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

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682 Part 4 Functional Materials

C. Transport Properties

Tables 4.1-165 – 4.1-167.

Table 4.1-165 Electronic transport, general description

Cadmium oxide (CdO)

Owing to a high degree of nonstoichiometry, CdO is generally a highly degenerate n-type semiconductor. The

conductivity is related to an excess of Cd in the lattice. Usually the electron concentration is several times

−3

. Values of the electrical resistivity at 300 K range from 1.2to1.5×10

−3

Ω cm.

Cadmium sulﬁde (CdS)

Electrical transport in CdS is performed by electrons in the Γ

conduction band and holes in the Γ

valence

band. Because of compensation effects during the preparation of the samples and the large ratio µ

/µ

> 10,

CdS is normally n-type conducting; p-type conductivity is observed only in a few special cases. The carrier con-

centration depends on the impurity or defect content and on temperature. Furthermore, the carrier concentration

can be changed markedly by illumination: CdS is known to be a model substance for photoconductivity.

Cadmium selenide (CdSe)

Electrical transport in CdSe is governed by electrons in the Γ

conduction band and holes in the Γ

valence band.

CdSe is mainly n-type conducting, owing to compensation effects during the preparation of the samples and to

a ratio of the mobilities of electrons and holes of order 10. The carrier concentration depends on the impurity or

defect content and on temperature. Furthermore, it depends strongly on irradiation. Photoconductivity in CdSe

can be produced by electromagnetic illumination (photon energy > band gap) and by high-energy particles.

Cadmium telluride (CdTe)

CdTe bulk crystals can be doped to become n- or p-type conductive. High-resistivity crystals (ρ>10

Ω cm)

can be obtained under various growth and doping conditions.

Table 4.1-166 Electron and hole mobilities µ

and µ

of cadmium compounds

Crystal µ

(cm

/Vs) µ

(cm

/Vs) Temperature Remarks

(K)

Cadmium oxide CdO 180 300 Hall mobility, cold-pressed CdO, n = 1.1×10

−3

Cadmium sulﬁde CdS 160 300 In-doped, n =5×10

−3

>10 000 30–40 Peak mobility, ultrapure crystals

15 300 Highly resistive crystals

Cadmium selenide CdSe 660 300 Polycrystal and single-crystal material

5000 80 Dc Hall effect

200 800

40 300 N-doped epitaxial ﬁlms

Cadmium telluride CdTe <110 000 32 Hall mobilities

60 300

1200 170

Table 4.1-167 Thermal conductivity κ of cadmium compounds

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

dependence

Cadmium sulﬁde CdS 0.20 300 Fig. 4.1-171

Cadmium selenide CdSe 0.09 300

Cadmium telluride CdTe 0.071 298 Fig. 4.1-172 Single crystal

10 8 Theoretical maximum for a pure crystal

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 683

468

262

–1

T (K)

(W/cm K)

c axis

⊥ ∆T

⎢⎢ ∆T

CdS

Fig. 4.1-171 CdS. Thermal conductivity vs. temperature for

c axis parallel and perpendicular to the heat ﬂow ∆T [1.145,

146]

D. Electromagnetic and Optical Properties

Tables 4.1-168 and 4.1-169.

Table 4.1-168 Dielectric constant ε of cadmium compounds

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

Cadmium oxide CdO 21.9 300 Infrared reﬂectivity

2.1 300 Transmittance, absorption

Cadmium sulﬁde CdS ε(0)

perpend

8.28 ε(∞)

perpend

5.23 300 Spectroscopic ellipsometry

ε(0)

parall

8.73 ε(∞)

parall

5.29

Cadmium selenide CdSe ε(0)

perpend

9.29 300 Infrared spectroscopy

9.15 100

ε(0)

parall

10.16 300

9.29 100

Cadmium telluride CdTe 10.4 7.1 (1) 300

–1

–2

–3

101

T (K)

(W/cm K)

CdTe

Pure crystal

Samples 2 ( ) and 4 ( )

Samples 1 ( ) and 3 ( )

Fig. 4.1-172 CdTe. Thermal conductivity of several differ-

ent specimens vs. temperature. The results for specimens

1 and 3 have been plotted reduced by a factor

of 10. The point defect concentrations of the sam-

ples are (1) 3.42× 10

−3

;(2)3.99 × 10

−3

;(3)

3.42× 10

−3

;(4)2.66× 10

−3

[1.147]

Part 4 1.3

684 Part 4 Functional Materials

Table 4.1-169 Refractive index n of cadmium compounds

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

Cadmium oxide CdO 1.95–2.65 600 Fig. 4.1-173

Cadmium sulﬁde CdS n

parall c

Fig. 4.1-174

perpend c

Cadmium selenide CdSe Fig. 4.1-175

Cadmium telluride CdTe 2.70 2500 300 Prism refraction

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

Refractive index n Absorption index k

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.02

Wavelength λ (nm)

300 400 500 600 700 800 900

CdO

Fig. 4.1-173 CdO. Dispersion of the optical constants

n and k of a ﬁlm [1.148]

2.80

2.75

2.70

2.65

2.60

2.55

hv (eV)

2.24 2.28 2.32 2.36 2.40 2.44

CdS

⊥

⏐⏐

Fig. 4.1-174 CdS, hexagonal. Dispersion of the refractive

index. The symbols are experimental values and the curves

correspond to polynomial ﬁts [1.149]

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 685

3.5

3.0

2.5

2.0

1.5

1.0

0.5

01234567

hω (eV)

n, k

ZnSe

Fig. 4.1-175 CdSe, hex, cub. The real refractive index

n(E) and the extinction coefﬁcient k(E), forming the

complex refractive index n ∗(E) = n(E) +ik(E),for

both hexagonal and cubic CdSe. The circles represent

experimental data, the solid lines numerically calculated

energy dependences [1.150]

Part 4 1.3

686 Part 4 Functional Materials

4.1.3.6 Mercury Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-170 – 4.1-177.

Table 4.1-170 Crystal structures of mercury compounds

Crystal Space group Crystal system Structure type Figure

Mercury oxide HgO D

Trigonal

Mercury sulﬁde HgS Red α-HgS

Mercury selenide HgSe T

F43m fcc Zinc blende Fig.4.1-131

Mercury telluride HgTe T

F43m fcc Zinc blende Fig.4.1-131

Table 4.1-171 Lattice parameters of mercury compounds

Crystal Lattice parameters (nm) Remarks

Mercury oxide HgO a = 0.3577 X-ray diffraction

b =0.8681

c =0.2427

Mercury sulﬁde HgS a =0.414 X-ray diffraction

b =0.949

c =0.2292

Mercury selenide HgSe a = 0.5997 (5) Angle-dispersion X-ray diffraction, pressure p =2.25 GPa

Mercury telluride HgTe a =0.6453 Energy-dispersive X-ray diffraction

Table 4.1-172 Densities of mercury compounds

Crystal Density (g/cm

)

Mercury oxide HgO 11.080

Mercury selenide HgSe 8.11

Mercury telluride HgTe 8.21

Table 4.1-173 Melting point T

of mercury compounds

Crystal Melting Remarks

point T

(K)

Mercury sulﬁde HgS 1093 Zinc blende structure

Mercury selenide HgSe 1072 Assessed

Mercury telluride HgTe 943

–2

–4

HgTe

0 50 100 150 200 250 300

T (K)

α (10

–6

–1

)

Fig. 4.1-176 HgTe. Linear thermal expansion coefﬁcient α

vs. T . Symbols, experimental points; solid line, calculated

values [1.151]

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 687

Table 4.1-174 Elastic constants c

of mercury compounds

Crystal c

(GPa) c

(GPa) Remarks

Mercury sulﬁde HgS 35.0 (14) 48.6 (5) 13.0 (5) 300 K

Mercury selenide HgSe 62.2 (1) 46.4 22.7 (1) 292 K, ultrasound measurements

Mercury telluride HgTe 53.6 36.6 21.10 300 K

58.7 40.5 22.3 77 K

Table 4.1-175 Linear thermal expansion coefﬁcient α of mercury compounds

Crystal Linear thermal expansion Temperature Remarks

coefﬁcient α(10

−6

−1

)

Mercury sulﬁde HgS α

parall

18.8 (8) 20–200

◦

C Parallel to c axis

perpend

18.1 (5) Perpendicular to c axis, trigonal HgS

Mercury selenide HgSe 28.61 30–380

◦

C From temperatur dependence of lattice constant a

Mercury telluride HgTe 4.0 77–300 K See Fig. 4.1-176 for temperature dependence

Table 4.1-176 Heat capacity c

and Debye temperature Θ

of mercury compounds

Crystal Heat capacity c

Temperature Debye temperature Θ

Remarks

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

Mercury sulﬁde HgS 50.25 300 152 T = 0 K, calorimetry, extrapolated

Mercury selenide HgSe 49.79 300 142 T = 0 K, calorimetry, extrapolated

Mercury telluride HgTe 54.81 300 141.5

Table 4.1-177 Phonon frequencies/wavenumbers at symmetry points for mercury compounds. Mercury sulﬁde (HgS),

80 K, from infrared reﬂectance; mercury selenide (HgSe), RT, from resonance Raman scattering; mercury telluride

(HgTe), 290 K, from neutron scattering

HgS HgSe HgTe

Mode Symmetry Wavenumber Mode Wavenumber Mode Symmetry Phonon

point (cm

−1

) (cm

−1

) point energy (meV)

356

130 hν

Γ 14.86 (16)

347.6

174 hν

Γ 14.63 (17)

296 hν

X 16.86 (12)

284.2 hν

X 16.64 (10)

156 hν

X 10.56 (7)

115.5 hν

X 1.97 (2)

98 hν

L 18.07 (24)

92 hν

L 15.86 (18)

50 hν

L 9.97 (6)

42 hν

L 2.28 (2)

Part 4 1.3

688 Part 4 Functional Materials

B. Electronic Properties

Tables 4.1-179 – 4.1-183.

Table 4.1-178 Band structures of mercury compounds

Mercury selenide (HgSe)

Mercury selenide is a zero-gap material (semimetal). The lowest conduction band minimum and the top of

the valence band are degenerate at the center of the Brillouin zone (Γ

). The Γ

level, which for most cubic

semiconductors is the conduction band minimum and has an energy larger than that of the Γ

state, is found to

be below the Γ

state in HgSe (“negativ energy gap”, inverted band structure).

Mercury telluride (HgTe)

Mercury telluride, like mercury selenide, is a zero-gap material (semimetal). The lowest conduction band

minimum and the top of the valence band are degenerate at the center of the Brillouin zone (Γ

). The Γ

level,

which for most cubic semiconductors is the conduction band minimum and has an energy larger than that of

the Γ

state, is found to be below the Γ

state in HgTe (“negativ energy gap”, inverted band structure) (see

Fig. 4.1-177).

Zero gap Positive gap

CrossoverHgSe Hg

1–x

Se CdSe

∆

Fig. 4.1-177 Schematic band structure of the Hg–Cd–Se

system near the Γ point [1.152]

Table 4.1-180 Energy gaps of mercury compounds

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

Mercury oxide HgO 2.19 Photoconductivity

2.80

Mercury sulﬁde HgS 2.03 300 Absorption

Mercury selenide HgSe −0.274 Γ

and Γ

4.2 Shubnikov–de Haas effect

−0.061 Γ

and Γ

300

Mercury telluride HgTe −0.304 Γ

and Γ

0 Extrapolated optical and

−0.141 (13) Γ

and Γ

300 magneto-optical data

Table 4.1-179 First Brillouin zones of mercury compounds

Crystal Figure

Mercury selenide HgSe Fig. 4.1-133

Mercury telluride HgTe Fig. 4.1-133

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 689

Table 4.1-181 Spin–orbit splitting energies ∆

of mercury compounds

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

Mercury selenide HgSe 0.383 (2) Γ

to Γ

4.2 Interband magnetoabsorption

0.45 Γ

15v

12 Reﬂectivity

Mercury telluride HgTe 1.08 (2) Γ

to Γ

300 Electroreﬂectance

Table 4.1-182 Effective masses of electrons (in units of the electron mass m

) for mercury compounds

Crystal Quantity Band Mass Temperature (K) Remarks

Mercury selenide HgSe m

Strongly dependent on electron concentration

Mercury telluride HgTe m

0.031 (1) 4.4 Interband magnetoabsorption

Table 4.1-183 Effective masses of holes (in units of the electron mass m

) for mercury compounds

Crystal Quantity Band Mass Temperature (K) Remarks

Mercury selenide HgSe m

0.78

Mercury telluride HgTe m

[100] Γ

0.320 4.2 Interband magnetoreﬂection

[110] 0.406

[111] 0.445

0.3 4–100 Transport measurements

0.028 (1) 4.4 Interband magnetoabsorption

C. Transport Properties

Tables 4.1-184 and 4.1-185. See Fig. 4.1-179 for the

thermal conductivity of mercury telluride.

Table 4.1-184 Electronic transport, general description

Mercury sulﬁde (HgS)

In natural red cinnabar crystals (α-HgS), carrier concentrations n = 10

–10

−3

are found; in synthetic

crystals, the values range from 10

to 10

−3

. The observed values of the resistivity ρ are: parallel to the

c axis, 6400 Ω cm at 77 K, and perpendicular to the c axis, 3450 Ω cm at 300 K, both values being obtainded

from natural crystals.

Mercury selenide (HgSe)

All HgSe samples show n-type conductivity. As-grown crystals have carrier concentrations of about

electrons/cm

Mercury telluride (HgTe)

See Fig. 4.1-178 for the temperature dependence of the electrical conductivity.

Part 4 1.3

690 Part 4 Functional Materials

Table 4.1-185 Electron mobilities µ

of mercury compounds

Crystal µ

(cm

/Vs) Temperature (K) Remarks

Mercury sulﬁde HgS µ

parall

157 77 Natural crystal, maximum values

30 300

perpend

49 77

10 300

Mercury selenide HgSe 15 × 10

300 All HgSe samples show n-type conductivity

55× 10

Mercury telluride HgTe 35 × 10

300 Maximum mobility values

120× 10

800× 10

4.2

4682

2×

T (K)

σ (Ω

–1

)

HgTe

Fig. 4.1-178 HgTe. Electrical conductivity vs. tempera-

ture. Experimental data (circles), in comparison with

calculated curves assuming mixed scattering modes (solid

line) and neglecting interband optical-phonon scattering

(broken line) [1.153]

468

246822

–1

–2

4×

T (K)

(W/cm K)

Fig. 4.1-179 HgTe. Thermal conductivity vs. temperature

for three different samples; the solid lines represent theo-

retical ﬁts [1.154]

Part 4 1.3

Semiconductors References 691

D. Electromagnetic and Optical Properties

Tables 4.1-186 and 4.1-187.

Table 4.1-186 Dielectric constant ε of mercury compounds

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

Mercury sulﬁde HgS ε(0)

perpend

16.85 ε(∞)

perpend

5.38 80 Synthetic crystal

18.2 6.25 300

ε(0)

parall

21.5 ε(∞)

parall

7.4 80

23.5 7.9 300

Mercury selenide HgSe 25.6 12–21 Reﬂectivity and Kramers–Kronig

analysis of ﬁts to data on

plasmon–LO-phonon coupled mode

Mercury telluride HgTe 21.0 15.2 77 Reﬂectance

Table 4.1-187 Refractive indices n of mercury compounds

Crystal Refractive λ(nm) Temperature

index n (K)

Mercury oxide HgO 2.5 550

Mercury sulﬁde HgS n

2.9028 620 298

3.2560

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Part 4 1