Emerging Trends in Terahertz Engineering and System Technologies: Devices, Materials, Imaging, Data Acquisition and Processing 9811597650, 9789811597657

Citation preview

Arindam Biswas · Amit Banerjee · Aritra Acharyya · Hiroshi Inokawa   Editors

Emerging Trends in Terahertz Engineering and System Technologies Devices, Materials, Imaging, Data Acquisition and Processing

Emerging Trends in Terahertz Engineering and System Technologies

Arindam Biswas Amit Banerjee Aritra Acharyya Hiroshi Inokawa •

•

•

Editors

Emerging Trends in Terahertz Engineering and System Technologies Devices, Materials, Imaging, Data Acquisition and Processing

123

Editors Arindam Biswas School of Mines and Metallurgy Kazi Nazrul University Asansol, West Bengal, India Aritra Acharyya Department of Electronics and Communication Cooch Behar Government Engineering College Cooch Behar, West Bengal, India

Amit Banerjee Department of Physics Bidhan Chandra College Asansol, West Bengal, India Hiroshi Inokawa Research Institute of Electronics Shizuoka University Shizuoka, Japan

ISBN 978-981-15-9765-7 ISBN 978-981-15-9766-4 https://doi.org/10.1007/978-981-15-9766-4

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed 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

Contents

A Novel Integrated Power Module with Solid-State Diode at THz Frequency—The Concept and a Possible Way to Realize It . . . . . . . . . . Subal Kar Effects of Space Charges in IMPATT Source at Terahertz Regime . . . . Girish Chandra Ghivela and Joydeep Sengupta Performance Estimation of Defected Ternary Photonic Crystal-Based Bandpass Filter Beyond 100 THz for All-Optical Circuit . . . . . . . . . . . . Arpan Deyasi and Angsuman Sarkar Terahertz Radiation from Gallium Phosphide Avalanche Transit Time Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aritra Acharyya, Arindam Biswas, Bisal Sarkar, Amit Banerjee, and Hiroshi Inokawa Influence of Terahertz Frequency on the Elastic Constants in 2D Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. K. Das, R. Paul, S. Chakrabarti, B. Chatterjee, S. Pahari, and K. P. Ghatak

1 23

31

49

59

The Carrier Statistics, Terahertz Frequency, Extremely Degenerate Opto-electronic Materials and All That . . . . . . . . . . . . . . . . . . . . . . . . . 107 R. Paul, S. Chakrabarti, B. Chatterjee, P. K. Das, T. De, S. D. Biswas, and M. Mitra OFDM for Terahertz Wireless Communication Systems . . . . . . . . . . . . 141 Mohammed El Ghzaoui and Sudipta Das All Optical Universal Logic TAND Gate Using a Single Quantum Dot Semiconductor Optical Amplifier at 2 Tbit/s . . . . . . . . . . . . . . . . . . . . . 167 Kousik Mukherjee

v

vi

Contents

TOAD-Based Frequency-Encoded All Optical XOR Gate, Half Adder, and Half Subtractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Kousik Mukherjee, Kajal Maji, Ashif Raja, and Mrinal Kanti Mandal Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array for Short Range THz Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Mandeep Singh, Simranjit Singh, and Mohammad Tariqul Islam Ga2O3 Based Heterostructure FETs (HFETs) for Microwave and Millimeter-Wave Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 R. Singh, T. R. Lenka, D. Panda, R. T. Velpula, B. Jain, H. Q. T. Bui, and H. P. T. Nguyen

A Novel Integrated Power Module with Solid-State Diode at THz Frequency—The Concept and a Possible Way to Realize It Subal Kar

Abstract The basic concept and possible way to realize a novel power module with device and antenna integrated in the same structure using IMPATT diode has been proposed that might have useful applications at THz frequency. The power module judiciously used the idea of resonant-cap cavity for oscillator design normally used at microwave and millimetre–wave frequency, slotted disc for broadband operation and an improvised circular microstrip patch antenna integrated in the same structure. The structure is realizable with fully planer technology with some added steps in the device fabrication process. Since there is no need for transmission line or waveguide to connect the antenna with the oscillator, the transmission loss is minimized and the integrated structure will also lead to size miniaturization. The integrated power module is expected to have many applications especially at THz frequency regime.

1 Introduction From the beginning of twenty-first century THz signal generation, detection [1] and its application for security purposes in concealed weapon detection and standoff detection of explosives and abusive drugs [2–4] and medical purposes for early detection of skin and breast cancer [5] including that in pharmaceutical industry [6] have proliferated exponentially. However, till the end of twentieth century, the ‘THz gap’, vide Fig. 1, was the most neglected chunk of electromagnetic spectrum with very few applications for space and Earth science studies [1]. Nowadays, we have various techniques for THz signal generation including optical heterodyning [7], quantum cascade laser [8], free-electron laser [9] and so forth. Initially, it was observed that tube and solid-state devices used in the generation of microwave/millimetre-wave signal are limited for THz signal generation, as they are controlled by transit time of the charge carriers via the device causing lower output power and bandwidth of operation. But with the availability of device fabrication materials like GaN for high power devices and better fabrication facility, S. Kar (B) Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Biswas et al. (eds.), Emerging Trends in Terahertz Engineering and System Technologies, https://doi.org/10.1007/978-981-15-9766-4_1

1

2

S. Kar

Fig. 1 Electromagnetic spectrum showing the THz gap and various applications in other parts of the spectrum

solid-state devices, especially IMPATT device, have been found to be possible to design that can operate at THz frequency range [10]. It may be noted that GaN-based devices are attractive because they can deliver higher power output and higher efficiency at high frequencies. Their breakdown electric field is high together with high values of saturation drift velocity, electron mobility and thermal conductivity. Main problem of solid-state devices, even with IMPATT which is known to give higher power output compared to all other solid-state devices at microwave and millimetre-wave frequency, at THz frequency are their low power availability following the well-known relation: PO .(f r )2 = constant; where PO is the power output from the device and f r is the frequency of oscillation. When the THz signal source is to be connected to antenna via transmission line/waveguide, the transmission loss worsens the problem further. However, if some integrated power module can be designed in which the oscillator and the antenna can be integrated in the same structure, we can get rid of the transmission loss problem. The reported integrated power module with IMPATT device in this chapter is such a novel attempt to integrate the oscillator with antenna that does not need any transmission line or waveguide to connect the antenna with the oscillator making it efficient and size-miniaturized. The idea of this novel structure is derived from (i) the concept of resonant-cap oscillator (normally used at microwave and millimetre-wave frequencies) [11–14], (ii) slotted disc for resonant-cap structure useful for broadband operation of oscillator and amplifier [15–18], and (iii) circular microstrip patch antenna used in practice [19]: judiciously integrated together (conceptually and structurally, with planer fabrication idea in mind)—giving the power module (including the diode) realizable with fully planer technology.

A Novel Integrated Power Module with Solid-State …

3

2 Conceptual Visualization of the Integrated Power Module To visualize the concept, we first need to know some details of resonant-cap oscillator, broad banding with slotted-disc structure and microstrip patch antenna and the IMPATT diode as all the three has been combined in an improvised way to realize the integrated power module.

2.1 Resonant-Cap Oscillator Oscillator design at microwave and millimetre-wave frequency can be done by mounting the active device, for example, solid-state devices like IMPATT or Gunn, in a waveguide either via a bias-post or a resonant-cap structure, vide Fig. 2 [14]. The problem of mounting the device in a full-height waveguide with bias-post is that impedance matching between the device and the circuit is very poor (device impedance f out (f in and f out are determined respectively by the inner radius, Ri , and outer radius, R, of the slotted-disc structure); we can expect realization of broadband for slotted-disc resonant-cap compared to un-slotted disc resonant-cap structure. With the help of an empirical formula, the effective resonant frequency of the slotted-disc resonant-cap can be determined [13]. It will have two resonant frequencies f in and f out , the former being determined by the inner radius Ri and latter by the outer radius R (vide Fig. 3c). f in is due to the effectiveness of the inner circle of radius Ri and is given by:  f in =

f out +

nc df ·r · dR 2π Ri

 (1a)

where f out is practically due to the un-slotted disc of radius R, (df /dR) is the incremental change of frequency of the un-slotted disc with its radius, r is the depth of

A Novel Integrated Power Module with Solid-State …

5

Fig. 3 Realization of broadband operation for resonant-cap oscillator with slotted-disc structure a Cap structure and plan view of slotted disc b Skirt pattern showing broad banding c Plan view of slotted disc showing different parameters

cut in the direction of the radius of the disc and c is the circumferential cut-length, and n is the number of slots in the disc of the resonant-cap. The effective frequency of oscillation of the slotted-disc resonant-cap oscillator will then be given by: f effective = ( f in + f out )/2

(1b)

2.2 Microstrip Patch Antenna A microstrip patch antenna has a thin patch of metal having rectangular/square/circular shape which is etched on a thin dielectric substrate with printed circuit technology and the substrate being backed by a large ground plane [14]. The

6

S. Kar

Fig. 4 Microstrip patch antenna a Basic structure of the antenna showing the radiating and nonradiating edges; 1 and 2 are radiating edges while 3 and 4 are non-radiating edges b Electric field variation along non-radiating edges c Fringing electric field across the radiating edges

microstrip patch antenna of rectangular shape is basically a truncated microstrip having length L and width W as shown in Fig. 4a. A cavity is formed in the region between the patch and the ground plane. The top and bottom of the cavity being bounded by electric walls (short-circuited boundary) and on sides by magnetic walls (open-circuited boundary), resembling the resonantcap cavity discussed above. The length L of the patch is chosen to be approximately half a guide wavelengths (for circular patch, the patch radius will be thus nearly a quarter wavelengths). The field is seen to be ideally zero near the patch centre x = 0, that gradually increases on either side of the centre (with phase opposition) and becomes maximum near the patch edges x = ± L/2 (vide Fig. 4b), causing a pairwise cancellation of the electric field on either side of the patch centre along L. Thus, the lengthwise edges 3 and 4 act as non-radiating edges while the fringing electric field across truncated edges W of the microstrip has a non-vanishing electric field Ex which are in phase, making W the radiating edge (edges 1 and 2). The radiated field (caused by the fringing fields along the edge W indicated by radiating slots in the figure) finally comes out from the microstrip resonator in the broadside direction z, which is the direction of the Poynting vector for the corresponding electric and magnetic fields along E x and Hy , respectively.

A Novel Integrated Power Module with Solid-State …

7

2.3 IMPATT Diode IMPATT (IMPact Avalanche Transit Time) is a reverse-biased junction diode that exhibits negative resistance due to 180° to 270° phase difference between the applied bias voltage and the generated RF current [14]. It has an ‘avalanche region’, where electron shower, i.e. avalnce of electrons, is generated due to high-field effect at a p+ n junction (the avalanche process is an inductive process), and a ‘drift region’/‘transittime region’ where more than 90° phase difference is produced between the voltage being applied and the current being generated. When the predominantly capacitance impedance of the diode is resonated with the inductive impedance of an RF cavity (in which the diode is embedded), RF oscillation is obtained at microwave or millimetrewave frequency depending on the diode design parameters and cavity dimensions. The diode to be used in RF cavity is suitably packaged (either in S4 package or studtype package) [14] for mounting in the cavity. A simple schematic of S4 package and equivalent circuit of IMPATT diode mounted in S4 package is shown in Fig. 5. However, the IMPATT diode to be used for the purpose of designing the integrated power module may be the 1 THz diode structure reported earlier [10]. The diode structure is shown in Fig. 6. In the IMPATT diode design, certain issues are to be taken care of. The possibility of premature breakdown or edge (local) breakdown of the diode needs to be taken care of during device design, which is normally caused by crowding of electric field at edge of the device. Use of edge termination structures is found to realize high breakdown voltages and good figure-of-merits. Instead of using Sapphire [c(1000)Al2 O3 ] as the substrate for growing the entire DDR structure, it can be grown on GaN substrate. Since GaN has better thermal conductivity than Sapphire, this will lead to better heat-sinking by the diode which is a need for THZ diodes as they have lower DC to RF conversion efficiency. Further, the reduced crystalline defect in the epitaxial GaN film due to perfect lattice matching makes GaN substrate better than Sapphire.

Fig. 5 a Schematic illustrating the bonding and S4 packaging of the diode chip b Equivalent circuit of the S4 packaged IMPATT chip

8

S. Kar

Fig. 6 Schematic of the 1.0-THz GaN DDR IMPATT [10]

2.4 The Integrated Power Module In the integrated power module, the IMPATT diode to be used is the seed diode of the type mentioned in Fig. 6 and it need not be a packaged diode; the latter being used in waveguide mounted oscillator of different types discussed in Fig. 2. Further, in integrated power module, no actual resonant-cap structure mounting in waveguide is needed. In fact, two more metallization steps one at the beginning and the other at the end of the diode fabrication process complete the power module structure as shown in Fig. 7. The ground plane (of conventional microstrip antenna) at the bottom of the integrated module (vide Fig. 7) has to be formed first of suitable material (highly conducting). Then the 1 THz seed IMPATT diode shown in Fig. 6 will be fabricated in different steps, and finally, a thin metallic slotted disc (of proper dimension) has to be realized with another metallization in the same planer fabrication process schedule. The whole module will act as an improvised slotted-disc-type microstrip patch antenna being fed by the seed IMPATT device embedded in the improvised resonant-cap cavity formed with top and bottom E-walls bounded by open H-wall

A Novel Integrated Power Module with Solid-State …

9

Fig. 7 Schematic of the integrated (Device + Cavity + Antenna) power module at THz

on sides—fringing field being responsible for radiation by the antenna as shown in Fig. 8. A few issues need to be considered while designing improvised resonant-cap structure for the oscillator of the integrated power module. Since the diode has to be grown epitaxially from the substrate, a hole needs to be provided in the ground plane. Under this condition, we need to include a perturbation factor in the analysis of the microstrip patch antenna. For analytical modelling and simulation, we have to resort to defected-ground-state (DGS) analysis of microstrip patch antenna. For oscillator operation, we need complex conjugate matching of the device and circuit impedances. Thus, the resonant-cap circuit impedance at the device location needs to be evaluated, which is expected to be dependent on cap design parameters, so that we can set the resistive component of resonator smaller than the absolute value of the negative resistance of IMPATT diode. Again, the scheme for applying DC bias signal

Fig. 8 Radial transmission line structure for source-antenna integration

10

S. Kar

to the IMPATT diode in such an integrated power module may be done by attaching gold ribbons to the ground plane and the cap structure as indicated in Fig. 7, via bonding pad especially for the disc structure. This will not affect the electromagnetic functioning of the module and also the radiation from the antenna (as E-field in the resonant-cap cavity will be perpendicular to the metallic ribbons and since the radiation field being transverse to the upper surface of the slotted resonant-cap disc, it will be unaffected by the presence of the metallic ribbons). Finally, the power module may have to be packaged in some form or the other in some innovative way—which may be decided as and when the power module design and testing is completed. At first, we need to proceed for the proof of principle with physical conceptualization, analysis, simulation, optimization, and finally, the fabrication of the diode chip and the integrated module and its experimental testing would establish the success of the proposed integrated power module. Here, the antenna (improvised microstrip patch type) needs no transmission line/waveguide to connect to the oscillator as it is integrated with the oscillator (with IMPATT device embedded in the improvised resonant-cap cavity); thus, transmission loss is minimized. This is an important advantage of the integrated device-antenna module because at THz frequency, power available from the device is inherently low. Further, the integrated structure will lead to size miniaturization too. Unlike conventional feeding mechanism in microstrip patch antenna (coaxial feed, microstrip feed, aperture feed, etc.), here the IMPATT source directly feeds input to the improvised microstrip patch antenna and the IMPATT diode is fed with the reverse bias with gold ribbons attached to the slotted disc via bonding pads and soldered to the ground plane as shown in Fig. 7.

3 Analytical Modelling to Realize the Power Module The analytical modelling will begin with the analytical characterization of resonantcap cavity, followed by device-circuit interaction and hence the oscillator characterization and finally to evaluate the radiation characteristics of the improvised slotted-disc microstrip patch antenna of the power module.

3.1 Analytical Characterization of Resonant-Cap Cavity It has already been mentioned that the lower face of the metallic disc of the cap structure and the upper face of the lower broad wall of the waveguide (or the ground plane of the improvised microstrip patch antenna of the integrated power module) forms the resonant-cap cavity. In such a cavity, formed between two circular conducting plates parallel to each other, electromagnetic energy is guided radially with no field variations either in the circumferential or axial direction. Thus, there will be only field

A Novel Integrated Power Module with Solid-State …

11

Fig. 9 Schematic showing the device embedded in the resonant-cap cavity that forms resonant–cap oscillator

components E z and H ϕ and the propagation vector k will be in the radial direction, vide Fig. 9. The E z component of electric field provides a total voltage of E z h between plates (where h is the plate separation) while the H ϕ component provides a total radial current of 2π rH ϕ (where r is the radius of the disc) that is directed outward from one plate and inward into the other plate. In such a radial transmission line, the E z and H ϕ field components are given by [21–23]:

Hφ =

E z = G 0 (kr )[Ae jθ(kr ) + Be− jθ(kr ) ]

(2)

G 1 (kr ) 1 ∂ Ez = [Ae jψ(kr ) − Be− jψ(kr ) ] jωμ ∂r η

(3)

where G 0 (x) = G 1 (x) =

 

J02 (x) + N02 (x)

(4a)

J12 (x) + N12 (x)

(4b)

and θ (x) = tan−1



   N0 (x) J1 (x) ψ(x) = tan−1 J0 (x) −N1 (x)

(5)

12

S. Kar

With, J m (kr) and N m (kr) being the mth-order Bessel and Neumman functions, respectively. The wave impedance of the outward travelling wave and inward travelling wave may be found by taking the ratio of E z and H ϕ in (2) and (3) with A and B set to zero in respective cases, when we have: For outward travelling wave: Z r+ = Z 0 (kr )e j[ψ(kr )−θ(kr )]

(6)

Z r− = Z 0 (kr )e− j[ψ(kr )−θ(kr )]

(7)

For inward travelling wave:

with Z 0 (kr ) = η1

The input impedance Z i =  Z i = Z 0i



Ez  , Hφ i

G 0 (kr ) G 1 (kr )

(8)

when load impedance Z L =



Ez  Hφ  L

Z L (cos(θi − ψ L ) + j Z 0L sin(θi − θ L ) Z 0L cos(ψi − θ L ) + j Z L sin(ψi − ψ L )

is given by:

 (9)

Thus, the cap circuit impedance at the device plane (i.e. at r = r i ) has the real and imaginary part expressions as [11]:

Re[Z i ] = Z 0 (ri )

⎡

⎤

ZL ⎢ ⎣ Z 0 (r L )

1 + νζ ⎥

2 ⎦ ZL 2 2 η ζ + Z 0 (r L )

⎡ ⎢ Im[Z i ] = Z 0 (ri )⎣

η2 ζ −



η2 ζ 2 +

ZL Z 0 (r L )



2 ⎤ ν ⎥

2 ⎦

ZL Z 0 (r L )

where Z 0 (ri,L ) = 377 η=

h G 0 (kri,L ) 2πri,L G 1 (kri,L )

sin(θi − θ L ) sin(ψi − ψ L )

(10)

(11)

A Novel Integrated Power Module with Solid-State …

ζ =− ν=

13

cos(ψi − θ L ) sin(θi − θ L )

cos(θi − ψ L ) sin(ψi − ψ L )

(12)

with k = 2π , λr is the resonant wavelength, h, r i , r L , and Z L are as shown in Fig. 9. λr Considering the oscillation condition for IMPATT diode placed in a resonant-cap cavity, i.e.: Z g + Z D = 0, where Z g = (h/2π r g )Z i, and Z D is given by: 1/ωC d ; Z i being given by Eq. (9). At r g = r L we have after some manipulation the expression for Z L as: 0.5  2πr L 2π Z 0 (ri )ζ fr Cd − ζ 2 ZL = Z 0 (r L )η h 1 + 2π Z 0 (ri )ν fr Cd

(13)

where C d is the diode capacitance and f r is the resonant frequency of the oscillator. The computed results based on analytical model equations reported by Kar [11] indicate the following about resonant-cap oscillator. 1. The load impedance (Z L ) at the terminating end of the cap cavity is very close to the characteristic impedance of the waveguide in which the cap cavity with the diode embedded in it resides. This indicates that the resonant-cap (with its radius approximately a quarter wavelength) acts as quarter-wave impedance transformer between the device impedance and the waveguide characteristic impedance ensuring efficient operation of resonant-cap oscillator in terms of maximum possible power transfer from the device to the load. 2. The cap diameter primarily responsible for determining the oscillation frequency (f r ) of the cap-type oscillator though cap height also changes oscillation frequency slightly. However, cap height is significantly responsible for influencing the real part of the cap impedance at the device plane which is useful for oscillator design as the oscillation condition demands that Re(RD ) ≥ RC . Tailoring of RC with cap height will be an important design criterion of cap-type oscillator design.

4 Device-Circuit Interaction and Oscillator Characterization The oscillator characteristics can be evaluated in terms of the interaction of the IMPATT device with the circuit (in this case the resonant-cap circuit whose analytical model equations have been developed above). For IMPATT diode, large-signal model equations will be used to derive the model equations for oscillator characterization in terms of device-circuit interaction.

14

S. Kar

The large-signal impedance of an IMPATT diode is given by the expression [24]: Z D = RD− j X D

(14)

where 1 (1 − cos θ )/θ   . ωCd 1 − ω2 /ωa2 (u)   1 sin θ/θ 1 1    +  XD = . 1− + 2 2 2 ωCd ωCa 1 − ω /ωa (u) 1 − ωa (u)/ω2 RD =

(15)

(16)

In the above equations, ω is the angular frequency, ωa (u) is the RF voltage2I1 (u) , where ωa is the usual avalanche dependent avalanche frequency: ωa2 (u) = ωa2 u.I 0 (u) 



vs frequency: ωa2 = 3αεvs Jdc , u = 3α V and α  is the derivative of the ionization ωW r. f coefficient with respect to the electric field, vs is the carrier saturation drift velocity, J dc is the DC current density, θ is the transit angle (which is typically 0.75π for maximum power and efficiency), I 0 (u) and I 1 (u) are the modified Bessel’s function of first kind having order 0 and 1, respectively, C a and C d are, respectively, the avalanche and drift region capacitances of the diode, W is the depletion region width (W A + W D ), vide Fig. 10, vr.f is the RF voltage across the diode. IMPATT is a current driven device and we need expressions for GD and BD which can be derived from the expression for RD and X D given by Eqs. (15) and (16) with suitable practical approximations viz.: ω2 >> ωa2 (u) and ω21C 2 ≈ |R D |2 = 1 |, |G D | .|R D

T

when we have [25]:

Fig. 10 IMPATT diode with avalanche and drift regions for a Single drift region (SDR) diode and b Double drift region (DDR) diode

A Novel Integrated Power Module with Solid-State …

G D = −2

15

Idc I1 (u) (1 − cos θ ) . . Vr. f I0 (u) θ

B D = ω(Cd + Ca ) ≈ ωCd

(17) (18)

where I dc is the DC bias current flowing through the diode from a constant current source and for thin avalanche zone practically C a  C d . Let us now apply the threshold approximation, i.e. near oscillation threshold vr.f → 0 and so u is very small and we can expand the modified Bessel’s functions I 0 (u) and I 1 (u) in power series which yields:   9 α 2 2 α 1 − (1 − cos θ )I V dc θ2 8 θ 2 r. f   3 α 9 α 2 2 = − 2 (1 − cos θ )Idc 1 − V 2θ 32 θ 2 r. f

G D | S D R = −3 G D |D D R

(19a)

(19b)

where the terms proportional to Vr.4 f and higher powers are neglected. Here: for SDR   diode, u = 3αθ Vr. f as ωW = θ ; while for DDR diode, u = 3α V as ωW = 2θ (vide vs 2θ r. f vs

u Fig. 10) and note that II01 (u) = u2 + 16 + ···. (u) Now, when a negative resistance device with an admittance: Y D = −G D + j B D is connected to a passive circuit whose admittance is: YC = G C + j BC , then the condition for stable oscillation due to device-circuit interaction is given by: 3

G D (V, ω) − G C (ω) = 0

(20a)

B D (V, ω) + BC (ω) = 0

(20b)

The net zero conductance of the circuit-diode combination ensures the stability of the oscillator and the frequency of oscillation is being determined by the resonant frequency of the system, when the total susceptance is zero. In general, an equivalent lumped circuit representation of IMPATT diode (including its series resistance) and the passive RF circuit may be given by Fig. 11. Referring to this circuit, the device and circuit admittances can be written as: Y D = −(−G D − B D2 Rs ) + j B D  YC = g L + −

j ω0 L c

(21a)

 (21b)

where BD and GD are given by Eqs. (18) and (19a, 19b), respectively, Rs is the diode’s parasitic series resistance, gL is the load conductance referred to the diode plane, and L C is the circuit inductance.

16

S. Kar

Fig. 11 Equivalent circuit of IMPATT diode with RF circuit and load

The condition for stable oscillation is obtained by equating the real parts of Y D and Y C in Eq. 21a, 21b, when we have: g L = −G D − B D2 Rs

(22)

But when the imaginary parts of Y D and Y C are equated, we obtain the frequency of oscillation as: f0 =

1 √ 2π L c Cd

(23)

The power output of the oscillator is given by: Pout =

1 g L Vr.2 f 2

(24)

At oscillation threshold when vr.f = 0, Eqs. (19a and 19b) simplifies to: α (1 − cos θ )Ith θ2

(25a)

3 α (1 − cos θ )Ith 2 θ2

(25b)

G D | S D R = −3 G D |D D R = −

In the practical situation, since B D2 Rs is fixed and the magnitude of GD increases with current, it is a good approximation to take gL = 0 at oscillation threshold. Because oscillation can only occur when the negative conductance exceeds the magnitude of B2 Rs , the oscillation threshold may be obtained from: −G D0 = B D2 Rs

(26)

A Novel Integrated Power Module with Solid-State …

17

From Eqs. (26), (25a, 25b), and (18) we have the expression for threshold current as: Ith | S D R =

θ 2 ω2 Cd2 Rs 3α  (1 − cos θ )

(27a)

Ith | D D R =

2θ 2 ω2 Cd2 Rs 3α  (1 − cos θ )

(27b)

Again, as the DC bias current increases above the oscillation threshold, which is the practical situation for oscillator operation, we continually adjust the load conductance gL by using EH tuner placed between the oscillator and the load to give maximum power output, this means that: ∂ Pout =0 ∂g

(28)

where Pout is given by Eq. (24). Using Eq. (24) and (22) in Eq. (28) and resorting to threshold approximation: (I dc – I th ) γ ] J=1 ∼ 1 − 1 − e−γ

(30)

The PAPR should then be considered as a random variable. The average PAPR value which has been shown in [22] is given by, E[P A P R] = 0.57721 + ln[N ]

(31)

In Fig. 8, we plot the average PAPR value as a function of the number of carriers. This curve shows that the average PAPR value of the OFDM increases with the number of subcarriers. For example for N = 200, the average value of PAPR is 6 dB while it is 6.7 dB for N = 1200 subcarriers. In [23], the authors give an upper limit of the distribution function for an oversampling factor greater than 2, Pr[PAPR{x} > γ ] J>2 < J N e

  2 γ 1− 2πJ 2

(32)

156

M. El Ghzaoui and S. Das 8 7

E[PAPR] (dB)

6 5 4 3 2 1 0

0

200

400

600

800

1000

1200

1400

1600

Number of subcarriers N Fig. 8 Average PAPR value as a function of N

In order to extrapolate the above results to the continuous case, it is then necessary to oversample the signal by a factor J > 1 and make J tend toward infinity. In Fig. 9, we depicted the complementary cumulative distrution function (CCDF) of the OFDM signal for N = 1024 and for various values of the oversampling factor. The discretization of a continuous signal does not appreciably modify the value of the mean power. Besides, this can modify the value of the maximum power. Thus, if the sampling does not correspond to the moment when the power is maximum, we can observe significant differences between the peak power in continuous and the peak power in discrete. By increasing the oversampling rate, we get closer to the peak power continuously, which explains the increase in CCDF effected when the oversampling factor increases. However, for J > 4, there is no longer a significant increase in CCDF. We can therefore draw the following conclusion: an oversampling factor of at least 4 is necessary to get as close as possible to the continuous peak power.

6.3 Frequency Equalization If we note x(t), the OFDM signal sent with the cyclic prefix, r(t) the received signal, h(t) the time domain response, and n(t) the noise of the channel, we can then write, if ⊗ represents the convolution:

OFDM for Terahertz Wireless Communication Systems

157

0

10

J=1 J=2 J=4 J=8 J=16

Pr[CCDF(x) = PAPRx>gama]

-1

10

-2

10

-3

10

-4

10

0

2

4

6

8

10

12

14

gama (dB)

Fig. 9 CCDF of the discrete OFDM signal for different values of the oversampling factor

+∞ r (t) = h(t) ⊗ x(t) + n(t) = x(τ )h(t − τ )dτ + n(t)

(33)

−∞

if R(f), H (f), X (f), and N (f) present, respectively, the Fourier transforms of r (t), h (t), x (t), and n (t), then the expression (32) is written in the frequency domain as: R( f ) = H ( f ) · X ( f ) + N ( f )

(34)

These equations, applied to continuous signals, remain valid for discrete signals if on the one hand, the number of symbols on which the discrete Fourier transform takes place, is large enough and if, on the other hand, one of the two signals convoluted is periodic, so that the temporal convolution of the signals is circular. This last condition is verified by the introduction of the cyclic prefix. OFDM equalization simple which can be done in the frequency domain after the FFT in reception. The channel being flat in each subband, an estimate of the channel using symbol and/or pilot frequency makes it possible to calculate the complex coefficients Hn of channel. So we can equalize the signal by introducing a factor H1ˆ k on the signal which allows us to estimate the symbols x[n].

158

M. El Ghzaoui and S. Das

7 Advantages and Drawback of OFDM System OFDM modulation is an old technology with recent success which consists in transmitting data in parallel on several different carrier frequencies. The OFDM is particularly well suited to long-distance radio transmission channels without multiple wave transmissions (echoes), so it significantly reduces inter-symbol interference. However, OFDM also has a number of drawbacks.

7.1 Advantages The OFDM modulation process has been mainly designed to fight against multiple paths with fading, by minimizing inter-symbol interference (ISI), and it guarantees us sufficiently high bit rates. Spectral congestion has been optimized, the transmission channel appears locally invariant, and frequency equalization is carried out in a very simple manner.

7.1.1

Low ISI

Using a guard interval enhances the robustness of the OFDM signal against frequency-selective channel. This allows an acceptable ISI to be received, i.e., OFDM symbols arriving at the receiver do not interfere with the sampling times.

7.1.2

Optimal Spectral Bulk

OFDM offer an effective use of frequency properties in comparison with conventional frequency multiplexing solutions. This is due to the fact that in OFDM, the subcarriers overlap while maintaining perfect orthogonality as shown in Fig. 10, and therefore optimizing the spectral occupancy of the modulated signal. f k − f k+1 = 1/TB

7.1.3

Frequency-Selective Channel

We can consider that the transfer function of the transmission channel is flat at the level of each subcarrier as shown in Fig. 11.

OFDM for Terahertz Wireless Communication Systems

159

Fig. 10 Orthogonal subcarrier in frequency domaine

0

Bu

H(f) in dB

-10

-20

-30

-40

-50 6 10

Bu/N

7

10

8

10

Frequency in Hz Fig. 11 Frequency response of a frequency-selective channel

7.1.4

Equalization

Channel equalization in OFDM is digital and simple due to the presence of the cyclic prefix. Moreover, channel coding technics connected with interleaving between frequencies achieves the performance of plat channel. This technique which is COFDM is used in particular by the DVB-T standard used in France for digital terrestrial television.

160

7.1.5

M. El Ghzaoui and S. Das

Robustness Against Noise

Unlike single-carrier modulations where noise can affect a the whole frame, in OFDM system, the loss of a symbol due to significant noise does not disturb other data.

7.2 Drawbacks Temporal characteristics of OFDM signal represent the main drawback of it in this signal [24, 25]. Indeed, on the one hand, OFDM modulation uses a rectangular frequency wave form which corresponds to a cardinal sine. Consequently, it is a very badly located frequency spectrum. In addition, the first secondary lobe of the DSP goes back to −13 dB which makes this modulation difficult to apply for THZ channels, having a very strict emission mask. The idea is therefore to substitute in OFDM a waveform having better localization properties and having, in particular, a frequency response with a higher attenuation. To overcome the time-frequency location problem associated with OFDM modulation, we can use the oversampled OFDM modulation. On the other hand, an OFDM signal in Fig. 12 has strong envelope fluctuations, and therefore, a sufficiently high PAPR. This needs a high linearity of the transmission chain, in particular at the level of the power amplifier which will then exhibit mediocre efficiency (linearity and divergent efficiency) and, therefore, incompatible with consumption optimized for a mobile application. In addition, the amplifier’s nonlinear transfer characteristic generates in-band falsification of the OFDM signal. This misrepresentation will have an effect on the N subcarriers which will then interfere with other subcarriers which lead to performance degradation in term of “BER” of the OFDM transmission system. 1 0.8

Amplitude (Volt)

0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1

Normalized Time in s Fig. 12 Envelop fluctuation of OFDM signal

OFDM for Terahertz Wireless Communication Systems

OFDM Transmier

Data In

Differenal Encoding

Data Out

Detecon

161

OFDM

OFDM demodulator + MLSE Esmaon + Equalizaon

Cp

DAC

Upconversio

PA

BPF

OFDM Receiver

IF/LPF

ADC

Downconversion

LNA

BPF

Fig. 13 OFDM structure

It is therefore essential to use linearization techniques for the amplifier or “PAPR” reduction techniques for the OFDM signal.

8 Numerical Results and Discussions 8.1 Structure of OFDM Transceiver The architecture of the OFDM transmitter is dipected in Fig. 13. The binary data is modulated with an M-QAM or M-PSK modulation, converted in parallel and then transmitted to an IFFT. The IFFT converts the OFDM signal from the frequency domain to the time domain. After that, a guard interval is adeed. The OFDM symbols are passed through two analog digital converters (DAC). Afterward, the OFDM signal will be up-converted and amplified by high power amplifier and then is filtered by low-pass filters in order to remove the aliasing generated by the DACs.

8.2 Simulation Parameters we chose to share the nominal speed of 10 Gbps between four independent OFDM subbands multiplexed. In order to be compatible with a spacing between channels of 50 GHz, each subband has a width of 8 GHz, while the spacing between the subbands is 10 GHz. The nominal bit rate to be addressed when considering 10 Gb payload Ethernet with 4% overhead dedicated to protocols and 7% for associated channel coding (FEC) is 11.1 Gbps. However, an OFDM signal requires a certain number of

162

M. El Ghzaoui and S. Das

Table 1 Main parameters of the proposed OFDM system used in THz communication system

Nominal rate

10 Gbps

Number of bands

4 bands

Data rate

128 Gbps

Bandwidth

8 GHz

Baseband

4 GHz

Modulation type

OFDM

Signal-to-noise ration

0–30 dB

Carrier frequency

300 GHz

Sampling frequency

12 GHz

Sampling period

0.32552 ns

FFT size (NC)

2048

Cyclic prefix length

18 samples

Data subcarriers

512, 1024, 2048

additional overheads, linked to the addition of the cyclic prefix, training sequences, and pilot subcarriers. The cyclic prefix gives OFDM its robustness in the face of interference between symbols and has been dimensioned here for a THZ channel. The pilot subcarriers are there to allow synchronization, channel estimation, and phase noise compensation of the overall system. The effective bit rate to be transmitted is then ~12.8 Gbps. In order not to be too sensitive to the accumulation of nonlinear phase noise during the propagation and of the phase noise of the lasers, we have chosen to have each subcarrier carry QPSK modulation. The effective bit rate carried by each subband on a polarization is therefore ~1.6 Gbps. It is contained in ~8 GHz of bandwidth. The cyclic prefix, meanwhile, will occupy a time slot of 1.5 ns at the beginning of each OFDM frame. Among the 256 carriers, 85 subcarriers equal to zero (on the edges of the spectrum) in order to induce oversampling, making it possible to separate the useful OFDM signal from the aliasing generated by the DACs. Each of the four OFDM subbands then has 170 subcarriers. Note that the central subcarrier is set to zero. The duration of the OFDM symbols is 227.5 ns (Table 1).

8.3 Channel Model In this work, we use the multi-path THz channel module including LOS and NLOS propagation [26]: H ( f, r, δ) = HL O S ( f, r )e− j2π f τ L O S + HNi L O S ( f, δi )e− j2π f τ NLOS

(35)

where HL O S ( f, r ) is the transfer function of the LOS propagation path, HNi L O S ( f, δi ) represent the transfer function of the i-th NLOS path, δi is coordinates of all the

OFDM for Terahertz Wireless Communication Systems

163

scattering points, r is the distance from transmitter and receiver, and N represent the whole number of NLOS paths. In this chapter, scaled versions of different normalized delay profiles are used to generate taps for the channel model.

8.4 Numerical Results In simulation part, we study the performance of multi-carrier systems through a Thz channel described above. We try to minimize the average BER of the system for a given bit rate. In fact, to define the quality of a digital transmission chain, BER is used as a metric, depending on the type of modulation used. There is a relationship between BER and the SNR. To compare the performances of the different types of M-PSK and M-QAM technics, we choose to plot the variations of the BER according to the SNR at constant bandwidth. The curves of Fig. 14 represent the variation of the BER according to SNR for three values of N. It should be noted that the bit rate transmitted by the 16-PSK modulation is twice higher than the bit rate transmitted by the 4-PSK modulation. The number of carriers N is an interesting parameter for the implementation of our system. To implement the IFFT and FFT calculations, the number of carriers must be a power of 2. In our case, we are considering the following three architectures: OFDM with 512, 1024, 2048 carriers. We can notice from the figure that the number

Fig. 14 Performance of OFDM over THZ for deferent value of N with 4-PASK and 16-PSK

164

M. El Ghzaoui and S. Das

Fig. 15 Performance of OFDM over THZ for deferent value of M (M-QAM)

of subcarriers has no significant effect on the performance of OFDM modulation. On the other hand, the number of bits per symbol plays a critical role in determining the performance of our system. Indeed, for the same SNR ratio, the more the speed is increased, the more the BER increases, on the other hand these curves clearly show that if we want the BER to remain below 10-4, we must have an SNR above 12 dB for 4-PSK and higher than 16 dB for 16-PSK. To increase the flow, we will increase the number of cocks per symbol. For this, we will examine, in Fig. 15, the performance of our system with 32-QAM, 64-QAM, 124-QAM, and 256-QAM. It is clear from this figure that the more data rate increases the more the BER increases. So there are a tradeoff between spectral efficiency and performance, high spectral efficiency result in poor performance.

9 Conclusion The key motivation of this chapter is to decrease the transmission errors produced during signal propagation in the THz system as well as the robustness of multi-carrier THz systems, so that they can be used effectively to exchange data. The problem of reducing the BER for multi-carrier systems is considered under the constraints of data rate. This chapter has been devoted to a general presentation of multi-carrier transmission techniques such as OFDM. The basic principle of OFDM modulation has been explained. In order to combat interference between symbols or between

OFDM for Terahertz Wireless Communication Systems

165

carriers, time or frequency equalization techniques must be used, and we have tried to highlight some characteristic points of these techniques. Thus, we have described the advantages and disadvantages of OFDM modulation, which we have answered in the last parts of this chapter and in the next chapter. Then, we described the THz channel. We have optimized high-speed data transmission over such a channel. Thus, we were able to reach a BER of 10-4 without coding for SNR less than 18 dB. Consequently, the OFDM modulation seems more robust in the face of ISIs caused by multi-path propagation phenomena THz communication system. Others’ solutions can be used to reduce BER in THz communication system such as MIMO technique which is an effective method to increase capacity in radio communication system.

References 1. H.J. Song, Present and future of terahertz communications. IEEE Trans. Terahertz Sci. Technol. 1(1), 256–263 (2011). https://doi.org/10.1109/TTHZ.2011.2159552 2. C. Han, A. Bicen, I. Akyildiz, Multi-wideband waveform design for distance-adaptive wireless communications in the terahertz band. IEEE Trans. Signal Process. 64(4), 910–922 (2015). https://doi.org/10.1109/TSP.2015.2498133 3. V. Petrov, A. Pyattaev, D. Moltchanov, Y. Koucheryavy, Terahertz band communications: applications, research challenges, and standardization activities, in 8th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Lisbon, Portugal, Oct. 2016 4. I. Akyildiz, J. Jornet, C. Han, Terahertz band: next frontier for wireless communications. Phys. Commun. (2014). https://doi.org/10.1016/j.phycom.2014.01.006 5. T. Kürner, S. Priebe, Towards THz communications—status in research, standardization and regulation. J. Infrared Milli Terahz Waves 35, 53–62 (2014). https://doi.org/10.1007/s10762013-0014-3 6. M. El Ghzaoui, S. Das, Data transmission with terahertz communication systems, in Book: Emerging Trends in Terahertz Solid-State Physics and Devices, pp. 121–141. Springer, Singapore (2020). https://doi.org/10.1007/978-981-15-3235-1_9 7. H. Yuan, N. Yang, K. Yang, C. Han, J. An, Hybrid Beamforming for MIMO-OFDM Terahertz Wireless Systems over Frequency Selective Channels, pp. 1–6 (2018). https://doi.org/10.1109/ glocom.2018.8647835 8. D. Asiedu, R. Ahiadormey, S. Shin, K.-J. Lee, Performance comparison of single-carrier and multi-carrier systems in a terahertz wireless communication environment. J. Adv. Information Technol. Convergence 9, 11–24 (2019). https://doi.org/10.14801/jaitc.2019.9.1.11 9. J. Mestoui, M. El Ghzaoui, M. Fattah, et al.: Performance analysis of CE-OFDM-CPM modulation using MIMO system over wireless channel. J. Ambient Intell Human Comput. (2019). https://doi.org/10.1007/s12652-019-01628-0 10. R. Van Nee, P. Ramjee, OFDM for Wireless Multimedia Communications. Artech House Publishers (2000) 11. N. Benvenuto, S. Tomasin, L. Tomba, et at., Equalization methods in OFDM and FMT systems for broadband wireless communications. IEEE Trans. Commun. 50(9), 1413–1418, September 2002. https://doi.org/10.1109/tcomm.2002.802571 12. E.P. Lawreybe, Adaptative Techniques for Multiuser OFDM. Ph.D. Thesis, Jam Cook University, Townsville (2001) 13. M. Jamal, G. El Mohammed, H. Abdelmounim, F. Jaouad, BER performance improvement in CE-OFDM-CPM system using equalization techniques over frequency-selective channel. Proc. Comput. Sci. 151, 1016–1021 (2019). https://doi.org/10.1016/j.procs.2019.04.143

166

M. El Ghzaoui and S. Das

14. W. Shieh, I. Djordjevic, OFDM for Optical Communications. Academic Press, Elsevier (2010). https://doi.org/10.1016/C2009-0-19354-6 15. R. Vallet, K. Haj Taieb, Fraction spaced multi-carrier modulation transmission. IEEE Wireless Personal Commun. 2, 97–103, Mars 1995 16. S. Weinstein, P. Ebert, Data transmission by frequency-division multiplexing using the discrete fourier transform. IEEE Trans. Comm. Techn. 19, 628–634 (1971) 17. J.G. Proakis, Digital Communication. Mc Graw Hill international Editions (1995) 18. M. Joindot, A. Glavieux, Communication Numérique. Edition Masson (1996) 19. R. Haas, Application des transmissions à porteuses multiples aux communications radiomobiles (Thése de doctorat, ENST, France, 1996) 20. C. Tellambura, Improved phase factor computation for the PAPR reduction of an OFDM using PTS. IEEE Commun. Lett. 5(4), April 2001 21. H. Ochiai, H. Imai, On the distribution of the peak-to-average power ratio in OFDM signals. IEEE Trans. Commun. 49(2), 282–289 (2001) 22. H. Ochiai, H. Imai, Peak-power reduction schemes in OFDM systems: a review, in WPMC, pp. 247–252 (1998) 23. M. Sharif, M.G. Alkhansari, B.H. Khalaj, On the peak-to-average power of OFDM signals based on oversampling. IEEE Trans. Commn. 51(1), 72–78 (2003) 24. J. Belkadid, A. Benbassou, M. El Ghzaoui, PAPR reduction in CE-OFDM system for numerical transmission via PLC channel. Int. J. Commun. Antenna Propagation 3(5), 267–272 (2013) 25. M. El Ghzaoui, A. Hmamou, J. Foshi, J. Mestoui, Compensation of non-linear distortion effects in MIMO-OFDM systems using constant envelope OFDM for 5G applications. J. Circuits Syst. Comput. https://doi.org/10.1142/S0218126620502576 26. M. Bharathi, A. Amsaveni, S. Sasikala, Orthogonal frequency division multiplexing for improving the performance of terahertz channel. J. Infrared Millim. Waves 38(3), 1001–9014 (2019). https://doi.org/10.11972/j.issn.1001-9014.2019.03.001

All Optical Universal Logic TAND Gate Using a Single Quantum Dot Semiconductor Optical Amplifier at 2 Tbit/s Kousik Mukherjee

Abstract All optical universal logic TAND is designed and simulated for performance analysis using rate equation model of quantum dot semiconductor optical amplifier. Extinction ratio(ER), contrast ratio (CR), and quality factor are calculated. A large eye opening with low value of amplitude modulation ensures efficient performance also. This TAND gate is used to design basic gates NOT, OR, and AND which shows that TAND is a universal gate. Keywords Universal logic · Quantum dot SOA · Cross gain modulation · Q factor · Contrast ratio

1 Introduction Quantum Dot Semiconductor Amplifiers (QDSOAs) are important nonlinear devices for the design of all optical communication and computation applications [1– 5]. QDSOA is an effective gain media and have higher gain at lower injection current compared to ordinary Semiconductor Optical Amplifiers (SOAs). Moreover, QDSOAs have higher saturation output power, wider gain bandwidth, and low noise Fig. 1. TAND gate is a universal gate with only one high output is proposed using Tera Hertz Asymmetric Demultiplexer (TOAD) is proposed in [6]. In [7], reflective SOA is used for the implementation of TAND gate. In this chapter, TAND gate using QDSOA is proposed and analyzed. The universality of TAND gate is established by designing three basic gates NOT, AND, and OR. Most of the QDSOA-based logic designs deal with Mach Zehnder interferometer. But, in this chapter, the device presented uses no Mach Zehnder interferometer. The Mach Zehnder-based designs requires special techniques for maintaining balance in terms of amplitude and phase [4]. Section 2 describes the simulated results of operation of the proposed logic gates using MATLAB. Section 2 gives the basic principle of working of QDSOA-based

K. Mukherjee (B) Department of Physics, B.B. College, Asansol 713303, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Biswas et al. (eds.), Emerging Trends in Terahertz Engineering and System Technologies, https://doi.org/10.1007/978-981-15-9766-4_8

167

168

K. Mukherjee

TAND gate. In Sects. 4.1, 4.2 and 4.3, the designs of NOT, OR, and AND gates are described. Section 5 deals with overall conclusions.

2 Working Principle of the TAND Gate The cross-gain modulation (XGM) in QDSOA is the basic mechanism behind the working of the proposed logic gate. This XGM results in inverted output at probe wavelength (Fig. 1). When pump is absent, the input probe experiences high gain and QDSOA gives high output. When pump is present, the input probe signal passes the gain saturated QDSOA and hence the output is low. All optical universal logic TAND gate using Quantum Dot Semiconductor Optical Amplifier is shown in Fig. 1. It is made by a single QDSOA. It has two outputs P ˜ corresponding to two inputs A and B as shown in the truth table = A and Q = AB (Table 1). The operation of the gate is discussed for different cases: Case 1: When the input signals A = B = 0 or low, both probe and pump signals are absent in the QDSOA resulting P = 0 and Q = 0. Case 2: A = 0 and B = 1, i.e., only the probe signal is present. In this situation, no gain saturation (which results in high QDSOA output) occurs and hence gives P = 0 and Q = 1. Fig. 1 QDSOA-based TAND gate

Beam splitter

P

A

Q

QDSOA

B

Table 1 Truth table of TAND gate

Input A

Output B

P

Q

0

0

0

0

0

1

0

1

1

0

1

0

1

1

1

0

All Optical Universal Logic TAND Gate Using a Single …

169

Case 3: When A = 1 and B = 0’, only pump signal is present and the output Q of the QDSOA becomes high and output P becomes low (as no probe signal is present there), i.e., P = 1 and Q = 0. Case 4: When both the inputs A and B becomes ‘1’ both pump & probe signals are present and the output Q of the QDSOA becomes low and output P is high, i.e., P = 1 and Q = 0.

3 Modeling and Results of Simulations For modeling and simulations, the QDSOA rate equations and the parameters are used from Dimitriadou et al. [1]. J N (1 − h) NQ N ∂N = − + − ∂t eL w τw2 τ2w L w τw R

(1)

∂h h N (1 − h)L w f (1 − h) (1 − f )h = − − + − ∂t τ2w τw2 N Q τ21 τ12

(2)

∂f f (1 − h) f2 L w gmax (2 f − 1)P (1 − f )h = − + − ∂t τ21 τ12 τ1R N Q Aeff hv

(3)

∂P [gmax (2 f − 1) − αint ]P = ∂z Aeff hv

(4)

The values of different parameters are : gmax = 14 cm−1 , α int = 2 cm−1 , J = 1A/cm2 , L w = 250 nm, NQ = 5.0 × 1010 , spontaneous radiative lifetime in the WL(τ wR) = 0.2 ns, electron relaxation time from the WL to ES(τ w2 ) = 3 ps, electron relaxation time from ES to GS(τ 21 ) = 0.16 ps, group velocity(V g ) = 8.3 × 107 m/s, escape time (electron) from ES to WL(τ 2w ) = 1 ns, escape time(electron) from GS to ES(τ 12 ) = 1.2 ps, radiative lifetime (spontaneous) in Quantum Dot(τ 1R ) = 0.4 ns, Aeff = 0.75 μm2 . The input signals are taken of the form P = P0 exp [−(t/T F )2 ], where P0 is peak power of control signal, and T F = 0.1 ps. We have analyzed the TAND gate by calculating extinction ratio (ER) = 10log(P1 max /P0 min )dB, contrast ratio (CR) = 10log(P1 m /P0 m )dB, amplitude modulation (AM) = 10log(P1 max /P1 min )dB, Quality factor (Q) = (P1 m – P0 m )/(σ1 + σ0 ), and relative eye opening (REO) = [1–(P0 max /P1 min )] × 100%, where (P1 max , P1 min, P1 m , σ1 ) and (P0 max , P0 min , P0 m , σ0 ) are maximum, minimum, average, and standard deviations of 1 and 0 states, respectively. For all the calculations, the unsaturated gain is taken 10 dB. Figure 2 shows the variations of ER with control power. With control power, ER increases and becomes maximum at 0.3 mW, and then becomes almost constant above 9 dB. The ER is plotted up to 1mW of control power beyond which it shows decrease.

170

K. Mukherjee ER

9.4 9.2 9.0

ER (dB)

8.8 8.6 8.4 8.2 8.0 7.8 7.6 0.0

0.2

0.4

0.6

0.8

1.0

C ontrol Power (m W ) Fig. 2 Variation of ER with control power

CR 11.4 11.3

CR (dB)

11.2 11.1 11.0 10.9 10.8 0.0

0.1

0.2

0.4 0.5

0.3

0.6

0.7

Control Power (mW)

Fig. 3 Variation of CR with control power

0.8

0.9

1.0 1.1

All Optical Universal Logic TAND Gate Using a Single …

171 AM

0.35 0.30

AM (dB)

0.25 0.20 0.15 0.10 0.05 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Control Power (mW) Fig. 4 Variation of AM with control power

Figure 3 describes variation of CR with control power and is similar to ER variations and becomes maximum at 0.3 mW. CR value more than 11.3 dB is achieved. Figure 4 gives the variations of AM with control power. It is desired to have AM value less than 1 dB. In this case, it is well beyond 1 dB and a minimum value of 0.076 dB is obtained for 0.3mW of control power. Quality factor Q is another important parameter for analysis of optical logic gates and processors. A Q value greater than 6 is well for errorless transmissions. In this device, the maximum Q is 14.4, which ensures negligible bit error rate. This maximum value is achieved for 0.3mW of control power as shown in Fig. 5. The variations of BER with Q is shown in Fig. 6. Figure 6 shows for Q > 6 BER is almost zero. Relative eye opening (REO) signifies the difference between maximum of 1’s and maximums of 0’s, and helps in understanding the opening of the switching window. Figure 7 shows that REO is also maximum (88%) for control power of 0.3 mW. Output bit pattern is shown in Fig. 8 corresponding to A = 00,110,011, and B = 01,010,101. The output bit pattern is 10,100,010. All simulations are done at a rate of 2 TBit/s.

172

K. Mukherjee Q

15 14 13

Q

12 11 10 9 8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Control Power (mW) Fig. 5 Variation of Q with control power

0.16 0.14 0.12

BER

0.1 0.08 0.06 0.04 0.02 0 1

2

3

4

5

Q Fig. 6 Variation of BER factor with Q factor

6

7

8

All Optical Universal Logic TAND Gate Using a Single …

173 REO

88

REO (%)

87 86 85 84 83 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Control Power (mW)

Output Power(a.u)

Fig. 7 Variations of REO with control power

1

0.5

0 10

10.5

11

11.5

12

12.5

13

13.5

14

14.5

Time(ps)

Fig. 8 Output bit pattern at a speed of 2 TBit/s

4 TAND as a Universal Logic TAND gate can be used to design all basic gates and is universal one. In the following sections, NOT, AND, and OR gates are designed and explained.

174

K. Mukherjee

Fig. 9 QDSOA-based NOT gate

4.1 NOT Gate QDSOA-based NOT gate using TAND gate as shown in Fig. 9. Here, the input signal B = 1 and is connected with QDSOA as a data signal and A is connected with RSOA as a control signal. Operation principle of this gate is given below. Case 1: When input A = 0, the output Q is high, i.e., in ‘1’ state. Case 2: When input A = 1 the output Q is low, i.e., ‘0’. This gives the NOT operation of input control signal A. So the output of NOT gate is Q = A.

4.2 AND Gate QDSOA-based AND gate using TAND gate as shown in Fig. 10. It consists of two TAND gates. The output Q of the TAND1 gate is connected to the control input of the TAND2 gate. Detailed operational principle of AND gate is given below. Case 1: When A = 0 and B = 0, there is no control signal present in the QDSOAbased TAND1 gate and data signal on the TAND2 gate so the output Q is low, i.e., ‘0’. Case 2: When A = 0 and B = 1, i.e., control signal is absent for the TAND1 gate and data signal is present on the TAND2 gate so the output Q is low, i.e., ‘0’. Fig. 10 QDSOA-based AND using TAND gate

A TAND1 P

1 TAND2 B

Q

All Optical Universal Logic TAND Gate Using a Single … Fig. 11 QDSOA-based OR gate using TAND gate

175

A

TAND

Q

B

Case 3: When A = 1 and B = 0, i.e., control signal is present on the TAND1 gate and data signal is absent of the TAND2 gate so the output Q is low, i.e., ‘0’. Case 4: When both A = 1 and B = 1, output of the TAND 1 gate becomes low, i.e., control signal of the TAND2 is zero so the output Q is high, i.e., ‘1’. From above discussion, we observed that the output of this gate is Q = AB which is the output of AND gate.

4.3 OR Gate QDSOA-based OR gate using TAND gate as shown in Fig. 11. It consists of only one TAND gate. Detailed operational principle of OR gate is given below. Case 1: When both the inputs A and B are zero or low, there are no probe and pump signals are present in the QDSOA, both outputs (P and Q) of this QDSOA becomes zero, i.e., P = 0 and Q = 0. Case 2: When the input A becomes ‘0’ and B becomes ‘1’ or high, i.e., only probe signal is present, the output Q of the QDSOA becomes high and output P is low, i.e., P = 0 and Q = 1. Case 3: When the input A becomes ‘1’ and B becomes ‘0’, i.e., only pump signal is present so that the output Q of the QDSOA becomes high and output P is also high, i.e., P = 1 and Q = 1. Case 4: When both the inputs A and B become ‘1’ both pump & probe signals are present so the output Q of the QDSOA becomes high and output P is high, i.e., P = 1 and Q = 1. From above discussion, we observed that the output of this gate is Q = A + AB which is the output of OR gate.

5 Conclusions We have analyzed all optical universal logic TAND gate using QDSOA. The maximum values of both ER and CR are found to be nearly 9.2 dB and 11.35 dB for

176

K. Mukherjee

an unsaturated gain of 10 dB of the QDSOA, we also found higher Q value which is 14.5 dB and negligible BER. A higher Q value represents error less performance. We also designed NOT, AND, and OR gates using this universal TAND gate. It is interesting to note that QDSOA shows high speed performance compared to reflective SOA-based similar devices [7].

References 1. E. Dimitriadou, K.E. Zoiros, On the feasibility of all optical AND gate using quantum dot semiconductor optical amplifier based Mach Zehnder Interferometer. Prog. Electromagnet. Res. B 50, 113–140 (2013) 2. X. Zhang, S. Thapa, N. Dutta, All-optical XOR gates based on dual semiconductor optical amplifiers. Cogent Phys. 6(1), 1660495 (2019) 3. D.K. Gayen, T. Chattopadhyay, Designing of optimized all-optical half adder circuit using single quantum-dot semiconductor optical amplifier assisted mach-zehnder interferometer. J. Lightwave Technl. 31(12), 2029–2034 (2013) 4. K. Komatsu, G. Hosoya, H. Yashima, All optical NOR gate using a single quantum dot SOA assisted an optical filter. Opt Quant Electron 50(131), 1–18 (2018) 5. D.K. Gayen, T. Chattopadhyay, Simultaneous all optical basic arithmetic operations using QDSOA assisted Mach Zehnder interferometer. J. Comp. Electrn (2016) 6. T. Chattopadhyay, All optical clocked delay flip flop using a single terahertz optical asymmetric demultiplexer based switch: a theoretical study. Appl. Opt. 49(28), 5226 (2010). https://doi.org/ 10.1364/AO.49.005226 7. K. Maji, K. Mukherjee, M.K. Mondal, Simulative performance analysis of all optical universal logic TAND gate using Reflective Semiconductor Optical Amplifier (RSOA), in Communicated to Advanced intelligence system and computing, AISC series, Proceeding of COMSYS2020, Jailpaiguri (Springer, 2020)

TOAD-Based Frequency-Encoded All Optical XOR Gate, Half Adder, and Half Subtractor Kousik Mukherjee, Kajal Maji, Ashif Raja, and Mrinal Kanti Mandal

Abstract Tera Hertz Optical asymmetric Demultiplexer or TOAD is an important optical switch in optical computational and communication applications. It is used to design different types of logic gates and logic circuits. In this chapter, we have utilized it to design a frequency-encoded optical XOR gate, half adder, and half subtractor using TOAD-based switch for the first time. The input/output bit patterns along with ON/OFF ratio is also investigated. Keywords TOAD · Frequency encoding · XOR gate · Half adder · Half subtractor

1 Introduction Semiconductor amplifiers (SOAs) are important modules for the realization of next-generation optical network [1]. Many proposals for frequency-encoded all optical logic gates and circuits have been implemented using SOA-based nonlinearities like cross-gain modulation (XGM), cross-phase modulation (XPM), four wave mixing (FWM), polarization rotation, etc. [2–8]. Frequency encoding uses two different frequencies ν1 and ν2 for representing ‘0’ and ‘1’, respectively. Conventional encoding has many drawbacks compared to frequency encoding technique like intensity dependence, or polarization dependence, etc. This is because frequency is a characteristic of light that remains unchanged in reflection or transmission [2]. TOAD is an important interferometric device for the implementation of optical logic processors at high speed [9, 10]. Recently, TOAD is utilized to design optical frequencyencoded logic gates by us in [10]. In this present chapter, frequency-encoded X-OR gate, half adder, half subtractor are designed and analyzed using TOAD as switch for K. Mukherjee (B) · K. Maji · A. Raja Department of Physics, B.B. College, Asansol, India e-mail: [email protected] K. Mukherjee · A. Raja Centre of Organic Spintronics and Optoelectronics Devices, KNU, Asansol, India K. Maji · M. K. Mandal Department of Physics, National Institute of Technology Durgapur, Durgapur, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Biswas et al. (eds.), Emerging Trends in Terahertz Engineering and System Technologies, https://doi.org/10.1007/978-981-15-9766-4_9

177

178

K. Mukherjee et al.

the first time since no literature is found in similar topic. These devices are analyzed considering input/output bit patterns, on/off ratio and its dependence on control power and amplified spontaneous emission noise (ASE). This chapter is divided as follows: Section 2 deals with basic switching of TOAD, Sect. 3 mathematical modeling and in subsequent sections sum, carry, and borrow generations are discussed. Operations of half adder, half subtractor along with simulation results are given in Sects. 5, 6 and 7, respectively. Section 8 concludes the chapter.

2 Working Principle of TOAD Figure 1 shows TOAD-based optical switch. It has one control signal input(C), one data signal (D), and two output ports: output port 1 is called transmitted port and output port 2 is called reflected port. When the only data signal enters into the TOAD, it splits into two components: clockwise (Dcw) and counter-clockwise (Dccw), experiences same high SOA gain, and recombines at the coupler. Therefore, no phase difference is introduced between them; the data signal comes out of the reflected port. When the control signal and data signal enter into the TOAD, the two components will experience a phase shift (can be adjusted to be π ) and data signal will pass to the transmitted port. Now equations of these two ports are [10]   Transmitted port = 0.25Pin ( G c (t) + G cc (t))2

(1)

  Reflected port = 0.25Pin ( G c (t) − G cc (t))2

(2)

where Gc (t) and Gcc (t) are the power gains. When control signal enters the TOAD, gain of the SOA decreases [10] ∆X

SOA

td

Control Signal, C

Dcw

Dccw

Data Signal

Output port 1 Filter

Output port 2 Filter

Fig. 1 TOAD-based switch

TOAD-Based Frequency-Encoded All Optical …

179

G(t) = exp[h(t)]

(3)

     E c (t) 1 exp − h(t) = − ln 1 − 1 − G0 Es

(4)

where h(t) is [11]

Es being saturation energy and E c (t), control pulse energy of the SOA. We have used the Soliton pulses as control inputs [10, 11] Pi (t) =

  (t − nχ ) an A,B Psoli sec h 2 1.763 τfwhm n=1

n=N 

(5)

2 Aeff λ3 Dm  where Psoli = 1.763 gives the Soliton peak power, Dm , the disper2 2π n 2 cτfwhm sion constant, n2 is the nonlinear refractive index coefficient, λ and c denote the wavelength and velocity of light, respectively, Aeff is the effective area of the fiber,τfwhm gives the full width half maximum, χ gives the bit period. E cp (t → ∞) = Psoli × τfwhm = E c , total control pulse energy. The control signal and data signal have different frequencies υ 1 or υ 2 for proper operation in co propagation scheme.

3 Frequency-Encoded XOR Gate for SUM Generation Frequencies υ1 and υ2 with corresponding wavelengths are 1550 nm and 1560 nm, respectively, denotes the states ‘0’ and ‘1’. Design of frequency-encoded XOR gate using TOAD as shown in Fig. 2. It has two inputs A, B and one output. It is consist of 7 TOADs, T 1 , T 2 , T 3 , T 4 , T 5 , T 6 , T 7 . The following is the operation of the XOR gate: Case (1): When input A is a signal of frequency υ 1 , the small portion of signals through the υ 1 pass filter makes the control input of the TOAD T 1 is υ 1 and rest of the signal passes through the υ 1 pass filter to make output of the TOAD T 5 to be υ 1 . In this condition, the control signal of the TOAD T 1 forces the data signal of frequency υ 2 transmitted through the port 1 of the TOAD T 1 and output of the TOAD T 1 is υ 2 . Similarly, when input B is a signal at υ 1 , the small portion of signals through the υ 1 pass filter makes the control input of the TOAD T 3 is υ 1 and remaining portion of the signal, through the υ 1 pass filter makes the output of the TOAD T 6 at υ 1 . In this condition, the control signal of the TOAD T 3 forces the data signal of frequency υ 2 transmitted through the port 1 of the TOAD T 3 and output of the TOAD T 3 is υ 2 . So both the outputs of TOAD T 5 and T 6 are signal frequency υ 1 , i.e., there is no control signal receives of TOAD T 7 . During the absence of control, the SOAs remains unsaturated, hence, the data signal of frequency υ 1 comes out at the port 2 of the TOAD T 7 thus the final output of the gate will be at frequency υ 1 , i.e., ‘LOW’.

180

K. Mukherjee et al.

A

BS ∆X

BS

SOA

υ1 pass filter

υ1 Filter

td

∆X

Control Dcw

SOA

Dccw

td

Filter

Dcw

∆X

Dccw

Filter

υ2

SOA

Filter

υ2 pass filter

td Control

Dcw

Filter

Dccw

BS

υ2

∆X

Filter

SOA

υ1 Filter

∆X

Filter

BS

B

Dcw

Dccw

td

SOA

υ1 pass filter

S/D

td

SOA

∆X

υ1

Dcw

Dccw

td Control Dcw

Dccw

Filter

υ2 Filter

Filter

Filter

Filter ∆X

Filter

SOA

υ2 pass filter

td Control

Dcw

Dccw

Filter

Filter

Fig. 2 Frequency-encoded SUM generation

Case (2): When input A is a signal of frequency υ 1 , the small portion of signals through the υ 1 pass filter makes the control input of the TOAD T 1 is υ 1 and rest of the signal passes through the υ 1 passing filter makes the output of the TOAD T 5 is υ1. In this condition, the control signal of the TOAD T 1 forces the data signal of frequency υ 2 transmitted through the port 1 of the TOAD T 1 and output of the TOAD T 1 is υ 2 . Similarly, when input B is at υ 2, the small portion of signals through the υ 2 pass filter makes the control input of the TOAD T 4 is frequency υ 2 and there is no signal receives of the TOAD T 6 . At this condition, there is no control signal present at the TOAD T 6 and the data signal of frequency υ2 is reflected through the port 2 of the TOAD T 6 and output of the TOAD T 6 becomes at frequency υ 2 . So the outputs of TOAD T 5 and T 6 are signal frequencies υ 1 and υ 2 , i.e., a signal passes through the υ 2 pass filter makes the output of the TOAD T 7 is frequency υ 2 thus the final output becomes at frequency υ 2 , i.e., ‘HIGH’. Case (3): When input B is a signal of frequency υ 1 , the small portion of signals through the υ 1 pass filter makes the control input of the TOAD T 3 at υ 1 and rest of the signal passes through the υ 1 passing filter makes the output of the TOAD T 6 is υ 1 . In this condition the control signal of the TOAD T 3 forces the data signal of frequency υ 2 transmitted through the port 1 of the TOAD T 3 and output of the TOAD T 3 is υ 2 . Similarly, when input A is at frequency υ 2 , the small portion of signals through the υ 2 pass filter makes the control input of the TOAD T 2 at frequency υ 2 and there is no signal receives of the TOAD T 5. At this condition, there is no control signal present of the TOAD T 5 and the data signal of frequency υ 2 is reflected through the port 2 of the TOAD T 5 and output of the TOAD T 5 is at υ 2 . So the outputs of TOAD T 6 and T 5 are signal at frequencies υ 1 and υ 2 , i.e., a signal passes through the υ 2 pass

TOAD-Based Frequency-Encoded All Optical …

181

filter makes the output of the TOAD T 7 at frequency υ 2 and thus the final output is at υ 2 , i.e., ‘HIGH’. Case (4): When input A is at frequency υ 2 , the small portion of signals through the υ2 pass filter makes the control input of the TOAD T 2 is υ 2 . In this condition the control signal of the TOAD T 2 forces the data signal of frequency υ 1 transmitted through the port 1 of the TOAD T 2 and output of the TOAD T 2 is υ 1 . Similarly, when input B is at frequency υ 2 , the small portion of signals through the υ 2 pass filter makes the control input of the TOAD T 4 is υ 2 . In this condition, the control signal of the TOAD T 4 forces the data signal of frequency υ 1 transmitted through the port 1 of the TOAD T 4 and output of the TOAD T 4 is υ 1. So both the outputs of TOAD T 2 and T 4 are signal frequency υ 1 and this signals passes through the υ 1 pass filter makes the output of the TOAD T 5 is υ 1 and TOAD T 6 is υ 1 . In this situation, there is no control signal receives of TOAD T 7 . As the control is absent, SOA gain is unsaturated; hence, the data signal of frequency υ 1 comes out at the port 2 of the TOAD T 7. This makes the final output at frequency υ 1 , i.e., ‘LOW’. Therefore, from the above discussions, we found the output becomes signals at frequencies υ 1 υ 2 υ 2 υ 1 which is the output of frequency-encoded XOR gate.

4 Frequency-Encoded AND Gate for Carry Generation Diagram of frequency-encoded AND gate as shown in Fig. 3 will be utilized for carry generation. It is consisting of only one TOAD-based switch. When both the inputs A and B are signals at frequency υ 1 , the small portion of signals passes through the υ 1 pass filter makes the control input of the TOAD at υ 1 and other portion of the signal from beam splitter makes the output of the TOAD at frequency υ 1 . At this condition, A

B

υ1 Filter ∆X SOA

AND / CARRY

td Control Signal

Dcw

Dccw

BS Filter Output port Filter

Fig. 3 Frequency-encoded carry generation

182

K. Mukherjee et al.

Table 1 Truth table of frequency-encoded half adder Input

Output (Y )

A

B

SUM = A ⊕ B

CARRY = AB

υ 1 (0)

υ 1 (0)

υ 1 (0)

υ 1 (0)

υ 1 (0)

υ 2 (1)

υ 2 (1)

υ 1 (0)

υ 2 (1)

υ 1 (0)

υ 2 (1)

υ 1 (0)

υ 2 (1)

υ 2 (1)

υ 1 (0)

υ 2 (1)

no signal is present at the port 2 of the TOAD. Therefore, the output of the gate is signal at frequency υ 1 . When input A is a signal at frequency υ 1 or υ 2 and input B is a signal of frequency υ 2 or υ 1 , small portion of signals through the υ 1 pass filter makes the control input of the TOAD at υ 1 and other portion of the signal passes through the beam splitter makes the output of the TOAD is signal of frequency υ 1 . At this condition, there is no signal present of the port 2 of the TOAD. Therefore, the output of this TOAD is at υ 1 . When both the input A and B are signal at frequencies υ 2 , there is no control signal receives of TOAD; hence, the data signal of frequency υ 2 comes out from port 2 of the TOAD making final output at frequency υ 2 .

5 Frequency-Encoded Half Adder Half adder is a device which can add two binary digit at a time and generates ‘SUM’ and ‘CARRY’ and for we use the XOR gate and AND gate described above (Table 1).

6 Frequency-Encoded Half Subtractor Half Subtractor is a device which can subtract two binary digit at a time generates ‘Difference’ and Operation of ‘Borrow’ generation: Case (1): When A is at frequency υ1, signal through the υ1 pass filter makes the control input of the TOAD T 1 is υ 1. In this condition, the control signal of the TOAD T 1 forces the data signal of frequency υ 2 to be transmitted through the port 1 of the TOAD T 1 and output of the TOAD T 1 is υ 2 and input B is a signal of frequency υ 1, the small portion of signals through the υ 1 pass filter makes the control input of the TOAD T 3 is υ 1 and other portion of the signal from beam splitter makes the output of the TOAD T 3 at frequency υ 1. At this condition, there is no signal present of the port 2 of the TOAD T 3 . Thus, the output of the TOAD T 3 is at frequency υ 1 , i.e., ‘LOW’. Case (2): If A is at frequency υ 1, the signal through the υ 1 pass filter makes the control input of the TOAD T 1 is υ 1. In this condition, the control signal of the TOAD

TOAD-Based Frequency-Encoded All Optical …

183

T 1 forces the data signal of frequency υ2 transmitted through the port 1 of the TOAD T 1 and output of the TOAD T 1 is υ 2 and B, a signal at υ 2, there is no signal goes to TOAD T 3 , hence the data signal of frequency υ 2 comes out of the port 2 of the TOAD making final output of the gate is at frequency υ 2 , i.e., ‘HIGH’ (Fig. 4). Case (3): Similarly, when A is at frequency υ 2, the signal through the υ2 pass filter makes the control input of the TOAD T 2 is υ 2. In this condition, the control signal of the TOAD T 2 forces the data signal of frequency υ1 transmitted through the port 1 of the TOAD T 2 and output of the TOAD T 2 is υ 1 and input B is at υ 1, the small portion of signals through the υ 1 pass filter makes the control input of the TOAD T 3 is υ 1 and other portion of the signal divided at the beam splitter makes output of TOAD T 3 is signal of frequency υ 1. At this condition, all signal are absent at port 2 in TOAD T 3 . Thus, the output of the TOAD T 3 is at frequency υ 1 . Case (4): When A is at frequency υ 2, the signal through the υ 2 pass filter makes the control input of the TOAD T 2 is υ 2. In this condition, the control signal of the TOAD T 2 forces the data signal of frequency υ1 transmitted through the port 1 of the TOAD T 2 and output of the TOAD T 2 is υ 1, the small portion of signals through the υ 1 pass filter makes the control input of the TOAD T 3 is υ 1 and other portion of the signal divided at beam splitter makes the output of the TOAD T 3 is signal of frequency υ 1 and input B is at υ 2 , and the final output is at frequency υ1 , i.e., ‘LOW’ (Table 2). ∆X SOA

υ1 pass filter

td Control Dcw

Dccw

Data Signal

υ2

Filter

A

∆X SOA

υ2 pass filter

td Control

Dcw

Dccw

Data Signal υ1 Filter

Filter

υ1 pass ∆X

passFilter

SOA

B td

Dcw

Borrow

Dccw

υ2 Filter

Fig. 4 Frequency-encoded BORROW generation

184

K. Mukherjee et al.

Table 2 Truth table of the frequency-encoded half subtractor Input

Output (Y )

A

B

DIFFERENCE = A ⊕ B

BORROW = AB

υ 1 (0)

υ 1 (0)

υ 1 (0)

υ 1 (0)

υ 1 (0)

υ 2 (1)

υ 2 (1)

υ 2 (1)

υ 2 (1)

υ 1 (0)

υ 2 (1)

υ 1 (0)

υ 2 (1)

υ 2 (1)

υ 1 (0)

υ 1 (0)

7 Simulation and Result For simulation performance of this TOAD-based switch, control pulse and incoming pulse both considered as a Soliton pulses. Figure 5 shows output bit patterns when the control pulse absent of the TOAD-based switch and when control pulse is present of the TOAD base switch. Input and output bit patterns of the XOR gate or sum/difference are shown in Fig. 6a–d for various conditions. When A is at frequency υ1 (1550 nm), input B is at υ1 ( 1550 nm), output power spectrum is signal of frequency υ1 as 1550 nm. When A is at υ 1 (1550 nn), input B is at υ 2 (1560 nm), output power spectrum is signal of frequency υ 2 as 1560 nm. When A is at frequency υ 2 (1560 nm), input B is at υ 1 as 1550 nm, output power spectrum is signal of frequency υ 2 as 1560 nm. When A is at frequency υ 2 (1560 nm), input B is at frequency υ 2 (1560 nm), output power spectrum is signal of frequency υ 1 as 1550 nm. Input and output power optical spectrums of AND or CARRY bit as shown in Fig. 7a–d. When the input A is at frequency υ 1 (1550 nm), input B is at frequency υ 1 (1550 nm), output is at frequency υ 1 as 1550 nm. When A is at frequency υ 1 (1550 nm), input B is at frequency υ 2 (1560 nm), output is at frequency υ 1 as 1550 nm.

Fig. 5 Output power of port 2 of the TOAD-based switch

TOAD-Based Frequency-Encoded All Optical …

a

185

Power spectrum of Input and output

1 0.9

Input A= u1 Input B=u1 Output u1

Power(a.u.)

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

b

Power spectrum of Input and output 1 0.9 Input A=u1

0.8

Input B=u2 Output u2

Power(a.u.)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

Fig. 6 a Input and output optical power spectrum when A = υ 1 and B = υ 1 b Optical power spectrum when A = υ 1 and B = υ 2 c Optical power spectrum when A = υ 2 and B = υ 1 d Optical power spectrum when A = υ 2 and B = υ 2

When A is at frequency υ 2 (1560 nm), input B is at frequency υ 1 (1550 nm), output is at frequency υ 1 as 1550 nm. When A is at frequency υ 2 (1560 nm), input B is at frequency υ 2 (1560 nm), output is at frequency υ 2 as 1560 nm. The optical spectrum of BORROW bit is shown in Fig. 8a–d. When A is at frequency υ 1 (1550 nm), input B is at υ 1 (1550 nm), output is at frequency υ 1 (1550 nm).

186

K. Mukherjee et al.

Power spectrum of Input and output

c 1 0.9

Input A=u2 Input B=u1 Output u2

0.8

Power(a.u.)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

Power spectrum of Input and output

d 1 0.9

Input A=u2

0.8

Input B=u2 Output u1

Power(a.u.)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

Fig. 6 (continued)

When A is a signal of frequency υ 1 (1550 nm), input B is at frequency υ2 (1560 nm), output is at frequency υ 2 as 1560 nm. Figure 8c shows the input and output optical power spectrums when A is at frequency υ 2 (1560 nm), B is at frequency υ 1 (1550 nm), output is at frequency υ 1. Figure 8d shows the input and output optical power spectrums when A is at frequency υ 2 (1560 nm) B is at frequency υ 2 (1560 nm), output is at υ 1 or wavelength 1550 nm. Table 3 shows the SOA parameter used in simulations [10, 11].

TOAD-Based Frequency-Encoded All Optical …

a

187

Power spectrum of Input and output

1

Input A=u1 Input B=u1 Output=u1

Power(a.u.)

0.8 0.6 0.4 0.2 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

b

Power spectrum of Input and output 1 Input A=u1 Input B=u2

0.8

Power(a.u.)

Output=u1

0.6 0.4 0.2 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

c

Power spectrum of Input and output 1 Input A=u2 Input B=u1 output=u1

Power(a.u.)

0.8 0.6 0.4 0.2 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

Fig. 7 a Optical power spectrum when A = υ 1 and B = υ 1 b Input and output optical power spectrums when A = υ 1 and B = υ 2 c Input and output optical power spectrums when A = υ 2 and B = υ 1 d Input and output optical power spectrums when A = υ 2 and B = υ 2

188

d

K. Mukherjee et al. Power spectrum of Input and output 1 Input A=u2 Input B=u2

Power(a.u.)

0.8

Output=u2

0.6

0.4

0.2

0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

Fig. 7 (continued)

ON−OFF ratio [12] is equal to the ratio of maximum output of the transmitted port 1 to the minimum output of the reflected port 2 and it is found to be 11.34 dB. The variation of ‘On–Off’ ratio with control pulse energy at different maximum gains (15 dB, and 20 dB) is shown in Fig. 9 and it is decreases with increases control pulse energy. The effect of ASE noise is added to TOAD-based switch and it is [11] Pase = N sp (G0 − 1) (hc/λ) × B0 , where h is the Planck’s constant, λ is the wave length, B0 is the bandwidth, c is the velocity of light, G0 is the unsaturated gain and N sp is ASE factor. Figure 10 depicts dependence of on–off ratio with ASE noise factor for different gains and it is almost constant with increase the amplified spontaneous noise factor.

8 Conclusions We have successfully designed and analyzed the frequency-encoded XOR gate, half adder, and half Subtractor. We also included the effect of ASE noise power in the TOAD-based switch. These designs will be extended to implement more complex devices like full adder and full subtractor in the future. This is the first time TOAD is utilized to design half adder and subtractor in frequency-encoded format.

TOAD-Based Frequency-Encoded All Optical …

a

Power spectrum of Input and output

1

Input A=u1

0.8

Power(a.u.)

189

Input B=u1 Output=u1

0.6 0.4 0.2 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

b

Power spectrum of Input and output

1

Input A=u1 Input B=u2

Power(a.u.)

0.8

Output=u2

0.6 0.4 0.2 0 1540

1545

1550

1555

1565

1560

1570

Wavelength(nm)

c

Power spectrum of Input and output

1

Input A=u2 Input B=u1

Power(a.u.)

0.8

Output=u1

0.6

0.4

0.2 0 1540

1545

1550

1555

1560

1565

1570

Wavelength(nm)

Fig. 8 a Optical power spectrum when A = υ 1 and B = υ 1 b Optical power spectrum when A = υ 1 and B = υ 2 c Optical power spectrum when A = υ 2 and B = υ 1 d Optical power spectrum when A = υ 2 and B = υ 2

190

d

K. Mukherjee et al.

Power spectrum of Input and output

1

Input A=u2 Input B=u2

Power(a.u.)

0.8

Output=u1

0.6

0.4

0.2

0 1540

1545

1555

1550

1560

1565

Wavelength(nm)

Fig. 8 (continued) Table 3 Parameters of SOA used in simulation Symbol

Parameter

Value

C

Velocity of light

3 × 108 m/s

I

Injection current

200 mA

G

Confinement factor

0.48

αN

Differential gain

3.3 × 10–20 m2

Nt

Carrier density at transparence

1.0 × 1024 m−3

W

Width(active region)

1.5 μm

D

Depth (active region)

250 nm

L

Length(active region)

150 μm

αD

Internal waveguide loss

2700 m−1

λ

Wavelength of light

1550 nm

te

Gain recovery time

90 ps

Ec

Control pulse energy

50 fJ

Tfwhm

Full width half maximum

1 ps

T

Eccentricity

20 ps

n2

Nonlinear coefficient

2.6 × 10–20 m2 /w

D

Dispersion constant

1 ps/(nm-km)

Aeff

Fiber effective area

5 × 10–13 m2

N sp

Spontaneous emission factor

2

1570

TOAD-Based Frequency-Encoded All Optical …

191

Fig. 9 Variation of on–off ratio with control pulse energy

Fig. 10 Variation of on–off ratio with N sp

References 1. K. Mukherjee, A. Raja, K. Maji, All-optical logic gate NAND using semiconductor optical amplifiers with simulation. J. Optics (Springer, 2019) 2. K. Mukherjee, A novel frequency encoded all optical logic gates exploiting polarization insensitive four wave mixing in semiconductor optical amplifier, filtering property of add/drop multiplexer and non linearity of reflective semiconductor amplifier. Optik 122(10), 891–895 (2011) 3. K. Mukherjee, Method of implementation of frequency encoded all optical half adder, half subtractor and full adder based on semiconductor optical amplifiers and add drop multiplexers.

192

K. Mukherjee et al.

Optik 122, 1188–1194 (2011) 4. K. Mukherjee, Semiconductor optical amplifier based frequency encoded logic gates exploiting nonlinear polarization rotation only. J. Circuits Syst. Comput. 23(09) (2014) 5. K. Mukherjee, All optical frequency encoded combinational logic devices utilizing polarization independent four-wave mixing in semiconductor optical amplifiers. J. Circuits Syst. Comput. 23(09) (2014) 6. K. Maji, K. Mukherjee, A. Raja, Frequency encoded all optical tri-state logic gates NOT and NAND using semiconductor optical amplifier based interferometric switches. Nanosci. Nanotechnology-Asia (2019). https://doi.org/10.2174/2210681209666190620110027 7. B. Ghosh, S. Hazra, N. Haldar et al., A novel approach to realize of all optical frequency encoded dibit based XOR and XNOR logic gates using optical switches with simulated verification. Opt. Spectrosc. 124, 337 (2018). https://doi.org/10.1134/S0030400X1803013X 8. K. Mukherjee, Method of implementation of frequency encoded all optical half adder, half subtractor and full adder based on semiconductor optical amplifiers and add drop multiplexers. Optik (2011) 9. D.K. Gayan,T. Chattopadhyay,A. Bhattacharyya, S. Basak, D. Dey, All-optical half-adder/halfsubtractor using terahertz optical asymmetric demultiplexer. Appl. Optics (2014) 10. K. Maji, K. Mukherjee, A. Raja, An alternative method for implementation of frequencyencoded logic gates using a terahertz optical asymmetric demultiplexer (TOAD).J. Comput. Electronics (2019). https://doi.org/10.1007/s10825-019-01393-5 11. K. Maji, K. Mukherjee, A. Raja, Performance of all optical logic Soliton based AND gate using Reflective Semiconductor Optical Amplifier (RSOA), Book chapter of Springer Lecture Notes in Electrical Engineering (LNEE), Book Series (2019). https://doi.org/10.1007/978-981-150829-5 12. J.K. Rakshit, J.N. Roy, T. Chattopadhay, Design of micro-ring resonator based all-optical parity generator and checker circuit. Optics Commun. 303, 30–37 (2013)

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array for Short Range THz Applications Mandeep Singh, Simranjit Singh, and Mohammad Tariqul Islam

Abstract In this chapter, a highly efficient and ultra-wideband MIMO patch antenna array are studied and analyzed for short-range sub terahertz wireless communications. The polyimide material with thickness 50 μm and a dielectric constant of 3.5 is used as the substrate material. First, a single octagonal shape patch antenna is developed from a rectangular shape patch antenna then such an octagonal antenna is optimized by using a genetic algorithm (GA) for the terahertz frequency range. The microstrip line feed with 50  impedance is used to feed the radiating patch for proper impedance matching between the source and load. Furthermore, to tackle the highly attenuated, path loss environment for the terahertz frequency range, a 4 × 2 MIMO patch antenna array is developed by using the proposed optimized antenna. From the measured results, it is found that the developed MIMO antenna array is resonating on 0.660 and 0.833 THz frequency with an effective −23.98 dB and −29.29 dB reflection coefficient, respectively. The developed antenna is efficiently covering 57.96% bandwidth. The optimized antenna has maximum directivity 9.77 dB and gain 8.28 dB within the resonance band. Also, the mutual coupling between the antenna element is low as the transmission coefficient and envelope correlation coefficient (ECC) is less than −14 dB and 0.01 between the respective MIMO antenna element. The proposed MIMO antenna array can be a good candidate for future short-range terahertz wireless applications. Keywords Terahertz · MIMO · Bandwidth · Antenna

M. Singh (B) · S. Singh Department of Electronics and Communications Engineering, Punjabi University Patiala, Patiala 147002, Punjab, India e-mail: [email protected] M. T. Islam Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia, 43600 Bangi, Malaysia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Biswas et al. (eds.), Emerging Trends in Terahertz Engineering and System Technologies, https://doi.org/10.1007/978-981-15-9766-4_10

193

194

M. Singh et al.

1 Introduction The modern world’s reliance on digital technologies and the use of high-speed internet in exchanging information, images, photographs, and videos has put a burden on the present microwave electromagnetic spectrum. New frequency bands are needed to meet customer requirements. It is continuously observed from the last three decades that wireless traffic is projected to be double every eighteen months [1]. The fifth-generation (5G) network is already moved to the millimeter waves to fulfill the demands of high-speed networks. According to the Federal Communications Commission (FCC), the millimeter-wave from 24 to 100 GHz has been allotted for 5G millimeter-wave-based communications. Recently, it is significantly noted that in developed countries like the USA, China, UK, Canada, and South Korea 5G networks based upon millimeter wave are already been established and under trials [2]. Following this trend, it is anticipated that sometime in the next five to ten years, sixth-generation (6G) wireless communications having data speed of Terabit-per-second (Tbps) connectivity will become a reality. So, to accommodate the upcoming demands of higher transmission speeds, FCC has already unlocked the spectrum around 95 to 3,000 GHz for innovative usage and unlicensed applications to encourage the advancement of new wireless communication systems [3]. There are some hurdles like atmospheric loss and molecular absorption loss at the THz regime for wireless communications. But for short-range or indoor wireless communications, the molecular absorption losses for distances far below 1 m seem to be almost negligible, and thus the THz band performs as a kind of 3 THz wide transmission window. Moreover, many resonances become significant for transmission distances of over 10 m, and the transmission windows become shorter. From the past experiments, it is observed that some low loss transmission windows like w1 = [0.38–0.44 THz], w2 = [0.45–0.52 THz], w3 = [0.62–0.72 THz], and w4 = [0.77–0.92 THz] can be a good option for future high-speed short-range wireless communication in the terahertz band. The influence of molecular absorption loss inside each transmission window is marginal, well under 10 dB/km [4, 5]. Nonetheless, the total path loss is very strong due to the scattering loss, which encourages the utilization of highly efficient antennas as well as advanced MIMO antenna system technologies. The significant disadvantage for the terahertz communications network is the atmospheric loss as already mentioned. As reported, to resolve this challenge, the high-power transmitters and efficient detectors need to be developed [5–7]. The planar antennas can play a revolutionary role to realize the terahertz shortrange wireless communications due to its significant properties like compact size, ease of fabrications, and low cost. Despite several advantages, it has some disadvantages like narrow bandwidth and low gain which can’t be considered in proper utilization of terahertz band for communications. But one can increase the gain, bandwidth, and efficiency of the antenna by deploying some techniques like slot inside patch, defected ground surface, use of multiple layers of substrate, etc. Also, the on-chip deployment of MIMO antenna array is only possible by utilizing the planar

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array …

195

antenna. Otherwise, it will be not possible by using horn antenna, lens antenna, and Yagi-Uda antenna [8, 9]. If we speak about the previous research, for several terahertz applications several researchers recorded terahertz antenna. Some of the most generally recognized terahertz antennas, to the best of the author ‘s knowledge, are mentioned here. Several researchers achieved a high degree of directness and gain by designing lens antenna, leaky-wave antenna, reflector-based antenna, and Yagi-Uda antenna but at the cost of a large, voluminous, and complex three-dimensional structure [10–16]. Because of their large and complicated configurations, compatibility of the these kinds of antenna with the on-chip processor is thus unlikely. So, the antenna researchers switch to planar antenna configuration with on-chip integration. Hossein. D and Behbod. G had developed a highly efficient wideband THz antenna having a bandwidth of 118% (0.434–1.684 THz) and a maximum gain of 5.72 dB [17]. Singh proposed a multiband antenna using a photonic band structure resonating at the THz frequency with a peak gain of 10.5 dB [18]. Mittal developed a planar antenna at 0.63 THz frequency by using the polyimide substrate and achieved 7.93 dB gain for defense applications [19]. Hocini et al. in Ref. [20] developed five THz patch antennas based on a modified photonic bandgap (PBG) substrate in the frequency range from 0.5 to 0.8 THz and obtained maximum 9.19 dB gain. Paul et al. proposed a compact size wideband antenna for THz band using PBG and DGS techniques at resonating frequency of 0.703 THz for THz applications and achieved a gain of 5.95 dB [21]. Azam et al. investigated the graphene patch antenna at resonating frequency of 6.8 THz, 6.94 THz, 7.1 THz, and 7.13 THz with a peak gain of 16.7 dB [22]. Jha et al. proposed a dual-band antenna resonating on 0.6 and 0.8 THz with peak gain 10.9 dB and bandwidth 11.6% [23]. Kushwaha et al. proposed a dual-band novel antenna using a photonic crystal with a peak gain of 7.94 dB and 10.1% bandwidth [24]. Zhou et al. [25] presented a tunable compact size antenna at 1.03 THz by using the graphene as the conducting patch and get 9.7% bandwidth. Anand et al. [26] proposed the antenna at 0.75 THz by using the graphene nanoribbon wires for tea hertz applications and achieved 5.09 dB gain with 6.67% bandwidth. Tamagone et al. [26] presented at reconfigurable THz antenna at resonance 0.8 THz and achieved radiation efficiency of 93%. Jha et al. [27] proposed a dual-band antenna by using the double-layer substrate technique with a peak gain of 7.968 dB. Cheng [28] increased the gain of an antenna by using epsilon-near-zero (ENZ) metamaterial superstrate and found that the peak gain of the antenna is increased from 5.37 to 7.79 dB. The numerous methodologies, such as PBG, electronics bandgap (EBG), DGS, multilayered structures, nanoribbon wires, and complex substrate content, are used to increase the antenna’s gain, bandwidth, and efficiency performance. From literature, it is found that mostly antennas are resonating on different bands, didn’t cover the low loss transmission window. Some are suffering from low gain, narrow bandwidth, large size. Also, most of the authors developed only the single antenna element for traditional single input single output communications systems but to realize the highspeed communications in the terahertz regime, there is a need to develop and analyze the MIMO antenna design.

196

M. Singh et al.

2 Design of Single Antenna Element for Terahertz Applications 2.1 Design of Proposed Single Antenna Element To develop the proposed terahertz planar antenna, a polyimide substrate material having a dielectric constant of 3.5 and height 50 μm is used. The copper with thickness of 2.1 μm is chosen as the conducting material. The dimension of rectangular patch is computed by using the equations below [29]. Here the length and width of the rectangular patch are calculated by using Eqs. (1–2) Pl =

(2N + 1) λ × − L √ εeff 2

(1)

(2N + 1) λ  × 2 εr +1

(2)

Pw =

2

where N is an integer, effective, and relative dielectric constants are given by εeff and εr, respectively. Also, the following expression may be used to measure the upper limit of substrate thickness h to mitigate the surface wave effect in the printed circuit board. λ h= √ 4 εr And the effective dielectric constant has been computed by using equation a εreff =

  h −1/2 εr + 1 εr − 1 + 1 + 12 2 2 Pw

(3)

And here due to fringing effect, the increase in length is given by using the following equation L = 0.412h

(εreff + 0.3)

 Pw

+ 0.264



  (εreff − 0.258) Phw + 0.8 h

(4)

The length (L f ) and width (F w ) of 50  transmission feed line is calculated by [30] Fw =

  9.5138h 1 √ − t 0.8 e λ(εeff + 1.41)/Pw

L f = (2M + 1) × λ/2

(5) (6)

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array …

197

Table 1 The various dimension of patch antenna developed for terahertz communications (μm) Sa

400

Pw

230.14

Sb

400

Ra

112.69

Sc

392.98

Rb

109.29

Sd

376.12

Fw

28.34

Pl

271.11

Fa

30.06

Here, M is an integer and h is the substrate thickness (Table 1).

2.2 Performance Evaluation of Proposed Antenna Here in this section, the different stages to develop a highly efficient and ultrawideband planar antenna are discussed. First, the low profile rectangular patch antenna, as shown in Fig. 1a, is developed by using the Eqs. (1–6). In the second, an octagonal patch is formed into rectangular shape planar antenna as shown in Fig. 1b. Furthermore, in the third stage to optimized the reflection coefficient and bandwidth of developed octagonal patch antenna, the genetic algorithm (GA) is used. The octagonal patch and ground plane are optimized to achieve the target values as shown in Fig. 1c. The CST microwave studio is used to design, optimize, and analyze the proposed antenna for terahertz communications. The time-domain analysis is done of terahertz antenna. The various performance parameters such as reflection coefficient, gain, antenna, and radiation efficiency are measured against frequency. Here in Fig. 2, the frequency versus reflection coefficient is plotted to evaluate the performance of antennas at three different stages. From the plot, it is clear that at first stage, antenna is resonating on the single narrow band at 0.822 THz and having a reflection coefficient −14.08 dB. So further in the second stage, the octagonal patch is developed from a rectangular patch antenna, and it is observed that the octagonal Ground Patch

(a) Computed Antenna Design A

(b) Developed Antenna Design B

(c) Optimized Antenna Design C

Fig. 1 Design and development of new DGS irregular octagonal shape patch antenna at terahertz

198

M. Singh et al.

Fig. 2 Reflection coefficient versus frequency

antenna has dual wideband resonating frequencies. The developed antenna at 2nd stage is resonating on 0.642 and 0.878 THz with a reflection coefficient −23.4 dB and −33.42 dB. The developed antenna at stage 2nd is covering 0.605 to 0.683 THz and 0.762 THz to 1 THz or it can be said that it has 12.14 and 27.08% bandwidth at the respective resonating band. Furthermore, to enhance the reflection coefficient and bandwidth, the GA is applied to the 2nd stage antenna. The 3rd final octagonal patch antenna is transformed into an elliptical octagonal patch antenna with the defected ground plane. Thus, the 3rd stage antenna has dual-band resonating with ultra-wide bandwidth. The 3rd stage proposed antenna is resonating on 0.658 and 0.858 THz with a reflection coefficient of −35.93 dB and −60.14 dB. Also, after applying the optimization algorithm, the bandwidth of the 3rd stage antenna enhanced and it is covering the entire band from 0.618 to 1 THz or can be said it is enhanced to 57.96%. Also, from Fig. 3, it is noted that the optimized patch antenna has high gain as compared to the 2nd stage patch antenna. Also, the other important parameters are analyzed and measured for various stages of terahertz patch antenna and are listed in Table 2. In Fig. 4, the surface current distribution of optimized patch antenna is shown for both the resonating frequency. From Fig. 4, it is noticed that for resonating frequency 0.658 and 0.858 THz, the maximum surface current density of 128 dBm A/m and 131dBm A/m is shown in the figures. To characterize the radiation character of the optimized antenna, in Fig. 5, a polar plot is plotted for both the resonating frequencies.

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array …

199

Fig. 3 Gain versus frequency Table 2 Measured performance parameters for terahertz antenna of Stage 1st, 2nd and 3rd Antenna design

Resonating frequency (THz)

Reflection coefficient (dB)

Radiation efficiency (%)

Gain (dB)

Directivity (dB)

Antenna at 1st stage

0.822

−14.08

69.8

7.43

8.85

Bandwidth (%) 8.91

Antenna at 2nd stage

0.642

−23.44

75.42

4.13

5.32

12.14

0.878

−33.62

72.45

6.84

8.22

27.08

Antenna at 3rd stage

0.658

−35.93

75.14

4.38

5.62

57.96

0.858

−60.14

72.85

7.13

8.49

(a) Surface current density at 0.65THz

(b) Surface current density at 0.85THz

Fig. 4 Surface current distribution for elliptical octagonal patch antenna at both resonating frequency

200

M. Singh et al. E-Plane H-Plane

0 330

Gain (dB)

0

300

-20 270

0

90

-10 0 10

240

330

10

60

-10

120

300

60

-20 270

90

-10 0

240

120 210

150

150 180

180

(a) Polar plot for 3rd stage developed planar antenna at 0.65THz

30

-10

10

210

E-Plane H-Plane

0

Gain (dB)

10

30

(b) Polar plot for 3rd stage developed planar antenna at 0.85THz

( )

Fig. 5 Radiation pattern for optimized patch antenna at dual bands

3 MIMO Antenna for THz Applications 3.1 Design of 4 × 2 MIMO Antenna Array for Short-Range Wireless Terahertz Wireless MIMO antenna communications system could provide an effective solution to the multi-path issue by generating additional signal pathways. Here, MIMO antenna system mainly consists of multiple antennas and multiple signal paths to acquire communication channel knowledge. By using a communication link’s spatial dimension, MIMO systems can achieve significantly higher data rates than traditional single input single output (SISO) communication channel [31]. In this section, the 4 × 2 MIMO antenna is designed for terahertz applications. In Section ii, the various stages to develop a highly efficient and wideband antenna are being discussed and analyzed. So, the optimized antenna element of 3rd stage is being used to design the 4 × 2 MIMO antenna array. Here in this arrangement, the eight radiating elements are designed on a single substrate having dimensions (800 × 1600 × 50) μm as shown in Fig. 6. The performance of the MIMO antenna array arrangement is analyzed based upon their various performance parameters like the reflection coefficient, diversity gain, transmission coefficient. From Fig. 7, it is noted that each element of MIMO antenna array is resonating on 0.658 and 0.846 THz frequencies. Also, the mutual coupling between the antenna elements is plotted in Figs. 8 and 9. It is noted that the transmission coefficient between the respective antenna elements is less than −13 dB. which is acceptable for the efficient working of MIMO antenna system. Diversity gain and ECC are investigated to test the MIMO antenna array’s diversity capabilities. The ECC is used to evaluate the correlation between symmetric antenna components. To get a higher value of diversity between the MIMO antenna components, ECC values between the symmetric element must be small. The ECC is determined using Eq. (7) based on S-parameters and takes into account the form

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array … Port 1

Port 2

Port 8

Port 7

Port 3

Port 6

201 Port 4

Port 5

Reflection Coefficient (dB)

Fig. 6 4 × 2 Proposed MIMO antenna array for terahertz communications

Frequency (THz)

Fig. 7 Reflection coefficient versus frequency of MIMO antenna

of the radiation pattern, the polarization, and the relative phase between two antenna elements in a MIMO system [32]. From Fig. 10, it is clear that the values of ECC for ECC(1,2), ECC(1,3), ECC(1,4), ECC(1,5), ECC(1,6), ECC(1,7), ECC(3,8), ECC(4,8), and ECC(6,8) are less than 0.001, which is acceptable for working on two independents antenna on a single substrate (7).

M. Singh et al.

Transmission Coefficient

202

Frequency (THz)

Transmission Coefficient (dB)

Fig. 8 Transmission coefficient versus frequency of MIMO antenna

Frequency (THz) Fig. 9 Transmission coefficient versus frequency of MIMO antenna

 2  ∗  sii si j + s ∗ji s j j  2       pi j =  1 − sii |2 +s ji |2 1 − s j j |2 +si j |2

(7)

sij is the coupling factor between the ij th and jith elements used pi2j is the envelop correlation coefficient The diversity gain is being used to evaluate the MIMO antenna system’s diversity performance. The relationship between the gain in diversity and ECC is provided by using the equation below (8).

203

ECC

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array …

Frequency (THz)

Fig. 10 ECC versus frequency of MIMO antenna

 DG = 10 ×

1 − |ECC|2

(8)

dB

In Fig. 11, the MIMO antenna array’s diversity gain is plotted and found that it has an approximately constant value of 10 dB all across the band. In parallel, the MIMO antenna gain and directivity are plotted in Fig. 11 which shows that at resonating frequency 0.825 THz, it has the highest gain and directivity value that can be more useful in deeply attenuated situations.

Frequency (THz)

Fig. 11 Directivity, diversity gain and gain versus frequency of proposed MIMO antenna array

204

M. Singh et al.

4 State-of-Art-of Comparison In this section, the comparisons between the proposed optimized antenna with the previously reported antennas are done for terahertz applications as listed in Table 3. The comparison is done based on performance parameters like resonating bands, radiation efficiency, gain, bandwidth, and size of the antenna elements, see Table 3. In Ref. [17, 19, 21, 25, 26] the reported antennas are resonating on a single band and suffering from low gain and narrow bandwidth so these antennas are not a suitable candidate for wideband short wireless terahertz communications. On the other hand, the antennas reported in [18, 22, 24, 28] are resonating on multiple bands and having efficient gain but these antennas didn’t cover the important low loss terahertz transmission windows, so these are not a suitable for terahertz applications. In Ref. [20], the reported antenna is claiming the wide bandwidth and high gain but such antenna is resonating on a single band, also the size of the antenna is large as Table 3 Performance comparison between the proposed antenna and previously reported antennas Reference

Resonating frequency (THz)

Radiation efficiency (%)

Maximum Gain (dB)

Bandwidth (%)

Size MIMO (L × W × configuration H)μm3

[17]

1.65

77.5

5.72

118

150 × No 150 × 9.6

[18]

0.96, 1.28, 1.43, 1.56

–

11.01

51.88

950 × 950 No × 185

[19]

0.67

–

5.2

5.97

208.90 × 422 × 20

No

[20]

0.65

87.73

9.19

46.15

600 × 600 × 90

No

[21]

0.704

–

5.090

3.78

180 × 510 × 10

No

[22]

6.8,6.94 7.1,7.13

–

8.92,12.5, 14.3, 16.7

–

24 × 24 × 0.0485

No

[23]

0.6, 0.8

96.1, 95.7

10.9, 9.13

8.33, 3.33

500 × 500 × 50

No

[24]

1.03

10

–

9.7

–

No

[25]

0.75

86.58

5.09

6.67

208.98 × 433.2 × 20

No

[26]

0.8

20

–

–

–

No

[27]

0.6, 0.542

71.98,73.12

7.968

–

400 × 410 No × 400

[28]

1.85

78.55

7.88

3.78

–

No

Proposed optimized antenna

0.658 0.858

75.14 72.85

8.28

57.96

400 × 400 × 50

Yes

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array …

205

compared to the proposed antenna. The antenna reported in Ref. [23] has resonance on dual-band with high gain and efficiency but having low bandwidth as compared to propose optimized antenna. From Table 3, it is clear that the proposed antenna is providing better performance as compared to the previously reported terahertz antenna. The optimized antenna is resonating on dual-band and covering the entire bandwidth from 0.61 to 1 THz of the terahertz regime. The entire band has a high constant value of radiation and antenna efficiency over the resonance. Moreover, many researchers have developed only the single antenna for terahertz communications, didn’t characterize the MIMO antenna system for proposed geometry.

5 Conclusion This chapter is having research-oriented content of the design of MIMO antenna for THz applications. In this chapter, we have presented a new dual wideband optimized MIMO patch antenna array that is developed for terahertz indoor wireless applications. This research is focused to design a low profile, highly efficient, easy to fabricate, wideband, and high gain planar MIMO antenna. The proposed antenna is resonating on 0.65 and 0.85 THz band having −35 dB and −60.14 dB reflection coefficient, so very low power is reflected back. The antenna will be fully utilized the input power. Such antenna attained 8.41 dB maximum gain and 70.01% antenna efficiency. Furthermore, there is a requirement of the MIMO antenna system to tackle the multiple losses in the terahertz environment so a 4 × 2 MIMO antenna is developed and analyzed. The developed MIMO antenna system has same resonance character as that of the optimized antenna when eight antenna elements are arranged on a single substrate. The developed MIMO antenna has less than −13 dB values of transmission coefficient and less than 0.01 dB values of ECC between respective antenna elements. The proposed MIMO antenna array can be a good candidate for on-chip devices for next-generation wireless short-range communications.

6 Acknowledements The authors would like to acknowledge the Visvesvaraya Ph.D. scheme, Meity (India) and Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India and for financial support under grant number EEQ/2019/000,115.

206

M. Singh et al.

References 1. J. Ma, R. Shrestha, J. Adelberg, C. Yeh, Z. Hossain, E. Knightly et al., Security and eavesdropping in terahertz wireless links. Nature 563(7729), 89–93 (2018) 2. Home—5G Americas [Internet]. 5G Americas (2020), https://www.5gamericas.org/. Accessed 7 Aug 2020 3. FCC Opens Spectrum Horizons for New Services & Technologies [Internet]. Federal Communications Commission (2020), https://www.fcc.gov/document/fcc-opens-spectrum-horizonsnew-services-technologies. Accessed 7 Aug 2020 4. S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther et al., Wireless sub-THz communication system with high data rate. Nat. Photonics 7(12), 977–981 (2013) 5. I. Akyildiz, J. Jornet, C. Han, Terahertz band: Next frontier for wireless communications. Phys. Commun. 12, 16–32 (2014) 6. K. Jha, G. Singh, Terahertz planar antennas for future wireless communication: A technical review. Infrared Phys. Technol. 60, 71–80 (2013) 7. M. Tamosiunaite, S. Tamosiunas, M. Zilinskas, G. Valusis, Atmospheric attenuation of the terahertz wireless networks, in Broadband Communications Networks—Recent Advances and Lessons from Practice, ed. by A. Haidine, A. Aqqal (IntechOpen, 2017) 8. H. Kim, W. Choe, J. Jeong, A Terahertz CMOS V-Shaped Patch Antenna with Defected Ground Structure. Sensors 18(8), 2432 (2018) 9. K. Jha, G. Singh, Patch array antenna on EBG substrate, In Terahertz Planar Antennas for Next Generation Communication, ed. by K. Jha, G. Singh. 1st ed. Switzerland: Springer international publishing (2014), pp. 39–58. 10. K. Mak, K. So, H. Lai, K. Luk, A Magnetoelectric Dipole Leaky-Wave Antenna for MillimeterWave Application. IEEE Trans. Antennas Propag. 65(12), 6395–6402 (2017) 11. F. Formanek, M. Brun, T. Umetsu, S. Omori, A. Yasuda, Aspheric silicon lenses for terahertz photoconductive antennas. Appl. Phys. Lett. 94(2), 021113 (2009) 12. L. Guo, F. Huang, X. Tang, A novel integrated MEMS helix antenna for terahertz applications. Optik 125(1), 101–103 (2014) 13. K. Wu, Y.J. Cheng, T. Djerafi, W. Hong, Substrate-integrated millimeter-wave and terahertz antenna technology. Proc. IEEE 100(7), 2219–2232 (2012) 14. Y. Sirmaci, C. Akin, C. Sabah, Fishnet based metamaterial loaded THz patch antenna. Opt. Quant. Electron. 48(2) (2016) 15. K. Han, T. Nguyen, I. Park, H. Han, Terahertz Yagi-Uda antenna for high input resistance. J. Infrared Millim. Terahertz Waves (2009) 16. A. Gonzalez, K. Kaneko, T. Kojima, S. I. Asayama, Y. Uzawa, Terahertz corrugated horns (1.25–1.57 THz): design, gaussian modeling, and measurements. IEEE Trans. Terahertz Sci. Technol. 7(1), 42–52 (2017) 17. H. Dabadifarahani, B. Ghalamkari, High efficiency miniaturized microstrip patch antenna for wideband terahertz communications applications. Optik 194, 163118 (2019) 18. A. Singh, S. Singh, A trapezoidal microstrip patch antenna on photonic crystal substrate for high speed THz applications. Photonics Nanostruct Fundam. Appl. 14, 52–62 (2015) 19. R. Kushwaha, P. Karuppanan, L. Malviya, Design and analysis of novel microstrip patch antenna on photonic crystal in THz. Phys. B 545, 107–112 (2018) 20. A. Hocini, M. Temmar, D. Khedrouche, M. Zamani, Novel approach for the design and analysis of a terahertz microstrip patch antenna based on photonic crystals. Photonics Nanostruct Fundam. Appl. 36, 100723 (2019) 21. L. C. Paul, M. Islam, Proposal of wide bandwidth and very miniaturized having dimension of μm range slotted patch THz microstrip antenna using PBG substrate and DGS, in 20th International Conference of Computer and Information Technology, ICCIT (2017), pp. 1–6 22. S. Azam, M. A. K. Khan, et al., Graphene based circular patch terahertz antenna using novel substrate materials, in 2017 6th International Conference on Informatics, Electronics Vision, 2017 7th International Symposium in Computational Medical and Health Technolog ICIEVISCMHT (2018), pp. 1–6

Highly Efficient Ultra-Wide Band MIMO Patch Antenna Array …

207

23. K. Jha, G. Singh, Dual-band rectangular microstrip patch antenna at terahertz frequency for surveillance system. J. Comput. Electron. 9(1), 31–41 (2009) 24. T. Zhou, Z. Cheng, H. Zhang, M. Le Berre, L. Militaru, F. Calmon, Miniaturized tunable terahertz antenna based on graphene. Microw. Opt. Technol. Lett. 56(8), 1792–1794 (2014) 25. S. Anand, D. Sriram Kumar, R. Wu, M. Chavali, Graphene nanoribbon based terahertz antenna on polyimide substrate. Optik 125(19), 5546–5549 (2014) 26. M. Tamagnone, J. Gómez-Díaz, J. Mosig, J. Perruisseau-Carrier, Reconfigurable terahertz plasmonic antenna concept using a graphene stack. Appl. Phys. Lett. 101(21), 214102 (2012) 27. K. Jha, G. Singh, Analysis and design of rectangular microstrip antenna on two-layer substrate materials at terahertz frequency. J. Comput. Electron. 9(2), 68–78 (2010) 28. M. Shalini, M. Madhan, Design and analysis of a dual-polarized graphene based microstrip patch antenna for terahertz applications. Optik 194, 163050 (2019) 29. M. Rabbani, H. Ghafouri-Shiraz, Size improvement of rectangular microstrip patch antenna at MM-wave and terahertz frequencies. Microw. Opt. Technol. Lett. 57(11), 2585–2589 (2015) 30. R. Garg, Microstrip Antenna Design Handbook (Artech House, Boston, 2001). 31. M. Irshad Khan, M. Khattak, S. Rahman, A. Qazi, A. Telba, A. Sebak, Design and Investigation of Modern UWB-MIMO Antenna with Optimized Isolation. Micromachines 11(4), 432 (2020) 32. Y. Usha Devi, M. T. Boddapati, T. Anil Kumar, Ch. K. Sri Kavya, P. Pardhasaradhi, Conformal printed MIMO antenna with DGS for millimeter wave communication applications. Int. J. Electron. Lett. 1–15 (2019)

Ga2 O3 Based Heterostructure FETs (HFETs) for Microwave and Millimeter-Wave Applications R. Singh, T. R. Lenka, D. Panda, R. T. Velpula, B. Jain, H. Q. T. Bui, and H. P. T. Nguyen

Abstract The rapid development of the power electronic devices over the last few decades to cater demands of ever increasing wireless communication technologies, traditional as well as new military applications, and many more, have been further fueled by work-from-home (WFH) due to unprecedented global pandemic COVID19. These high frequencies and high-power applications have necessitated the introduction and development of wide bandgap semiconductors over the period because of their suitable material properties. However, these wide bandgap materials, such as silicon carbide (SiC) and gallium nitride (GaN), based device technologies have already extended their cycle of development and optimization due to various reasons. Moreover, still facing critical challenges like producing large-size, cost-effective, and high-quality substrates. In the quest of better material properties suitable for highvoltage and high-frequency applications, a new ultra-wide bandgap (UWB) semiconductor material gallium oxide (Ga2 O3 ), although studied and reported way back in mid of twentieth century, has attracted research community only in last few years as a supplement to existing silicon carbide (SiC) and gallium nitride (GaN) technologies. Ga2 O3 is an ultra-wide bandgap (UWB) semiconductor having different crystal structures with energy bandgap values up to 5.3 eV, and bulk crystals can be grown using melt-growth techniques which facilitate the availability of large-size, cost-effective, single-crystal substrates. Gallium oxide crystallizes into five different structures: monoclinic, rhombohedral, defective spinel, cubic, and orthorhombic structures, and represented as β-, α-, γ-, δ-, and ε-Ga2 O3, respectively. Among these R. Singh · T. R. Lenka (B) Department of Electronics and Communication Engineering, National Institute of Technology Silchar, Silchar, Assam 788010, India e-mail: [email protected] R. Singh e-mail: [email protected] D. Panda School of Electronics, VIT-AP University, Amaravati, Andhra Pradesh 522237, India R. T. Velpula · B. Jain · H. Q. T. Bui · H. P. T. Nguyen Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102, USA © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Biswas et al. (eds.), Emerging Trends in Terahertz Engineering and System Technologies, https://doi.org/10.1007/978-981-15-9766-4_11

209

210

R. Singh et al.

Ga2 O3 polymorphs, β-Ga2 O3 is most thermally stable and widely studied as well as reported. Apart from an edge on high-quality native-substrate over existing GaN technology, β-Ga2 O3 offers other promising features relating to power device applications, such as large bandgap of 4.9 eV and critical electric field up to 8 MV/cm. This high critical electric field enables significant improvement in the performance of the β-Ga2 O3 based high-voltage Schottky rectifiers and enhancement mode (e-mode) metal–oxide–semiconductor field-effect transistors (MOSFETs) over SiC and GaN power devices. Nonetheless, β-Ga2 O3 also faces some issues such as relatively low electron mobility that limits DC and on-state performance, the high thermal resistance of the material requires device level thermal management and absence of p-type doping restricts device structure types. In this chapter the overview of state-of-the-art β-Ga2 O3 technologies as a supplement to existing SiC or GaN counterparts with a perspective on the growth and development of β-Ga2 O3 heterostructure is presented. The device design, microwave, and millimeter-wave (mmW) performance as well as challenges are also presented. Keywords FET · Gallium oxide · Heterostructure · Microwave · Millimeter-wave · Ultra-wide bandgap

1 Introduction Apart from the new addition of power generation capacity to match ever increasing worldwide energy demands, improving efficiency of power devices is equally important as it enables a significant reduction of power consumption in a wide variety of power converters. More matured silicon (Si) technology hugely underperforms on this front since most of the power consumed in intermediate processing. Over the years, wide bandgap semiconductors such as SiC and GaN have been explored and are currently in the development stage for commercial usage, for high-power and highfrequency power devices due to their suitable material properties [1]. However, some critical issues like producing high-quality, large-size native-substrate still remains a challenge in GaN technology [2]. Furthermore, new application areas like electric vehicles (EV) and automation require introduction of new semiconductor devices capable to operate at multiple kVs [3]. Recently, research community for high-voltage applications has shown great interest in UWB semiconductors like Ga2 O3 , AlN, and diamond [1]. Table 1 shows the UWB physical properties together with those for wide bandgap semiconductor, GaN. Considering major properties of these UWB materials suitable for practical applications, Ga2 O3 emerges as the ultimate choice and looks promising for future power device applications. Out of the five different phases of Ga2 O3 , β phase of Ga2 O3 with monoclinic structure is the most thermally stable and widely studied as well as reported [4–8]. It has large energy bandgap values, between 4.5 to 4.9 eV as reported in [9–11]. These values are much larger than those for wide bandgap semiconductors SiC (3.3 eV) and GaN (3.4 eV). Due to the large bandgap, the estimated

Ga2 O3 Based Heterostructure FETs (HFETs) for Microwave …

211

Table 1 Comparative material properties of UWB semiconductors Properties

GaN

AlN

Diamond

β-Ga2 O3

Energy band gap, E g (eV)

3.4

6

5.5

4.5–4.9

10–10

10–34

10–27

10–24

Electric breakdown field, E BR (MV/cm)

3.3

6

5

8

Relative dielectric constant, εr

9.0

8.5

5.7

10

Intrinsic carrier concentration, ni

Electron mobility, μn

(cm2

(cm−3 )

2000

300

2200

200

Saturation velocity, vsat (107 cm/ s)

/V s)

2.0–2.5

1.5

2.7

2.0

Thermal conductivity, k(W/cm K)

1.3

2.85

20

0.27 (010)

JFoMSi , (vsat E MAX / 2π)

27.5

36

45.7

40

BFoMSi (μn εr E MAX 3 )

1503

1280

3645

2380

BHFFoMSi (μn E MAX 2 )

179.2

89

453

105

breakdown electric field in β-Ga2 O3 is up to 8 MV/cm [12]. The high breakdown field facilitates optimization of vertical power devices with thinner drift region and lower on-resistance and reduced conduction losses [13]. Therefore, β-Ga2 O3 looks promising material for at least certain classes of power electronics, currently non-accessible with SiC and GaN, if not capable to replace them fully [1–3]. For high-voltage unipolar devices, different figure of merits (FoMs): Johnson (JFoM), Balliga (BFoM), and BHFFoM for low and high frequency, respectively, also indicate its superior RF performance and are shown in Table 1. Although, maturity of process technology may take a long time, β-Ga2 O3 based electronic devices have already shown promising results vis-à-vis DC and RF performance. The β-Ga2 O3 high-voltage Schottky rectifiers with breakdown voltage up to 3 kV employ field-plate technology and low on-resistance (RON ) [14], FETs with I ON /I OFF in the range of 106 –1010 and carrier mobility upto 100 cm2 /Vs, maximum drain current of 700 mA/mm [12, 15–19], modulation-doped FETs (MODFETs) with electron mobility of 180 cm2 /Vs at 300 K [20]. More recently, AlN/β-Ga2 O3 highelectron-mobility transistor (HEMT) resulting in maximum achievable drain current of 11 A/mm, peak transconductance of 0.9 S/mm, intrinsic unity current gain cut-off frequency f T of 166 GHz, maximum frequency of oscillation f MAX of 292 GHz, and X-band output power POUT of 2.91 W/mm [21], has been reported. Looking at these promising results of β-Ga2 O3 devices, it is expected that it could outperform existing GaN technology for high-power RF device applications in low frequency regime [22]. In this work, we focus on key physical properties of β-Ga2 O3 covering crystal structure and anisotropic properties, potential capabilities, defects, impurities, and scattering phenomena concerning intrinsic mobility, in addition to, latest progress of β-Ga2 O3 based heterostructures with a focus on evolution of β-Ga2 O3 HEMT and their RF performance. Finally, the outlook of the β-Ga2 O3 HEMTs for potential microwave and millimeter-wave applications is also analyzed.

212

R. Singh et al.

2 Properties of β-Ga2 O3 Apart from large bandgap of 4.9 eV, what makes β-Ga2 O3 most competitive and compelling for power device applications is availability of inexpensive, large-size, and high-quality single-crystal substrates. Also, latest advances in β-Ga2 O3 bulk crystal growth bring to the table renewed interest in Ga2 O3 , and remain as a key driver for its potential applications in power electronics. These bulk substrates can be grown using economical melt-growth techniques: Czochralski (CZ), floating-zone (FZ) and edge-defined film-fed growth (EFG) [23–26]. In addition, experimental, βGa2 O3 devices have shown high breakdown field of 3.8 MV/cm [16], saturation velocity vsat ~1.1 × 107 cm/s [27], and reasonable carrier mobility ~180 cm2 /Vs [20]. Owing to these properties, β-Ga2 O3 based power devices can offer reasonable advantages in terms of size, weight, and output delivery power. Concerning β-Ga2 O3 electronic and structural properties, most of the earlier studies [28–31] used density functional theory (DFT), largely due to difficulty in isolation of different Ga2 O3 polymorphs in crystalline form, to calculate its electron effective mass, lattice, and structural parameters, and reported β-Ga2 O3 band structure. The β-Ga2 O3 band structure has conduction band minima (CBM) at the center and almost flat balance band which suggests large effective mass for holes [28, 29]. The effective mass of electron, largely responsible for transport properties, was reported ~0.342m0 , where m0 is electron rest mass [28]. Anionic (O-2p with Ga-3d and -4s states) and cationic (Ga-4s states) constitute the valence band top and conduction band bottom, respectively. As valence band states are made up of O-2p states and are slightly dispersed, resulting in large effective mass for holes and high valence band densities of states. Therefore, p-type conduction either intrinsic or extrinsic does not look feasible due to the tendency of holes to form localized polarons alias self-trapped holes (STHs) [32], and due to deep acceptor dopants with ionization energy levels higher than 1 eV. However, some groups demonstrated the p-type conductivity in Ga2 O3 : p-type Ga2 O3 based nanowires using nitrogen and zinc as acceptor dopants [33, 34]; by manipulating hydrogen incorporation in the lattice [35], and by finding Ga-vacancy as possible acceptor [36]. On the other hand, wide variety of intentional n-type dopants like Si, Ge, and Sn for both β-Ga2 O3 bulk crystals and epitaxial films are available with very controllable carrier concentrations ranging from 1016 to 1020 cm−3 [10, 11, 37, 38]. To date, EFG has been proved as most successful technique for growing β-Ga2 O3 bulk crystals, and conductive as well as semi-insulating (S.I.) wafer sizes up to 4 inch diameter are commercially available from novel crystal technologies [1]. EFG grown bulk β-Ga2 O3 crystals have major impurities like Si, Ir, and Fe originated from the crucible and primary source material. This unintentional doping causes background n-type conductivity which can be compensated by adding deep acceptors like Fe and Mg to obtain semi-insulating β-Ga2 O3 bulk [39]. In the crystal structure of β-Ga2 O3 , each unit cell contains two inequivalent gallium and three inequivalent oxygen ions commonly mentioned as Ga(I) , Ga(II) , and O(I) , O(II) , O(III) , respectively. Due to this low symmetry of β-Ga2 O3 crystal,

Ga2 O3 Based Heterostructure FETs (HFETs) for Microwave …

213

it shows anisotropic physical, electrical, and optical properties. For example, [010] oriented β-Ga2 O3 crystal has thermal conductivity of 0.27 W/cm K while 0.1 W/cm K along [100] direction [40], as shown in Fig. 1. It is observed that for various device applications, different orientations of β-Ga2 O3 crystal like [2 01], [010], and [001] are commonly used, and also EFG grown [010] crystal planes can be cut to obtain crystal with [2 01] orientation. Figure 2 shows β-Ga2 O3 crystal and bulk in different directions [3]. This practical aspects has rendered growing III-nitrides (GaN, AlN, and InN) epitaxial layers on [2 01] β-Ga2 O3 possible and can further facilitate the formation of potential heterostructures between AlN and β-Ga2 O3 enabled by low lattice mismatch of 2.4% [41] between the two. Earlier few research groups [41, 42] have demonstrated growth of GaN and AlN epi-layers on β-Ga2 O3 and also calculated conduction and valence band offset (CBO and VBO) due to band bending at the interface. Very recently, Singh et al. [21] reported highly scaled novel designed AlN/β-Ga2 O3 HEMT and achieved improved RF performances: intrinsic current gain cut-off frequency (f T ) of 166 GHz and X-band output power (POUT ) of 2.91 W/mm at 10 GHz using 2D device simulations.

Fig. 1 Thermal conductivity of β-Ga2 O3 along different crystal directions, figure adopted from Ref. [40]

214

R. Singh et al.

Fig. 2 β-Ga2 O3 crystal structure and bulk growth, a (010) and (201) surfaces, b EFG grown single crystal, figures adopted from Refs. [2, 3]

3 Defects, Scattering, and Transport Properties in β-Ga2 O3 It is widely accepted that crystal defects negatively affect the power device performance, and largely leads to increased leakage current and decreased breakdown voltage. Both issues are more pronounced in vertical devices as increased current demands larger device area enclosing a larger number of defects or dislocations. Therefore, defect densities should be at an insignificant level using improved process technologies. Currently, defect densities in β-Ga2 O3 crystals grown using meltgrowth methods are limited to 103 /cm3 . Nakai et al. [43] reported two types of defects in EFG grown [010] β-Ga2 O3 wafer as dislocations and nanopipes using X-ray topography, transmission electron microscopy (TEM), and selective etching. Screw dislocations with burgers vector parallel to [010] near the wafer surface, and nanopipes of diameter ~0.1 μm and length ~15 μm along [100] were found. These defects resulted in different pits of dimensions 2 and 10 μm, and density 102 and 106 cm−3 , respectively. Subsequently, Hanada et al. [44] identified groove-shaped void defects of length varying from 50–1200 nm in [001] and 40 nm in [100] β-Ga2 O3 un-etched single crystal. Furthermore, Kasu et al. [45] also investigated different shapes of etch pits and named them as type-A to F. Among these pits, type-A etch pit (changes to B, C, and D during etching) was considered as a void defect as it contains void in the center, whereas type-E as well as type-F pits (unchanged during etching) contain a core and hence named as dislocations. In β-Ga2 O3 Schottky barrier diodes (SBDs), between the void- and dislocation-type defects, only the former along the [100] plane were anticipated responsible for leakage current path.

Ga2 O3 Based Heterostructure FETs (HFETs) for Microwave …

215

As electron mobility in β-Ga2 O3 based experimental devices is comparatively low and reported in the range of 60 to 200 cm2 /Vs at room temperature. Earlier this variation in electron mobility was interpreted as due to anisotropy in electron effective mass [10]. However, subsequent theoretical studies [26, 38, 46–49] suggested almost isotropic conduction band effective mass. So different mechanism affecting transport properties is of critical importance for relatively new and immature βGa2 O3 semiconductor. The first-principles study was reported to explain the scattering mechanism considering the role of polar and non-polar optical phonons, and ionized impurities. Parisini et al. [50] suggested non-polar optical (NOP) phonons scattering as the main mechanism in β-Ga2 O3 crystals and estimated lattice deformation potential of about 4 × 109 eV/cm. However, subsequent reports [51–53] advocated and suggested polar optical (PO) phonon with energy between 21 and 48 meV scattering as most likely scattering phenomena in β-Ga2 O3 limiting room temperature electron mobility of