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

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672 Part 4 Functional Materials

hv (eV)

–5

–10

2345601

+ ∆

, ε

ZnTe

Fig. 4.1-156 ZnTe. Dielectric-function spectrum ε(ω),

measured by spectroscopic ellipsometry at RT (ﬁlled and

open circles); the solid and dashed lines show calculated

values [1.130]. The triangles are experimental data from

[1.131]

D. Electromagnetic and Optical Properties

Tables 4.1-147 – 4.1-149.

Table 4.1-147 Dielectric constant ε of zinc compounds

Crystal ε(0) ε(∞) Temperature (K) Remarks

Zinc oxide ZnO ε

parall c

perpend c

parall c

perpend c

300

8.75 7.8 3.75 3.70

Zinc sulﬁde ZnS 300 See Fig. 4.1-157 for spectral dependence

and Fig. 4.1-158 for the temperature

dependence

Zinc selenide ZnSe 8.6 5.7 300 Ellipsometry

Zinc telluride ZnTe 10.3 RT Reﬂectivity derived from refraction data

7.28 300 See Fig. 4.1-160 for spectral dependence

Table 4.1-148 Refractive index n of zinc compounds

Crystal Refractive index n λ(nm) Temperature (K) Spectral dependence

Zinc oxide ZnO n

parall c

2.151 436 293 Fig. 4.1-161

perpend c

2.137

Zinc sulﬁde ZnS 300

Zinc selenide ZnSe 300 Fig.4.1-163

Zinc telluride ZnTe 300 Fig. 4.1-164

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 673

123456

–2

hv (eV)

, ε

ZnS (cubic)

Fig. 4.1-157 ZnS, cubic. Dielectric-function spectrum

ε(E), measured by spectroscopic ellipsometry at 300 K af-

ter chemomechanical polishing of the sample (circles). The

solid lines show values calculated from a model dielectric

function for interband critical points. The dashed lines rep-

resent the best-ﬁt standard critical-point lineshapes [1.132]

ZnS (hex)

2.75

2.65

2.55

2.45

2.35

2.25

λ (nm)

ω,

350 600 850 1100 1350 1600

T = 298 K

Fig. 4.1-159 ZnS, hexagonal. Index of refraction vs. wave-

length. n

, ordinary ray; n

, extraordinary ray [1.134]

8.8

8.6

8.4

8.2

8.0

T (K)

0 50 100 150 200 250 300

ZnS (hex)

Fig. 4.1-158 ZnS, hexagonal. Dielectric constant vs. tem-

perature [1.133]. At 300 K, the dielectric constant of

hexagonal ZnS is isotropic

1.2

1.0

0.8

0.6

0.4

0.2

1.6

1.2

0.8

0.4

Dielectric constant ε

Photon energy hv (eV)

0 40 80 120 160

Dielectric constant ε

ZnTe

Fig. 4.1-160 ZnTe. Spectral dependence of the real and

imaginary parts of the complex dielectric constant,

and ε

[1.135]

Part 4 1.3

674 Part 4 Functional Materials

⏐⏐

⊥

2.5

2.0

1.5

1.0

0.5

Reflective index n

⊥

Photon energy hv (eV)

4.0 5.04.52.0 3.01.5 2.5 3.5

2.5

2.0

1.5

1.0

0.5

Absorption index k

⊥

2.5

2.0

1.5

1.0

0.5

Refractive index n

⏐⏐

Photon energy hv (eV)

4.0 5.04.52.0 3.01.5 2.5 3.5

2.5

2.0

1.5

1.0

0.5

Absorption index k

⏐⏐

ZnO ZnO

Fig. 4.1-161 ZnO. Numerically calculated spectral dependence of the complex refractive index n

∗

= n(E) +ik(E) for

ZnO (solid lines). The circles represent experimental data at 300 K [1.136]

ZnS (cubic)

3.88

3.84

3.80

3.76

3.72

3.68

0 50 100 150 200 250 300

T (K)

g,dir

(eV)

Fig. 4.1-162 ZnS, cubic. Direct energy gap (Γ

15v

to Γ

)

vs. temperature [1.137]. Solid line, theoretical result. Cir-

cle, experimental data from [1.138]. Triangle, experimental

data from [1.139]

3.5

3.0

2.5

2.0

1.5

1.0

0.5

01234567

hω (eV)

n, k

ZnSe

Fig. 4.1-163 ZnSe. Numerically calculated spectral depen-

dence of the real refractive index n and the extinction

coefﬁcient k (solid lines). The ﬁlled circles (n)andopen

circles (k) are experimental data [1.140]

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 675

Table 4.1-149 Electro-optical constants of zinc compounds. Under the inﬂuence of an electric ﬁeld, the refractive index

changes in accordance to the nonlinearity of the dielectric polarization (Pockels effect). Crystals with hexagonal symmetry

have three electro-optical constants r

, r

; crystals with cubic symmetry have only one electro-optical constant r

Crystal Electro-optical constant λ(nm) Temperature (K) Remarks

(10

−9

cm/V)

Zinc oxide ZnO r

, r

−1.4 400 295 Electrotransmission

−0.31

Zinc sulﬁde ZnS r

0.21 650 Retardation angle

Zinc telluride ZnTe r

−4.71 Calculated

hv (eV)

0123456

n, k

ZnTe

Fig. 4.1-164 ZnTe. Numerically calculated spectral depen-

dence of the complex refractive index (n and k)(solid lines).

The circles are measured ellipsometry data [1.130]. The

triangles are experimental data taken from [1.131]

Part 4 1.3

676 Part 4 Functional Materials

4.1.3.5 Cadmium Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-150 – 4.1-157.

Table 4.1-150 Crystal structures of cadmium compounds

Crystal Space group Crystal system Structure type Figure

Cadmium oxide CdO O

Fm3m fcc NaCl Fig. 4.1-138

Cadmium sulﬁde CdS C

mc hex Wurtzite Fig. 4.1-130

Cadmium selenide CdSe T

F43m fcc Zinc blende Fig. 4.1-131

Cadmium telluride CdTe T

F43m fcc Zinc blende Fig. 4.1-131

Cadmium oxide is the only II–VI semiconductor which crystallizes in the NaCl structure at standard pressure.

CdS crystallizes in several different structures. Besides the most common wurtzite structure, it is found also in the zinc blende structure and

in the high-pressure NaCl structure. Epitaxial layers of CdS are frequently found in one of the cubic modiﬁcations.

Under ambient conditions, CdSe crystallizes in the zinc blende structure. Ab initio calculations show that the energy of the zinc blende

structure is lower than that of the wurtzite structure by 1.4meV/atom. Under increasing pressure, the wurtzite structure transforms to the

NaCl structure, the β-tin structure, and as yet unidentiﬁed structures. If not stated otherwise, the data in this section concern CdSe in the

zinc blende structure.

Table 4.1-151 Lattice parameters of cadmium compounds

Crystal Lattice parameters (nm) Remarks

Cadmium oxide CdO a =0.4689

Cadmium sulﬁde CdS a = 0.41348 X-ray diffraction

c =0.67490

Cadmium selenide CdSe a =0.6077 (5) Perpendicular to surface, X-ray diffraction

a =0.6078 (1) Parallel to surface

Cadmium telluride CdTe a =0.646 X-ray diffraction

Table 4.1-152 Densities of cadmium compounds

Crystal Density (g/cm

) Temperature (K) Remarks

Cadmium oxide CdO 8.15 X-ray crystal density method

Cadmium sulﬁde CdS 4.82 300

Cadmium selenide CdSe 5.81 300

Cadmium telluride CdTe 5.87 4

Table 4.1-153 Elastic constants c

of cadmium compounds

Crystal c

(GPa) c

(GPa) Remarks

Cadmium sulﬁde CdS 90.7 51.0 93.8 15.04

Cadmium selenide CdSe 74.6 46.1 81.7 13.0 14.3 Ultrasound measurements, RT

Table 4.1-153 Elastic constants c

of cadmium compounds, cont.

Crystal c

(GPa) c

(GPa) Temperature (K)

Cadmium telluride CdTe 53.8 37.4 20.18 298

56.2 39.4 20.61 77

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 677

9.0

7.5

6.0

4.5

3.0

1.5

– 1.5

– 3.0

T (K)

α (10

–6

–1

)

0 100 200 300 500 700 900

CdS

Table 4.1-154 Melting point T

of cadmium compounds

Crystal Melting point T

(K) Remarks

Cadmium oxide CdO >1773

Cadmium sulﬁde CdS 1750 Under pressure p > 3.85 bar

Cadmium selenide CdSe 1537 Assessed

Cadmium telluride CdTe 1366.6 (70) Mean of experimental values

Table 4.1-155 Linear thermal expansion coefﬁcient α of cadmium compounds

Crystal Expansion coefﬁcient α(K

−1

) Temperature (K) Remarks

Cadmium oxide CdO 14× 10

−6

300–770 Dilatometer measurements

Cadmium sulﬁde CdS See Fig. 4.1-165 for temperature

dependence

Cadmium selenide CdSe

Cadmium telluride CdTe 4.96 × 10

−6

20–420

Fig. 4.1-165 CdS, hexagonal. Temperature dependence of

the linear thermal expansion coefﬁcients α

⊥

(perpendicular

to the c axis, curve 1)andα



(parallel to the c axis, curve 2),

measured by dilatometer experiments [1.141,142]

T (K)

0 300 600 900

(J/mol K)

CdO

Fig. 4.1-166 CdO. Heat capacity c

vs. temperature. Mea-

surements from two authors [1.143]

Part 4 1.3

678 Part 4 Functional Materials

Table 4.1-156 Heat capacity c

and Debye temperature Θ

of cadmium compounds

Crystal Heat capacity c

Temperature Debye temperature Remarks

(J/mol K) (K) Θ

(K)

Cadmium oxide CdO 43.639 298.15 See Fig. 4.1-166 for temperature dependence

255 (6) Calculated from X-ray diffraction measurements

Cadmium sulﬁde CdS 55.10 300 T = 298–1678 K

219.32 From elastic constants

Cadmium selenide CdSe 49.58 300 Monocrystalline sample, T =400–700 K

181.7 T = 0K

Cadmium telluride CdTe 25.63 300 Polycrystalline sample, T =300–530 K

140 (3) Single crystal, X-ray diffraction

Table 4.1-157 Phonon frequencies/wavenumbers at symmetry points for cadmium compounds. Cadmium oxide (CdO), Funda-

mental optical-mode frequencies; cadmium sulﬁde (CdS), 25 K; cadmium selenide (CdSe), 300 K, from infrared and Raman

spectroscopy; cadmium telluride (CdTe), 300 K, from inelastic neutron scattering

CdO CdS

Mode Symmetry Frequency Temperature Mode Symmetry Wavenumber

point (THz) (K) point (cm

−1

)

Γ 7.85 300

, perpendicular to c 307

ΛO

Γ 15.83 300

LO, 1

, parallel to c 305

L 14.4 2

TO, 1

, perpendicular to c 242

X 15.6 2

TO, 1

, parallel to c 234

X 7.2 2

LO, 2

, perpendicular to c 256

TO, 3

, perpendicular to c 43

CdSe CdTe

Mode Symmetry Wavenumber Mode Symmetry Frequency

point (cm

−1

) point (THz)

LO, 1

, parallel to c 210 ν

Γ 5.08 (10)

TO, 1

, perpendicular to c 169 ν

Γ 4.20 (10)

LO, 2

, perpendicular to c 212 ν

X 4.44 (6)

TO, 2

, parallel to c 166 ν

X 1.05 (3)

43.5 ν

L 4.33 (6)

TAO

L 4.33 (7)

L 3.25 (8)

L 0.88 (3)

B. Electronic Properties

Tables 4.1-158 – 4.1-164.

Table 4.1-158 First Brillouin zones of cadmium com-

pounds

Crystal Figure

Cadmium oxide CdO Fig. 4.1-133

Cadmium sulﬁde CdS Fig. 4.1-132

Cadmium selenide CdSe Fig. 4.1-133

Cadmium telluride CdTe Fig. 4.1-133

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 679

Table 4.1-159 Band structures of cadmium compounds

Cadmium oxide (CdO) (Fig. 4.1-167)

The lowest conduction band has its minimum at the Γ

point in the center of the Brillouin zone. Within an energy

range of a few tenths of an electron volt above its bottom, the band is isotropic but highly nonparabolic. The

nonparabolicity is revealed by the strong dependence of the optical electron mass on the electron concentration.

The lowest conduction band is separated from the higher bands by a small gap. The valence band consists of

several branches, with maxima at L

and Σ.

Cadmium sulﬁde (CdS) (Fig. 4.1-168)

Hexagonal CdS is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone

(Γ). The topmost valence band (Γ

+Γ

) is split owing to the crystal ﬁeld and spin–orbit coupling into three

spin-degenerate states. The exciton states formed with holes in these valence band states are referred to as the

A, B, and C excitons, respectively.

Cadmium selenide (CdSe)

See Fig. 4.1-170.

Cadmium telluride (CdTe) (Fig. 4.1-169)

Cadmium telluride is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin

zone (Γ). The topmost valence band is split owing to spin–orbit coupling into a fourfold (Γ

) and a twofold (Γ

)

state.

1.5

1.0

0.5

– 0.5

– 1.0

– 1.5

– 2.0

Γ WΓ XW LΣ∆ΛZK Q

E (Ry)

Wave vector k

CdO

∆

25'

2,5

∆

25'

∆

25'

Fig. 4.1-167 Band structure of cadmium oxide

–2

–4

ΓΣ∆ ΓARLUM A SHPK T

E (eV)

Wave vector k

1,3

CdS (hex)

2,4

5,6

1,2

1,3

5,6

1,3

1,2

Fig. 4.1-168 Band structure of hexagonal cadmium sulﬁde

Part 4 1.3

680 Part 4 Functional Materials

–3

–6

–9

–12

–15

XW Γ K Γ

E (eV)

Wave vector k

CdSe (cubic)

Cd 4d energy

–2

–4

–6

–8

–10

–12

U,KXL ΓΓΣΛ∆

0 0.5 1.0 1.5

Wave vector kg (states/eV atom)

E (eV)

CdTe

4,5

a) b)

Fig. 4.1-169a,b CdTe. (a) Band structure and (b) electron

density of states from a pseudopotential calculation [1.144].

Dashed curve: Experimental data

Fig. 4.1-170 Band structure of cubic cadmium selenide

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 681

Table 4.1-160 Energy gaps of cadmium compounds (for the letters A, B, C see CdS band structure, Fig. 4.1-168)

Crystal Band gap (eV) Between bands Temperature (K) Remarks

Cadmium oxide CdO E

(1)

g, ind

1.09 (5) Σ

and Γ

100 Thermoreﬂectance

(2)

g, ind

0.84 L

and Γ

g, dir

2.28 Γ

15v

and Γ

Cadmium sulﬁde CdS E

g, dir

2.482 Γ

and Γ

300 Band gaps of the three subbands;

2.496 Γ

and Γ

Ellipsometry

2.555 Γ

and Γ

Cadmium selenide CdSe E

g, dir

1.74 E

300 Ellipsometry

Cadmium telluride CdTe E

g, dir

1.475 Γ

and Γ

RT Photoelectrochemistry

Table 4.1-161 Spin–orbit splitting energy ∆

of cadmium compounds

Crystal Splitting energy (meV) Bands Temperature (K) Remarks

Cadmium selenide CdSe 470 Calculation

Cadmium telluride CdTe 950 (20) Γ

to Γ

300 Photoemission

Table 4.1-162 Effective masses of electrons (in units of the electron mass m

) for cadmium compounds

Crystal Quantity Mass Temperature (K) Remarks

Cadmium oxide CdO m

0.33–0.46 81 Comparison of low-temperature mobilities,

n = 0.4–6.3×10

−3

Cadmium sulﬁde CdS m

0.25 300 Thermoelectric power

Cadmium selenide CdSe m

0.12 Calculation

Cadmium telluride CdTe m

[110] 0.096 (3) 1.5 Cyclotron resonance

[100] 0.094 (4) 1.8

[111] 0.095 (4) 1.8

Table 4.1-163 Effective masses of holes (in units of the electron mass m

) for cadmium compounds

Crystal Quantity Mass Temperature (K) Remarks

Cadmium sulﬁde CdS m

p, perpend

0.7 (1) 1.6 Exciton magnetoabsorption

p, parall

Cadmium selenide CdSe m

p, heavy

[111] 2.14 Calculation

p, heavy

[100] 0.9

p, heavy

[110] 1.7

p, light

[111] 0.16

p, light

[100] 0.18

p, light

[110] 0.16

Cadmium telluride CdTe m

p, heavy

[110] 0.81 (5) 1.5 Cyclotron resonance

p, light

[110] 0.12 (2)

Table 4.1-164 g-factors in the conduction band (g

) and valence band (g

) for cadmium compounds

Crystal Quantity g-factor Temperature (K) Remarks

Cadmium oxide CdO g

1.806 (5) 77 Electron spin resonance measurements

Cadmium sulﬁde CdS g

c, perpend

1.78 (5) 1.6 Exciton absorption

c, parall

1.72 (10) (for the letters A, B, C see

v, parall

1.15 (5) 16 CdS band structure, Fig. 4.1-168)

v, perpend

0.8 1.8 Lineshape analysis of excitonic polaron reﬂectivity

Cadmium selenide CdSe g 0.23 Calculation

Cadmium telluride CdTe g

1.652 1.5 Spin-ﬂip Raman measurements

Part 4 1.3