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

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632 Part 4 Functional Materials

H,n

(cm

/V s)

2468 2468

2×

T (K)

GaN

Fig. 4.1-93 GaN. Electron Hall mobility vs. temperature

for two samples [1.85]

H,n

(cm

/V s)

300

200

100

100 200 300 400 500 600

H,p

(cm

/V s)

300

200

100

100 200 300 400 500 600

T (K)T (K)

GaP

5 × 10

–3

2 × 10

–3

2.5 × 10

–3

7.5 × 10

–3

1.2 × 10

–3

8 × 10

–3

5×10

–3

3×10

–3

6×10

–3

1×10

–3

2×10

–3

a) b)

Fig. 4.1-94a,b GaP. Hall mobility in n-type (a) and p-type (b) LPE-grown layers vs. temperature [1.86]

Part 4 1.2

Semiconductors 1.2 III–V Compounds 633

2468 2

4×10

4×

T (K)

H,n

(cm

(V s)

–1

)

GaAs

Deformation

potential mobility

Polar

mobility

Ionized-impurity

mobility

Fig. 4.1-95 GaAs. Temperature variation of Hall mobility

at 5 kG for three n-GaAs samples. In the temperature range

from 300 K to 77 K, the electron mobility of sample a is

dominated bypolar optical scattering. Samples b and c show

increased effects of ionized-impurity scattering [1.88]

–1

4×10

2468

T (K)

(W/cm K)

GaN

2×

Fig. 4.1-97 GaN. Thermal conductivity along the c axis vs.

temperature [1.90]

2468 2

4×10

T(K)

H,n

(cm

(V s)

–1

)

GaAs

MBE

MOCVD

Fig. 4.1-96 GaAs. Hall mobility of holes vs. tem-

perature for MBE- and MOCVD-grown samples. The

solid line represents the empirical relation µ

H,n

= 450 ×

(300/T)

2.3

[1.89]

–1

–2

468

2468262

T (K)

(W/cm K)

GaP

3.8

2×

Fig. 4.1-98 GaP. Thermal conductivity vs. temperature for

a p-type sample [1.69,70]

Part 4 1.2

634 Part 4 Functional Materials

Table 4.1-68 Thermal conductivity κ of gallium compounds

Crystal κ(W/cmK) Temperature (K) Remarks

Gallium nitride 1.3 300 See Fig. 4.1-97 for temperature dependence.

Gallium phosphide 0.77 300 See Fig. 4.1-98 for temperature dependence.

Gallium arsenide 0.455 300 See Fig. 4.1-99 for temperature dependence.

Gallium antimonide See Fig. 4.1-100 for temperature dependence.

–1

–2

–3

4×10

468

246822

T (K)

7 × 10

5 × 10

14 × 10

2.7 × 10

2.6 × 10

≈ 5 × 10

(W/cm K)

GaAs

Doping (cm

)

Fig. 4.1-99 GaAs. Thermal conductivity vs. temperature

for seven samples with impurity concentrations between

7×10

−3

and 2.6×10

−3

[1.91]

–1

–2

4268

4×10

T (K)

6×10

–3

(W/cm K)

GaSb

Fig. 4.1-100 GaSb. Thermal conductivity of two n-type

samples with impurity contents of 4 ×10

−3

(1)

and 1.4×10

−3

(2) and of two p-type sam-

ples with impurity contents of 1 × 10

−3

(3) and

2×10

−3

(4) [1.92]

Part 4 1.2

Semiconductors 1.2 III–V Compounds 635

D. Electromagnetic and Optical Properties

Tables 4.1-69 – 4.1-72 and Figs. 4.1-101 – 4.1-105.

Table 4.1-69 Dielectric constant ε and refractive index n of gallium compounds

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

(K) or hν(eV)

Gallium nitride GaN 300 9.5 (3) E perpendicular to c Fig. 4.1-101

10.4 (3) E parallel to c

5.8 (4) E parallel to c

5.35 (20) E perpendicular to c

2.29 (5) 500 nm Optical interference

Gallium phosphide GaP 300 11.11 Low-frequency capacitance Fig. 4.1-103

75.7 10.86 measurements

300 9.11 Derived from refractive index

3.334 2.0eV Spectroscopic ellipsometry

Gallium arsenide GaAs 300 12.80 (5) Microwave technique Fig. 4.1-102

10.86 Optical-transmission

interference

3.878 2.0eV Spectroscopic ellipsometry

Gallium antimonide GaSb 300 15.7 Reﬂectance and oscillator ﬁt Fig.4.1-105

14.44

5.239 2.0eV Spectroscopic ellipsometry

2.7

2.6

2.5

2.4

2.3

hω (eV)

1.0 2.0 3.01.5 2.5 3.5

GaN

Fig. 4.1-101 GaN. Refractive index vs. photon energy at

300 K; E⊥c [1.93]

3.8

3.7

3.6

3.5

3.4

hω (eV)

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

GaAs

Fig. 4.1-102 GaAs. Refractive index vs. photon energy in

the range 1.0–1.7 eV [1.94]. Solid line, calculated; symbols,

experimental data from three sources

Part 4 1.2

636 Part 4 Functional Materials

Table 4.1-70a Optical constants of gallium phosphide

hν(eV) ε

n k R K (10

−1

)

1.5 10.102 0.000 3.178 0.000 0.272 0.00

2.0 11.114 0.000 3.334 0.000 0.290 0.00

2.5 12.996 0.046 3.605 0.006 0.320 1.63

3.0 16.601 1.832 4.081 0.224 0.369 68.26

3.5 24.833 8.268 5.050 0.819 0.458 290.4

4.0 9.652 16.454 3.790 2.171 0.452 880.1

4.5 11.073 17.343 3.978 2.180 0.461 994.3

5.0 0.218 26.580 3.661 3.631 0.580 1840

5.5 −10.266 10.974 1.543 3.556 0.677 1983

6.0 −5.521 7.041 1.309 2.690 0.583 1636

Table 4.1-71 Optical constants of gallium arsenide

hν(eV) ε

n k R K (10

−1

)

1.5 13.435 0.589 3.66 0.080 0.327 12.21

2.0 14.991 1.637 3.878 0.211 0.349 42.79

2.5 18.579 3.821 4.333 0.441 0.395 111.7

3.0 16.536 17.571 4.509 1.948 0.472 592.5

3.5 8.413 14.216 3.531 2.013 0.425 714.2

4.0 9.279 13.832 3.601 1.920 0.421 778.7

4.5 6.797 22.845 3.913 2.919 0.521 1331

5.0 −11.515 18.563 2.273 4.084 0.688 2070

5.5 −6.705 8.123 1.383 2.936 0.613 1637

6.0 −4.511 6.250 1.264 2.472 0.550 1503

Table 4.1-72a Optical constants of gallium antimonide

hν(eV) ε

n k R K (10

−1

)

1.5 19.135 3.023 4.388 0.344 0.398 52.37

2.0 25.545 14.442 5.239 1.378 0.487 279.4

2.5 13.367 19.705 4.312 2.285 0.484 579.1

3.0 9.479 15.838 3.832 2.109 0.444 641.2

3.5 7.852 19.267 3.785 2.545 0.485 902.8

4.0 −1.374 25.138 3.450 3.643 0.583 1477

4.5 −8.989 10.763 1.586 3.392 0.561 1547

5.0 −5.693 7.529 1.369 2.751 0.585 1394

5.5 −5.527 5.410 1.212 2.645 0.592 1475

6.0 −4.962 4.520 0.935 2.416 0.610 1469

Table 4.1-70b GaP. Refractive index in the infrared

Wavelength Refractive Remarks

(µm)

index n

20 2.529 Reﬂectance and transmission at 300 K

10 2.90

5 2.94

2 3.02

1 3.17

Table 4.1-72b GaSb. Refractive index in the infrared

Wavelength Refractive Temperature Remarks

(µm)

index n (K)

14.9 3.880 300 Reﬂectance and

transmission

10 3.843

4 3.833

2 3.789 Prism method

1.9 3.802

1.8 3.820

Part 4 1.2

Semiconductors 1.2 III–V Compounds 637

GaP

11.5

11.4

11.3

11.2

11.1

11.0

10.9

10.8

0 0.2 0.4 0.6 0.8 1.0

–1

–2

–3

0 100 200 300 400 500 600

T (K)

–0.04

–0.08

–0.12

∆ε (0)

tan δ

p (GPa)

ε (0)

298.4 K

T = 75.4 K

1 kHz

10 kHz

100 kHz

1 kHz

10 kHz

100 kHz

ε (0)

tan δ

Fig. 4.1-103a,b GaP. (a) Static dielectric constant ε(0) and

dielectric loss tan δ vs. temperature, obtained from low-

frequency capacitance measurements. For clarity, the actual

data points at only one frequency (100 kHz) are shown. The

data have been corrected for dimensional changes due to

thermal expansion.

(b) Change in static dielectric constant

vs. pressure at two temperatures [1.95]

, ε

–10

hω (eV)

23456

GaP

Fig. 4.1-104 GaP. Real and imaginary parts of the dielec-

tric constant vs. photon energy [1.47]

–10

23456

hω (eV)

GaSb

Fig. 4.1-105 GaSb. Real and imaginary parts of the dielec-

tric constant vs. photon energy [1.47]

Part 4 1.2

638 Part 4 Functional Materials

4.1.2.4 Indium Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-73 – 4.1-81.

Table 4.1-73 Crystal structures of indium compounds

Crystal Space group Crystal system Structure type Remarks Figure

Indium nitride InN C

mc hex Wurtzite Phase transition to NaCl Fig. 4.1-3

structure under pressure

Indium phosphide InP I T

F43m fcc Zinc blende Stable at normal pressure Fig. 4.1-2

InP II

Fm3m fcc NaCl Pressure > 34 GPa

Indium arsenide InAs I T

F43m fcc Zinc blende Stable at normal pressure Fig. 4.1-2

InAs II

Fm3m fcc NaCl Pressure > 4GPa,RT

Indium antimonide InSb I T

F43m fcc Zinc blende Stable at normal pressure

Fig. 4.1-2

Quite a number of phase transitions have been observed at high pressures (> 2.1 GPa).

Table 4.1-74 Lattice parameters of indium compounds

Crystal Lattice parameters (nm) Temperature (K) Remarks

Indium nitride InN a =0.35446 Epitaxial layers, X-ray

c =0.57034 diffraction

Indium phosphide InP a = 0.58687 (10) 291.15 Powder, X-ray diffraction

Indium arsenide InAs a =0.60583 298.15

Indium antimonide InSb a =0.647937 298.15 Powder, X-ray diffraction

Table 4.1-75 Densities of indium compounds

Crystal Density (g/cm

) Temperature (K) Remarks

Indium nitride InN 6.78 (5) Pycnometric

Indium phosphide InP 4.81

Indium arsenide InAs 5.667 300 X-ray diffraction

Indium antimonide InSb 5.7747 (4) 300 X-ray diffraction

Table 4.1-76 Elastic constants c

(in GPa) of indium compounds

Crystal c

Remarks

Indium nitride InN 190 (7) 104 (3) 121 (7) 182 (6) 9.9(11) Calculated from the mean square displacements

of the lattice atoms measured by X-ray diffraction

Indium phosphide InP 101.1 56.1 − − 45.6 Ultrasonic-wave transit times, RT

Indium arsenide InAs 83.29 45.26 − − 39.59 Ultrasound, f = 15 MHz, n-type, RT

Indium antimonide InSb 69.18 37.88 − − 31.32 T = 0 K, extrapolated from 4.2K,

ultrasound, f = 10 MHz

Part 4 1.2

Semiconductors 1.2 III–V Compounds 639

Table 4.1-77 Melting point T

of indium compounds

Crystal Melting Remarks

point T

(K)

Indium nitride InN 1900 Estimated;

at 80 kbar N

Indium phosphide InP 1327 Optimized

Indium arsenide InAs 1221(1)

Indium antimonide InSb 800 (1) Drop calorimetry

Table 4.1-78 Linear thermal expansion coefﬁcient α of indium compounds

Crystal Expansion coefﬁcient Temperature (K) Temperature Remarks

α(10

−6

−1

) dependence

Indium nitride InN α

3.6 (2) 100–673 Fig. 4.1-106 X-ray diffraction

2.6 (3)

Indium phosphide InP 4.75 (10) 298 Fig. 4.1-107

Indium arsenide InAs 4.52 20–250 Fig. 4.1-108 Average value, X-ray diffraction

Indium antimonide InSb 5.37 (50) 283–343 Fig. 4.1-109 X-ray diffraction

–0.5

4.0

2.0

T (K)

α (10

–6

–1

)

0 100 200 300

InP

Fig. 4.1-107 InP. Temperature dependence of the coefﬁ-

cient of linear thermal expansion, obtained by the Bond

method [1.96]

⊥

⏐⏐

0 100 200 300 400 500

T (K)

α (10

–6

–1

)

600

InN

Fig. 4.1-106 InN. Coefﬁcient of linear thermal expansion

vs. temperature [1.75]

α (10

–8

–1

)

T (K)

–30

–60

–90

–120

–150

10 15 20 25 30 35 4005 45

InSb

InAs

Fig. 4.1-108 InAs, InSb. Linear thermal expansion coefﬁ-

cient vs. temperature, measured with a variable-transformer

dilatometer [1.97]

Part 4 1.2

640 Part 4 Functional Materials

Table 4.1-79 Heat capacity c

and Debye temperature Θ

of indium compounds

Crystal Heat capacity Temperature Debye Remarks

(J/mol K) (K) temperature (K)

Indium nitride InN 41.74 300 660 Calorimetry

Indium phosphide InP 321

Indium arsenide InAs 247

Indium antimonide InSb 206 Average value

Table 4.1-80 Phonon wavenumbers of indium compounds. Indium nitride (InN), T = 300 K; indium phosphide (InP),

RT, from coherent inelastic neutron scattering, carrier concentration n = 10

−3

; indium arsenide (InAs), from

Raman scattering; indium antimonide (InSb), T = 300 K, from inelastic neutron scattering, carrier concentration n =

8×10

−3

InN InP

Symmetry Branch Wave- Temperature Remarks Symmetry Branch Frequency

point number (K) point

(cm

−1

) (THz)

ν(Γ)

TO 478 300 Reﬂectivity, ν(111)(0.05) LO 10.3 (3)

Kramers–Kronig analysis

LO 694 Reﬂectivity, ν(Γ

) TO 9.2 (2)

Kramers–Kronig analysis

ν (A

) TO 400 Experimental data ν (X

) TA 2.05 (10)





TO 484 ν (X

) LA 5.8 (3)

LO 570 ν (X

) TO 9.70 (10)



(1)



TO 190 ν (X

) LO 9.95 (20)

ν (E

(2)

) TO 590 ν (L

) TA 1.65 (2)

ν (L

) LA 5.00 (10)

ν (L

) TO 9.50 (15)

ν (L

) LO 10.2 (3)

InAs InSb

Symmetry Branch Wave- Temperature Symmetry Branch Frequency

point number (K) point

(cm

−1

) (THz)

ν(Γ)

TO 217.3 300 ν(Γ

) LO 5.90 (25)

LO 238.6 TO 5.54 (5)

ν (X)

TA 53 ν (X

) TA 1.12 (5)

LA 160 ν (X

) LA 4.30 (10)

TO 216 ν (X

) LO 4.75 (20)

LO 203 100 ν (X

) TO 5.38(17)

ν (L)

TA 44 300 ν (L

) TA 0.98 (5)

LA 139.5 ν (L

) LA 3.81 (6)

TO 216 LO 4.82 (10)

LO 203 100 ν (L

) TO 5.31 (6)

Part 4 1.2

Semiconductors 1.2 III–V Compounds 641

α (10

–8

–1

)

T (K)

–40

–80

–120

–160

–2

0 10 20 30 0 100 200 300

T (K)

α (10

–6

–1

)

InSb

a) b)

Fig. 4.1-109a,b InSb. Linear thermal expansion coefﬁcient vs. temperature: (a) low-temperature region [1.97], (b) high-

temperature region [1.98]

Table 4.1-81 Phonon dispersion curves of indium com-

pounds

Crystal Figure

Indium phosphide InP Fig. 4.1-110

Indium arsenide InAs Fig. 4.1-111

Indium antimonide InSb Fig. 4.1-112

ΓΓ

Frequency ν

(THz)

Wave vector q

KX L X W L

InP

Fig. 4.1-110 InP. Phonon dispersion curves. Experimental neutron

data (diamonds) [1.99] and Raman data (triangles) [1.100] and

ab initio pseudopotential calculations (solid curves) [1.101]. From

[1.101]

Part 4 1.2