often overlapped and cross-penetrated each other to produce better performance of the devices. The detailed methods as how to fabricate and experimentally measure the

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solar materials and devices are described in Sects. 11, 12, respectively, with their broad applications given in Sect. 13. There is certainly room for continuous study of the solar selective absorber devices used to harvest more of the solar energy under wide application conditions with great efforts that are paying to benefit our society in the long run of future.

Index

A Admittance locus method, 57 AM1.5, 6, 54 Ampère’s law, 14, 15 Angular dispersion power, 110 Angular frequency, 16, 19, 88 Anodization, 10, 13, 60 Anti-reflection layer, 8, 53 Atomic force microscopic lithography, 90 Atomic layer deposition, 63, 72 Attenuation constant, 29 Azimuthal angle, 5, 58

B Blackbody radiation, 3, 5, 6, 30, 31, 45–47, 125, 126, 130, 132, 135, 138 Blazed angle, 112 Blaze wavelength, 112 Bloch-Floquet theory, 86 Boltzmann constant, 100 Brewster angle, 26 Bruggeman model, 71, 72 B-spline function, 72

C Calorimetry, 124, 134 Carnot efficiency, 135, 144, 150 Cauchy model, 39 Central solar power, 4, 145 Cermet absorbers, 8, 12 Characteristic matrix, 48 Chemical etching, 90 Chemical Vapor Deposition (CVD), 13, 51, 99

Clausius-Mossotti relation, 36, 37 Complex dielectric function, 35, 42 Concentrating Solar Collectors (CSCs), 144 Conective heat, 3–5 Constitutive equation, 15, 16, 27 Courant number, 88 Courant stability condition, 88 Critical angle, 25, 26 Cutoff wavelength, 45, 51, 53, 63

D Damping coefficient, 34 Damping factor, 36 DC sputtering, 102–105 Deep Q learning method, 57 Deep Reactive Ion Etching (DRIE) technique, 71, 92 Deep-Ultraviolet Lithography (DUV), 90 Destructive interference, 8, 56 Detailed balance limit theory, 32 Dielectric function, 13, 16, 17, 33–40, 42, 43, 72, 85, 93, 94, 98, 136 Dielectric polarization, 34, 36 Diffusion barrier, 8, 13, 56, 63 Drude model, 33, 35, 36, 38, 167

E E-beam evaporation, 63 E-beam lithography, 82, 90 Effective Medium Approximation (EMA), 36–38, 71, 72, 167 Electro-chemical plating, 13 Electrodeposition, 60 Electroless deposition, 60

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170 Electromagnetic theory, 13, 167 Electromagnetic wave, 18, 31, 85, 86, 88, 124 Electron Beam Evaporation (EBE), 99–102 Ellipsometric parameter, 41, 43, 44 Evacuate Tube Collector (ETC), 143, 144 Evanescent wave, 26, 93 Extinction coefficient, 7, 13, 35, 39–41, 57, 73, 97, 136

F Faraday’s law, 14 Fast Atom Beam (FAB) etching, 77 Finite-Difference Frequency-Domain method (FDFD), 89 Finite-Difference Time-Domain method (FDTD), 87–89, 92, 96 Finite Element Method (FEM), 26, 86, 87, 92 Flat Plate Collector (FPC), 139, 143, 144 Fourier Transform Infrared Spectrometer (FTIR, FT-IR), 122, 132, 133 Free spectral range, 111, 112 Fresnel coefficients, 23 Fresnel equations, 23, 26

G Gauss’s law, 14 Genetic algorithm, 59, 60, 138 Glalerkin’s method, 87 Global-modified Levenberg-Marquardt method, 58 Graded cermet, 10, 71, 75 Grating constant, 110–112 Group velocity, 18

H Heat flux, 3, 144, 146 Heat-to-electricity conversion efficiency, 135 Heat Transfer Fluid (HTF), 139, 143, 144, 146, 147 Heliostat field, 137, 144 Hemispherical thermal emittance, 135 High Metal Volume Fraction (HMVF), 10, 74, 142 Holographic grating, 109, 110

I Imaginary part of the permittivity, 16

Index Impedance, 10, 66, 76, 97–99 Independent blackbody method, 129 Inductor-Capacitor (LC) model, 96, 99 Integrating sphere reflectometer, 122, 126, 132, 134 Interband transition, 9, 33–35, 39 Interferometric spectrometer, 109, 113 Intrinsic absorbers, 7 Intrinsic absorption, 7, 56, 76, 81 Intrinsic solar selective material, 50, 53, 167 Ion beam sputtering, 102 Ion-beam treatment, 11 Ionic liquids, 143, 146, 147

K Kirchhoff’s law, 30, 31, 46, 124–126, 132

L Lambert’s law, 114 Laser holographic lithography, 90 Laser interference lithography, 80, 90 Laser polarization method, 127, 128 Law of charge conservation, 27 Laws of reflection, 21 Laws of refraction, 21 LC model, 96–99 Lenz’s Law, 96 Levelized Cost of Energy (LCOE), 135 Life time of free electrons, 36 Linear Fresnel Reflector (LFR), 137, 144– 146 Line dispersion power, 110, 111 Liquid metals, 143, 146, 147 Lorentz-Lorenz model, 37 Lorentz model, 17, 33–35 Loss angle, 17 Low Metal Volume Fraction (LMVF), 10, 12, 73, 74, 142

M Magnetic dipole, 14, 15 Magnetic flux density, 14 Magnetic induction, 14 Magnetic polariton resonance, 96 Magnetic resonance frequency, 98 Magnetic susceptibility, 15 Magnetizing current, 15 Magnetron sputtering, 60, 61, 63, 99, 102, 104 Mask manufacturing, 90

Index Maxwell equations, 13–15, 17, 21, 24, 27– 29, 84, 85, 87–89, 167 Maxwell-Garnett (MG) model, 37 Mechanical preparation method, 90 Metal-dielectric composite, 8, 9, 12, 33, 71, 72, 138 Metalorganic Chemical Vapor Deposition (MOCVD), 99 Michelson interferometer, 113, 129, 130, 132 Micro-cavity effect, 95, 96 Molten salt, 146, 147 Monochromatic spectrometer, 109 Multilayer absorbers, 8, 11, 12

N Nanoimprinting, 90, 91 Nanoparticle-laden fluids, 146 Nano-textured surface, 76, 167 Needle optimization method, 58 Non-concentrating solar collector, 139

O Optical admittance, 48, 49, 57 Oxynitride, 8, 9, 51, 57, 61

P Parabolic dish concentrator, 4, 145 Parabolic dish reflector, 137, 144 Parabolic Trough Collector (PTC), 4, 137, 144–146 Particle-swarm optimization method, 59 Penetration depth, 29, 97 Perfect Matched Layer (PML), 89 Performance Criterion (PC), 50 Permeability, 15, 16, 18 Permittivity, 15–17, 94, 97 Photonic Crystal (PhC), 11, 12, 84, 86, 87, 90–93, 96, 149 Photon-to-electron conversion, 32, 167 Photo-thermal conversion, 12, 54, 59, 60, 71 Photovoltaic, 2, 33, 92, 132, 147 Physical Vapor Deposition (PVD), 8, 9, 13, 60, 99, 102, 106 Picosecond laser, 77 Plane Wave Expansion method (PWE), 84 Plasma frequency, 36, 97 Plasmonic Metamaterial Absorbers (PMAs), 82 Poynting vector, 24, 25 Propagation constant, 29

171 Protection layer, 8, 57 Pulsed Laser Deposition (PLD), 99, 106– 109 R Radiation energy method, 128 Radiative heat, 139 Radio Frequency sputtering (RF), 99, 102, 105 Reactive sputtering, 99, 102 Real part of the permittivity, 16 Reflection coefficients, 24 Refractive angle, 23, 25, 26 Refractive index, 7, 8, 10, 11, 13, 18, 35, 38, 39, 41, 53, 55, 73, 76, 77, 136 Refractivity, 18, 25, 30 Relaxation time of free electrons, 36 Replica grating, 109 Resistance-heating thermal evaporation method, 100 Resolving power, 111 Rigorous Coupled-Wave Analysis (RCWA), 89, 92 Ritz method, 87 Root Mean Square Error (RMSE), 44 S Scribed grating, 109 Seebeck effect, 149 Sellmeier model, 38, 39 Semiconductor-based multilayer solar absorber, 12 Semiconductor-metal tandems, 7, 53, 167 Semiconductor nanowire array, 12 Semi-empirical method, 57 Sidewall lithography, 90, 91 Snell’s law, 23, 25, 26, 30, 42 Solar absorptance, 3, 5, 9–11, 45, 46, 48–54, 57–59, 61, 62, 65, 67–70, 73, 76, 77, 81, 82, 136, 138, 139 Solar cell, 2, 32, 33, 148 Solar collectors, 4, 139, 143, 147 Solar concentration, 5, 7, 54, 55, 60, 135, 137–139, 145, 150 Solar desalination, 3, 4 Solar power station, 12 Solar thermoelectric, 3, 4, 137 Solar Thermoelectric Generators (STEGs), 147, 149, 150 Solar thermophotovoltaic, 3, 4, 147 Solar-to-electricity conversion efficiency, 137, 149

172 Solar-to-heat conversion, 75, 134, 135, 137– 140, 167 Solar-to-power conversion efficiency, 59, 138 Solar-to-thermal conversion efficiency, 138, 139 Sol-gel, 60 Solution-based methods, 60 Spectroscopic ellipsometry, 41, 43–45, 72 Specular reflection, 116, 119 Static permittivity, 17 Steady-state calorimetry, 134 Stefan-Boltzmann constant, 5 Surface Plasmon Polariton (SPP), 93–95 Surface texturing, 11 Synthetic aromatic fluid, 143, 146 Synthetic oil, 146 T Template stripping method, 80 Textured surface, 11, 76, 77, 79, 83 Thermal cavity reflectometer, 126, 127 Thermal emission, 11, 32 Thermoelectric Generator (TEG), 149, 150 Total reflection, 25, 26, 77, 79 Transfer matrix method, 8, 48, 57, 84, 138 Transient calorimetry, 134 Transition metal, 7, 8, 39, 40, 51, 57, 136

Index Transition wavelength, 5 Transmission coefficients, 24 Transmittance, 25, 40, 41, 45–47, 56, 57, 126, 137 Transverse Electric wave (TE), 48, 49, 94, 95 Transverse Magnetic wave (TM), 48, 49, 93–95

U Ultrafast laser, 11, 77 Ultraviolet lithography, 90

V Vacuum evaporation, 99, 101

W Wave number, 19, 113 Wave vector, 19, 22, 28, 84, 86, 88, 93, 95 Weighting factor, 5, 6 Wien’s displacement law, 31

X X-ray lithography, 90