Semiconductors - Basic Data [2, Revised] 9783642976773, 9783642976759

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Otfried Madelung (Editor) Semiconductors - Basic Data

Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo

Otfried Madelung (Editor)

Semiconductors Basic Data 2nd revised Edition

With 359 Figures

Springer

Prof. Dr. Otfried Madelung Am Kornacker 18 D-35041 Marburg

The 1St ed. was published in 2 volumes in the series "Data in Science and Technology" under title Semiconductors.

Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnabme Semiconductors - Basic Data / ed.: Otfried Madelung. 2.,rev. ed. Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer, 1996 FrUher mehrb. begrenztesWerk u.d.T.: Semiconductors NE: Madelung,Otfried [Hrsg.J

ISBN-13: 978-3-642-97677-3 e-ISBN-13: 978-3-642-97675-9 DOl: 10.1007/978-3-642-97675-9

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfllm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law. © Springer-Verlag Berlin Heidelberg 1991, 1992, and 1996

Softcover reprint of the hardcover 3rd edition 1996 The use of general descriptive names, registered names, trademarks, 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. production: PRODUSERV Springer Produktions-Gesellschaft, Berlin Cover layout: Lewis & Leins, Berlin Typesetting: Camera ready copy from editor

SPIN: 10532384

63/3020 - 543 2 1 0 - Printed of acid-free paper

Preface The frequent use of well known critical data handbooks like Beilstein, Gmelin and Landolt-Bomstein is impeded by the fact that merely larger libraries - often far away from the scientist's working place - can afford such precious collections. To satisfy an urgent need of many scientists working in the field of semiconductor physics for having at their working place a comprehensive, high quality, but cheap collection of at least the basic data of their field of interest this volume contains the most important data of semiconductors. All data were compiled from information on semiconductors presented on more than 6000 pages in various volumes of the New Series of Landolt-Bomstein. We hope to meet the needs of the community of semiconductor physicists with this volume, forming a bridge between the laboratory and additional information sources in the libraries.

Marburg, January 1996

The Editor

Table of contents A Introduction

1 General remarks .......................................................................................................................................................... 1 2 The corresponding Landolt-Bomstein volumes .......................................................................................................... 2 3 Physical quantities tabulated in this volume ............................................................................................................... 3

B Physical data Elements of the IVth group and IV-IV compounds 1.1 Diamond (C) ................................................................................................................................................... 5 1.2 Silicon (Si) .................................................................................................................................................... 11 1.3 Germanium (Ge) ........................................................................................................................................... 28 1.4 Grey tin (a-Sn) ............................................................................................................................................. .42 1.5 Silicon carbide (SiC) ................................................................................................................................... .47 1.6 Silicon germanium alloys (SixGel_x) ............................................................................................................ 57 2 III-V compounds 2.1 Boron nitride (BN) ...................................................................................................................................... 60 2.2 Boron phosphide (BP) ................................................................................................................................. 65 2.3 Boron arsenide (BAs) .................................................................................................................................. 68 2.4 Aluminium nitride (AIN) ............................................................................................................................. 69 2.5 Aluminium phosphide (AlP) ....................................................................................................................... 72 2.6 Aluminium arsenide (AlAs) ........................................................................................................................ 75 2.7 Aluminium antimonide (AISb) .................................................................................................................... 80 2.8 Gallium nitride (GaN) ................................................................................................................................. 86 2.9 Gallium phosphide (GaP) ............................................................................................................................ 91 2.10 Gallium arsenide (GaAs) ........................................................................................................................... 101 2.11 Gallium antimonide (GaSb ) ....................................................................................................................... 114 2.12 Indium nitride (InN) .................................................................................................................................. 122 2.13 Indium phosphide (InP) ............................................................................................................................. 124 2.14 Indium arsenide (InAs) .............................................................................................................................. 133 2.15 Indium antimonide (InSb) ......................................................................................................................... 141 2.16 Ternary and quaternary alloys between III-V compounds .......................................................................... 155

3 Elements (other than group IV elements) 3.1 Group III elements ...................................................................................................................................... 160 3.2 Group IV elements ....................................................................................................................... see chapter 1 3.3 Group V elements ....................................................................................................................................... 161 3.4 Group VI elements ...................................................................................................................................... 162 4 Binary compounds (other than III-V compounds) 4.1 IA-IB compounds ....................................................................................................................................... 164 4.2 Ix-Vy compounds ........................................................................................................................................ 164 4.2.1 I-V compounds ................................................................................................................................ 164 4.2.2 I3-V compounds ............................................................................................................................... 165 4.2.3 I2-I-V compounds ............................................................................................................................ 166 4.3 Ix-VIy compounds ....................................................................................................................................... 167 4.4 I-VII compounds ........................................................................................................................................ 170 4.5 IIx-IVy compounds ..................................................................................................................................... 173 4.5.1 IIrIV compounds ............................................................................................................................ 173 4.5.2 II-IV2 compounds ............................................................................................................................ 175 4.6 IIx-Vy compounds ...................................................................................................................................... 175 4.6.1 II3-V2 compounds ............................................................................................................................ 175

4.7

4.8 4.9 4.10

4.11 4.12

4.13

4.14 4.15 4.16

4.6.2 II4-V3 compounds ............................................................................................................................ 177 4.6.3 II-V compounds ............................................................................................................................... 177 4.6.4 II-V2 compounds ............................................................................................................................. 178 4.6.5 II-V4 compounds ............................................................................................................................. 179 4.6.6 Further II-V compounds .................................................................................................................. 179 II-VI compounds ........................................................................................................................................ 180 4.7.1 IIA-VIB compounds ........................................................................................................................ 180 4.7.2 Zinc chalcogenides .......................................................................................................................... 182 4.7.3 Cadmium cha1cogenides .................................................................................................................. 184 4.7.4 Mercury chalcogenides .................................................................................................................... 186 II -VII2 compounds ...................................................................................................................................... 188 III-V compounds ......................................................................................................................... see chapter 2 Ill x - Vly compounds .................................................................................................................................... 190 4.10.1 III-VI compounds .......................................................................................................................... 190 4.10.2 III2-VI3 compounds ....................................................................................................................... 192 4.10.3 Further Ill x - Vly compounds .......................................................................................................... 192 4.10.4 III-Ill-VI compounds ..................................................................................................................... 193 III-VII compounds ...................................................................................................................................... 194 IV x- Vy compounds ..................................................................................................................................... 196 4.12.1 IV -V compounds ........................................................................................................................... 196 4.12.2 IV-V2 compounds .......................................................................................................................... 197 IV x- Vly compounds .................................................................................................................................... 197 4.13.1 IV-VI compounds .......................................................................................................................... 197 4.13.2 IV-VI2 compounds ........................................................................................................................ 200 4.13.3 IV2-VI3 compounds ....................................................................................................................... 202 IV -VII2 compounds .................................................................................................................................... 203

5 Ternary compounds 5.1 Tetrahedrally bonded ternary and quasi-binary compounds ....................................................................... 209 5.1.1 1I12-VI3 compounds ......................................................................................................................... 209 5.1.2 I-III-VI2 compounds ........................................................................................................................ 211 5.1.3 II-IV-V2 compounds ........................................................................................................................ 216 5.1.4 12-IV-V3 compounds ........................................................................................................................ 219 5.1.5 12-V-VI4 compounds ........................................................................................................................ 220 5.1.6 II-Ill2-VI4 compounds ..................................................................................................................... 221 5.1.7 Other ordered vacancy compounds ................................................................................................. 224 5.1.8 Quaternary compounds .................................................................................................................... 225 5.2 Further ternary compounds ......................................................................................................................... 226 5.2.1 Ix-IVy-VIz compounds ..................................................................................................................... 226 5.2.2 Ix - V y-VIz compounds ...................................................................................................................... 227 5.2.3 II x -III y-Vl z compounds .................................................................................................................... 230 5.2.4 III x - V y-VIz compounds .................................................................................................................... 231 5.2.5 IVx-Vy-Vl z compounds ................................................................................................................... 232 5.2.6 V-VI-VII compounds ...................................................................................................................... 233 5.2.7 Other ternary compounds ................................................................................................................ 235 6 Further compounds with semiconducting properties 6.1 Boron compounds ....................................................................................................................................... 237 6.2 Binary transition metal compounds ............................................................................................................ 238 6.2.1 Compounds with elements of the IVth group .................................................................................. 238 6.2.2 Compounds with elements of the Vth group ................................................................................... 238 6.2.3 Oxides .............................................................................................................................................. 239 6.2.4 Chalcogenides .................................................................................................................................. 240 6.3 Binary rare earth compounds ...................................................................................................................... 241

6.4

6.5

Ternary transition metal compounds .......................................................................................................... 242 6.4.1 Pnigochalcogenides ......................................................................................................................... 242 6.4.2 Spinels and related compounds ....................................................................................................... 242 6.4.3 Oxides .............................................................................................................................................. 243 6.4.4 Further chalcogenides ...................................................................................................................... 243 Ternary rare earth compounds .................................................................................................................... 243

7 Figures to chapters 3, 4 and 5 ................................................................................................................................. 247 Appendix

1 Index of Substances ................................................................................................................................................ 299 2 Synopsis of the sections of this book and the corresponding sections of volumes III/17, III/22 and III123a of the New Series of Landolt-Bornstein ................................................................................................ 307 3 Contents of the volumes of the New Series of Landolt-Bornstein dealing with semiconductors ........................... 311

A Introduction 1 General remarks This volume contains basic data of semiconductors. All data were compiled from volumes of the New Series of the Landolt-Bomstein data handbook. They comprise the information a scientist working on semiconductors is needing in his every-day work. The volume consists of three parts: A. Introduction, B. Physical data, C. Appendix. In part B the chapters 1 and 2 cover data on the most important semiconductors, the elements of the IVth group and the III-V compounds. Here detailed information is given on all physical properties of these substance groups. Chapters 3 to 7 present basic data on more than 600 other substances with semiconducting properties. The scope and the arrangement of data is as follows: Chapters 1 and 2 on group IV elements and III-V compounds The data presented in these chapters are ordered under the following headings: - Electronic properties: band structure / energies at symmetry points of the band structure / energy gaps (direct energy gap, indirect energy gap) / exciton energies / intra conduction band energies / intra valence band energies / critical point energies / spinorbit splitting energies / camel's back structure of the conduction band edge / structure of the top of the valence band / effective masses (effective masses, electrons; effective masses, holes) / g-factor of electrons / valence band parameters. - Lattice properties: structure / high pressure phases / transItIOn temperature (pressure) or decomposition temperature / lattice parameters / linear thermal expansion coefficient / density / melting point / phonon dispersion relations / phonon frequencies (wavenumbers) / second order elastic moduli / third order elastic moduli. - Transport properties: electrical conductivity (intrinsic conductivity) / (intrinsic) carrier concentration / carrier mobilities (electron mobility, hole mobility) / thermal conductivity (resistivity). - Optical properties: optical constants / absorption coefficient / reflectance / extinction coefficient / refractive index / dielectric constants. - Impurities and defects: solubility of impurities / diffusion coefficient (self-diffusion, impurity diffusion) / binding energies of (shallow) impurities / energy levels of impurities, defects and complexes or of deep centers. For alloys bowing parameters and crossover concentrations are also given. Chapters 3 to 7 on further semiconducting elements and compounds To cover the properties of more than 600 semiconductors several restrictions were necessary: - Only diagrams showing lattice structures and band structures have been included. Thus, no temperature or pressure dependence of parameters, no optical spectra etc. could be presented. Most data are values at room temperature and normal pressure. - No references have been given. For all references as well as for all supplementary information (experimental conditions, experimental method, further data, errors etc.) the reader has to consult the respective subvolumes of volumes NS IIIIl7 and 22 of Landolt-Bomstein (see below). - For technical reasons the figures to chapters 3 ... 5 are presented in chapter 7. In Chapters 3, 4 and 5 all data have been grouped into eight colums: - Substance: The name of the semiconducting substance. - Structure: symmetry type of the lattice and space group for normal conditions. Further information about the locations of atoms in the unit cell, about high temperature phases or high pressure phases have been omitted. - Static and dynamical lattice parameters:

2

Introduction

Lattice constants. Density, melting temperature (in some cases peritectic temperature). Data on second order elastic constants have been added in simple cases only where the elastic properties are determined by a small number of tensor components. Dielectric constants. Phonon frequencies are given only if the phonon spectrum is characterized by a small number of frequencies e.g. TO and LO modes at the center of the Brillouin zone or some infrared active or Raman-active modes. For complicated phonon spectra no data are given. - Band structure parameters: Energy gaps. Data were given here mostly for room temperature, but characteristic data at other temperatures were added if necessary. If possible the type of the transition (optical, thermal, direct, indirect etc.) has been indicated. Effective masses of electrons and holes, polaron masses. - Transport properties: In most cases only the mobilities are listed. Since such data represent upper limits or are accidentally measured values carrier densities or conductivities (resistivities) have been added when necessary. Activation energies for conductivity have been included in some cases. In Chapter 6 data on compounds are listed, for which the information on semiconducting properties is scarce, or for which semi conductivity is only of minor importance. In this chapter the tables have been restricted to six col urns giving information on structure, optical and thermal energy gaps and carrier mobilities. Here activation energies for conductivity have been indicated, if this was stated explicitely in the original paper. In many cases the references do not differentiate between thermal energy gaps and activation energies. The following restrictions should be taken in mind when using these tables: - If not stated otherwise all data are room temperature values. Only for parameters which do not depend strongly on temperature (e.g. effective masses) data measured at other temperatures were included without mentioning it. - Physical data can be judged confidentally only by added information about measuring and evaluation methods, about the reference the value has been taken from etc. All this valuable information is lacking here because of the restriction of the number of pages for this data collection. The reader has to go back to the corresponding LandoltBornstein volumes for such information. Adding such informations in the present text - and the references to the original papers too - had surpassed the frame of this volume. - The data presented here had often to be chosen from several values, given in the Landolt-Bornstein volumes, if no unique choice had been possible for the author of the respective chapter. In such cases the "most reliable one" according to the judgement of the editor - or the "newest" one has been listed. Appendices

To facilitate the use of this book three Appendices have been added: 1. Index of Substances, 2. Synopsis of the sections of this book and the corresponding sections of volumes IIIIl7 and III/22 of the New Series of LandoltBornstein, 3. Lists of Contents of the volumes of the New Series of Landolt-Bornstein dealing with semiconductors.

2 The corresponding Landolt-Bornstein volumes Although the most relevant data have been summarized here the respective volumes of the New Series of LandoltBornstein contain much more information about these topics. In addition data on other properties can be found on the more than 6 000 pages of volumes 17a ... i, 22a,b and 23a of Group III of the New Series: Volume III/17a (and its supplement and extension III/22a) present data on group IV elements and III-V compounds. Additional information is given on topics as temperature and pressure dependence of energy band parameters, critical point energies, Kane and Luttinger band structure parameters, exciton parameters and deformation potentials; temperature and pressure dependence of lattice parameters, Debye temperatures, sound velocities, bulk modulus, Griineisen parameters; carrier concentrations, drift velocities, galvanomagnetic, thermomagnetic and thermoelectric coefficients; optical constants and spectra, elasto- and piezooptic coefficients, Raman spectra; magnetic susceptibility, heat capacity, thermodynamical data and many other topics. Volume IIII22b is devoted to an extensive representation of all relevant data on impurities and defects in group IV and III-V semiconductors as solubilities and segregation constants, diffusion coefficients, shallow defect levels, deep defects and impurities, luminescence data, ESR and ENDOR data, local vibrational modes. In addition to these physical data the volumes III/17c and d concentrate on technological data of the group IV, III-V and some other semiconductors. The volumes III1l7b, e ... h present data on elements other than group IV elements and on binary, ternary and polynary semiconductors. Volume III/17i adds data on amorphous and organic semiconductors as well as on some special topics. Chapter 2.1 of volume IIII23a presents photoemission spectra and related band structure and core level data of tetrahedrally bonded semiconductors. The organization and tables of contents of these volumes are described in the Appendix.

Introduction

3

3 Physical quantities tabulated in this volume Data on the following physical quantities are given in the tables and figures of Part B: Electronic structure energies (unit eV): energy of a band state at wave vector k. Instead of the value of k often the respective symmetry point in the Brillouin zone is given (r, X, L, L: ... for the meaning of the symbols see Fig. 2 in section 1.1 for the diamond and zincblende structure, Fig. 5 in section 2.1 for the wurtzite structure). Subscripts to these letters designate the irreducible representation of the energy state (I, I', 2, 12, 25' ... ). Indices c or v differentiate between states lying in the conduction or valence band, respectively. energies of the edges of conduction and valence bands, respectively. energy gap between conduction and valence band. Further subscripts refer to: dir: direct gap, ind: indirect gap, opt: optical gap (threshold energy for optical transitions), pseu: pseudodirect energy gap, th: thermal gap (energy gap extrapolated to OK from transport measurements), x: excitonic gap (energy gap minus exciton binding energy), 11,1- electric field parallel or perpendicular to a crystal axis; L(T) superscripts for longitudinal (transverse) exciton energies. binding energy of the exciton. mostly spin-orbit splittings of energy levels (subscripts 0, so, I, 2 and dashes (') refer to the location of the level as explained in the tables), also other splittings of energy levels (cf: crystal-field splitting, ex: exciton exchange interaction energy, L-T: longitudinal-transverse exciton splitting energy) the letter E with other subscripts refers to intra- and interband transitions as explained in the tables (Eo, EI, E2 ... ).

E(k)

Eo···

effective masses (in units of the electron mass trio): trln, trip

effective mass of electrons (holes); other subscripts refer to: c: conductivity effective mass, cr: cyclotron resonance effective mass, ds: density of states mass, p,h: heavy holes, p,l: light holes, so: effective mass in the spin-orbit split band, (X ... ): effective mass at symmetry point X ... , II, 1-: effective mass parallel or perpendicular to a principal axis

ellipsoidal energy surfaces as occuring in the conduction band of group IV and III-V semiconductors are characterized by the longitudinal and transverse effective masses trill, trI-L

defined by the equation where

K=

k - ko and

Kx

II ko,

Ky, Kz

1- ko·

camel's back structure occurs at the conduction band edge in several III-V compounds. The relevant parameters LI, Llo, LIE, trill etc. are explained in Fig. 2 and the accompanying equation in the tables of section 2.9. warped energy surfaces as occuring in the valence band of group IV and III-V semiconductors are characterized by valence band parameters A, B, C defined by the equation

g-factor of electrons: gc Lattice parameters crystal lattice, phase transitions:

a, b, c

a, [3, u

a d

r

lattice parameters (unit A or nm) angles ratio of lattice parameters coefficient of linear thermal expansion (unit K-I) density (unit g cm- 3 ) (dx : density determined from X-ray data)

4

Introduction

Tm Ttr Tperil Ptr

melting temperature (unit K) transition temperature (unit K) peritectic temperature (unit K) transition pressure for phase transitions (unit Pa)

phonon parameters:

v I{k)

phonon frequency (unit s-I) wavenumber phonon dispersion relation (dependence of phonon frequency on wave vector), instead of k often the reduced wave vector 1; = klkmax is used. Subscripts to the frequencies (wavenumbers) refer to transverse and longitudinal optical and acoustic branches (TO, LO, TA, LA) and to the symmetry points in the Brillouin zone as for the band structure energies. Further subscripts refer to Raman active (R) and infrared active (ir) modes.

elastic moduli: Gim, Gimn second (third) order elastic moduli (unit dyn cm-2)

Transport properties R RH a; (OJ) p K

EA

resistance (unit n) Hall coefficient (unit cm3C-I) (intrinsic) electrical conductivity (unit n-1cm- I) electrical resistivity (unit ncm) thermal conductivity (subscript L: lattice contribution) (unit Wcm-IK-I) activation energy (mostly for temperature dependence of conductivity) (unit eV)

carrier concentrations (unit cm- 3) and carrier mobilities (unit cm2Ns): electron concentration hole concentration intrinsic carrier concentration electron and hole mobilities, respectively. Further subscripts refer to: dr: drift mobility, c: conductivity mobility, H: Hall mobility, 11,1..: parallel (perpendicular to a principal axis)

n

Optical properties absorption coefficient (unit cm- I) reflectance (dimensionless) (real) refractive index (dimensionless) extinction coefficient (dimensionless)

K R n k E,

Bik

dielectric constant (component of the dielectric tensor); subscripts and brackets refer to: 1: real part of the complex dielectric constant, 2: imaginary part of the complex dielectric constant, 0: low frequency limit, Si II Si II --> Si III

84H, 85MI

high purity single crystal measured in vacuum

82BI

8401

transition pressures (in GPa):

Ptr

11.2(2) .. ·12.5(2) 13.2(2) .. ·16.4(5) 14.5 .. ·11.0 10.8 .. ·8.5

lattice parameter (in nm):

a

0.543102018 (34)

295.7 K

temperature dependence of the lattice parameter: a(T) in high-purity material can be approximated in the range 20 .. ·8oo°Cbya(T) = 5.4304 + 1.8138·1O- 5 (T - 298.15 K) + 1.542·1O- 9 (T - 298.15 K)2 [73Y2J, see also Fig. 7. linear thermal expansion coefficient:

a. 2.59(5)·1O- 6 K- 1 8402 298.2K Temperature dependence: Fig. 8 [8402]. The data of Fig. 8 can be approximated in the temperature range 120··· 1500 K by the formula: a.(T) = (3.725 [I - exp ( - 5.88 '10- 3 [T - 124J)J + 5.548' 10 - 4 n 10 - 6 K - 1 (T in K). density:

d

2.329002 g cm - 3

25C

hydrostatic weighing, high purity crystal

64H

melting point:

1685(2)K phonon dispersion relations: Fig. 9.

73H

1.2 Silicon (Si)

16 Numerical value

Physical property

Experimental conditions

Experimental method, remarks

Ref.

296K

from inelastic neutron scattering

63D

phonon frequencies (in THz):

15.53 (23) 4.49 (6) 12.32 (20) 13.90(30) 3.43 (5) 11.35 (30) 12.60(32) 14.68 (30)

VLTo(r 25') VTA (X 3 )

vLAo(Xd VTQ(X 4 ) vTA (L 3 ) VLA (L 2 ,)

vLO(Ld vT o(L 3 ,)

5.0 .10- 6

5.447

!

Si

5.444

r 5.441 t:J

5.438

5.435

/a

V

/

V

V

/

K- 1

./

I I

2.5

1.5

300

I

3.0

5.429

200

V

3.5

2.0

100

o

4.0

5.432

o

Si

4.5

400

500

600

700 'C BOO

T-

/

Va

__

i-""'"

./

J

f

1.0

Fig. 7. Si. Lattice parameter vs. temperature in the range 20 .. ·740°C, measurements on various samples [6lH].

0.5

o Fig. 8. Si. Linear thermal expansion coefficient vs. temperature. Experimental data from [77L1J (full circles) and [8402J (open circles).

-0.5

.a 1

15

200

400

600

l"

THz

800

1000

T_

w,

5

OL-________ r

t:J.

______

x

______

ErA

L -__- L____

LL

__

w

Fig. 9. Si. Phonon dispersion relation. Solid lines: theoretical [77WIJ, data points from [63DJ and [72N].

1200 1400 K1600

1.2 Silicon (Si) 1.676

'10'2

em 2

-........ "-.,

17

6.50 .10 11 dyn

Si -.......

r

11.668

G 1.664

'-'

1.656

6.40

-120

-80

o '(

-40

T-

Fig. 10. Si. Second-order elastic modulus C II vs. temperature [53M].

8.010 .10 11 dyn

!

-150

-120

-80

'"

-40

T_

o '(

Si

em 2

C'66 -

I

ls.o

I

1

7990 .

I

J 7.980 I 7.970

I

i i

,

-7.5

I

-160

I

-120

C111 -

I 1

I I

I

7.960

Cm

u I

i

7.950 -200

40

Fig. II. Si. Second-order elastic modulus C 12 VS. temperature [53M].

I Si

!

'\

5.38 -200

40

"\

5.44 5.42

-160

"'"

6.46

1.660

1.652 -200

Si

em 2

-80

-40

\

-10.0

o '(

o

50

100

150

200

250 K 300

T-

'\

1.0 ·10'2 dyn

40

T-

Fig. 12. Si. Second-order elastic modulus C 44 vs. temperature [53M].

Crn2

I

0 C'44

\

:;; -0.5

G

-1.0

C456

\

.., ..,............

-1.5

Fig. 13. Si. Third-order elastic moduli vs. temperature. Solid lines: best fit to the data [83P].

-2.0

em

v-

o

50

100

150 T_

200

250

K 300

1.2 Silicon (Si)

18 Physical property

Experimental conditions

Numerical value

Experimental method, remarks

Ref.

p-type sample, from ultrasound sound measurements for temperature dependence, see Figs. 10··· 12

64M

ultrasonic harmonic generation combined with pressure derivative of elastic constants for full temperature dependence, see Fig. 13

SIP

second order elastic moduli (in 1011 dyn cm - 2): 16.577 6.393 7.962

298 K I! = 410acm

third order elastic moduli (in 10 12 dyncm- 2): C 111 C 112 C 144 C 123 C 166 C456

- 8.34 (II) - 5.31 (32) -0.95(24) -0.02(18) -2.96(12) -0.074(22)

298K

Transport properties Contributions to the electric transport are exclusively made by electrons in the [100J-conduction band minima and (heavy and light) holes in the two uppermost valence bands. In samples with impurity concentrations below 10 12 cm - 3 the mobilities are determined by pure lattice scattering down to temperatures of about 10 K (n-type) or 50 K (p-type), respectively. For electrons the lattice mobility below 50 K is dominated by deformation potential coupling to acoustic phonons. At higher temperatures, intervalley scattering between the equivalent minima of the conduction band is added to the intra valley process, modifying the familiar T - 1.5 dependence to T - 2.42. At temperatures below 100 K, the lattice mobility of holes is dominated by acoustic scattering, but does not follow the T-1.5 law due to the non-parabolicity of the valence bands. The proportionality of flp to T- 2.2 around RT is a consequence of optical phonon scattering. intrinsic conductivity: O"j 3.16'10- 6 0-1 cm -1 300 K 54M The intrinsic conductivity up to 1273 K is given by the phenomenological expression 10glo O"j = 4.247 - 2.924 .10 3 T- 1 (O"j in a- 1 Cm- 1, Tin K).

intrinsic carrier concentration: 1.02·10 10 cm- 3

see Fig. 14 for temperature 77W2 dependence nj can be expressed in the range 200···500 K by nj(T) = 5.71·10 19 (T/300)2.365 'exp ( - 6733/T) cm - 3 [77W2], in the range 450··· 700 K by nj(T) = 3.87'10 16 T 3/2'exp( - 1.21/2 k T)cm - 3 (Tin K, k TineY).

nj

300K

electron mobility: fln 1450 cm 2jYs Around RT fln can be expressed by Fig. 15.

fln

300 K

lattice scattering mobility

54M

82H, 83S1, 83S2, 83S3

= 1.43 '109 T - 2.42 cm 2IVs (T in K). For temperature dependence, see

hole mobility ().l in cm 2IV s): flH.p

370 2.10 5

300K 20K

ultrapure sample see Fig. 16 (b)

fl c . p

505 1.6'10 5

300K 20K

see Fig. 16 (a)

1.2 Silicon (Si)

19

-T

1200 K800 600 500

\

Si

'I

400

I

-computed

28=

1\

H \ i

I

t-

I

0.5

'"

t\

7', 4.1013 "t-

H

I

I

:

tr-

\

!

I

. I -s+-

t-

T -2.42

Il::

.\

1.3.10 17

t-

\

-.

0

'\

Vo I

1\

t-

\

t-

U

1.0 1.5 '10-) K-1 2.5 1!T-

=+

L',

t-

102 T-

Fig. 14. Si. Carrier concentration in the intrinsic range vs. reciprocal temperature [54M].

Fig. IS. Si. Electron mobility vs. temperature; data points from three authors. solid line: theoretical lattice scattering mobility. dash-dotted line: T- 2.42 dependence of iJn around RT [771].

ts1\

tt-

10 5

S'I

cm 2

Vs

1\

1\

11

!'Slight-hale bond

\

1\

f\;totOI

\

,),totol-heavy - hole bond

1\

'l.

b light -hole and

'l.

heOVy\ hole bond

,

1\

'\

\

\

.1

1 1

\\

spin-orbit bond

8

Fig. 16. Si. (a) Conductivity hole mobility vs. temperature (circles from [82M]. triangles from [56L]). Solid lines: calculated contributions from the three valence bands. (b) Hall hole mobility vs. temperature (circles from [82M]). Solid lines as in (a) [83S I. 83S2].

I

spin-orbit bond

,

a

4

5

810 2

T-

K 4.10 2

\\ \ ....

\..\

\\

10 2 10

\

,\

1\ \ 10 )

1

I:',.

10 2 10 b

iI450K substitutional substitutional acceptor boron-carbon pair, X-center B(substitu tional)-F e(interstitial) donor-acceptor pair hydrogenation of B acceptor, atomic hydrogen substitutional, Is(Ad ground state, double substitutional acceptor Cd(Oj - ), single charge state double substitutional acceptor Cd( - j - - ), double charge state interstitial, Cr(Oj +), 3d 6 j3d 5 double donor, interstitial? many levels reported, uncertain identification inactive at T < 850°C, several irradiation defects at T> 850°C triple acceptor most likely Cu-related, frequently reported values passivated by hydrogen interstitial after quenching substitutional acceptor Ga(substitutional)-C(substitutional) pair (X-center) Fe(interstitial)-Ga(substitutional) donor-acceptor pair, configuration bistability passivation by atomic H substitutional acceptor, In(substitutional)-C(substitutional), (X-center) F e(interstitial)-In(substitutional) donor-acceptor pair passivation by atomic H, interstitial Li(interstitial)-AI(substitutional) donor-acceptor pair

83F 83S4 86Gl

Impurity, defect

E

Al

Au B B-C B-Fe

[eV]

a a d a

B-H Bi Cd

Cr

-0.0710 +0.55

d a

-0.45

a

-0.22 +0.128

d d

Cu

Fe Ga Ga-C Ga-Fe Ga-H In In-C In-Fe In-H Li Li-AI

+0.222 +0.411 +0.385 +0.07273 +0.0572

d a a

+0.14 +0.23

d d

+0.15558 +0.1128

a

+0.160 +0.27

d d

-0.03381

d

87S 79T2 82W

87S 85Hl 81D

86Gl 81K2 86Gl 86C2 85F2 86C2 85W2 86Gl 82S 85Ft 86Gl 87S 83S4 82S 86Gt 87Pl 81S 65Wl (Continued)

1.2 Silicon (Si) Impurity, defect

E [eV]

Type

Li-B -0.1075 -0.2565 +0.26 -0.42 -0.12 +0.34 -0.43

d d d d a d a

-0.19

d

-0.061

d

-0.132

d

O-Vac

-0.17

a

P

-0.04558 -0.0037

d a

P-Vac Pd

-0.45 -0.23

a a

+0.33

d

+ 0.32··· + 0.36 - 0.23 ... - 0.26 -0.3182

d a d

-0.6132

d

Sb-Vac

-0.1875 -0.3700 -0.44

d d a

Sb Se

-0.04277 -0.3065

d d

-0.5932

d

-0.2064

d

-0.3892

d

Mg Mn

N Ni 0

Pd-H Pt S

S-S

Se-Se

25

Remarks

Ref.

Li(interstitial)-B( substitu tional) donor-acceptor pair interstitial Mg(O) interstitial Mg( +), Td-symmetry Mn+ +/+ 3d 5 interstitial, Mn+/o 3d 6 Mno/3d 7 Mn+/o 3d z substitutional, Mno/3d 5 N-N pairs main incorporation ofT-center substitutional partial uncertain identification, 15Ni-related complexes Si-O-Si bridging, displaced [lllJ-axis, electrically inactive "thermal donor" TD, double donor (0/ + ), formation at 350···500 °e "thermal donor" TD, double donor ( + / + + ), formation at 350···500 °e, structure uncertain, ezv-symmetry A-center, after irradiation ezv-symmetry, (lOO)-orientation substitutional, single donor D - -center, binding of a second electron at 4 K E-center, irradiation damage, Pd( - /0) predominant incorporation, T = 900· .. 1200 °e annealing and quenching Pd( + /0) predominant incorporation, T = 900· .. 1200 °e annealing and quenching passivation by atomic H substitutional Pt( + /0) substitutional Pt(O/ - ) substitutional S( + /O)double donor, T d-symmetry substitutional S( + + / + )double donor, T d-symmetry sulfur pair Sz( + /0) e 3v -symmetry sulfur pair Sz( + + /0) E-center, irradiation, anneals at T=460K substitutional single donor substitutional double donor Se( +/0), Td-symmetry, Is(Al) substitutional double donor Se( + + / + ), Td-symmetry Is(Al) Se-pair, double donor, Se z( + /0), D 30-symmetry Se-pair, double donor, Se z( + + / + ), D 30-symmetry

65W2 72H 86Gl 86Gl 86S4 86S4 86Gl 87L 87P2 87P2 87P2 87P2 82G 82N 77K 86S2 84L 87Pl 87N 86S2 86P 86P 86P 86P 79T2 84S 86P 86P 86P 86P (Continued)

References for 1.2

26 Type

Remarks

Ref.

-0.21 -0.1987

d

86P

-0.4112

d

Te-Te

-0.1580

d

Ti

+ 0.25 ... + 0.28 -0.28 -0.08 +0.2460 +0.1800

d d a a a

+0.32

d

-0.45

d

+0.05 +0.20 -0.23 +0.32 -0.47 ( +0.66)

d d a a a

substitutional double donor Te( + /0), T d-symmetry substitutional double donor Te( + + / + ), T d-symmetry double donor pair Te 2 ( + /0), D 3D-symmetry double donor 3d 3 - 3d 2 , interstitial single donor 3d4 - 3d 3 , interstitial single acceptor 3d 5 - 3d 4 , interstitial substitutional acceptor X-center passivation by atomic H double donor V( + + / + ), interstitial 3d4 - 3d 3 , single donor V( + /0), interstitial 3d 5 - 3d4 , metastable center, single charge divacancy, stable at T 300 DC double acceptor Zn(O/ - ), substitutional double acceptor Zn( - / - - ), substitutional

Impurity, defect

E [eV]

Ta Te

Tl Tl-C TI-H V

Vac Vac-Vac Zn

77B

86P 84W2 83Wl 83WI 83Wl 83S4 83S4 87Pl 86Gl 86Gl 84W3 85H2 86Gl 86GI

Reference for 1.2 53M McSkimin, H.I.: J. Appl. Phys. 24 (1963) 988. 54M Morin, F.I., Maita, J.P.: Phys. Rev. 96 (1954) 28. 56L Ludwig, G.W., Watters, R.L.: Phys. Rev. 101 (1956) 1699. 57C Carlson, R.O.: Phys. Rev. 108 (1957) 1390. 60P Philipp, H.R., Taft, E.A.: Phys. Rev. 120 (1960) 37. 6lH Hall, R.O.A.: Acta Crystallogr. 14 (1961) 1004. 630 Dolling, G.: in "Inelastic Scattering of Neutrons in Solids and Liquids", IAEA, Vienna 1963, Vol. II, p. 37. 64H Hennis, J.: 1. Res. Nat. Bur. Stand. 68A (1964)529. 64M McSkimin, H.I., Andreatch jr., P.: J. App\. Phys. 35 (1964) 2161. 65B Balslev, I., Lawaetz, P.: Phys. Lett. 19 (1965) 6. 65H Hensel, J.e., Hasegawa, H., Nakayama, M.: Phys. Rev. 138 (1965) A225. 65Wl Weltzin, R.D., Swalin, R.A., Hutchinson, T.E.: Acta Metall. 13 (1965) 115. 65W2 Waldner, M., Hiller, M.A., Spitzer, W.G.: Phys. Rev. AI40 (1965) 172. 66K Kodera, H.: J. Phys. Soc. Jpn. 21 Suppl. (1966) 578. 67B Barber, H.D.: Solid State Electron. 10 (1967) 1039. 68F Fulkerson, W., Moore, J.P., Williams, R.K., Graves, R.S., McElroy, D.L.: Phys. Rev. 167 (1968) 765. 681 . Ichimiya, T., Furuichi, T.: Int. 1. Appl. Radiat. Isot. 19 (1968) 573. 69W Wolf, H.F.: Semiconductors, New York: Wiley-Interscience 1971. 72A Aspnes, D.E., Studna, A.A.: Solid State Commun. 11 (1972) 1375. 72H Ho, L.T., Ramdas, A.K.: Phys. Rev. B5 (1972) 462. 72N Nilsson, G., Nelin, G.: Phys. Rev. B6 (1972) 3777. 72Z Zorin, E.I., Pavlov, P.V., Tetelbaum, 0.1., Khokhlov, A.F.: Fiz. Tekh. Poluprovodn. 6 (1972) 28. 73H Hultgren, R., Desai, P.O., Hawkins, D. T., Gleiser, M., Kelly, K.K., Wagman, D.O.: The Thermodynamic Properties of the Elements, American Society for Metals, Metals Park, Ohio 1973. 73Yl Yatsurugi, Y., Akiyama, N., Endo, Y., Nozaki, T.: J. Electrochem. Soc. 120 (1973) 975. 73Y2 Yin, W.M., Pall R.I.: J. Appl. Phys. 45 (1973) 1456. 74A Akasaka, Y., Horie, K., Nakamura, G.: Jpn. J. Appl. Phys. 13 (1974) 1533. 74B Bludau, W., Onton, A., Heinke, W.: J. Appl. Phys. 45 (1974) 1846. 74F Foreman, R.A., Aspnes, D.E.: Solid State Commun. 14 (1974) 100. 75L Lisiak, K.P., Milnes, A.G.: Solid State Electron. 18 (1975) 533. 74N Nishino, T., Takeda, M., Hamakawa, Y.: Solid State Commun. 14 (1974) 627.

References for 1.2 76B 76H 760 76P 77B 77FI 77F2 77J 77K 77L1 77L2 77WI 77W2 78D 78S 78V 79T1 79T2 80E 80S 8ID 81KI 81K2 81L 81P 81S 82BI 82B2 82G 82H 82M 82N 82S 82W 83A 83C 83F 83GI 83G2 83J 83K 83L 83M 83N 83P 83S1 83S2 83S3 83S4 83WI 83W2 84H 84L 8401 8402 84S 84WI 84W2 84W3 850 85FI 85F2 85HI 85H2 85L 85S 85T 85WI 85W2

27

Belikova. M.N., Zastavnyi, A.V., Korol, V.M.: Fiz. Tekh. Poluprovodn. 10 (1976) 535. Hensel, J.C: unpublished. Ousset, J.C, Leotin, J., Askenasy, S., Skolnick, M.S., Stradling, R.A.: J. Phys. C9 (1976) 2802. Pavlov, P.V., Zorin, EL, Tetelbaum, DJ., Khokhlov, A.F.: Phys. Status Solidi ta) 35 (1976) II. Busta, H.H., Waggener, H.A.: 1. Electrochem. Soc. 124 (1977) 1424. Fair, R.B.: Semiconductor Silicon 1977, Hull H.R., Sirtl, E. (eds.), The Electrochem Soc. 1977 p. 968. Fair, R.B., Tsai, J.Ce.: 1. Electrochem. Soc. 124 (1977) 1107. Jacoboni, C, Canali, C, Ottaviani, G., Alberigi Quaranta, A.: Solid State Electron. 20 (1977) 77. Kimerling, L.C: Radiation EfTects in Semiconductors 1976, in: Inst. Phys. Conf. Ser. 31 (1977) 221. Lyon, K.G., Salinger, G.L., Swenson, CA., White, G.K.: 1. Appl. Phys. 48 (1977) 865. Lipari, N.O., Altarelli, M.: Phys. Rev. B15 (1977) 4883. Weber, W.: Phys. Rev. BI5 (1977) 4793. Wasserrab, Th.: Z. Naturforsch. 32a (1977) 746. Daunois, A., Aspnes, D.E.: Phys. Rev. B18 (1978) 1824. So, L., Whiteley, J.S., Ghandi, S.K., Baliga, B.1.: Solid State Electron. 21 (1978) 887. Vydianath, H.R., Lorenzo, J.S., Kriiger, FA: J. Appl. Phys. 49 (1978) 5928. Troxel, J.R., Chatterjee, A.P., Watkins, G.D.: Phys. Rev. B19 (1979) 5336. Troxel, J.R.: Ph.D. Thesis, Lehigh University, U.S.A. 1979. Edwards, D.F., Ochoa, E.: Appl. Opt. 19 (1980) 4130. Schmid, W.: Phys. Rev. Lett. 45 (1980) 1726. Dyunaidov, S.S., Urmanov, N.A., Gafurova, M.Y.: Phys. Status Solidi (a) 66 (1981) K79. Keller, W.: Diplomarbeit Univ. Erlangen 1981. Kunio, T., Nishino, T, Ohta, E, Sakata. M.: Solid State Electron. 24 (1981) 1087. Lampert, M.O., Koebel, J.M., SifTert, P.: J. Appl. Phys. 52 (1981) 4975. Philip, J., Breazeale, M.A.: J. Appl. Phys. 52 (1981) 3383. Szablak, 8., Altarelli, M.: Solid State Commun. 37 (1981) 341. Becker, P., Seyfried, P., Siegert, H.: Z. Physik 848 (1982) 17. Budzak, YaS, Mavrin, OJ.: Phys. Status Solidi (a) 69 (1982) K61. Grimmeiss, H.G., Janzen, E., Larsson, K.: Phys. Rev. B25 (1982) 2627. Haug, A., Schmid, W.: Solid State Electron. 25 (1982) 665. Mitchel, W.C, Hemenger, P.M.: J. Appl. Phys. 53 (1982) 6880. Narita, S., Shinbashi, T, Kobayashi, M.: J. Phys. Soc. Jpn. 51 (1982) 2186. Searle, CW., Ohmer, M.C, Hemenger, P.M.: Solid State Commun. 44 (1982) 1597. Wu, R.H., Peaker, A.R.: Solid State Electron. 25 (1982) 463. Aspnes, D.E., Studna, A.A.: Phys. Rev. B27 (1983) 985. Cerofolini, G.F., Pignatel, G. U., Riva, F.: Thin Solid Films 10 (1983) 275. Fischer, D.W., Rome, 1.1.: Phys. Rev. B27 (1983) 4826. Giisele, u., Tan, TY.: Aggregation Phenomena of Point Defects in Si, Sirtl, E. (ed.), The Electrochem. Soc. 1983, p. 17. GrafT, K.: Aggregation Phenomena of Point Defects in Si, Sirtl, E (ed.), The Electrochem. Soc. 1983. p. 121. Jellison, G.E., Modine, FA: Phys. Rev. B27 (1983) 7466. Kolbesen, 8.0.: Aggregation Phenomena of Point Defects in Si, Sirtl, E. (ed.), The Electrochem. Soc. 1983, p. 155. Lang, J.E., Madarasz, F.L., Hemenger, P.M.: 1. Appl. Phys. 54 (1983) 3612. Masovic, D.R., Vukajlovic, F.R., Zekovic, S.: 1. Phys. C16 (1983) 6731. Nobili, D.: Aggregation Phenomena of Point Defects in Si, Sirtl, E. (ed.), The Electrochem Soc. 1983. p. 189. Philip, J., Breazeale, M.A.: 1. Appl. Phys. 54 (1983) 752. Szmulowicz, F.: Appl. Phys. Lett. 43 (1983) 485. Szmulowicz, F.: Phys. Rev. B28 (1983) 5943. Szmulowicz, F., Madarasz, F.L.: Phys. Rev. B27 (1983) 2605. Searle, CW., Hemenger, P.M., Ohmer, M.C: Solid State Commun. 48 (1983) 995. Weber, E.: Appl. Phys. A30 (1983) I. Wacker Chemitronics Co.: Silicon calculator 1983. Hu, J.Z., Spain, LL.: Solid State Commun. 44 (1984) 263. Lemke, H.: Phys. Status Solidi (a) 86 (1984) K39. Olijnuk, H., Sikka, S.K., Holzapfel, W.B.: Phys. Lett. A103 (1984) 137. Okada, Y., Tokumaru, Y.: 1. Appl. Phys. 56 (1984) 314. Scalar, N.: Appl. Phys. 55 (1984) 2972. Wagner, P., Holm, C, Sirtl, E., Oeder, R., Zulehner, W.: Festkiirperprobleme XXIV (1984) 191. Wagner, P., Holm, C: 13th Int. Conf. on Defects in Semiconductors 1984. Watkins, G.D.: Festkiirperprobleme XXIV, Grosse, P. (ed.), Braunschweig: Vieweg 1984. p. 163. Danilicheva, TA., Markvicheva, V.S., Nisnevich, J.D.: Izv. Akad. Nauk SSSR Neorg. Mater. 21 (1985) 525. Fischer, D.W., Mitchel, W.e.: 1. Appl. Phys. 58 (1985) 3118. Fazzio, A., Caldas, M.1., Zunger, A.: Phys. Rev. B32 (1985) 934. Hertel, N., Materlik, G., Zegenhagen, 1.: Z. Phys. B58 (1985) 199. Harris, R.D., Watkins, GD.: Proc. Defect. Conf. Coronado, Kimmerling, L.C,(ed.), The Met. Soc. of AIME 1985. p. 799. Lautenschlager, P., Allen, P.B., Cardona, M.: Phys. Rev. B31 (1985) 2163. Sieh, K.S., Smith, P.V.: Phys. Status Solidi (b) 129 (1985) 259. Tan, TY., Giisele, U.: Appl. Phys. A37 (1985) I. Weber, E.R.: Proc. SPIE (Proc. Soc. Photo-Opt. Instrum. Eng.) 524 (1985) 160. Wang, Z., Chen, K., Qin, G.: Chin. 1. Semicond. 6 (1985) 437.

28 86CI 86C2 860 86GI 86G2 86MI 86M2 86P 86S1 86S2 86S3 86S4 87AI 87A2 87L 87N 87P1 87P2 87R 87S 87T 88J 88M 88S1 88S2 88U 88W 89N

1.3 Germanium (Ge) Carlberg, T.: J. Electrochem. Soc. 133 (1986) 1941. Chen, K.-M., Qin, G.-G.: Proc. 14th Int. Conf. on Defects in Semiconductors, Paris 1986. Dominguez, E., Jaraiz, M.: J. Electrochem. Soc. 133 (1986) 1895. Graff, K.: Semiconductor Silicon 1986, H.R. Huff et a!. (eds.), The Electrochem. Soc. 1986, p. 751. Gilles, D., Bergholz, W., Schriiter, W.: J. App!. Phys. S9 (1986) 3590. Mononi, e.S., Hu, J.Z., Spain, I.L.: Phys. Rev. 834 (1986) 362. Mikkelsenjr., J.e.: Mater. Res. Soc. Symp. Proc. S9 (1986) 19. Pensl, G., Roos, G., Holm, e., Wagner, P.: Proc. 14th Int. Conf. on Defects in Semiconductors, Paris 1986. Stolwijk, N.A., Hiilzl, 1., Frank, W., Weber, E.R., Mchrer, H.: App!. Phys A39 (1986) 37. Stiiffier, W., Weber, J.: Proc 14th Int. Conf. on Defects in Semiconductors, Paris 1986. Schulz, HJ.: European Semiconductor Device Research Conference (ESSDERC) 1986. Stein, HJ.: Proc. MRS Meeting Boston 1986, Mikkelsen, J. (ed.) MRS Pittsburgh, Pa. 1986, p. 523. Angelucci, R., Armigliato, A., Landi, E., Nobili, D., Solmi, S.: ESSDERC Conference Bologna 1987. Azomov, S.A., Yunusov, M.S., Nurkuziev, G.: Fiz. Tekh. Poluprovodn. 21 (1987) 1555; Sov. Phys. Semicond. (English Trans!.) 21 (1987) 944. Lemke, H.: Phys. Status Solidi (a) 99 (1987) 205. Nolte, D.O., Walukiewicz, W., Haller, E.E.: Phys. Rev. B36 (1987) 9392. Peart on, SJ., Corbett, 1.W., Shi, T.S.: App!. Phys. A43 (1987) 153. Pensl, G.: Proc. 5th Int. School ISPPME 1987. Rollert, F., Stolwijk, N.A., Mehrer, H.: 1. Phys. D20 (1987) 1148. Stavola, M., Peart on, SJ., Lopata, J., Dautremont-Smith, W.e.: App!. Phys. Lett. SO (1987) 1086. Tsai, 1.e.e., Schimmel, D.G., Fair, R.B., Maszara, W.: J. Electrochem. Soc. 134 (1987)1508. Jantsch, 0.: private communication. Mathiot, D., Hocine, S.: 15. Int. Conf. Defects in Semiconductors Budapest 1988. Stuempel, H., Vorderwuelbecke, M., Mimkes, 1.: App!. Phys. A46 (1988) 159. Stolwijk, N.A., Griinebaum, D., Perret, M., Brohl, M.: Proc. 15th Int. Conf. on Defects in Semiconductors, Budapest 1988, Trans. Tech. Pub!. 1988. Utzig, J., Gilles, D.: Proc. 15th Int. Conf. on Defects in Semiconductors, Budapest 1988, Ferency, G. (ed.), Trans. Tech. Pub!. 1988. Watkins, G.D.: Proc. 15th Int. Conf. on Defects in Semiconductors, Budapest 1988, Ferency, G. (ed.), Trans. Tech. Pub!. 1988. Nobili, D., Angelucci, R., Armigliato, A., Landi, E., Solmi, S.: 1. Electrochem. Soc. 136 (1989) 1142.

Physical property

Numerical value

Experimental conditions

Experimental method, remarks

Ref.

1.3 Germanium (Ge) Electronic properties band structure: Fig. 1 (Brillouin zone, see Fig. 2 of section l.l). The conduction band is characterized by eight equivalent minima at the end points of the [1 I I]-axes of the Brillouin zone (symmetry L6)' The surfaces of constant energy are ellipsoids of revolution with major axes along [Ill]. Higher minima are located at the r-point and (above this) on the [IOO]-axes. The valence band has its maximum at the r-point (symmetry r 8), the (warped) light and heavy hole bands being degenerate at this point. The third spin-orbit split-ofT band has r 7-symmetry. The spin-orbit splitting is considerable. Thus, the symmetry notation of the double group of the diamond lattice is used in the following tables. energies of symmetry points of the band structure (relative to the top of the valence band) (in eV): E(r 6v) E(r 7.) E(r 8v) E(r 7e) E(r 6e) E(r 8e) E(Xs.) E(Xs.) E(X se ) E(L6v)

-12.66 -0.29 0.00 0.90 3.01 3.22 -8.65 -3.29 1.16 -10.39

theoretical data (Fig. I)

for experimental data from angular resolved photoemission, see [85W2] and [84H, 85N]

76C

1.3 Germanium (Ge) Numerical value

Physical property

29

Experimental conditions

Experimental method, remarks

Ref.

1.5K 291 K

magnetotransmission optical absorption temperature dependence of intrinsic conductivity

59Z 57M 54Ml

magnetoabsorption

59Z

-7.61 1.63 -1.43 0.76 4.16 4.25

E(L6J E(L 6.) E(L4 •S.) E(L 6c ) E(L6C) E(L4 •Sc )

indirect energy gap (in eV): 0.744(1) 0.664 0.785

OK

(extrapol.) Temperature dependence, see Fig. 2. direct energy gap:

r 7C)

0.898 (1) eV 0.805 (1) eV Temperature dependence, see Fig. 3. Eg.di,(f 8. -

15K 293K

0 eV

J -0.1 -2

"'\ 1\ Ge

'\

J--0.2 --0...0...

I

2.2

c:i'

-.".,..

'"

2.0 1.8 1.6

k

Fig. I. GaP. Band structure calculated by a pseudo potential method neglecting spin-orbit interaction [76C]; circles: data from angle resolved photoemission [84SI].

78H

o

zoo

400

600

800

T-

1000 K 1200

Fig. 3. GaP. Indirect energy gap vs. temperature from various authors. The solid curve was calculated by the formula given in the tables [69P].

E

2.875

r 2.850

""

'"

2.825 2.800 2.775

x Fig. 2. GaP. Camel's back structure of the conduction band minima at the ll.-axes near the zone boundary X. Dashed curves: diamond structure, solid curves: zincblende structure. The higher band has X3 (X 7 ) symmetry, the lower band XI (X 6 ) symmetry at the zone boundary.

2.750

o

50

100

150

200

" '\ 250 K 300

T-

Fig. 4. GaP. Direct exciton edge Eo and spin-orbit split edge Eo + Lio vs. temperature measured with wavelength modulated reflectivity [83T].

2.9 Gallium phosphide (GaP) Physical property

93

Numerical value

Experimental conditions

Experimental method, remarks

Ref.

2.637(1O)eV

78K

electroabsorption

78K

direct energy gap (in eV):

Eg •dir (r l5v -

OK, extraphotoconductivity 64N polated 300K 2.780(2) excitonic gap, wavelength 83T Egx.dir 2.866 OK, extrapolated modulated reflectance Temperature dependence: Fig. 4; the curve in Fig. 4 can be approximated by Eo( T) = Eo(O) - 0.1081 '(coth (I 64/T) - 1) (E in eV, Tin K).

ric)

2.895 (4)

spin-orbit splitting energy (in eV): (splitting of r 15v into r 8v (upper level) and

.10

0.080(3)

r 7v (lower level)) 100···2ooK

wavelength modulated reflectivity

83T

camel's back structure of conduction band edge: The camel's back structure near the minimum can be described by the formula:

E(k) = h 2k 2/2ml

+ h2ki/2m, -

((.1/2)2

+ .1oh2k2/2ml)I/2

with k and k.l: components of the wave vector parallel and perpendicular to the [lOOJ-direction, respectively, mt: effective mass perpendicular to the [looJ-direction; .10: parameter describing the non-parabolicity; all other parameters are explained in Fig. 2. .1

355meV

.10 mt m) tJ.E m km

433 meV 0. 25mo 0.91 mo 3.5meV 10.9 mo 0.025 (2n/a)

fitting of cyclotron resonance data obtained in very high magnetic fields

83Ml, 83M2

from tJ.E = (.10/4)(1 - .1/.10)2 from m . =ml(l-(.1/.1o)2)-1 from km = (2m)tJ.E/h2)1/2

effective mass, electrons (in units of mol:

m*n m*n.l

0.254 (4) 4.8 (5)

apparent effective masses from cyclotron resonance data at 11911m (337 11m) assuming .ellipsoidal energy surfaces at X 1 neglecting camel's back structure

83Ml

cyclotron resonance at 1.6 K

12S

calculated from k·p model

83S1

calculated using k· p theory

75W

effective masses, holes (in units of mol:

0.67 (4) 0.17(1) 0.4649

11[111] 11[111]

valence band parameters:

A B

ICI

-4.20 -1.97 4.60

2.9 Gallium phosphide (GaP)

94

5.451 r---,----,,...----,----,----r-----,

5.475

A

A

5.470

,/

15.465

15.449

t:>

t:>

5.460

I

5.455

7

I III

/

/ 0

/

5.450 5.446

_ _....I.-_---L_ _..J...-_.....J

8 .10-6

50

100

150

T_

200

250 K 300

5.445

0 200 400 600 800 K 1000 T_ b Fig.s. GaP. Lattice parameter vs. temperature. (a) below RT [830], (b) above RT, circles and broken line: ["12K], solid line: data from (a).

a

o

V

/0

GaP

K-l

0

" 00 0 0 0 0

0 0

2

0 0 0

0

o

300

600

T-

K 900

Fig. 6. GaP. Linear thermal expansion coefficient vs. temperature; circles: [830], other symbols: data taken from literature.

400 r---''""""lr_ _

300

I

1;0.

200

100

x

W(ll

X

A

Fig. 7. GaP. Phonon dispersion relations calculated with an eleven parameter rigid ion model. Solid lines calculated to fit neutron dilTraction data from [798] (full symbols), dashed lines calculated to fit data from [68Y] (open symbols [82P]).

2.9 Gallium phosphide (GaP) Numerical value

Physical property

Experimental conditions

Experimental method, remarks

95 Ref.

Lattice properties Structure

GaP I GaP II

space group - F43m (zincblende structure) tetragonal - 14,/amd (fJ-tin structure)

stable at normal pressure high-pressure phase

82BI

215 (8) kbar

beginning of phase transition

82BI

transition pressure:

Ptr lattice parameter:

5.4505 (2) A

a

RT, single crystal

80B

300K

77M

For temperature dependence, see Fig. 5. linear thermal expansion coefficient: Fig. 6. density:

4.138gcm- 3

d melting point:

84T

1730 (5) K

Tm

phonon dispersion relations: Fig. 7. 14.40 ·10"

GoP

"'L

LU

r-r--

1

300 'C 350

Fig. 6. GaSb. Electron mobility in (a) the r-band and (b) the L-band vs. temperature for a sample with n = 1.49.10 18 cm - 3 (/i,o,) and the contributions from various scattering mechanisms (ac - longitudinal acoustic phonon scattering, po - polar optical mode scattering, ii - ionized impurity scattering, sc - space charge scattering. r - L - intervalley scattering) [81 L].

0

'" "

fr"

,,"

a

t:,o,c,,,, p,;000 o

..'

'"

r:.!!

a •

.

a •

•

o.

-

b

o

Ga5b

f--

"

I 10-1 B

a

'"

I

c.

i7

o.

"

I

I

D..

I

I '" 7

. . . '" . .=' 00

Q)

,

,,2 oJ .;

.

I

v

I

-

I

.fl 4

6 B 10

2

6

810 2

1

K 4.10 2

T-

Fig, 8, GaSb, Thermal conductivity of two n-type samples with impurity content of 4.10 18 cm - 3 (I) and 1.4' 10 18 cm - 3 (2) and of two p-type samples with 1,10 17 cm -3 (3) and 2' 10 17 cm - 3 (4) [64H].

120

2.11 Gallium antimonide (GaSb)

optical constants real and imaginary parts of the dielectric constant measured by spectroscopical ellipsometry; n, k, R, K calculated from these data [83A1]; see also Fig. 9. hw[eV]

£1

£2

n

k

R

K[10 3 cm -I]

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

19.135 25.545 13.367 9.479 7.852 -1.374 -8.989 -5.693 -5.527 -4.962

3.023 14.442 19.705 15.738 19.267 25.138 10.763 7.529 6.410 4.520

4.388 5.239 4.312 3.832 3.785 3.450 1.586 1.369 1.212 0.935

0.344 1.378 2.285 2.109 2.545 3.643 3.392 2.751 2.645 2.416

0.398 0.487 0.484 0.444 0.485 0.583 0.651 0.585 0.592 0.610

52.37 279.43 579.07 641.20 902.86 1477.21 1547.17 1394.02 1474.51 1469.28

Impurities and defects diffusion coefficients Element

Do[cm 2 s- l ]

Self-diffusion coefficients 3.2.10 3 Ga Sb 3.4-104 Impurity diffusion coefficients 1.2.10- 7 In In dependence on stoichiometry 2.4-10 - 5 Sn Sn dependent on carrier density 3.8.10- 4 Te 1.5-10- 6 Cd Zn

isoconcentration = 1.8.10- 11 cm 2 S-I at 560°C 4.0.10- 2

Q[eV]

T[°C]

Remarks

Ref.

3.15 3.45

680··· 700 680··· 700

radiotracer radio tracer

57E 57E

radiotracer SIMS radiotracer radiotracer radiotracer pn-junction depth measurement radiotracer (isoconcentration and chemical diffusion) pn-junction

60B 80M 60B 75U 60B 68B

0.53 0.80 1.20 0.72

D

Zn

30

1.6

74D

81K

GaSb

flw_

eV

6

Fig. 9. GaSb. Real and imaginary parts of the dielectric constants vs. photon energy [83A 1].

References for 2.11

121

donors Undoped, relatively pure GaSb is usually p-type. Thus, neutral donor states are not populated in equilibrium. No observations of inter-donor transitions have been reported. Conductivity and Hall coefficient relaxation experiments give evidence of a trap which is related to the S donor [79D]. binding energies of donors Impurity

Te(L) Te(X) Se(L) Se(L)*(?) Se(X) S(L) S(X)

Eb [meV]

20(5) l:>

I

I

I

I

\, 1'\.\

\.\

'\

T-

Fig. S. InAs. Electron Hall mobility of pure material vs. temperature [75RJ. Open triangles: n=1.7·lO'·cm- 3 , circles: n=4'lO'6 cm -3, full triangles: 4·IO,scm- 3 •

\r

213

'\ 6

thermal tanductivity: Fig. 10.

7

B

K 10 3

T-

Fig. 9. InAs. Hole mobility (SURH/37t) vs. temperature for two samples [54F].

Optical properties dielectric constants: 8(0)

15.15

8(00)

12.25

300K

infrared reflectance and oscillator fit

62H

optical constants: real and imaginary parts ofthe dielectric constant measured by spectroscopical ellipsometry; n, k, R, K calculated from these data [83A]; see also Fig. 11. hw[eV] 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

81

13.605 15.558 15.856 6.083 5.973 7.744 -1.663 -5.923 -3.851 -2.403

82

n

k

R

K[10 3 cm-']

3.209 5.062 15.592 13.003 10.550 11.919 22.006 8.752 6.008 6.005

3.714 3.995 4.364 3.197 3.008 3.313 3.194 1.524 1.282 1.434

0.432 0.634 1.786 2.034 1.754 1.799 3.445 2.871 2.344 2.112

0.337 0.370 0.454 0.412 0.371 0.393 0.566 0.583 0.521 0.448

65.69 128.43 452.64 618.46 622.13 729.23 1571.19 1455.26 1306.62 1284.15

2.14 Indium arsenide (InAs)

139

10 1

W

em K - - I - - - -t-+---+------i

20 10

P r---t I

---'--+--l-lf--I,___f-----I

c--

It.

10' 1

H--h

I

iii 810

5

i I

2

5

810 2

2

-10 L--:!;-------::!------..I..-----L.-----1

K 1..10 2

4

T-

flw_

Fig. 10. InAs. Thermal conductivity below 200 K for three samples with 1: n= 1.6·IO '6 cm- 3 • 2: n=2·10 '7 cm- 3 • 3: p = 2'10 '7 cm- 3 [71T].

5

eV

6

Fig. 11. InAs. Real and imaginary parts of the dielectric constant vs. photon energy [83A].

Impurities and defects solubility of impurities in InAs Impurity Cd S,Se, Te Zn

ceq

[cm - 3]

3.5' 10 '9 (max) full curves determined >3·1O '9 (max)

T[cC]

Remarks

Ref.

800

radiotracer micro hardness and Hall effect studies

67A 76G 67B2

800

diffusion coefficients Element

Q[eV]

Remarks

Ref.

4.0 4.45

radio tracer radiotracer

69K 69K

0.26 0.65 1.15 2.4 0.52 1.17 1.17 2.20 1.17 2.20 1.28 1.32 0.96 ± 0.02

radiotracer radiotracer radiotracer pn-junction radiotracer pn-junction pn-junction pn-junction pn-junction pn-junction pn-junction radiotracer isoconcentration technique not known

67Bl 67R 67A 81H 67F 62S 62S 62S 62S 62S 62S 71S 67B2 73C

Self-diffusion coefficients In As

6.0,10 5 3.0'10 7

Impurity diffusion-coefficients Ag Au Cd Cd Cu Ge Mg S Sn Se Te Hg Zn Zn

7.3'10- 4 5.8'10- 4 7.4'10- 4 3.6'10- 3 3.74,\0-6 l.98·\O-6 6.78 l.49·10- 6 12.6 3.43 '10- 5 l.45·10- 5 4.2'10- 3 complex profiles

140

References for 2.14

shallow impurities Little is known about impurities in this material. The binding energies of some acceptors and donors are determined from photoluminescence experiments. It is, however, not known whether these impurities are point defects or complexes. acceptor binding energies Impurity

Sn Ge Si (?)

structure defect

T

[K]

Remarks

Ref.

[meV] 10 14 20 20 35

77

photoluminescence of implanted material photoluminescence

75G 74G

photoluminescence of Sn-doped material

76Z

Eb

4.2

References for 2.14 54F 58S 62H 62S 63G 63M

630 67A 67B1 67B2 67P 67R 67S 69G 69K 69R 70Z 71S 71T 73C 74G 74L 75G 75R 75V 75WI 76C 76G 76Z 77L 78S 80C 81H

8IT

82P 82Y 83A

Folberth, O.G., Madelung, 0., Weiss, H.: Z. Naturforsch. 9a (1954) 954. Sirota, N.N., Pashintsev, Yu.l.: Inzh. Fiz. Zh. Akad. Nauk BSSR 1 (1958) 38. Hass, M., Henvis, B.W.: l Phys. Chern. Solids 23 (1962) 1099. Schillmann, E.: Compound Semiconductors - Preparation of III-V Compounds, Vo!. 1, Willardson, R.K., Goering, H.L. (eds.), New York: Reinhold 1962, p. 358. Gerlich, D.: lApp!. Phys. 34 (1963) 2915. Mikhailova, M.P., Nasledov, D.N., Siobodchikov, S.V.: SOy. Phys. Solid State (English Trans!.) 5 (1964) 1685; Fiz. Tverd. Tela 5 (1963) 2317. Ozolin'sh, lV., Averkieva, G.K., I1vin'sh, A.F., Goryunova, N.A.: SOy. Phys. Cryst. (English Trans!.) 7 (1963) 691. Arseni, K.A., Boltaks, B.I., Rembeza, S.l.: SOy. Phys. Solid State 8 (1967) 2248. Boltaks, B.I., Rembeza, S.I., Sharma, B.L.: SOy. Phys. Solid State 1 (1967) 196. Boltaks, B.I., Rembeza, S.I.: SOy. Phys. Solid State 8 (1967) 2117. Pidgeon, CR., Groves, S.H., Feinleib, J.: Solid State Commun. 5 (1967) 677. Rembeza, S.l.: SOy. Phys. Solid State 1 (1967) 516. Sparks, P.W., Swenson, CA.: Phys. Rev. 163 (1967) 779. Glazov, V.M., Chizhevskaya, S.N., Evgen'ev, S.B.: Zh. Fiz. Khim. 43 (1969) 373. Kato, H., Yokozawa, M., Kohara, R., Okabayashi, Y., Takayanagi, S.: Solid-State Electron. 12 (1969) 137. Reifenberger, B., Keck, M.J., Trivisoono, J.: J. App!. Phys. 40 (1969) 5403. Zucca, R.R.L., Shen, Y.R.: Phys. Rev. 155 (1970) 2668. Sharma, B.L., Purohit, R.K., Mukerjee, S.N.: J. Phys. Chern. Solids 32 (1971) 1397. Tamarin, P. V., Shalyt, S.S.: SOY. Phys. Semicond. (English Trans!.) 5 (1971) 1097; Fiz. Tekh. Poluprovodn. 5 (1971) 1245. Casey, H.C: Quoted unpublished measurements of M.G. Buehler and G.L. Pearson, in "Atomic Diffusion in Semiconductors", Shaw, D. (ed.), New York: Plenum Press 1973, p.351. Guseva, M.I., Zotova, N.V., Koval, A.V., Nasledov, D.N.: SOY. Phys. Semicond. (English Trans!.) 8 (1974) 34; Fiz. Tekh. Poluprovodn. 8 (1974) 59. Ley, L., Pollak, R.A., McFeely, F.R., Kowalczyk, S.P., Shirley, D.A.: Phys. Rev. 89 (1974) 600. Guseva, M.I., Zotova, N.V., Koval, A.V., Nasledov, D.N.: SOY. Phys. Semicond. (English Trans!.) 8 (1975) 1323; Fiz. Tekh. Poluprovodn. 8 (1974) 2034. Rode, D.L.: in "Semiconductors and Semimetals", Vo!. 10, R.K. Willardson, A.C Beer eds., Academic Press, New York 1975. Varfolomeev, A.V., Seisyan, R.P., Yakimova, R.N.: SOY. Phys. Semicond. (English Trans!.) 9 (1975) 530; Fiz. Tekh. Poluprovodn. 9 (1975) 804. Wiley, J.D.: in "Semiconductors and Semimetals", Vo!' 10, R.K. Willardson, A.C Beer eds., Academic Press, New York 1975. Chelikowsky, J.R., Cohen, M.L.: Phys. Rev. 814 (1976) 556. Glazov, V.M., Akopyan, R.A., Shvedkov, E.l.: SOY. Phys.-Semicond. 10 (1976) 378. Zotova, N.V., Karataev, V.V., Koval, A.V.: SOY. Phys. Semicond. (English Trans!.) 9 (1976) 1275; Fiz. Tekh. Poluprovodn. 9 (1975) 1944. Lukes, F.: Phys. Status Solidi (b) 84 (1977) K113. Semikolenova, N.A., Nesmelowa, I.M., Khabarov, E.N.: SOY. Phys. Semicond. (English Trans!.) 12 (1978) 1139; Fiz. Tekh. Poluprovodn. 12 (1978) 1915. Carles, R., Saint-Cricq, N., Renucci, lB., Renucci, M.A., Zwick, A.: Phys. Rev. 822 (1980) 4804. Horikoshi, Y., Saito, H., Takanashi, Y.: Jpn. J. App!. Phys. 20 (1981) 437. Takayama, J., Shimomae, K., Hamaguchi, C: Jpn. J. App!. Phys. 20 (1981) 1265. Pascher, H.: Opt. Commun. 41 (1982) 106. Yang June Jung, Byung Ho Kim, Hyung Jae Lee, Wolley, lC: Phys. Rev. 26 (1982) 3151. Aspnes, D.E., Studna, A.A.: Phys. Rev. 827 (1983) 985.

2.15 Indium antimonide (JnSb) 83K 83W 85V

141

Kanskaya, L.M., Kokhanovskii, S.I., Seisyan, R.P., Efros, Al.L., Yukish, V.A.: Sov. Phys. Semicond. (English Transl.) 17 (1983) 449; Fiz. Tekh. Poluprovodn. 17 (1983) 718. Williams, G.P., Cerrina, F., Anderson, l., Lapeyre, GJ., Smith, RJ., Hermanson, 1., Knapp, l.A.: Physica 117B & 118B (1983) 350. Vohra, Y.K., Weir, S.T., Ruoff, A.L.: Phys. Rev. B31 (1985) 7344.

Physical property

Numerical value

Experimental conditions

Experimental method, remarks

Ref.

2.15 Indium antimonide (InSb) Electronic properties band structure: Fig. 1 (Brillouin zone: see Fig. 2 of section 1.1) InSb is a direct semiconductor. The minimum of the conduction band (r 6) is situated in the center of the Brillouin zone. Near the minimum, E(k) is isotropic but non-parabolic. Thus the effective mass of the electrons is scalar and depends strongly on the electron concentration. Higher band minima (about 0.63 eV above the lowest minimum) seem to be established by transport measurements in heavily doped n-InSb [75F]. The valence band shows the structure common to all zincblende semiconductors i.e. two subbands degenerate at r 8 and one spin-split band (r 7)' A small crystal field splitting of the heavy hole band is negligible for most phenomena. energies of symmetry points of the band structure (relative to the top of the valence band) (in eV): E(r 6v) E(r 7v) E(r 8v) E(r 6e) E(r 7cl E(r 8e) E(X6vl E(X6vl E(X6vl

E(X 7v ) E(X6cl E(X 7e )

E(L6v) E(L6vl

-11.71 -0.82 0.00 0.25 3.16 3.59 -9.20 -6.43 -2.45 -2.24 1.71 1.83 -9.95 -5.92

symmetry symbols in double group notation first row: theoretical data of [76C, 85C], see Fig. 1 second row: experimental data deduced from (a): [85L1], (b): [83L], (c):[81M]), (d): [74L]

-11.7(d) -0.850(a) 0.235 (b) 3.141 (a) 3.533 (a, c) -9.5(d) -6.4(d) -2.4(d) 1.79 (a, d) - 10.5 (d)

eV

0

L3

"-'

-6

Fig.!. InSb. Band structure obtained with a non-local pseudopotential calculation [76C], corrected in [84C] (Fig. from [84C]). Experimental data from angular resolved photoemission from a InSb (001) surface [83H] have been included (circles).

-9 -1 Z L

X5 l5

15 A

r

U.K

/:;

k

r

2.15 Indium antimonide (InSb)

142

Physical property

Experimental conditions

Numerical value

E(L 6v ) E(L4.SJ E(L 6 cl E(L 6c ) E(L 4 . Sel

Experimental method, remarks

Ref.

exciton ground state, from luminescence and absorption calculated from E(1S) resonant two-photon photoHall effect, two-photon magnetoabsorption

79K2

- 1.4 (d)

-1.44 -0.96 1.03 4.30 4.53

-O.9(a,d) 4.32 (a, d) 4.47 (a, d)

energy gaps (in eV): E(IS)

0.2363 (2)

2K,n 77K = 6·t0 13 cm- 3

0.2368 (2) 0.2352

1.8 K

77K

0.230

79K2 85L2, 82G

temperature dependence of energy gap: Eg(O) - aT2 j(b

+ T) with

a = 0.6 meV K -}, b = 500 K, Fig. 2

85L2

For camel's back structure of the conduction band X-minima, see [85K]. spin-orbit splitting energies (in e V): L10(r Bv - r 7.) L1} (A 4 . Sv - A 6 .) 7c - r Bel

0.850 0.498 (4) 0.392 (12)

tOOK

ellipsometry

85Ll

ellipsometry

81M

ellipsometry

85Ll 81M 85Ll

Faraday effect

83Z

critical point energies (in eV):

Bv -

r 7c)

E 2(X 6 . 7v - X6c ) E'} (L 4 . sv - L6cl

1.968 (1) 1.872 (2) 3.141 (12) 4.186(2) 5.22(3)

lOOK RT

effective masses, electrons (in units of mol: 0.01359 (3)

4.2 K,n = 4.6 .t013cm -3

Dependence of electron effective mass on carrier concentration: see Fig. 3; energy dependence caused by the non-parabolicity of the conduction band: see Fig. 4. 0.09m o

electro reflection

79Z

-50.6

intra conduction band magnetoabsorption

83G

cyclotron resonance

63B2

magnetoplasma resonance (decreases to 0.0147 at 150K)

80S

electron g-factor: gc

effective masses, holes (in units of mol: 0.45 (3)

T=4···77K, 1I[111J

0.42 (3) 0.34(3) 0.0158 (5)

II [ltOJ I [looJ

77 K, p-type

2.15 Indium antimonide (InSb) Numerical value

Physical property

Experimental conditions

143

Experimental method, remarks

Ref.

calculated using k· p theory

75W

valence band parameters:

-35

A B

- 31.4 20.92

lei Lattice properties Structure

InSb I

stable at normal pressure

space group (zincblende structure)

Data on high-pressure phases are conflicting [78Y]. 0.24 eV

80

InSb

on

50

K

on

sf.

.,..../

L--'

.-J.

...---

V

20

1 0.21 ...:J'

I

In Sb

'\

0.20 0.19

oa

50

1\

\6

0.18 0.17

\

ob OJ

0.4

0.5

0.5

0.7

0.8

0.9

1.0

E_

0.15

o

80

150 T-

240

320

Fig. 2. InSb. Energy gap vs. temperature below RT measured by resonant two-photon photo-Hall effect (full circles); open circles and triangles: earlier literature data for comparison. Solid curve: fit by Varshni's formula as given in the tables [85L2].

Fig. 4. InSb. Dependence of electron effective mass and gfactor on energy in the conduction band tJ.E = E - E,. (a) reciprocal mass and (b) g-factor vs. E = Eg/(E g + 2tJ.E) [83K].

0.D7 r - - - , - - - - , - - - - . , - - - . , - - - - - ,

In Sb

0.D51----t----+----+----+-----hI

i

0.05

to o

Faraday and VOigt} '" 77 K Faraday

f. 0.04

• • • • ..

magnetoplasma plasma magnetoplasma Faraday plasma

Ef

0.03

,,300 K -+-1------1 •• ••

ODZI----r-------I-----=:7"f"'--=---+-----.j

n-

Fig. 3. InSb. Electron effective mass vs. carrier concentration. Comparison of results of several experimental measurements. Solid line: Kane's theory [77S].

144

2.1 S Indium antimonide (InSb)

Physical property

Numerical value

Experimental conditions

Experimental method, remarks

Ref.

6.47937 A

298.1S K

X-ray

6SS

lattice parameter: a

Temperature dependence in the range 10···60 °C and coefficient oflinear thermal expansion, see Figs. Sand 6. density:

S.7747(4)gcm- 3

d

X-ray

6SS

melting point:

800(3) K

73H

phonon dispersion relations: Fig. 7.

6.4810

t

InSb

6.4805

V

16.4800 tJ

6.4795

V

6.4790 /

6.4785

o

V 10

V

V

30

40

lr .10

InSb i

5

./

}/

20

50

T_

60

z ____

o

70 '( 80

Fig. 6. InSb. Linear thermal expansion coefficient vs. temperature measured with an interferometer [58G]. High temperature range.

7,----------------,---,------------,-------,

InSb

6,.-----._

300 T-

Fig. 5. InSb. Lattice parameter vs. temperature [65S].

TNz

_____ ____--'

LO

4

3

r

A

Fig. 7. InSb. Phonon dispersion relations calculated with a six parameter dynamic model [85R]. Experimental points from [7IP].

2.15 Indium antimonide (lnSb) Numerical value

Physical property

145

Experimental conditions

Experimental method, remarks

Ref.

300K, n = 8'I0 13 cm- 3

coherent inelastic neutron scattering

71P

zone center phonons, Raman spectroscopy

84L

phonon frequencies (in THz): yLO(r 15)

5.90(25)

YTO(r 15) YTA(X 5 ) yLA (X 3 ) YLO(X I ) YTQ(X 5 ) yTA (L 3 ) yLA(Ld YLO(Ld YTQ(L 3 ) vTQ(r)

5.54 (5) 1.12 (5) 4.30(10) 4.75 (20) 5.38 (17) 0.98 (5) 3.81(6) 4.82 (10) 5.31 (6) 5.49 5.39 5.83 5.72

VLO(r) 10 .10 11 dyn

00

Crii2

In'Sb

'l....

OK, extrapol. RT -T

! I

a

OK, extrapol. RT

1041000 500 K 300

I (C 11

+2c I 2+

Q.l cm -l

4C44 )/3

f-

200

150

InSb

I

I

...............

I !

)

'""

I

--

."'-'l\.......

B

\

5 3.14 0

A a

bcx:Il

3.12

0

a

, \\ \ \ ,,\ 1?

C44

r 110

a

\ .\\\.\

I I

cJ08

-

'-'

I

106

10

104

\

102

1.58

'\

'T\\

\

\

0

1.56

\

5

J

-

\

0

6

2




g

(1)

[

(1)

-
0

til

::I 0-

0 C

'0

3

0

0.21

mp:

mn:

1.4 .. ·2.4

0.33

temperatures

all at low

m Lex : II

mp,h:

mp,l :

mn:

all at 4.2 K

20 L m ex : 2.5 mTex : 2.5

mp:

mn:

m [m o]

films have been prepared so far. Band structures of AgCl and AgBr: Fig. 38 (p. 257).

The silver halogenidcs AgF, AgCl and AgBr crystallize in the cubic NaCI structure. These materials are light-sensitive at room temperature. For AgF only crystalline thin

y-CuI

y-CuBr

zincblende

y-CuCI

T2d - F 43m

Structure

Substance

-..I

-

Ul

0-

;:l

r::

0

0

()

a '"0

"""

-

Structure

Tm[K] Cik [lOlldyn cm-2]

V

[THz]

m [mol

OSh - Tm3m

NaCllattice

OSh - Tm3m

NaCllattice

OSh - Tm3m

NaCllattice

3.18 =2 =3

VIO: VLO:

VIA: VLA:

Cll: 5.985 CI2: 3.611

0.624

a: 5.77475

Eg,dir:

3.92

VIO: VLO:

Cll: 5.610

3.270 0.724

C44:

4.14

2.37

4.62

&(00):

C12:

12.44

&(0) :

5.88

d: 6.4753 703 Tm:

C44:

Egx,dir:

11.14

&(0) : &(00) :

VLO:

Eg,dir:

Egx,dir:

Eg,ind:

Egx,ind:

Egx,ind:

Egx,dir:

d: 5.5667 728 Tm:

9.60

VIO:

Egx,ind:

a: 5.55023

2.99 5.10

&(00) :

10.6

&(0) :

d: 5.852 708 Tm:

a: 4.936

4.2

4.292

4.2

300

4.3 .. ·4.8 3.96 .. ·4.40

1.8

1.8

4.2

4.2

1.8

4.8

4.8

2.7125

2.6845

5.15

5.13

3.2476

4.63

2.8

mn:

0.302

1.25

0.215 mpil : mp.l: 0.52

mn:

mn,pol: 0.431

f.lp:

f.l n :

f.lp:

f.l n :

AgI

T2d - F 43m

zincblende

y-phase

a: 6.473

d: 6

Brillouin zone. The band structures are shown in Figs. 40 and 41 (p. 258). Eg,dir:

2.82

2.91

4 300

r

in the

at 4.2 K

500 .. ·2000 3.104

2

60

at 4.2 K

104 ... 4.104

For silver iodide two phases coexist at room temperature: P-AgI and the metatable y-AgI. Both are direct gap semiconductors with band extrema at the point

AgBr

AgCI

AgF

f.ln,H:

f.l [cm2Ns]

at T [K]

Eg [eV]

&(0), &(00)

a [A] d [g cm- 3]

Transport parameters

Band structure parameters

Static and dynamical lattice parameters

AgF, AgCI and AgBr are indirect gap semiconductors with the uppermost valence band located at L and the lowest conduction band at r.

Substance

en

P-

= ::s

0

'0

0

a

0

I

N

..... .....,

00

00 00

-

Hgl2

b: 12.445

in unit cell)

7.32

(4 molecules

c:

b: 13.76

4.674

a:

13-phase

orthorhombic

(2 molecules in unit cell)

a:

c: 12.36

tetragonal DI5 4h

4.357

6.798

a-phase

c:

CI22v

4.624

a:

orthorhombic

HgBr2

6.109

Ttr

0.35

C44: C66:

6.094 Tm: 532

0.727

C33 :

d:

1.526

C12: 0.559 CI3 : 1.168

CII: 3.16

6.36 400 (a

d: :

Tm: 509

d:

(3)

[THz]

E g,

L1 leV]

at T[K] m [mol

Vir:

See chapter 2.

mp.1:

mpll:

1.72 (2.106)

(0.37)

0.56 (1.03) polaron masses

90

0.25 (0.31 )

m n.1: 0.29

mnll:

3.75 3.05

4.2

4.2 300 4.2

values in brackets: Eg :

2.3707 2.140 1.012 0.199

0.85 3.45 4.38 3.15

0.54

L1cf:

.,(00).1: 5.15 VR:

L1so :

Eg,dir:

.,(00) II: 6.8

.,(0) II : 8.5 ., (0) .1 : 25.9

semiconducting properties proved, but no reliable data

V

Band structure parameters

4.9 111-V compounds

Cik [lOlldyn cm- 2]

Tm, Ttr [K]

Static and dynamical lattice parameters .,(0), .,(00) d [g cm- 3] a, b, c [A]

Structure

Substance

Jl n,dr.1 : 65

···100

Jl dr,n II: 50

Jl [cm2Ns]

Transport parameters

00 '-0

en

::l 0-

0

'"0

3

0

(")

\0

--.

Structure

Cjk

Eg [eV]

at T [K]

Band structure parameters

4.10 IH.-VIy compounds

[10lldyn cm-2]

Tm [K]

Static and dynamical lattice parameters a,c[A] d[gcm- 3] &(0),&(00)

m [mol

I-' [cm 2/Vs]

Transport parameters

Dl3h - P 6m2

on poly types

8 : C46v - P63mc

E :

ell : 10.24 Cl2 : 3.24

depending

y: C53v - R3m

poly types)

6.18

80

80

16

12

3.5

C66 :

I-' p l.,dr :

I-' p II ,dr :

50

250

60

210

I-' 0 1. ,dr :3000

l-'o,H:

0.8

0.2

I-' 0 II ,dr :

I-'p,H:

mpl.:

mpll :

0.5

0.70

4.2

mol.:

C55 :

2.103

300

3.07

Eg,iod:

2.021

4.2

Egx,dir:

2.1275

77

3.028

Eg,dir:

I-' p,dr :

I-' o,H : I-' p,H :

l.6

5

77

moll:

mo:

300

l.5

3.05

2.495

2.593

Eg,dir:

Egx,iod:

C33 :

&(00) 1.: 7.44

&(00) II: 5.76

&(0) II : &(0) 1. : 10.6

5.03

Tm:

13 : D46h - P63/mmc

&(00)11 : 5.3 &(00) 1.: 6.7

&(0) II : 5.9 &(0) 1. : 10.0

l211

d:

a: 3.755

C : 16 .. ·34

hexagonal layers

GaSe

(several

1233

Tm:

c: 15.492

D46h - P63/mmc

3.86

3.587 d:

a:

I3-GaS

hexagonal layers

Figs. 81 (p. 271) shows the Brillouin zone and Figs. 82 ... 84 (p. 271, 272) the band structures for GaS, GaSe and InSe.

p. 271), TIS, TISe and InTe in the tetragonal TlSe structure (Fig. 80, p. 271).

polytypes are known (Fig. 77, p. 270). The GaTe lattice is a monoclinic distorted GaSe lattice (Fig. 78, p. 270). InS crystallizes in an orthorhombic structure (Fig. 79,

GaS, GaSe and InSe crystallize in a hexagonal layer structure (Fig. 76, p. 270). The bonding is strongly covalent within the layers and weaker between them. Four basic

4.10.1 III-VI compounds

Substance

til

0-

§

.go

8

.........

- 0.005

(A,B) 77

300

(A,B,C)

m [mol

L1so :

1.53

at T [K]

Transport parameters

L1cf:

Eg,dir:

E g,

Band structure parameters

£(0) 1-: 16.0

£(0) II: 15.2

VLO:

VTO:

4.74

d:

a:

c: 11.08

5.52

V [THz]

£(0), £(00)

Tm [K]

d [g

DI2 2d - I 42d

CulnS2

a, c [A] cm- 3 ]

Static and dynamical lattice parameters

chalcopyrite

Structure

Substance

AglnS2

AgGaTe2

AgGaSe2

4.97 1150

d:

Tm:

c: 10.88

6.29

c: 11.95

5.82

a:

a:

c: 11.l7

Dl22d - I 42d

chalcopyrite

Dl22d - I 42d

chalcopyrite

phase

a: 6.954

b: 8.264

c: 6.683

orthorhombic

phase

wurtzite-type

Dl22d - 142d

d: 6.08 Tm: 950

5.98

5.70 1130

d:

Tm:

···1320

a:

1220

Tm: 5.50

11.8

VLO:

(A) 300

Eg,dir:

LIef:

(A) 300 2.168

(C) 300

(B) 300

2.081 2.144

300

- 0.15

(B,C) 300

::l

6.63

VLO:

2.02

'0

0

U>

0-

s::

3

6.12

0

0-

5·

s::

.0

0-

§

(1)

a

....

0(1) 0-

0 ::l

cr

""

(1)

..,0-

>-:l

!J'

VTO:

1.87

300

77

77

105

108

0

Eg,dir:

1.32

0.31

- 0.25

p:

p:

IV

-"""

&(00).L:l1.86

&(00)11: 11.0

&(O).L: 15.0

Eg,dir:

Llso :

8.22

VLO:

&(0) II: 14.5

LIef:

7.44

2.29

&(00).L: 6.80 VTO:

(B) 77

2.02

&(00)11: 6.95 (C) 77

(A) 77

1.83

77

&(0) .L: 9.05

0

77

(B,C) 77

3.01 - 0.28

(A) 77

300

2.73

2.638

300

Eg,dir:

Llso :

LIef:

Eg,dir:

p[Qm]

Eg, LI [eV] at T [K]

Transport parameters

Band structure parameters

1.80

&(0) II: 10.48

11.0

VTO:

&(00).L: 5.90

&(00)11:

&(O).L : 8.51

8.21

&(0) II:

4.70

d:

chalcopyrite

5.75

a:

V [THz]

Tm [K]

c: 10.29

&(0),&(00)

d [g cm-3]

Dl22d - I 42d

AgGaS2

a, b, c [A]

Static and dynamical lattice parameters

chalcopyrite

Structure

Substance

chalcopyrite DI22d - I 42d

chalcopyrite DI2 2d - 142d

AglnSe2

AglnTe2

5.82 1055

d:

Tm:

d: 1.96 Tm: 960

a: 6.095 c: 11.69

a: 6.43 c: 12.59

Tm [K]

d [g cm-3]

&(00)11: 6.38 &(00) 1.: 6.48

&(0) II : 7.68 &(0) 1.: 8.10

&(00)11: 7.16 &(00)1.: 7.20

&(0) II: 10.73 &(0)1.: 11.94

&(0), &(00)

Static and dynamical lattice parameters

a, c [A]

300 300

- 0.12 0.30

Acf: Aso:

Eg,ind: Eg,lh:

300 300

1.12 0.99 0.95

Eg,dir:

AgFeTe2

AgFeSe2

tetragonal

a: c: 6.58 8.96

Tm:

953

Tm: 1009

0':

J.J n

0':

:

:

700

2000

1500

250

0':

J.J n

50 400

J.J p :

700 0':

Tm: 1015

20 J.J p :

850

100 0':

30

750 8·1011 10-4

... 1150

Tm: 1120

CuFeTe2

a: 5.29 c: 10.41 Tm:

chalcopyrite DI22d - I 42d

CuFeSe2

CuFeS2

J.J p :

0':

J.J n :

n:

(A) 300

(C) 300

1.33 1.60

1.24

n [cm-3]

0' [Q-1cm-1]

J.J [cm2Ns]

Transport parameters

(B) 300

Eg,dir:

at T[K]

Band structure parameters Eg, A [eV]

These are a few data available on the mineral chalcopyrite (CuFeS2, band structure: Fig. 148, p. 293) and related compounds:

Structure

Substance

VI

IV .....

Co en

::I

0 &::

3 '0

0

0

I

cS·

&::

gj Co .c

act

Co

CD

Co

::I

o

c-

'
'

c:

.0

0-

I>'

::;

("0

0-

.... ...::;

("0

0-

0 ::;

0-

0-

...e:..

("0

-l

!""

d:

3.97 Tm: 1390

Tm: >1120

a: 6.273 c: 12.546

a: 5.679 c: 10.431

a: 5.885 c: 10.881

a: 5.740 c: 10.776

chalcopyrite DI2 2d - I 42d

chalcopyrite DI2 2d - I 42d

chalcopyrite DI2 2d - I 42d

chalcopyrite DI2 2d - I 42d

ZnSnSb2

CdSiP2

CdSiAs2

CdGeP2 Tm:

1073

Tm [K]

VLO:

VTO:

VLO:

VTO:

Static and dynamical lattice parameters d [g cm-3] a, c [A] V [THz]

Structure

Substance

11.52 12.0

14.67 15.36

Llso :

Lief:

Eg,dir:

Llso :

Lief:

Eg,dir:

Llso :

Lief:

Eg,pseu: Eg,dir:

Eg,opt:

1.72 1.90 1.99 - 0.2 0.11

1.55 1.74 1.99 - 0.24 0.297

2.2 2.75 2.945 2.71 2.75 0.20 0.07

0.4 0.7

(A) 300 (B) 300 (C) 300 300 300

(A) 300 (B) 300 (C) 300 300 300

0.025 0.031 0.25

mnll: 1.068 mn.L: 0.124

mp2 : mp3 :

300 300 (A) 90 (B) 90 (C) 90 300 300

mn:

77

m [mol

300

Band structure parameters Eg, LI [eV] at T [K]

30 .. ·60 107 ... 2.10 7 J1 p : p:

n:

100 1012 ... 1015

300 .. ·500 6.1015

80 .. · 150 1014 ... 1015

1020

70

J1 n :

p:

J1 p :

n:

J1 n :

J1 p : p:

n,p [cm-3]

p[Qm]

Transport parameters J1 [cm 2/Vs]

.....

tv

Vl

::l 0-

c:

0

'0

3

(")

0

S'

0-

c:

..c

0-

§

("1)

a

cr" 0 ::l 0("1) 0-

.z

eo.

0...,

("1)

g.

-l

00

chalcopyrite DI2 2d - I 42d

CdSnAs2

6.089

c: 11.925

a:

c: 11.514

5.6 943

5.71

Tm: 868

d:

Tm: 840

Tm:

d:

[K]

d [g

11.8

(B) 300 (C) 300 300 300

0.30 0.79 - 0.06 0.48

Lief: Llso :

(A) 300

12.1

&(0) : 0.26

300

0.48

Llso :

Eg,dir:

300

- 0.10

Lief:

10.59

VLO:

(C) 300

1.33

(B) 300

(A) 300

11.67

1.25

1.17

VTO:

Eg,dir:

300

0.33

Llso :

&(00) : 10.0

&(0) :

300

(C) 300

1.02 - 0.21

Lief:

8.40

VLO:

(B) 300

(A) 300

at T [K]

8.16

VTO:

0.57 0.73

Eg,dir:

E g, LI leV]

&(00)1-: 15.2

&(00)11: 15.4

V [THz]

&(0), &(00)

Band structure parameters

mn:

mp:

0.05

0.035

mn: 0.26

m [mol

:

1000 .. ·4000

:

p,h :

:

J1 p,l :

J1

J1 n

p:

J1 p :

n:

J1 n

:

== 540

== 36

11000 ... 15000

90 .. · 150 10 14

400 .. ·2000 1015 .. · 1018

140 ... 400 p: 7.1015 ... 10 16 J1 p

n: 4.10 16 ... 1018

J1 n

n,p[cm- 3 ]

J1 [cm 2/Vs]

Transport parameters

CU2GeS3

formation.

tetragonal

5.317

c: 10.438

a: 4.45

1220

d:

Tm:

Eg,th:

0.3

:

p:

J1 p :

J1 n

360 3.10 17

3

The structures of the IrIV-V3 compounds are not known in detail. They generally adopt a disordered zincblende-like lattice with the tendency of superstructure

5.1.4 I,-IV-V, compounds

5.901

a:

chalcopyrite DI2 2d - I 42d

CdSnP2

5.943

a:

c: 11.220

DI2 2d - 142d

CdGeAs2

a, c [A]

cm- 3]

Static and dynamical lattice parameters

chalcopyrite

Structure

Substance

0-

S'

tv

'"

0-

;:I

-=

o

8 -0

o

n

Q

0-

..0 C

§

Q

:3

ct

0-

(1;

0-

;:I

o

cr"

0-

e.

(1;

§.

-l

..,

VI

590

Eg,th :

0.08

293

77

:

:

p:

J..l p :

p:

J..lp:

p:

J..l p

p:

J..l p :

p:

J..lp:

p:

J..l p :

J..l n n:

p:

J..l p :

p [cm-3]

600 5.1017

910 lOIS

720 8.1017

850 2·1017

870 5.1.10 17

605 6.1.10 17

0.5 1.2.1020

283 1.5.1017

J..l [cm2Ns]

Transport parameters

Little is known about the members of this group. Two structures are predominant the enargite structure (Fig. 154, p. 294) and the famatinite structure (Fig. 155, p. 294).

5.1.5 Iz-V-VI4 compounds

Tm:

0.7 Eg,th:

zincblende-like

0.81 Eg,opt:

760

Tm:

Eg,th:

Ag2SnSe3

0.9 0.25

0.91

Eg,opt:

Eg,th:

Ag2SnTe3

293

293

at T [K]

293 0.6 .. ·0.83

0.96

600

Eg,th:

Eg,opt:

Tm:

970

Ag2GeTe 3

Tm:

810

a: 5.6877

0.59

0.91

0.94

Tm:

cubic

disordered

Eg,th:

Eg,opt:

Eg,opt:

Eg [eV]

Band structure parameters

Ag2GeSe3

CU2SnSe3

Tm: 1120

5.445

a:

cubic

disordered

CU2SnS3

Tm: 2050

a: 5.5913 c: 10.977

tetragonal

CU2GeSe3

Tm [K]

Static and dynamical lattice parameters

a, c [A]

Structure

Substance

.., e:.

en

0-

c:: ::s

'"0 0

3

0

(")

0-

:i"

c::

.0

§

0-

c> 3

0-

."

0-

::s

cr" 0

'


N

{Il

0-

0 C ::l

'"0

3

0

(")

Q

3

10 12 p: fJ n,H :

'Tj

w w

tv

0.3

COP2 COAS2 COSb2 RhP2 RhAs2 IrP2 IrAs2 IrAsSb

arsenopyrite C5 2h - P21/c

NiP2 PdP2 PdPAs

C6 2h - C2/c

0.5 0.6 .. ·0.7 0.45

marcasite 0122h - Pnnm pyrite T6 h - Pa3

= 0.05

NiAs2

239

W)

PtP2 PtPAs PtAs2 PtSb2

> 0.02 0.15 .. ·0.35 0.17 =1 1.15 =0.4 1.1 =0.4

= 0.10 (ind.) >0.4 (dir. )

> 0.6 > 0.4 0.17 ... 0.5 0.05 .. ·0.11

COP3 COAS3 COSb3

skutterodite T5 h - 1m3

0.45 0.6 0.25

2.0

> 0.2 >1.5

0.8

> 0.45 1 ... 5

0.27

0.14

0.38 .. ·0.64

0.4 0.1

242 Substance

6.3 Binary rare earth compounds Structure, space group

Energy gaps leV]

Eg,opt

Carrier mobilities

Eg,th leV]

2

f.l n [cm Ns]

2

f.l p [cm Ns]

6.3 Binary rare earth compounds In rare earth compounds f- and d-bands play an important role. Optical energy gap data below are transitions between such bands or from f-bands into the conduction band. Instead of thermal gaps Eg,th we list here activation energies EA for conductivity. SmS

cubic 0\ -Fm3m

SmSe SmTe EuO EuS EuSe EuTe TmTe YbS YbSe YbTe

13-LaIOS140

tetragonal D204h - I41/acd

::0.2 2.3 0.46 1.4 0.63 l.l2 3.9 1.65 2.3 1.80 2.0 0.22···0.35 1 ... l.l 1.5 1.8 ... 2.0

(4f-5d) (3p6_5d) (4f-5d) (4p6_5d) (4f-5d) (4f-5d) (2p6_5d) (4f-5d) (3p6_5d) (4f-5d) (4f-5d)

2.6 2.69

0.132 (EA) 0.22, 0.32 (EA)

Sm3S4 EU3S4 y-La2S3 y-La2Te3 y-Ce2S3 y-Nd2S3 EU2Se3 y-Gd2S3 y-DY2S3

Th3P4-type T6d- I43d

O-DY2S3 O-H02S3

monoclinic C22h - P21/m

0.34 (EA) 0.5 (EA)

E-Yb2S3

rhombohedral D6 3d - R 3c

0.29 (EA)

1.7 2.9

2.0···2.3 1.02 3.4 3···3.8

0.43 (EA) 2.33 (EA) 2.7···3.8 (E A) 1.6 ... 1.9 (EA) 1.5 (EA)

20···25

20···30 30 0.5 33···58

6.4 Ternary transition metal compounds Substance

Structure, space group

Energy gaps E g•opt [eV]

243 Carrier mobilities

Eg.th

[eV]

J.in [cm 2Ns]

J.ip [cm 2Ns]

6.4 Ternary transition metal compounds 6.4.1 Pnigochalcogenides Most of the semiconducting compounds of transition metals with pnictides and chalcogenides (T -V-VI) are ternary analogs of the corresponding binary phases with the same cation d-electron configuration. FePS FeAsS FeAsSe FeSbTe RuPS RuAsS RuSbSe RuSbTe OsPS OsAsS OsSbS OsPSe

arsenopyrite-type C52h - P2!/c

CoSbS CoAsSe

pararammelsbergite-type D!5 2h - Pbca

PdPS PdPSe

PdPS-type D!42h - Pbcn

CoPS CoAsS

pyrite-type C5 2v - Pca2!

0.25 0.3···0.5 0.6 0.04 (EA)

>1.4 = 1.2 = 0.9

0.35 0.5

>1.4 =1.3 1.2 =1.4 0.5 0.2 1.4 1.38

0.15 (EA)

0.4 0.60···0.75

6.4.2 Spinels and related compounds MnGa2S4

MnSb2S4 CdCr2S4 FeCr2S4 HgCr2S4 CdCr2Se4 CuCr2S3Se CuCr2S2.5Se!.5 HgCr2Se4 ZnCr2Se4 BaCr2S4

1.2

monoclinic C6 4h - C2/c spinel-type

0\ - Fd3m

>1.5 1.42 1.2··· 1.7

1.0 0.17 ... 0.35 (EA) 0.02 (EA) 0.36 (EA)

0.3

0.050 (EA)

0.15 0.70

0.066 0.84 1.285 hexagonal

1.0 ... 1.5

0.36 (EA)

1 ···6

244 Substance

6.5 Ternary rare earth compounds Structure, space group

Energy gaps Eg,opt [eV]

Carrier mobilities Eg,th [eV]

2

Jl n [cm Ns]

2

Jl p [cm Ns]

6.4.3 Oxides Many of the semiconducting transition metal oxides are of interest as ferroelectrics. Reliable semiconductor data as optical energy gaps (mostly> 3 eV) or activation energies for conductivity are available only for a small number of compounds. As examples of such ternary oxides we mention BaTi03, PbTi03, NaNb03, KNb03, KTa03, SrTi03, PbZr03, CaV03, LiV03, LaV03, MnV03, SbNb04, PbMo04, PbW04,K2Cr04, CuFe204, C03V20g, BhPt20 7.

5.4.4 Further chalcogenides MnO.3NbS2 Feo.3NbS2 COo.3NbS2 Nio.3NbS2

hexagonal planes, Mn,Fe,Co,Ni intercalated

0.85 1.05 0.90 0.85

cubic T3 d - 143m

1.76

6.3 4.4 5.1 4.3

6.S Ternary rare earth compounds For a large number of ternary rare earth compounds data on energy gaps or activation energies for conductivity are published. We list only compounds where RT data are available. NdTi03 SmTi03 GdTi03 TbTi03 HoTi03 ErTi03 YbTi03 LaV03 CeV03 PrV03 NdV03 SmY03 EuY03 GdV03 TbV03 DyV0 3 HoY03 ErV03 TmV03 YbY03 LaCr03 NdCr03 SmCr03 DyCr03

orthorhombic D16 2h - Pbnm

=1

0.06 (EA) 0.15 (EA) 0.19 (EA) 0.2 (EA) 0.2 (EA) 0.24 (EA) 0.24 (EA) 0.16 (EA) 0.054 (EA) 0.103 (EA) 0 (EA) 0.130 (EA) 0.132 (EA) 0.141 (EA) 0.101 (EA) 0.125 (EA) 0.128 (EA) 0.173 (EA) 0.166 (EA) 0.169 (EA)

0.15

=

4.7

0.18 ... 0.6 (EA) 0.29 (EA)

0.36

0.005

6.5 Ternary rare earth compounds Substance

Structure, space group

Energy gaps Eg,opt leV]

Carrier mobilities Eg,th leV]

0.33 0.37 0.13 0.39 0.89 1.l0

HoCr03 YbCr03 LaMn03 LaFe03 GdFe03 HoFe03

(EA) (EA) (EA) (EA) (EA) (EA)

HoMn03 YbMn03

hexagonal C3 6v - P63cm

0.57 (EA) 0.73 (EA)

LaCo03

rhombohedral D6 3d - R 3c

0.2 (EA)

monoclinic P21/b

1.81 1.62 0.15

CU3TbS3 CU3DyS3 CU3YS3 CU3HoS3 CU3YbS3 CU3LuS3 CU3SCS3 CU3GdSe3 CU3TbSe3 CU3DySe3 CU3YSe3 CU3HoSe3 CU3YbSe3 CU3ScSe3 CU3SmTe3 CU3GdTe3 CU3TbTe3 CU3DyTe3 CU3YTe3 CU3HoTe3 CU3ErTe3 CU3TmTe3

trigonal P3

1.62 1.60 1.78 1.65 1.56 1.50 1.86 0.14 0.16 0.20 0.88 0.16 0.20 0.30 0.23 0.52 0.46 0.34 0.72 0.26 0.24 0.14

CUSHOS4 CUSLUS4 CUsGdSe4 CUsTbSe4 CuSYbSe4 CUSLuSe4

hexagonal

0.53 0.50 0.64 1.04 0.80 1.00

ZnTm2S4 ZnYb2S4 ZnLu2S4

orthorhombic

ZnSc2S4

spinel

CU3SmS3 CU3GdS3 CU3SmSe3

CS2h -

245

f..I.n [cm 2Ns]

f..I.p [cm2Ns]

0.0002

3.6 2.5 3.7

2::

2.1

3 .. ·40 doped with Ag,Cr,Ga

246 Substance

6.5 Ternary rare earth compounds Structure, space group

Energy gaps [eV]

Eg,opt

C dLa2S4 CdPr2S4 CdDY2S4

cubic trigonal

2.1

CdEr2S4 CdTm2S4 CdYb2S4 CdSC2S4

spinel

1.8

La2GeSes La2SnSes Ce2GeSeS Ce2SnSeS Pr2GeSeS Pr2SnSeS Nd2GeSeS Nd2SnSeS Sm2GeSeS Sm2SnSeS Gd2GeSes Gd2SnSes

2.3 1.7 1.65 1.55 1.52 1.82 1.65 1.90 1.70 2.00 1.88 1.90 1.70

Carrier mobilities Eg,th [eV]

f.ln [cm 2Ns]

f.lp [cm 2Ns]

40 doped with Li,Cr

7 Figures to chapters 3, 4 and 5

247

7 Figures to chapters 3, 4 and 5

Fig.I. 8. BI2 icosahedron wilh examples of 2-fold, 3-fold and 5-fold rotation axes.

,.12.5671

Fig.2. a-rhombohedral B. B12 icosahedra at the corners of the unit cell as viewed from above. Interatomic distances for the different types of bonds are indicated.

Fig.3. unit cell.

B. Model or the

FigA. a- and 13-rhombohedral B. Brillouin zone of the rhombohedral lattices.

7 Figures to chapters 3, 4 and 5

'"c:

"C

0

Fig.6. P. Perspective view of a portion of the black phosphorus structure; b-axis vertical and a-axis horizontal.

.0

Cl>

u

I, Z,

c: 0

:>

0.1

Fig.5. a-rhombohedral B. Band structure along the r - Z direction. Fig.7. P. Brillouin zone of orthorhombic black phosphorus.

-0.50'--_.,.,.-_'--_ _ _--'_ _ _-'--_ _-"--_ _-'-_ _-'

Z

r

r

k

r

Fig.8. P (black). Band structure calculated with the self-consistent pseudopotential method.

7 Figures to chapters 3, 4 and 5

249

..J "l' I

-/

/

(d- r+---7 I

I::::::::=:

V

I

I

_I V

a

b Fig.9. The A7 crystal structure (a) and the cubic NaCI structure

(b) from which it can be derived. The rhombohedral angle a is indicated. Open circles represent sublattice one, solid circles sublattice two.

Fig. 10. As, Sb, Bi. Brillouin zone of the rhombohedral lattice, showing points, lines and planes of symmetry. a indicates the hatched plane.

0.1

XVK

__ I

rAT

____ Q

W

LUSX k

(J

r

(J

LNUM

Fig.ll. Band structure of rhombohedral without spin along various symmetry lines, obtained from pseudopotential calculations. Solid lines and dashed lines indicate different symmetries.

250

7 Figures to chapters 3, 4 and 5

0.8

x,

K,

Sb

lJ l,

,

l,

r; EJ /

..... -

0.6

/

/

/

/

/

/

IT,

l l ' - - U,

l,

,-_ ......

' J', TJ

Il'

10.5 V>

Q.>

1i

0.4 XJ

l.

0.15

x,

l."

L,

I, I,

-6 A

T

k

l'ig.148. CuFeSz. Band slruclure of Ihe anliferromagnelic phase showing conduclion and valence and d-bands in Ihe fundamenlal gap.

24

cJ -4 I

'-'-'

-12

______________

- L_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Z

1\

r k

Fig,IS2. CdSnP2. Band slruclure.

7 Figures to chapters 3, 4 and 5

294 6

3 1

CdSnAs 2

eV

4

5 4

2-

I

3

1

--

o

'-