Semiconductors: Group IV Elements and III-V Compounds

169 Pages·1991·4.32 MB·English

by  O. Madelung (auth.), O. Madelung (eds.)

Data in Science and Technology
Editor in Chief: R. Poerschke
Semiconductors
Group IV Elements and III- V Compounds
Editor: O. Madelung
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
ISBN-13: 978-3-540-53150-0 e-ISBN-13: 978-3-642-45681-7
001: 10.1007/978-3-642-45681-7
Library of Congress Cataloging-in-Publication Data
Semiconductors: group IV elements and II I-V compounds I editor, o. Madelung.
p. cm. --(Data in science and technology)
Includes bibliographical references.
ISBN 978-3-54().53150.o (Springer-Verlag Berlin Heidelberg New York : acid-free paper)
I. Semiconductors--Handbooks, manuals, etc. I. Madelung, O. (Otfried) II. Series
QC611.45.S46 1991
537.6'22--dc20 90-26078 CIP
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Preface
The frequent use of well known critical data handbooks like Beilstein, Gmelin and Landolt
Bornstein 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
for having at their working place a comprehensive, high quality, but cheap collection of at least
the basic data oftheirfield of interest the series "Data in Science and Technology"is started now.
This first volume presents the most important data on two groups of semiconductors, the
elements of the IVth group of the periodic system and the III-V compounds. All data were
compiled from information on about 2500 pages in various volumes of the New Series of
Landolt-Bornstein.
For each critically chosen data set and each figure the original literature is cited. In addition,
tables of content refer to the handbooks the data were drawn from. Thus the presentation of data
in this volume is of the same high quality standard as in the original evaluated data collections.
We hope to meet the needs of the physical community with the volumes of the series "Data
in Science and Technology", forming bridges between the laboratory and additional information
sources in the libraries.
Berlin/Marburg, February 1991 The Editors
Table of contents
A Introduction
1 General remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Physical quantities tabulated in this volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
B Physical data
1 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 (Six Gel_x) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5"1
2 I II-V compollnds
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. . . . . . . . . . . . . . . . . . . . . . . . . . 150
Appendix:
Contents of the volumes of the New Series ofLandolt-B6rnstein
dealing with group IV and III-V semiconductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
A Introduction
1 General remarks
This volume contains basic data on Group IV and III -V Semiconductors. All data were compiled from
volumes of the New Series of the Landolt-Bornstein data handbook. They comprise the information a scientist
working on semiconductors is needing in his every-day work.
The data presented in this book 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 / spin-orbit 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 I 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.
Although the most relevant data have been summarized here the respective vofumes of the New Series of
Landolt-Bornstein contain much more information about these topics. In addition data on other properties can
be found on the about 2500 pages of volumes 17a, 17c, 17d, 22a, 22b and 23a of Group III of the New Series:
Volume III/17a (and its supplement and extension 11I/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 11I/22b 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 and III-V semiconductors.
Chapter 2.1 of volume 11I/23a 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.
2 Introduction
2 Physical quantities tabulated in this volume
Data on the following physical quantities are given in the tables and figures of Part B:
Sections on electronic properties
energies (unit eV):
E(k) 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, ~ ... ,
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 (1, 1',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)
th: thermal gap (energy gap extrapolated to 0 K from transport measurements)
x: excitonic gap (energy gap minus exciton binding energy)
binding energy of the exciton
mostly spin-orbit splittlngs of energy levels (subscripts 0, so, 1,2 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, E1, E2·· .).
effective masses (in units of the electron mass mo):
m mp effective mass of electrons (holes); other subscripts refer to:
n,
c: conductivity 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. .
further conduction and valence band parameters:
ellipsoidal energy surfaces as occuring in the conduction band of group IV and 111-V semiconductors are
characterized by the longitudinal and transverse effective masses
mil' m.L defined by the equation E(k) = E(ko) + h2K;/2mll + h2(K~ + K;)/2m.L
where K=k-ko and Kxllko,Ky,Kz~ko·
camel's back structure occurs at the conduction band edge in several 111-V compounds. The relevant
parameters
.1, .10, I1E, mil 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 E(k) = E(O) + (h2k2/2mO)(A ± (B2 + SC2)1/2)
S = (k2k2 + k2k 2 + k2k 2)/k4.
xy yz zx
Introduction 3
g-factor of electrons: gc
Sections on lattice properties
crystal lattice:
a, b, C lattice parameters (unit A or nm)
coefficient of linear thermal expansion (unit K -I)
(J.
d density (unit g cm -3)
Tm melting temperature (unit K)
Ptr transition pressure for phase transitions (unit Pal
phonon parameters:
v phonon frequency (unit s -I)
v phonon wavenumber (unit cm -I)
v(k) phonon dispersion relation (dependence of phonon frequency on wave vector); instead of k often the
reduced wave vector' = klkmax is used.
Subscripts to the frequencies (wavenumbers) refer to transverse and longitudinal optical and acoustic
branches (TO, LO, T A, LA) and to the symmetry points in the Brillouin zone as for the band structure
energies.
elastic moduli:
Clm,Clmn second (third) order elastic moduli (unitdyncm-Z)
Sections on transport properties
transport parameters:
resistance (unit Q)
Hall coefficient (unitcm3C-1)
(intrinsic) electrical conductivity (unit Q -1 cm -I)
electrical resistivity (unit Q cm)
thermal conductivity (subscript L: lattice contribution) (unit W cm -1 K -I)
carrier concentrations (unit cm -3):
n electron concentration
P hole concentration
nj intrinsic carrier concentration
carrier mobilities (unit cmzI V s):
I1n,l1p electron and hole mobilities, respectively. Further subscripts refer to:
dr: drift mobility
c: conductivity mobility
H: Hall mobility
Sections on optical properties
optical constants:
K absorption coefficient (unit cm -I)
R reflectance (dimensionless)
n (real) refractive index (dimensionless)
k extinction coefficient (dimensionless)
4 Introduction
G dielectric constant; 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
((fJ): high frequency limit
Sections on impurities and defects
(Substitutional impurities are designated by (s), interstitial ones by (i))
solubility:
ceq solubility of an impurity (maximum concentration incorporated in the solid in equilibrium without
inducing a phase transition) (unit cm ~ 3)
co,I1H parameters of the Arrhenius equation ceq = Co exp [ - H/kB T]
For a retrograde solubility a maximum solubility c~~x is observed at a temperature Tmax < Tm.
diffusion coefficient:
D diffusion coefficient (unit cm2 s ~ 1)
Do, Q parameters occurring in the equation D = Doexp[Q/kBT]
energy levels:
Eb binding energy of donors (Ee - Ed) or acceptors (Ea - Ev)
E for deep levels the type (d, a) is given; positive values refer to the valence band edge, negative values to
the conduction band edge
B Physical data
1 Elements of the IV th group and IV-IV compounds
Physical Numerical Experimental Experimental method, Ref.
property value conditions remarks
1.1 Diamond (C)
Electronic properties
band structure: Fig. 1 [84C] (Brillouin zone: Fig. 2)
Diamond is an indirect gap semiconductor, the lowest minima of the conduction band being located along
the A-axes. The valence band has the structure common to all group IV semiconductors: three at r degenerate
bands (spin neglected, symmetry r 25')' The spin orbit splitting of these bands is neglegible.
15r-~~-'----~--r-~~==~-'
eV
Diamond
-zo 1, r,
-ZSl...-___" --___- -'-_-'--___- ---'
L A r A U.K r r
k
Fig. I. Diamond. Band structure calculated by an ab mtio Fig. 2. Brillouin zone of the face centered cubic lattice, the
LCAO method [84C]. Bravais lattice of the diamond and zincblende structures.
550
I
eV
Ooa; Diamond
ru o~ ~
5.45
~
~
..;j' 5.40 '"
5.35
100 zoo 300 400 500 600 K 700
T--_ Fig. 3. Diamond. Indirect gap vs. temperature [64C].