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

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612 Part 4 Functional Materials

Table 4.1-43 Phonon wavenumbers of aluminium compounds: aluminium nitride (300 K, from Raman scattering); aluminium

Phosphide (from Raman spectroscopy);aluminium arsenide (from Raman spectroscopy; 0.5 µm layer of AlAs on GaAs; T =37 K);

aluminium antimonide (from Raman spectroscopy)

AlN AlP AlAs AlSb

Symmetry Wave- Symmetry Wave- Temperature Symmetry Wave- Symmetry Wave-

point,

number point, number (K) point, number point, number

polarization

(cm

−1

) polarization (cm

−1

) polarization (cm

−1

) polarization (cm

−1

)



(1)



248.6

(Γ) 504.5 (4) 5

(Γ) 404 (1)

(Γ) 334

) 611.0

(Γ) 501.0 (2) 300

(Γ) 361 (1)

(Γ) 316



(2)



657.4

(Γ) 442.5 (2) 5

(X) 403 (8)

(X) 64

) 670.8

(Γ) 439.4 (2) 300

(X) 335 (8)

(X) 153

) 890.0

(X) 109 (8)

(X) 290

) 912.0

(X) 222 (12)

(X) 343

Table 4.1-43 Wavenumbers of aluminium compounds, cont.

AlSb

Symmetry Wave-

point,

number

polarization

(cm

−1

)

(L) 49

(K) 149

(L) 306

(L) 327

(Γ) 340.0 (7)

(Γ) 318.7 (7)

Ab initio pseudopotential calculation.

First-order Raman scattering.

Γ Γ

1000

500

Wavenumber ν

–

(cm

–1

)

Wave vector q

KX L X W L

DOS

AlN

Fig. 4.1-62 AlN (wurtzite structure). Phonon dispersion curves (left panel) and phonon density of states (right panel),

from a rigid-ion model calculation [1.58,59]

Table 4.1-44 Phonon dispersion curves of aluminium

compounds

Crystal Figure

Aluminium nitride AlN Fig. 4.1-62

Aluminium phosphide AlP Fig. 4.1-63

Aluminium arsenide AlAs Fig. 4.1-64

Aluminium antimonide AlSb Fig. 4.1-65

Part 4 1.2

Semiconductors 1.2 III–V Compounds 613

ΓΓ

600

400

200

Wavenumber ν

–

(cm

–1

)

Wave vector q

KX L X W L

DOS

AlP

Fig. 4.1-63 AlP. Phonon dispersion curves (left panel) and phonon density of states (right panel), from ab initio

calculations [1.60]. The data points were obtained from Raman scattering [1.61]

ΓΓ

500

250

Wavenumber ν

–

(cm

–1

)

Wave vector q

KX L X W L

DOS

AlAs

Fig. 4.1-64 AlAs. Phonon dispersion curves (left panel) and phonon density of states (right panel). Experimental data

points [1.61, 62] and ab initio calculations [1.16]. From [1.16]

Part 4 1.2

614 Part 4 Functional Materials

ΓΓ

400

300

200

100

Wavenumber ν

–

(cm

–1

)

Wave vector q

KX L X W L

DOS

AlSb

Fig. 4.1-65 AlSb. Phonon dispersion curves (left panel) and phonon density of states (right panel). Experimental data

points [1.63] and ab initio calculations [1.16]. From [1.16]

B. Electronic Properties

Tables 4.1-45 – 4.1-48.

Band Structures of Aluminium Compounds. Alu-

minium Nitride (AlN). Aluminium nitride is a direct-gap

semiconductor. Since it crystallizes in the wurtzite struc-

ture, the band structure (Fig. 4.1-66) differs from that of

most of the other III–V compounds.

Aluminium Phosphide (AlP). Aluminium phosphide is

an indirect, wide-gap semiconductor. The minima of the

conduction bands are located at the X point of the Bril-

louin zone. The top of the valence band has the structure

common to all zinc blende semiconductors (Fig. 4.1-67).

Aluminium Arsenide (AlAs). Aluminium arsenide is

a wide-gap semiconductor with a band structure

(Fig. 4.1-68) similar to that of AlP. Measurements have

revealed a camel’s back structure near X.

Table 4.1-45 First Brillouin zones of aluminium com-

pounds

Crystal Figure

Aluminium nitride AlN Fig. 4.1-24

Aluminium phosphide AlP Fig. 4.1-23

Aluminium arsenide AlAs Fig. 4.1-23

Aluminium antimonide AlSb Fig. 4.1-23

Aluminium Antimonide (AlSb). Aluminium antimonide

(like AlAs) is an indirect-gap semiconductor with

camel’s back conduction band minima near X

(Fig. 4.1-69).

Part 4 1.2

Semiconductors 1.2 III–V Compounds 615

–5

–10

–15

–20

ΓKΓL Σ∆AR UM A S HP T

E (eV)

Wave vector k

AlN

1'3'

, Γ

1'3'

, Γ

Fig. 4.1-66 AlN. Band structure calculated by a semiem-

pirical tight-binding method [1.64]

–5

–10

–15

XL ΓΣΛ∆K Γ

E (eV)

Wave vector k

AlP

Fig. 4.1-67 AlP. Band structure calculated by an orthogonalized

LCAO method [1.65]

Part 4 1.2

616 Part 4 Functional Materials

–5

–10

–15

XL ΓΣΛ∆K Γ

E (eV)

Wave vector k

AlAs

Fig. 4.1-68 AlAs. Band structure calculated by an orthog-

onalized LCAO method [1.65]

Table 4.1-46 Energy gaps of aluminium compounds

Crystal Quantity Bands Energy (eV ) Temperature (K) Remarks

Aluminium nitride AlN E

g, dir

6.19 7 Optical absorption

6.13 300

Aluminium phosphide AlP E

g, ind

15v

to X

2.5 (1) 2 Excitonic gap;

2.45 300 Absorption

g, dir

15v

to Γ

3.63 (2) 4 Excitonic gap;

3.62 (2) 77 Photoluminescence

Aluminium arsenide AlAs E

g, ind

15v

to X

2.229 (1) 4 Excitonic gap;

2.153 (2) 300 Photoluminescence

g, ind

15v

to L

2.363 295 Transport

g, dir

15v

to Γ

3.13 (1) 4 Excitonic gap;

3.03 (1) 300 Photoluminescence

3.14 (1) 300 Transmission

Aluminium antimonide AlSb E

g, ind

15v

to ∆

1.615 (3) 300 Excitonic gap

1.686 (1) 27

g, ind

15v

to L

2.211 295 Electroreﬂectance

2.327 35

g, dir

15v

to Γ

2.300 295 Electroreﬂectance

2.384 25

–5

–10

–15

XL ΓΣΛ∆K Γ

E (eV)

Wave vector k

AlSb

Fig. 4.1-69 Band structure of aluminium antimonide

Part 4 1.2

Semiconductors 1.2 III–V Compounds 617

Table 4.1-47 Spin–orbit splitting energies of aluminium compounds

Crystal Spin–orbit splitting Symmetry points Energy (eV) Temperature (K) Remarks

AlAs ∆

15v

0.275 300 Electroreﬂectance

∆

15v

0.20

∆



15c

0.15

AlSb ∆

to Γ

0.673 295 Splitting of Γ

15v

∆

4,5v

to L

0.426 Splitting of L

Table 4.1-48 Effective masses of electrons (m

) and holes (m

) for aluminium compounds (in units of the electron

mass m

). Aluminium nitride (AlN), calculated values; aluminium phosphide (AlP), calculated from band structure;

aluminium arsenide (AlAs), calculated from band structure data; Aluminium antimonide (AlSb), theoretical estimates

AlN AlP AlAs AlSb

n, parall

0.33 m

n, parall

3.67 m

n, parall

(X) 1.1

n, perpend

(∆

) 0.26 estimated

n, perpend

0.25 m

n, perpend

0.212 m

n, perpend

(X) 0.19

n, parall

(∆

) 1.0

p, A, parall

3.53 m

p, heavy

0.513 m

n, parall

(L) 1.32 m

p, heavy

0.336

parallel to [100] parallel to [100]

p, A, perpend

11.14 m

p, heavy

1.372 m

n, perpend

(L) 0.15

p, heavy

0.872

parallel to [111] parallel to [111]

p, B, parall

3.53 m

p, light

0.211 m

p, heavy

0.409 m

p, light

0.123

parallel to [100] parallel to [100] parallel to [100]

p, B, perpend

0.33 m

p, light

0.145 m

p, heavy

1.022 m

p, light

0.091

parallel to [111] parallel to [111] parallel to [111]

p, C, parall

0.26 m

p, light

0.153

parallel to [100]

p, C, perpend

4.05 m

p, light

0.109

parallel to [111]

Effective masses at X, neglecting camel’s back structure.

Effective masses at L.

C. Transport Properties

Tables 4.1-49 and 4.1-50.

Electronic Transport, General Description. Aluminium

Nitride (AlN). Owing to the large energy gap, trans-

port is always extrinsic. Typical numerical values

for the electrical conductivity of undoped sin-

gle crystals lie in the range 10

−13

Ω

−1

σ<10

−11

Ω

−1

Aluminium Phosphide (AlP). At room temperature,

electrical conductivities σ of bulk crystals and layers be-

tween 1 and 10

Ω

−1

have been measured. For the

temperature dependence of the electrical conductivity,

see Fig. 4.1-70.

Aluminium Arsenide (AlAs). Only a small amount of reli-

able data exists on the transport properties of AlAs. Most

results are extrapolations from data obtained from the

technologically more important solid solutions of type

1−x

As. At roomtemperature, values of the elec-

trical conductivity of around 10 Ω

−1

have been

found.

Aluminium Antimonide (AlSb). Aluminium antimonide

grown without intentional doping is p-type and becomes

intrinsic at about 1000 K. For the temperature depen-

dence of the electrical conductivity, see Fig. 4.1-71.

Part 4 1.2

618 Part 4 Functional Materials

Table 4.1-49 Electron and hole mobilities µ

and µ

of aluminium compounds

Crystal Temperature (K) µ

(cm

/Vs) µ

(cm

/Vs) Remarks

Aluminium nitride AlN 290 14 Doped single crystal

Aluminium phosphide AlP 298 10–80 Single crystals

Aluminium arsenide AlAs 300 293–75 105 Single crystal layers, MBE-grown, Be-doped

Aluminium antimonide AlSb 295 200 Single crystal, Te-doped,

77 700 n = 4.7×10

−3

300 400 Single crystal, p = 10

−3

77 2000

Table 4.1-50 Thermal conductivity κ of aluminium compounds

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

Aluminium nitride AlN 300 3.19 See Fig. 4.1-72

Aluminium phosphide AlP 300 0.9

Aluminium arsenide AlAs 300 0.91

Aluminium antimonide AlSb See Fig. 4.1-73

ln σ

–1

(10

–3

–1

)

1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5

0.37 eV

0.15 eV

AlP

Fig. 4.1-70 AlP. Natural logarithm of electrical conductiv-

ity vs. reciprocal temperature for an undoped sample [1.66].

σ in Ω

−1

. Activation energies are also shown

02 46 8 12

1000 100 0 –100 –150 –200

–1

(10

–3

–1

)

T (°C)σ (Ω

–1

)

AlSb

Fig. 4.1-71 AlSb. Electrical conductivity vs. reciprocal

temperature for three different polycrystalline p-type sam-

ples [1.67]

Part 4 1.2

Semiconductors 1.2 III–V Compounds 619

–1

–2

–3

T (K)

101

(W/cm K)

AlN

Ceramic

Upper limit

Fig. 4.1-72 AlN. Temperature dependence of the thermal

conductivity for two single crystals (curves 1 and 2)and

several ceramic samples (curves 3 – 6). Other published

results are included (curves 7 – 10), as well as a theoretical

estimate of the upper limit [1.68]

D. Electromagnetic and Optical Properties

Table 4.1-51.

Table 4.1-51 Dielectric constant ε and refractive index n of aluminium compounds

Crystal Temperature (K) ε(0) ε(∞)

n at λ(µm)

Remarks

Aluminium nitride AlN 300 9.14 ε

perpend

4.71 (22) 2.17–2.34 0.25 Reﬂectivity and optical inter-

parall

4.93 (22) 2.04–2.18 0.30 ferometry, λ = 589.0nm,

CVD ﬁlms

Aluminium phosphide AlP 9.8 7.5 From refractive index

Aluminium arsenide AlAs 10.1 8.2 From infrared reﬂectivity

Aluminium antimonide AlSb 300 121.04 10.24 IR reﬂectance,

300 3.652 40 transmission and reﬂectance

2.995 20

2.080 15

3.100 10

3.182 4

3.300 2

3.445 1.1

See Fig. 4.1-74 for the spectral dependence of the refractive index.

See Fig. 4.1-75 for the spectral dependence of the refractive index.

See Fig. 4.1-76 for the spectral dependence of the refractive index.

See Fig. 4.1-77 for the spectral dependence of the refractive index.

–1

–2

T (K)

101

(W/cm K)

Fig. 4.1-73 AlSb. Thermal conductivity vs. temperature for

an n-typeand a p-type sample, low-temperaturerange [1.69,

70]

Part 4 1.2

620 Part 4 Functional Materials

2.8

2.6

2.4

2.2

2.0

λ (nm)

200 300 400 500 600250 350 450 550

AlN

Fig. 4.1-74 AlN. Spectral dependence of the refractive index (1,ordinaryray;2, extraordinary ray) [1.71]

3.1

3.0

2.9

2.8

2.7

hω (eV)

1.0 2.0 3.01.5 2.50.5

AlP

Fig. 4.1-75 AlP. Refractive index vs. photon energy at

300 K [1.72]

λ (µm)

20 23 26 29 32 35 38

AlSb

AlAs

hω (eV)

23456

n, k

Fig. 4.1-76 AlAs. Spectral variation of the complex refrac-

tive index calculated from the dielectric function [1.73]

Fig. 4.1-77 AlSb. Refractive index n and extinction co-

efﬁcient k vs. wavelength in the region of lattice

absorption [1.74]

Part 4 1.2

Semiconductors 1.2 III–V Compounds 621

4.1.2.3 Gallium Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-52 – 4.1-60.

Table 4.1-52 Crystal structures of gallium compounds

Crystal Space group Crystal system Structure type Remarks Figure

Gallium nitride GaN C

mc hex Wurtzite Stable at ambient pressure Fig. 4.1-3

F43m fcc Zinc blende Epitaxial growth Fig. 4.1-2

on cubic substrate

Gallium phosphide GaP T

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

/amd β-tin structure Pressure > 21–30GPa

Gallium arsenide GaAs I T

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

GaAs II

Orthorhombic Pressure > 17 GPa

Gallium antimonide GaSb I T

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

GaSb II

/amd β-tin structure Pressure > 8–10GPa

Table 4.1-53 Lattice parameters of gallium compounds

Crystal Lattice parameters (nm) Temperature (K) Remarks

Gallium nitride GaN a =0.3190 (1) X-ray diffraction,

c =0.5189 (1) monocrystal

Gallium phosphide GaP a = 0.54506 (4) RT Single crystal

Gallium arsenide GaAs a = 0.565359 RT

Gallium antimonide GaSb a =0.609593 (4) 298.15 X-ray powder diffraction

Table 4.1-54 Densities of gallium compounds

Crystal Density Temperature

(g/cm

) (K)

Gallium nitride GaN 6.07

Gallium phosphide GaP 4.138 300

Gallium arsenide GaAs 5.3161 (2) 298.15

Gallium antimonide GaSb 5.6137 (4) 300

Table 4.1-55 Elastic constants c

of gallium compounds

Crystal c

Temperature Remarks

(GPa) (GPa) (GPa) (GPa) (GPa) (K)

Gallium nitride GaN 377 160 114 209 81.4 300 Ultrasound resonance

technique

Gallium phosphide GaP 140.50 (28) 62.03 (24) − − 70.33 (7) Ultrasound

( f = 10 and 30 MHz)

Gallium arsenide GaAs 119 (1) 53.8 (1) − − 59.5 (1) 300

112.6 57.1 − − 60.0 0 Extrapolated data

Gallium antimonide GaSb 88.34 40.23 − − 43.22 296 Ultrasound

Part 4 1.2