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

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662 Part 4 Functional Materials

1.2

1.0

0.8

0.6

0.4

0.2

– 0.2

– 0.4

XL ΓΣΛ∆ KΓ

– 2.5

– 2.7

E (Ry)

– 0.9

– 1.1

– 1.3

– 1.5

Wave vector k

CaO

∆

4,1

∆

25'

∆

25'

∆

Fig. 4.1-146 Band structure of calcium oxide

Table 4.1-127 Band structure of calcium oxide

Crystal Figure Remarks

Calcium oxide CaO Fig. 4.1-146

Some controversy exists in the literature about the positions

of the lowest conduction band minima. One result shows the

lowest minimum at Γ

and the minimum of the d states at

, below some s states but above Γ

. Other results claim

the symmetry point of the conduction band bottom is at X

instead of Γ

, whereas according to other authors Γ

and X

are nearly degenerate.

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 663

C. Transport Properties

Tables 4.1-128 – 4.1-130.

Table 4.1-128 Electronic transport in oxides of Ca, Sr, and Ba, general description

Crystal Transport properties

Calcium oxide CaO For general remarks, see the comments on the transport properties of MgO on p. 659. The transport of charge

carriers in CaO has been discussed in various models, e.g. polaron band conduction and hopping conduction

through compensated semiconducting samples, and also a considerable contribution from ionic conductivity

has been taken into account. From measurements of the oxygen pressure dependence of the conductivity of

undoped CaO, it is concluded that n-type conduction occurs at low pressures (< 10

−2

–10

−4

mbar) and that

p-type conduction occurs at higher pressures (> 10

−2

–1 mbar). In some cases this conclusion is conﬁrmed

by Hall and thermoelectric measurements. For intermediate pressures, it is supposed that the lattice disorder

(presumably of Schottky type) gives rise to predominantly ionic conduction

Strontium oxide SrO The transport of charge carriers has been discussed in various models as in the case of CaO (see above). It is

supposed that the dominating scattering mechanism is optical-mode scattering

Barium oxide BaO The electrical transport has been discussed mainly on the assumption that it is due to electronic conduction.

The ionic contribution is small. Polaron conduction and predominant optical-mode scattering are assumed

Table 4.1-129 Electrical conductivity σ and electron mobility µ

of oxides of Ca, Sr, and Ba

Crystal Conductivity Electron mobility Remarks

at temperature at O

pressure

(cm

/Vs) (K) (mbar)

Calcium oxide CaO 8 700 < 10

−6

Single crystals, Hall mobility

Strontium oxide SrO 5 700 < 10

−6

Single crystals, Hall mobility

Barium oxide BaO Fig. 4.1-148 5 600 < 10

−6

Polycrystals, Hall mobility

Table 4.1-130 Thermal conductivity κ of oxides of Ca, Sr, and Ba

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

Calcium oxide CaO 300 0.3 See Fig. 4.1-147 for temperature dependence

Strontium oxide SrO 300 0.1 See Fig. 4.1-147 for temperature dependence

Barium oxide BaO 300 0.03 See Fig. 4.1-147 for temperature dependence

Part 4 1.3

664 Part 4 Functional Materials

–1

–2

T (K)

(W/cm K)

MgO

CaO

SrO

BaO

Fig. 4.1-147 MgO, CaO, SrO, BaO. Temperature de-

pendence of the thermal conductivity κ of single

crystals [1.124]. Dashed lines, κ ∝ T

−1

D. Electromagnetic and Optical Properties

Table 4.1-131.

Table 4.1-131 Dielectric constant ε of oxides of Ca, Sr, and Ba

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

Calcium oxide CaO 273 12.01 (10) Capacitance measurement at 1 kHz and 10 kHz

3.27 Compilation

Strontium oxide SrO

Barium oxide BaO 296 3.903–4.197 Calculated from refractive-index values in the spectral

range 624–436 nm

σ (Ω

–1

)

–1

–2

–3

–4

–5

–6

–7

–8

0.5 0.7 0.9 1.1 1.3 1.5

2.0

1.5

1.0

0.5

–1

(10

–3

–1

)

S (mV K

–1

)

BaO

Fig. 4.1-148 BaO. Electrical conductivity σ (solid lines)

and thermoelectric power S (dashed lines) of two crystals

vs. 1/T [1.125]. p

= 3×10

−5

mbar. n-type conduction

at temperatures below the discontinuity

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 665

4.1.3.4 Zinc Compounds

A. Crystal Structure, Mechanical and Thermal Properties

Tables 4.1-132 – 4.1-139.

Table 4.1-132 Crystal structures of zinc compounds

Crystal Space group Crystal system Structure type Figure

Zinc oxide ZnO C

mc hex Wurtzite Fig. 4.1-130

Zinc sulﬁde ZnS T

fcc Zinc blende Fig. 4.1-131

Zinc selenide ZnSe T

F43m fcc Zinc blende Fig.4.1-131

Zinc telluride ZnTe T

fcc Zinc blende Fig. 4.1-131

At room temperature, ZnS bulk material consists predominantly of the cubic phase, often with hexagonal inclusions, leading to

polytypic material. Epitaxial ZnS has mostly been grown on GaAs and thus has pseudomorphically assumed the cubic structure of

the substrate material. In this section, all data refer to the cubic modiﬁcation unless explicitly stated otherwise.

Table 4.1-133 Lattice parameters of zinc compounds

Crystal Lattice parameters (nm) Temperature Remarks

Zinc oxide ZnO a =0.3249 (6) X-ray diffraction

c =0.52042 (20)

Zinc sulﬁde ZnS a = 0.54053 RT X-ray diffraction

Zinc selenide ZnSe a = 0.5667 (4) 300 K X-ray diffraction

Zinc telluride ZnTe a =0.60882 RT X-ray diffraction

Table 4.1-134 Densities of zinc compounds

Crystal Density (g/cm

) Temperature Remarks

Zinc oxide ZnO 5.67526 (19) 293 K Hydrostatic weighing

Zinc sulﬁde ZnS Cubic: 4.088 RT

Hexagonal: 4.087 RT

Zinc selenide ZnSe 5.266 Shock wave experiment

Zinc telluride ZnTe 5.636 298 K

Table 4.1-135 Elastic constants c

(in GPa) of zinc compounds

Crystal c

(GPa) c

(GPa) Remarks

Zinc oxide ZnO 206 (4) 118 (10) 211 (4) 44.3 (10) 44.0 (10) ZnO ﬁlm on Si substrate, Brillouin

scattering

Table 4.1-135 Elastic constants c

(in GPa) of zinc compounds, cont.

Crystal c

(GPa) c

(GPa) Temperature Remarks

Zinc sulﬁde ZnS 103.2 (5) 64.6 (5) 46.2 (4) 293 K Resonance method

Zinc selenide ZnSe 90.3 (19) 53.6 (23) 39.4 (12) Brillouin scattering

Zinc telluride ZnTe 72.2 (2) 40.9 (6) 30.8 (3) RT Brillouin scattering

Part 4 1.3

666 Part 4 Functional Materials

ZnS (hex)

3.823

3.821

3.819

3.817

T (K)

(cm

)

23.84

23.80

23.76

23.72

6.264

6.256

6.248

1.640

1.638

1.636

0 70 140 210 280 350

c (Å)a (Å)

c/a

3.825

Two points

With silicone grease

c/a

Table 4.1-136 Melting point T

of zinc compounds

Crystal Melting point T

(K) Remarks

Zinc oxide ZnO 2242 (5)

Zinc sulﬁde ZnS 1991 Under normal pressure, ZnS sublimes before melting

Zinc selenide ZnSe 1799

Zinc telluride ZnTe 1563 (8)

Table 4.1-137 Linear thermal expansion coefﬁcient α of zinc compounds

Crystal Expansion coefﬁcient α(K

−1

) Temperature (K) Remarks

Zinc oxide ZnO α

parall c

:2.92× 10

−6

399 Interferometric and capacitance methods

perpend c

:4.75× 10

−6

300

Zinc sulﬁde ZnS See Fig. 4.1-149

Zinc selenide ZnSe 7.4×10

−6

300 Polycrystal, capacitance dilatometer

Zinc telluride ZnTe 0.083×10

−6

300

Fig. 4.1-149a,b ZnS, hexagonal. (a) Lattice parameters a

and c vs. temperature;

(b) molar volume and c/a ratio vs.

temperature [1.126]

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 667

Table 4.1-138 Heat capacities and Debye temperatures of zinc compounds

Crystal Heat capacity Debye temperature Θ

Temperature Remarks

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

Zinc oxide ZnO 440 (25) 300 Calorimetric data

Zinc sulﬁde ZnS 45.358 352 77 Zinc blende lattice, Θ

calculated from c

45.882 351 298 Wurtzite lattice; Θ

calculated from c

Zinc selenide ZnSe 51.88 339 (2) 298

Zinc telluride ZnTe 180 (6) 93–298 Θ

from X-ray intensities from powders

Table 4.1-139 Phonon frequencies/wavenumbers at symmetry points for zinc compounds. Zinc oxide (ZnO), fundamental

optical modes, T = 300 K, from Raman spectroscopy; zinc sulﬁde (ZnS), T = 300 K; zinc selenide (ZnSe), from Raman

spectroscopy and luminescence; zinc telluride (ZnTe), RT, from neutron scattering

ZnO ZnS

Mode

Symmetry Wavenumber Mode Symmetry Wavenumber

point (cm

−1

) point (cm

−1

)

101

Γ 350

437

Γ 274

1, perp c

407

X 332 (1)

1, parall c

380

X 318 (1)

1, perp c

583

X 212 (1)

1, parall c

574

X 88 (1)

L 334 (1)

L 298 (1)

L 192 (1)

L 72 (1)

ZnSe ZnTe

Mode

Symmetry Phonon energy Mode Symmetry Frequency

point (meV) point (THz)

hν

30.99 ν

Γ 6.20 (5)

hν

25.17 ν

Γ 5.30 (7)

hν

Γ 19.8 ν

X 5.51 (10)

hν

Γ 8.0 ν

X 5.21 (10)

hν

X 27.64 ν

X 4.29 (5)

hν

25.54 ν

X 1.62 (2)

hν

23.55 ν

L 5.39 (5)

hν

L 27.77 ν

L 5.20 (9)

hν

25.54 ν

L 4.06 (5)

hν W

24.9 ν

L 1.25 (2)

hν W

18.59

hν W



11.53

hν W



26.53

hν W



14.26

hν W



26.41

Part 4 1.3

668 Part 4 Functional Materials

B. Electronic Properties

Tables 4.1-140 – 4.1-145.

Band Structures of Zinc Compounds.

Zinc oxide (ZnO) (Fig. 4.1-150)

The topmost valence band (Γ

+Γ

) is split owing to

crystal-ﬁeld splitting and spin–orbit coupling into three

spin-degenerate states (Γ

, Γ

). The exciton states

formed with holes in these valence band states are re-

ferred to as the A, B, and C excitons, respectively. Owing

to the negative spin–orbit coupling (there is a contribu-

tion from Zn 3d states), the positions of the edges of the

two highest valence band states are reversed ascompared

with other II–VI compounds with the wurtzite structure.

The conduction band edge, originating from the 4s

states of Zn, possesses Γ

symmetry.

Zinc sulﬁde ZnS (Fig. 4.1-150)

Cubic ZnS is a direct-gap semiconductor with the small-

est energy gap at the center of the Brillouin zone (Γ).

When spin–orbit splitting is taken into account, the top-

most valence band state Γ

15v

splits into Γ

and Γ

;

further splitting into A, B, and C levels is caused by the

crystal ﬁeld.

E (eV)

12.5

10.0

7.5

5.0

2.5

–2.5

–5.0

–7.5

–10.0

–12.5

E (eV)

10.0

7.5

5.0

2.5

–2.5

–5.0

–7.5

–10.0

–12.5

–15.0

Wave vector k

ALMΓ ASH KRU Σ∆ PT

ΓLXWK

ZnO

1,3

5,6

1,3

1,2

1,3

2,4

1,3

5,6

1,3

1,2

ZnS (cubic)

∆

Fig. 4.1-150 Band structure of zinc oxide and cubic zinc sulﬁde

Table 4.1-140 First Brillouin zones of zinc compounds

Crystal Figure

Zinc oxide ZnO Fig. 4.1-132

Zinc sulﬁde ZnS Fig. 4.1-133

Zinc selenide ZnSe Fig. 4.1-133

Zinc telluride ZnTe Fig. 4.1-133

Zinc selenide ZnSe (Fig. 4.1-151)

Zinc selenide is a direct-gap semiconductor with the

smallest energy gap at the center of the Brillouin zone

(Γ). The topmost valence band (Γ

) is split owing to

spin–orbit coupling into a fourfold (Γ

)andatwofold

(Γ

) state.

Zinc telluride ZnTe (Fig. 4.1-152)

Zinc telluride is a direct-gap semiconductor with the

smallest energy gap at the center of the Brillouin zone

(Γ). The topmost valence band (Γ

) is split owing to

spin–orbit coupling into a fourfold (Γ

)andatwofold

(Γ

) state.

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 669

–3

–6

–9

–12

XL ΓΣΛ∆ Γ

E (eV)

U,K

Wave vector k

ZnSe

4,5

Fig. 4.1-151 Band structure of zinc selenide

Table 4.1-141 Energy gaps of zinc compounds

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

Zinc oxide ZnO E

3.4410 (1) 6 Two-photon absorption,

3.4434 (1) distance from A, B, and C valence bands

3.4817 (2) to conduction band

Zinc sulﬁde ZnS E

g, dir

3.723 (1) Γ

15v

and Γ

300 Luminescence;

g, dir

3.78 Γ

and Γ

295 For temperature dependence

g, dir

3.76 Γ

and Γ

298 see Fig. 4.1-162

Zinc selenide ZnSe E

g, dir

2.8222 (1) Γ

and Γ

6 Two-photon spectroscopy

Zinc telluride ZnTe E

g, dir

2.3945 Γ

and Γ

< 2 Transmission spectroscopy

2.35 Γ

and Γ

300 Reﬂectivity

Table 4.1-142 Exciton binding energies of zinc compounds

Crystal Binding energy (meV) Temperature (K) Remarks

Zinc oxide ZnO E

(A) 63.1 6 Two-photon absorption,

(B) 50.4

Zinc sulﬁde ZnS E

(1S) 38 (1) 10 Absorption,

(2S) 10 (2) Heavy-hole exciton

Zinc selenide ZnSe E

(1S) 20.8 1.8 Absorption, strained layers

(2P

1/2

)4.19 1.6 Two-photon absorption

(2P

5/2

,Γ

)4.80

(2P

5/2

,Γ

)5.15

a = 6.089 Å

–2

–4

–6

–8

–10

–12

Γ KΓ XW L

E (eV)

Wave vector k

ZnTe

∆

+∆

∆

+∆

Zn 3d

Fig. 4.1-152 Band structure of zinc telluride

Part 4 1.3

670 Part 4 Functional Materials

Table 4.1-143 Spin–orbit splitting energy ∆

of zinc compounds

Crystal Splitting energy Bands Temperature (K) Remarks

Zinc oxide ZnO −3.5 (2) meV 6 Two-photon absorption

Zinc sulﬁde ZnS 64 meV Γ

to Γ

293 Reﬂectivity

Zinc selenide ZnSe 0.42 eV Γ

to Γ

295 Reﬂectivity

0.20 eV Γ

4−5v

to Γ

300

Zinc telluride ZnTe 0.97 eV Γ

to Γ

80 Reﬂectivity

Table 4.1-144 Effective masses of electrons (in units of the electron mass m

) for zinc compounds

Crystal Quantity Mass Temperature (K) Remarks

Zinc oxide ZnO m

0.275 6 Cyclotron resonance

n, polaron

0.3 80 Polaron mass

Zinc sulﬁde ZnS m

n, polaron

0.22 Polaron mass, cyclotron resonance

Zinc selenide ZnSe m

0.160 (2) 4.2 Photoluminescence

Zinc telluride ZnTe m

0.122 (2) 3.5 Cyclotron resonance

n, polaron

0.124 (2) 1.5 Polaron mass

Table 4.1-145 Effective masses of holes (in units of the electron mass m

) for zinc compounds

Crystal Quantity Mass Temperature (K) Remarks

Zinc oxide ZnO m

p, parall

0.59 1.6 Magnetoreﬂection

p, perpend

0.59 Polaron mass

Zinc sulﬁde ZnS m

p, light

0.23 Calculated

p, heavy

1.76

Zinc selenide ZnSe m

0.75 2.1–200 Phonon-assisted exciton absorption

Zinc telluride ZnTe m

0.6 Estimated from hole mobility

C. Transport Properties

Table 4.1-146.

Electronic Transport, General Description.

Zinc oxide (ZnO)

The electronic conductivity of pure, stoichiometric

ZnO is still unknown. The concentration of foreign

admixtures in undoped crystals is of the order of

–10

−3

. Since E

g, opt

= 3.2 eV and impurity

ionization energies are about 0.01–0.1 eV at tempera-

tures below 900 K, impurity conduction is always

observed. At temperatures above 900 K, dissociation of

the intrinsic material occurs.

Table 4.1-146 Thermal conductivity κ of zinc compounds

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

Zinc oxide ZnO 0.54 300 Fig. 4.1-154 Steady-state heat ﬂow

Zinc sulﬁde ZnS 0.27 300 Pulse method

3.6 30

Zinc selenide ZnSe 0.19 300 Fig. 4.1-155

Zinc telluride ZnTe 0.18 300

The conductivity depends on the surrounding atmo-

sphere (which my be O

, Zn, or Ar). Nevertheless, it

is possible to investigate the inﬂuence of intentional

admixtures on the conductivity, the charge-carrier con-

centration, and the mobility as a function of temperature

and current direction.

Data for the electrical resistivityvary between values

of the order of 10

–10

Ω cm for ultrapure bulk single

crystals to values of the order of 10

−2

–10

−4

Ω cm for

doping concentrations of up to 10

−3

. Data for the

Part 4 1.3

Semiconductors 1.3 II–VI Compounds 671

electron mobility µ

at room temperature range between

0.5 and 200 cm

/V s. Figure 4.1-153shows theelectrical

conductivity of a crystal without intentional admixtures.

Zinc sulﬁde (ZnS)

The (photo)conductivity of ZnS depends strongly on

the growth conditions, dopants, doping characteristics,

etc. Data for the electrical resistivity vary between 10

−3

and 10

Ω cm depending on sample preparation. Val-

ues of the electron mobility around 100 cm

/V s and

600 cm

/V s have been found at room temperature, and

values around 3000 cm

/V s have been found at 77 K.

A value of 40 cm

/V s has been given for the hole mo-

bility.

Zinc selenide (ZnSe)

The (photo)conductivity of ZnSe depends strongly on

the growth conditions, dopants, doping characteristics,

etc. In undoped material, values of the electrical resistiv-

ity between 10

andafewΩ cm have been found. Values

of the electron mobility at room temperature reach up to

400 cm

/V s; for the hole mobility, µ

= 110 cm

/Vs

has been calculated as an upper limit.

–1

–2

–3

–4

–5

–1

(10

–3

–1

)

(Ω

–1

)

T (K)

50 10 3.35 2.5 2

0 100 200 300 400 500

I ⊥ c

ZnO

I ⊥ c

I⏐⏐ c

Fig. 4.1-153 ZnO. Electronic conductivity parallel and per-

pendicular to the c axis vs. temperature. Crystal grown in

ceramic without intentional admixtures [1.127]

Zinc telluride (ZnTe)

ZnTe is a p-type conductor owing to deviations from

stoichiometry when it is not intentionally doped; n-type

doping is extremely difﬁcult. The transport properties

of ZnTe depend strongly on the growth conditions,

dopants, doping characteristics, etc.

Typical data for the electrical resistivity at room

temperature are of the order of a few times 10

Ω cm;

at temperatures around 77 K, values of a few times

Ω cm have been found. The experimental values of

the electron and hole mobilities at room temperature

range from 300 to 350 cm

/Vs.

110

T (K)

(W/m K)

ZnO

T⊥c

T ⎢⎢ c

Fig. 4.1-154 ZnO. Thermal conductivity (lattice contribu-

tion) vs. temperature. Solid lines, calculated values [1.128]

T (K)

(W/cm K)

–1

11010

ZnSe

Fig. 4.1-155 ZnSe. Thermal conductivity vs. tempera-

ture [1.129]

Part 4 1.3