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

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602 Part 4 Functional Materials

α-Sn

hω (eV)

12345

K (10

–1

)

n, k

Fig. 4.1-47 α-Sn. Index of refraction n, extinction co-

efﬁcient k, and absorption coefﬁcient K vs. photon

energy [1.46]

T (K)

Dielectric constant ε (

∞

)

0 100 200 300 400 500

, ε

–10

23456

hω (eV)

Fig. 4.1-48 Ge. Real and imaginary parts of the dielectric

constant vs. photon energy [1.47]

Fig. 4.1-49 Ge. Temperature dependence of the high-

frequency dielectric constant [1.48]. Experimental data

points [1.49] and ab initio calculations (solid line); the dot-

ted line is the theoretical result without the effect of thermal

expansion, and the dashed line is the solid line shifted to

match the experimental data

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 603

Table 4.1-23 Optical constants of silicon

hν(eV) ε

n k K (10

/cm) R

1.5 13.488 0.038 3.673 0.005 0.78 0.327

2.0 15.254 0.172 3.906 0.022 4.47 0.351

2.5 18.661 0.630 4.320 0.073 18.48 0.390

3.0 27.197 2.807 5.222 0.269 81.73 0.461

3.5 22.394 33.818 5.610 3.014 1069.19 0.575

4.0 12.240 35.939 5.010 3.586 1454.11 0.591

4.5 −19.815 24.919 2.452 5.082 2317.99 0.740

5.0 −10.242 11.195 1.570 3.565 1806.67 0.675

5.5 −9.106 8.846 1.340 3.302 1840.59 0.673

6.0 −7.443 5.877 1.010 2.909 1769.27 0.677

Table 4.1-24 Optical constants of germanium

hν(eV) ε

n k K (10

/cm) R

1.5 21.560 2.772 4.653 0.298 45.30 0.419

2.0 30.361 10.427 5.588 0.933 189.12 0.495

2.5 13.153 20.695 4.340 2.384 604.15 0.492

3.0 12.065 17.514 4.082 2.145 652.25 0.463

3.5 9.052 21.442 4.020 2.667 946.01 0.502

4.0 4.123 26.056 3.905 3.336 1352.55 0.556

4.5 −14.655 16.782 1.953 4.297 1960.14 0.713

5.0 −8.277 8.911 1.394 3.197 1620.15 0.650

5.5 −6.176 7.842 1.380 2.842 1584.57 0.598

6.0 −6.648 5.672 1.023 2.774 1686.84 0.653

Table 4.1-25 Optical constants of silicon carbide

Crystal Refractive index Wavelength

range (nm)

3C-SiC n(λ) = 2.55378 +3.417 × 10

/λ

467–691

6H-SiC n

(λ) = 2.5531 +3.34 × 10

/λ

(λ) = 2.5852 +3.68 × 10

/λ

Part 4 1.1

604 Part 4 Functional Materials

4.1.2 III–V Compounds

4.1.2.1 Boron Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-26 – 4.1-32.

Table 4.1-26 Crystal structures of boron compounds

Crystal Space group Crystal Structure Remarks Figure

system type

Boron nitride, hexagonal BN

hex

/mmc hex h-BN Stable under normal conditions Fig. 4.1-50

Boron nitride, cubic BN

cub

F43m fcc Zinc blende Metastable under normal conditions Fig.4.1-2

Boron nitride, wurtzite BN

mc hex Wurtzite Metastable under all conditions Fig. 4.1-3

Boron phosphide BP T

F43m fcc Zinc blende Stable under normal conditions Fig. 4.1-2

Boron arsenide BAs T

F43m fcc Zinc blende Stable in presence of As vapor Fig. 4.1-2

up to 920

◦

Boron antimonide BSb T

F43m fcc Zinc blende Stable under normal conditions Fig. 4.1-2

Table 4.1-27 Lattice parameters of boron compounds

Crystal Lattice parameters (nm) Temperature (K) Remarks

Boron nitride, cubic BN

cub

a =0.36160 (3) RT X-ray diffraction

Boron nitride, hexagonal BN

hex

a =0.25072 (1) 297 Prepared from amorphous BN in

c =0.687 (1) 297 N

atmosphere at room temperature

Boron phosphide BP a = 0.45383 (4) 297

Boron arsenide BAs a = 0.4777

Boron antimonide BSb a = 0.512 Ab initio pseudopotential calculation

Fig. 4.1-50 The hexagonal lattice of h-BN (BN

hex

)

Table 4.1-28 Densities of boron compounds

Crystal Density Remarks

(g/cm

)

Boron nitride, cubic BN

cub

3.4863 X-ray

diffraction

Boron nitride, hexagonal BN

hex

2.279 X-ray density

Boron phosphide BP

Boron arsenide BAs 5.22

Part 4 1.2

Semiconductors 1.2 III–V Compounds 605

Table 4.1-29 Melting point T

or decomposition temperature of boron compounds

Crystal Melting point T

(K) Remarks

Boron nitride, cubic BN

cub

> 3246

Boron nitride, hexagonal BN

hex

3200–3400 N

ambient; pyrometric measurement

Boron phosphide BP 1400 Decomposition temperature

Table 4.1-30 Linear thermal expansion coefﬁcient α of boron compounds

Crystal Expansion coefﬁcient α(K

−1

) Remarks

Boron nitride, cubic BN

cub

1.15× 10

−6

X-ray measurement

Boron nitride, hexagonal BN

hex

40.6 (4) ×10

−6

Boron phosphide BP 3.65 × 10

−6

At 400 K

Boron arsenide BAs 4.1×10

−6

Calculated

Table 4.1-31 Heat capacities and Debye temperatures of boron compounds

Crystal Debye temperature Θ

(K) Remarks

Boron nitride, cubic BN

cub

1730 (70) See Fig. 4.1-51 for temp. dependence of c

Boron nitride, hexagonal BN

hex

598 (7) Calorimetry

Boron phosphide BP 985 See Fig. 4.1-52 for temp. dependence of c

Boron arsenide BAs 800

Table 4.1-32 Phonon wavenumbers/frequencies of boron compounds. Values for hexagonal boron nitride (BN

hex

)

obtained from infrared reﬂectivity; values for boron phosphide (BP) from ab initio pseudopotential calculations

Crystal

Phonon wavenumbers (cm

−1

)

Remarks

Boron nitride, cubic BN

cub

1305 (1)

1054.7 (6) RT; Raman scattering

Boron arsenide BAs

(Γ) 714

(Γ) 695 Raman scattering

Table 4.1-32 Phonon wavenumbers/frequencies, cont.

hex

Phonon branch Wavenumber (cm

−1

)

TO1

783

LO1

828

TO2

1510

LO2

1595

TO1

767

LO1

778

TO2

1367

LO2

1610

Table 4.1-32 Phonon wavenumbers/frequencies, cont.

Phonon branch Frequency (THz)

(Γ) 24.25

(X) 24.00

(X) 15.81

(X) 21.04

(X) 9.20

(L) 22.91

(L) 15.18

Part 4 1.2

606 Part 4 Functional Materials

Heat capacity c

(J K

–1

mol

–1

)

300

Temperature T (K)

0 50 100 150 200 250

h-BN

r-BN

c-BN

w-BN

T (K)

(J K

–1

mol

–1

)

10020304050

1.0

0.8

0.6

0.4

0.2

Fig. 4.1-51 BN. Heat capacities for four polymorphic

boron nitride modiﬁcations. Data taken from [1.50]

B. Electronic Properties

Tables 4.1-33 – 4.1-35.

Band Structures of Boron Compounds.

Boron Nitride, Cubic (BN

cub

). All band structure calcu-

lations lead to an indirect-gap structure (Fig. 4.1-53).

Boron Nitride, Hexagonal (BN

hex

). All recent

band structure calculations yield an indirect gap

(Fig. 4.1-54). The conduction band minimum is located

at P.

Boron Phosphide (BP). BP is an indirect-gap semicon-

ductor (Fig. 4.1-55).

Boron Arsenide (BAs). The calculated band structure

shows an indirect (Γ–X) gap of a few eV. The conduction

Table 4.1-33 First Brillouin zones of boron compounds

Crystal Figure

Boron nitride, cubic BN

cub

Fig. 4.1-23

Boron nitride, hexagonal BN

hex

Fig. 4.1-24

Boron phosphide BP Fig. 4.1-23

Boron arsenide BAs Fig. 4.1-23

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

Heat capacity c

(J g

–1

)

T (K)

1100

1000

900

800

700

600

Debye temperature Θ

(K)

320 400 500 600 700

Fig. 4.1-52 BP. Temperature dependence of speciﬁc heat

capacity and Debye temperature [1.51]

–7

–14

–21

KXL ΓΓ

E (eV)

c-BN

Wave vector k

Fig. 4.1-53 Band structure of cubic boron nitride

Part 4 1.2

Semiconductors 1.2 III–V Compounds 607

Table 4.1-34 Energy gaps of boron compounds

Crystal Quantity Bands Energy (eV) Remarks

Boron nitride, cubic BN

cub

g, ind

15v

to X

6.2 Soft-X-ray emission spectroscopy

g, dir

15v

to Γ

14.5 Reﬂectivity

Boron nitride, hexagonal BN

hex

5.9 (1) Inelastic electron scattering

g, th

7.1 (1) Temperature dependence of electrical resistivity

Boron phosphide BP E

g, ind

2.1 X-ray emission and absorption

g, dir

Γ 4.4

X 6.5

L 6.5

Boron arsenide BAs E

g, ind

0.67 Absorption

g, dir

1.46

Boron antimonide BSb E

Γ to ∆ 0.527 Calculated

Table 4.1-35 Effective masses of electrons (m

) and holes (m

) for cubic boron nitride (in units of the electron mass m

)

Crystal m

p, heavy

p, light

Remarks

Boron nitride, cubic BN

cub

0.752 Calculated from band structure data

0.375 0.150 Parallel to [100]

0.926 0.108 Parallel to [111]

band minimum is on the ∆ axis close tothe X point. As in

silicon, the Γ

15c

level is below the Γ

level (Fig. 4.1-56).

Boron Antimonide (BSb). Boron antimonide is an

indirect-gap semiconductor (Fig. 4.1-57).

–7

–14

–21

KH A LΓΓMA

E (eV)

h-BN

Wave vector k

Fig. 4.1-54 Band structure of hexagonal boron nitride

Fig. 4.1-55 Band structure of boron phosphide

–5

–10

–15

–20

ΓKΓ LΣ∆X Λ

E (eV)

Wave vector k

∆

Part 4 1.2

608 Part 4 Functional Materials

Energy E (eV)

–3

–6

–9

–12

–15

–18

Wave vector k

XΓ U,K ΓL Λ∆ Σ

BAs

15c

15v

15c

Fig. 4.1-56 Band structure of boron arsenide

C. Transport Properties

Electronic Transport, General Description. Boron Ni-

tride, Cubic (BN

cub

). Owing to the large gap, all

literature data refer to extrinsic conduction. For

the temperature dependence of the conductivity, see

Fig. 4.1-58. Hall measurements on nominally undoped

thin ﬁlms yield values of the carrier mobility of around

500 cm

/Vs.

Boron Nitride, hexagonal (BN

hex

). Figure 4.1-59 shows

the temperature dependence ofthe electrical resistivity at

high temperatures. In an undoped nanocrystalline ﬁlm,

resistivity values of the order of 2 ×10

Ω cm have been

found.

Boron Phosphide (BP). Boron phosphide is extrinsic at

room temperature, and the transport is limited by im-

purity scattering. Figure 4.1-60 shows the temperature

dependence of the conductivity, carrier concentration,

and Hall mobility of several samples. In n-doped

single crystals, electron mobilities of the order of

30–40cm

/V s have been found at 300 K; in p-doped

single crystals, mobilities around 500 cm

/Vs have

been measured at 300 K.

Boron Arsenide (BAs). There is almost no information

about the semiconducting properties of BAs.

Energy E (eV)

–3

–6

–9

–12

–15

–18

Wave vector k

XΓL ∆V

BSb

15c

15v

Fig. 4.1-57 Band structure of boron antimonide

123

–1

(10

–3

–1

)

σ (Ω

–1

)

–3

–4

–5

–6

–7

cub

Fig. 4.1-58 c-BN (BN

cub

). Electrical conductivity vs. re-

ciprocal temperature for several different polycrystalline

samples above RT [1.52, 53]

Part 4 1.2

Semiconductors 1.2 III–V Compounds 609

–1

(×10

–4

–1

)

ρ (Ω cm)

78956 1011

hex

Fig. 4.1-59 h-BN (BN

hex

). Resistivity vs. temperature

above 700

◦

C. A, from bulk resistance of a disk meas-

ured in the c direction; B – E, earlier literature data for

comparison [1.54]

2×10

4×10

–1

1.0 1.5 2.0 2.5 3.0 3.5

2×10

800 400 200 100 25

T (°C)

–1

(10

–3

–1

)

Concentration n (cm

–3

)

Conductivity σ (Ω

–1

)

Hall mobility µ

H,n

(cm

(V s)

–1

)

No. 1

H,n

No. 1

No. 3

Fig. 4.1-60 Temperature dependence of the conductivity

, the carrier concentration n, and the mobility µ

H,n

of n-type BP(100) wafers [1.55]. Sample No. 1 contains

autodoped Si with a concentration of 5 ×10

atoms/cm

and sample No. 3 contains 5 × 10

atoms/cm

Part 4 1.2

610 Part 4 Functional Materials

D. Electromagnetic and Optical Properties

Table 4.1-36.

Table 4.1-36 Dielectric constant ε and refractive index n of boron compounds

Crystal Temperature (K) ε(0) ε(∞) n at λ(nm) Remarks

Boron nitride, cubic BN

cub

300 7.1 2.097 712.5 IR reﬂectivity

Boron nitride, hexagonal BN

hex

300 5.09 4.10 2.13 Parallel to c axis, IR reﬂectivity

7.04 4.95 1.65 Perpendicular to c axis, IR reﬂectivity

Boron phosphide BP 300 11 7.8 Schottky barrier reﬂectance

RT 3.34 (5) 454.5 Brewster angle method

3.34 (5) 458

3.32 (5) 488

3.30 (5) 496

3.26 (5) 514.5

3.00 (5) 632.8

4.1.2.2 Aluminium Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-37 – 4.1-44.

Table 4.1-37 Crystal structures of aluminium compounds

Crystal Space group Crystal system Structure type Remarks Figure

Aluminium nitride AlN I C

mc hex Wurtzite At normal pressure Fig. 4.1-3

AlN II

Fm3m fcc NaCl structure At 21 GPa (shock

compression)

Aluminium phosphide AlP I T

fcc Zinc blende At normal pressure Fig. 4.1-2

AlP II O

Fm3m fcc NaCl structure High-pressure phase

Aluminium arsenide AlAs T

fcc Zinc blende Transition to NiAs structure Fig. 4.1-2

at high pressure

Aluminium antimonide AlSb I T

fcc Zinc blende At normal pressure Fig. 4.1-2

AlSb II Cmcm Orthorhombic At high pressure

Table 4.1-38 Lattice parameters of aluminium compounds

Crystal Lattice parameters (nm) Temperature Remarks

Aluminium nitride AlN a = 0.31111 300 K X-ray diffraction on ultraﬁne powder

c =0.49788

Aluminium phosphide AlP a = 0.54635 (4) 25

◦

C Epitaxial ﬁlm on GaP

Aluminium arsenide AlAs a = 0.566139 291 K High-resolution X-ray diffraction

Aluminium antimonide AlSb a = 0.61355 (1) 291.15 K Powder, X-ray measurement

Part 4 1.2

Semiconductors 1.2 III–V Compounds 611

Table 4.1-39 Densities of aluminium compounds

Crystal Density (g/cm

) Temperature (K) Remarks

Aluminium nitride AlN 3.255 X-ray diffraction

Aluminium phosphide AlP 2.40 (1)

Aluminium arsenide AlAs 3.760 Calculated from lattice parameter

Aluminium antimonide AlSb 4.26 293

Table 4.1-40 Elastic constants c

of aluminium compounds

Crystal c

(GPa) c

(GPa) Remarks

Aluminium nitride AlN 296 (18) 130 (11) 158 (06) 267 (18) 241 (20)

Aluminium phosphide AlP 140.50 (28) 62.03 (24) 70.33 (7) Ultrasound ( f = 10 and 30 MHz)

Aluminium arsenide AlAs 190 (1) 53.8 (1) 59.5 (1) T = 300 K

122.1 (3) 56.6 (3) 59.9(1) T = 77 K

112.6 57.1 60.0 T = 0 K; extrapolated data

Aluminium antimonide AlSb 88.34 40.23 43.22 T = 296 K; ultrasound

Calculated from the mean square displacement of the lattice atoms measured by X-ray diffraction.

Table 4.1-41 Melting point T

of aluminium compounds

Crystal Melting point T

(K)

Aluminium nitride AlN 3025

Aluminium phosphide AlP 2823

Aluminium arsenide AlAs 2013 (20)

Aluminium antimonide AlSb 1327(1)

Table 4.1-42 Linear thermal expansion coefﬁcient α of aluminium compounds

Crystal Expansion coefﬁcient α(K

−1

) Temperature Remarks

Aluminium nitride AlN α

perpend

4.35× 10

−6

300 K Powder; X-ray diffraction

parallel

3.48× 10

−6

Aluminium phosphide AlP

Aluminium arsenide AlAs 5.20 (5) ×10

−6

15–840

◦

C X-ray diffraction

Aluminium antimonide AlSb Fig. 4.1-61

–2

0 40 80 120 160 200 240 280 320 360

T (K)

α (10

–6

–1

)

AlSb

Fig. 4.1-61 AlSb. Coefﬁcient of linear thermal expansion

vs. temperature [1.56,57]

Part 4 1.2