Martienssen W., Warlimont H. (Eds.). Handbook of Condensed Matter and Materials Data

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572 Part 3 Classes of Materials

Table 3.4-30 Commercial infrared-transmitting glasses, cont.

Glass type Glass Transparency Refractive Density Thermal Transformation Manufacturer

name range

index n (g/cm

) expansion temperature

(µm) α(10

−6

/K) T

(

◦

Chalcogenide AMTIR1 0.8–12 2.5109

4.4 12 362 Amorph. Materials

IG1.1 0.8–12 2.4086

3.32 24.6 150 Vitron

AMTIR3 1.0–13 2.6173

4.7 13.1 278 Amorph. Materials

IG6 0.9–14 2.7907

4.63 20.7 185 Vitron

IG2 0.9–15 2.5098

4.41 12.1 368 Vitron

IG3 1.4–16 2.7993

4.84 13.4 275 Vitron

1.0–16 2.653

4.53 30 98 Corning France

IG5 1.0–16 2.6187

4.66 14.0 285 Vitron

IG4 0.9–16 2.6183

4.47 20.4 225 Vitron

1173 0.9–16 2.616

4.67 15 300 Texas Instruments

50% internal transmission for 5 mm path length.

Refractive index at 0.587 µm.

This glass contains SiO

Refractive index at 0.75 µm.

Refractive index at 5 µm.

References

4.1 S. R. Elliott: Physics of Amorphous Materials (Long-

man, Harlow 1990)

4.2 H. Bach, D. Krause (Eds.): Analysis of the Composition

and Structure of Glass and Glass Ceramics (Springer,

Berlin, Heidelberg 1999) 2nd printing

4.3 H. Bach (Ed.): Low Thermal Expansion Glass Ceramics

(Springer, Berlin, Heidelberg 1995)

4.4 W. Höland, G. Beall: Glass Ceramic Technology

(American Ceramic Society, Westerville 2002)

4.5 N. P. Bansal, R. H. Doremus: Handbook of Glass

Properties (Academic Press, Orlando 1986)

4.6 O. V. Mazurin, M. V. Streltsina, T. P. Shvaiko-

Shvaikovskaya: Handbook of Glass Data,PartA,

Silica Glass and Binary Silicate Glasses;PartB,Single

Component and Binary Non-silicate Oxide Glasses;

Part C, Ternary Silicate Glasses, Physical Sciences Data

Series, Vol. 15, (Elsevier, Amsterdam 1983–1987)

4.7 R. Blachnik (Ed.): Taschenbuch für Chemiker und

Physiker, D’Ans-Lax, Vol. 3, 4th edn. (Springer,

Berlin, Heidelberg 1998)

4.8 MDL SciGlass, Version 4.0 (Elsevier, Amsterdam)

4.9 INTERGLAD (International Glass Database), Version 5,

New Glass Forum

4.10 S. English, W. E. S. Turner: Relationship between

chemical composition and the thermal expansion

of glasses, J. Am. Ceram. Soc. 10, 551 (1927); J. Am.

Ceram. Soc. 12 (1929) 760

4.11 A. Paul: Chemistry of Glasses (Chapman and Hall,

New York 1982)

4.12 H. Bach, N. Neuroth (Eds.): The Properties of Optical

Glass, Schott Series on Glass and Glass Ceramics, 2nd

printing (Springer, Berlin, Heidelberg 1998)

4.13 A. Winckelmann, F. O. Schott: Über thermische

Widerstandskoefﬁzienten verschiedener Gläser in

ihrer Abhängigkeit von der chemischen Zusam-

mensetzung, Ann. Phys. (Leipzig) 51, 730–

746 (1894)

4.14 H. Scholze: Glass (Vieweg, Braunschweig 1965)

4.15 Schott: Schott Technical Glasses (Schott Glas, Mainz

2000)

4.16 H. R. Philipp: Silicon dioxide (SiO

) (glass). In: Hand-

book of Optical Constants of Solids, ed. by E. D. Palik

(Academic Press, New York 1985) pp. 749–763

4.17 C. R. Bamford: Colour Generation and Control in

Glass (Elsevier, Amsterdam 1977)

4.18 W. H. Dumbaugh: Infrared-transmitting oxide

glasses, Proc. SPIE 618, 160–164 (1986)

4.19 N. Neuroth: Zusammenstellung der Infrarotspektren

von Glasbildnern und Gläsern, Glastechn. Ber. 41,

243–253 (1968)

4.20 J. Lucas, J.-J. Adam: Halide glasses and their opti-

cal properties, Glastechn. Ber. 62, 422–440 (1989)

W. Vogel: Glass Chemistry (Springer, Berlin, Heidel-

berg 1994)

Part 3 4

573

Functional

Part 4

Part 4 Functional Materials

1 Semiconductors

Werner Martienssen, Frankfurt/Main, Germany

2 Superconductors

Claus Fischer, Dresden, Germany

Günter Fuchs, Dresden, Germany

Bernhard Holzapfel, Dresden, Germany

Barbara Schüpp-Niewa, Dresden, Germany

Hans Warlimont, Dresden, Germany

3 Magnetic Materials

Hideki Harada, Higashikaya, Fukaya,

Saitama, Japan

Manfred Müller, Dresden, Germany

Hans Warlimont, Dresden, Germany

4 Dielectrics and Electrooptics

Gagik G. Gurzadyan, Garching, Germany

Pancho Tzankov, Berlin, Germany

5 Ferroelectrics and Antiferroelectrics

Toshio Mitsui, Takarazuka, Japan

574

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575

Semiconducto

4.1. Semiconductors

The organization of this section follows a two-step

approach. The ﬁrst step corresponds to searching

for the substance of interest, that is, the relevant

group of substances. The second step corresponds

to the physical property of interest.

This section has three subsections, character-

ized by the groups of the Periodic Table that the

constituent elements belong to. The ﬁrst sub-

section, Sect. 4.1.1, deals with the elements of

Group IV of the Periodic Table and semiconduct-

ing binary compounds between elements of this

group (IV–IV compounds). The second subsection,

Sect. 4.1.2, treats the semiconducting binary com-

pounds between the elements of Groups III and

V (III–V compounds); Sect. 4.1.3 treats compounds

between the elements of Groups II and VI (II–VI

compounds). These two subsections are subdi-

vided further according to the ﬁrst element in the

formula of the compound.

The elements and compounds treated in

Sect. 4.1.1 (Group IV and IV–IV compounds) are

treated as one group; the data in the tables

are given for the whole group in all cases. In

Sects. 4.1.2 (III–V compounds) and 4.1.3 (II–VI

compounds), data are given separately for each

subdivision of those subsections.

For each group of substances, the physical

properties are organized into four classes. These

are

A. Crystal structure, mechanical and thermal

properties.

B. Electronic properties.

C. Transport properties.

D. Electromagnetic and optical properties.

These property classes, ﬁnally, are subdivided

into individual properties, which are described in

the text, tables, and ﬁgures.

4.1.1 Group IV Semiconductors

and IV–IV Compounds ......................... 578

4.1.2 III–V Compounds ................................ 604

4.1.2.1 Boron Compounds ................... 604

4.1.2.2 Aluminium Compounds............ 610

4.1.2.3 Gallium Compounds ................ 621

4.1.2.4 Indium Compounds ................. 638

4.1.3 II–VI Compounds ................................ 652

4.1.3.1 Beryllium Compounds.............. 652

4.1.3.2 Magnesium Compounds ........... 655

4.1.3.3 Oxides of Ca, Sr, and Ba ........... 660

4.1.3.4 Zinc Compounds...................... 665

4.1.3.5 Cadmium Compounds .............. 676

4.1.3.6 Mercury Compounds ................ 686

References .................................................. 691

Part 4 1

576 Part 4 Functional Materials

This section deals with the physical properties of semi-

conductors. Semiconductors are substances which, like

metals, are electronic conductors. In contrast to metals,

however, the density of freely mobile charge carriers in

semiconductors is, under normal conditions, smaller by

orders of magnitude than it is in metals. Therefore, in

semiconductors, a small change in the absolute value

of the charge carrier density can induce a large rela-

tive change in this carrier density and in the electrical

conductivity. In metals, on the other hand, the carrier

density is so high from the beginning that it is practi-

cally impossible to produce a reasonable relative change

by small changes of the absolute value of the carrier den-

sity. In conclusion, we can say that in semiconductors,

and only in semiconductors, is it possible to manipulate

the electronic conduction by small changes of the carrier

density.

Such changes can be effected by a number of tech-

niques, for instance by chemical doping, by temperature

changes, by the application of an electric ﬁeld, or by

light. The electronic conductivity of a semiconduc-

tor can be changed intentionally by these techniques

by orders of magnitude; some techniques allow sta-

tionary changes, and some techniques also allow

time-dependent changes on a very short timescale.

Semiconducting materials are functional materials

thanks to the above properties: they can be used as very

small, robust, energy-efﬁcient devices to control the cur-

rent in electrical networks, either on the basis of external

driving or on the basis of their internal, tailor-made

device characteristics.

During the last 50 years, a tremendous amount of

knowledge and experience has been collected world-

wide in research and development laboratories in the

ﬁeld of semiconductor physics, semiconductor engi-

neering, and semiconductor chemistry. During this

time, semiconductor technology laid the foundations

for the development of data processing and of com-

munication technology and, more generally, for the

establishment of the information society. Today, semi-

conductor technology is a basic technology of our

economy, business practice, and daily life with its mod-

ern comforts.

We can give an account of only a very small part of

the empirical knowledge about semiconductors in this

Handbook. Thus, a very limited selection of semicon-

ducting substances and of physical properties is treated

here. Only three major groups of substances are consid-

ered. These are, ﬁrst, the elements of the fourth group

of the Periodic Table, C, Si, Ge, and Sn, and binary

compounds between these (IV–IV compounds); second,

binary compounds between one element from the third

group of the Periodic Table, namely B, Al, Ga, or In, and

one element from the ﬁfth group of the Periodic Table,

N, P, As, or Sb, the so-called III–V semiconductors; and

third, binary compounds between one element from the

second group of the Periodic Table, namely Mg, Ca, Sr,

Ba, Zn, Cd, or Hg, and one element from the sixth group

of the Periodic Table O, S, Se, or Te, the so-called II–VI

semiconductors.

In fact, these three major groups form a kind of ba-

sic set for the physical understanding of semiconductor

phenomena and for the wide ﬁeld of semiconduc-

tor applications. It has to be kept in mind, however,

that ternary and higher compounds play a very im-

portant role in many semiconductor applications and,

furthermore, that a large number of semiconduct-

ing substances containing elements other than those

mentioned above have been developed for special

applications.

The limited number of pages of this Handbook

has forced us, furthermore, to be even more restric-

tive with regard to the properties of semiconductors,

which are considered as being of ﬁrst-order im-

portance for this data collection. So, semiconductor

chemistry is beyond the scope of this Handbook.

The very broad and important ﬁeld of semiconduc-

tor technology could not be included at all. Also,

the wide ﬁeld of the inﬂuence of chemical dop-

ing, impurities, and defects on the properties of

semiconductors had to be left out. The Handbook’s

emphasis is on the physical properties of a re-

stricted number of most important pure semiconducting

materials.

All the data have been compiled from Landolt–

Börnstein, Numerical Data and Functional Relation-

ships in Science and Technology, New Series, Group III,

Vol. 41, Semiconductors, published in eight subvolumes

between 1998 and 2003 [1.1].

The CD-ROM and the online version of the Landolt–

Börnstein volume present a completely revised and

supplemented version of the older Landolt–Börnstein

volumes III/17 and III/22 on semiconductors. The

printed edition of Vol. III/41 contains only a supplement

to the earlier Volumes III/17 and III/22, but neverthe-

less the printed version of Vol. III/41 extends to more

than 4000 pages in the eight subvolumes. If, in addition

to the data in this Handbook, further or more detailed

information is needed, the reader is recommended to

consult [1.1].

Only a very restricted number of references is given

in this chapter to the original publications in journals.

Part 4 1

Semiconductors 577

A very large number of references to all the original

papers are given, however, in the Landolt–Börnstein

volume mentioned above [1.1] (see also [1.2]).

The data are presented mainly in tables, which

always cover data concerning one or a few related

properties for a full group of substances. It is felt

that this synoptic presentation will provide an imme-

diate overview of the data for the group of substances.

This might be especially helpful if one is interested in

development or modeling of materials.

In many cases, functional relationships, in particular

temperature dependences, are of the utmost importance

in condensed-matter physics and materials science.

Therefore a large number of ﬁgures have been included,

in addition to short sections of text and the numerical

data in the tables. Figures in the form of graphs allow

one to see the general features of a functional relation-

ship at a glance; they also, of course, present information

in a very condensed form.

The physical properties of semiconductors treated in

this section are the following:

A. Crystal structure, mechanical and thermal proper-

ties:

•

Crystal structure (space group, crystal system, and

structure type) (tables and ﬁgures).

•

Lattice parameters a and c, given in nm.

•

Density , given in g/cm

•

Elastic constants c

, given in GPa.

•

Melting point T

, given in K.

•

Temperature dependence of the lattice parameters,

i. e. the functional relationships a(T ) and c(T ).

•

Linear thermal expansion coefﬁcient α,givenin

−6

−1

•

Heat capacity c

, given in J/mol K.

•

Debye temperature Θ

, given in K.

•

Phonon wavenumbers

ν, frequencies ν, energies

phon

at symmetry points, given in cm

−1

,THz,and

eV, respectively.

•

Phonon dispersion relations, i. e. wavenumber

ν ver-

sus wave vector q.

B. Electronic properties:

•

First Brillouin zone (ﬁgures).

•

Band structure (text and ﬁgures).

•

Energy gap, given in eV.

•

Exciton binding energies, given in eV.

•

Spin–orbit splitting energies, given in eV.

•

Effective masses, in units of the electron mass m

•

g-factor g

of conduction electrons.

C. Transport properties:

•

Electronic transport, general description.

•

Intrinsic carrier concentrations, n and p,givenin

−3

•

Electrical conductivity σ ,giveninΩ

−1

•

Electron and hole mobilities µ

and µ

,givenin

/Vs.

•

Thermal conductivity, given in W/cm K.

D. Electromagnetic and optical properties:

•

Dielectric constant ε.

•

Refractive index n.

•

Spectral dependence of the optical constants (tables

and ﬁgures).

The data given in this Handbook, if not stated oth-

erwise, are numerical data valid at room temperature

(RT) and at normal pressure (100 kPa). If the material

crystallizes in different modiﬁcations, the data given, if

not stated otherwise, concern the phase which is stable

under normal conditions (i. e. RT and 100 kPa).

Part 4 1

578 Part 4 Functional Materials

4.1.1 Group IV Semiconductors and IV–IV Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-1 – 4.1-10.

Table 4.1-1 Crystal structures of Group IV semiconductors and IV–IV compounds

Crystal Space group Crystal system Structure type Figure

Diamond C O

Fd3m fcc Diamond Fig. 4.1-1

Silicon Si O

Fd3m fcc Diamond Fig. 4.1-1

Germanium Ge O

Fd3m fcc Diamond Fig. 4.1-1

Gray tin

α-Sn O

Fd3m fcc Diamond Fig. 4.1-1

Silicon carbide

3C-SiC

fcc Zinc blende Fig. 4.1-2

2H-SiC

mc Hexagonal Wurtzite Fig. 4.1-3

Silicon–germanium alloys

Fd3m fcc Diamond Fig. 4.1-1

Below 290K (17

◦

C) and at ambient pressure.

Silicon carbide is said to be polytypic because it crystallizes in more than one hundred different modiﬁcations. This is due to the

small energy differences between the different structures.

The labels “3C”, “2H”, etc. indicate the stacking order along the c axis in a hexagonal system; the cubic form can be considered as

ﬁtting into this system by taking the [111] direction as the “c axis”.

Silicon and germanium form a continuous series of solid solutions with gradually varying properties.

Fig. 4.1-1 The diamond lattice. The elementary cubes of

the two face-centered cubic lattices are shown. In the dia-

mond lattice all the atoms in the two elementary cubes are

identical, they are atoms from the same chemical element.

Each atom in this lattice is surrounded tetrahedrally by four

nearest neighbour atoms

Fig. 4.1-2 The zinc blende lattice (a is the lattice parame-

ter). This is a diamond lattice in which the two elementary

cubes are occupied by different atomic species, for example

by Zn-ions and by S-ions of opposite charge. Each Zn-ion is

surrounded tetrahedrally by four nearest neighbour S-atoms

and vice versa

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 579

Table 4.1-2 Lattice parameters of Group IV semiconductors and IV–IV compounds

Crystal Lattice parameters (nm) Temperature (K) Remarks

Diamond C a = 0.356685 298 X-ray diffraction

Silicon Si a =0.543102018 (34) 295.7 High-purity single crystal, vacuum

Germanium Ge a =0.56579060 298.15 Single crystal

Gray tin α-Sn a =0.64892 (1) 293.15 X-ray diffraction

Silicon carbide 3C-SiC a = 0.43596 297 Debye–Scherrer method

2H-SiC

a =0.30763 (10) 300 Laue and Weissenberg patterns

c =0.50480 (10)

Silicon–germanium alloys There is a small deviation from Vegard’s law (Fig. 4.1-4)

Fig. 4.1-3 The wurtzite lattice (a and c are the lattice

parameters)

Table 4.1-3 Densities of Group IV semiconductors and IV–IV compounds

Crystal Density (g/cm

) Temperature (K) Remarks

Diamond C 3.51537 (5) 298 Flotation, type Ia

3.51506 (5) 298 Flotation, type IIb

Silicon Si 2.329002 298.15 High-purity crystal, hydrostatic weighing

Germanium Ge 5.3234 298 Hydrostatic weighing

Gray tin α-Sn 7.285 291

Silicon carbide 3C-SiC 3.166 293 Polycrystalline sample

6H-SiC

3.211 300

1–X

5.70

5.65

5.60

5.55

5.50

5.45

5.40

a (Å)

0 0.2 0.4 0.6 0.8 1.0

Fig. 4.1-4 Si

1−x

. Compositionaldependence of the lat-

tice parameter. Circles, experimental results from X-ray

diffraction; dashed curve, calculated by Vegard’s law from

the values for pure Ge and Si; solid curve, experimental

results from [1.3]

Part 4 1.1

580 Part 4 Functional Materials

Table 4.1-4 Elastic constants c

of Group IV semiconductors and IV–IV compounds

Crystal c

(GPa) c

(GPa) Temperature (K) Remarks

Diamond C 1076.4 (2) 125.2 (2.3) 577.4 (1.4) 296 Brillouin scattering

Silicon Si 165.77 63.93 79.62 298 Ultrasound measurement

Germanium Ge 124.0 41.3 68.3 298 Ultrasound measurement

Gray tin α-Sn 69.0 29.3 36.2

Silicon carbide 3C-SiC 289 234 55.4 300

4H-SiC 507 (6) 108 (8) 547 (6) 159 (7) RT Brillouin scattering

p-type sample, ρ = 410 Ω cm.

Calculated from an 11-parameter shell model ﬁtted to experimental data.

Table 4.1-5 Melting point T

of Group IV semiconductors and IV–IV compounds

Crystal Melting point (K) Remarks

Diamond C 4100 Diamond–graphite–liquid eutectic at p =12.5GPa

Silicon Si 1687 The coordination number changes from 4 in the diamond phase to 6.4in

the liquid phase with an increase in bond length from 0.235 to 0.25 nm. The

liquid phase shows metallic conduction

Germanium Ge 1210.4

Gray tin α-Sn Transforms into metallic β-Sn slightly below RT

Silicon carbide 3C-SiC 3103 (40) Peritectic decomposition temperature at p = 35 bar

Table 4.1-6 Temperature dependence of the lattice parameters of Group IV semiconductors and IV–IV compounds

Crystal Temperature dependence

of lattice parameter

Diamond C Fig. 4.1-5

Silicon Si Fig. 4.1-6

Germanium Ge Fig. 4.1-7

Gray tin α-Sn da/dT = 3.1×10

−6

nm/K; temperature range −130 to 25

◦

Silicon carbide 3C-SiC Fig. 4.1-8

6H-SiC

Fig. 4.1-9

The lattice parameter a of high-purity Si can be approxi-

mated in the range 20–800

◦

Cbya(T ) = 5.4304

+1.8138 × 10

−5

(T −298.15 K)+1.542 × 10

−9

(T −298.15 K)

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 581

Diamond

3.574

3.573

3.572

3.571

3.570

3.569

3.568

3.567

3.566

a (Å)

α (10

–6

–1

)

T (°C)

T (K)

0 100 200 300 400 500 600 700

0 200 400 600 800 1000 1200 1400 1600

Fig. 4.1-5a,b Diamond. (a) Lattice parameter vs. tem-

perature [1.4];

(b) linear thermal expansion coefﬁcient vs.

temperature [1.5]

5.447

5.444

5.441

5.438

5.435

5.432

5.429

a (Å)

T (°C)

0 100 200 300 400 500 600 700 800

Fig. 4.1-6 Si. Lattice parameter vs. temperature in the

range 20–740

◦

C, measurements on various samples [1.6]

5.69

5.68

5.67

5.66

5.65

a (Å)

T (°C)

0 100 200 300 400 500 600 700 800 900

Fig. 4.1-7 Ge. Lattice parameter vs. temperature [1.7]

Part 4 1.1