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

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592 Part 4 Functional Materials

–2

–4

–6

–8

–10

–12

–14

–16

ΓΣ RLTMASHPKKMT' U

E (eV)

Wave vector k

2H-SiC

1,3

1,2

1,3

2,4

1,3

1,2

5,6

1,2

1,3

1,2

1,3

1,2

1,3

2,4

1,2

5,6

1,3

Fig. 4.1-30 Band structure of 2H silicon carbide

Table 4.1-13 Energy gaps of Group IV semiconductors and IV–IV compounds

Crystal Between Gap Energy Temperature Remarks

bands (eV) (K)

Diamond C Γ



and ∆

g, indir

5.50 (5) RT Quantum photoyield

gx, indir

5.416 (2) 100 Indirect exciton gap with lower valence band

5.409 (2) Indirect exciton gap with upper valence band

Silicon Si Γ



and ∆

g, ind

1.1700 0 Extrapolated, wavelength-modulated

transmission

1.1242 300 Wavelength-modulated transmission

g, th

1.205 0 Extrapolated from temperature dependence of

conductivity above 200 K



and Γ



g, dir

4.185 (10) 4.2 Electroreﬂection

4.135 190

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 593

Table 4.1-13 Energy gaps of Group IV semiconductors and IV–IV compounds, cont.

Crystal Between Gap Energy Temperature Remarks

bands (eV) (K)

Germanium Ge Γ

and L

g, ind

0.744 (1) 1.5 Magnetotransmission

0.664 291 Optical absorption

g, th

0.785 0 Extrapolated from temperature dependence of

intrinsic conductivity

and Γ

g, dir

0.898 (1) 1.5 Magnetoabsorption

0.805 (1) 293

Silicon carbide 3C-SiC Γ

15v

and X

g, ind

2.417 (1) 2 Wavelength-modulated absorption

2.2 300 Optical absorption

g, dir

6.0 300 Optical absorption

2.390 2 Excitonic energy gap, wavelength-modulated

absorption

Silicon carbide 2H-SiC E

3.330 4 Excitonic energy gap; optical absorption

Silicon carbide 6H-SiC E

g, ind

2.86 300 Optical absorption

3.023 4

Table 4.1-14 Exciton energies of Group IV semiconductors and IV–IV compounds (E

= exciton binding energy)

Crystal Quantity State Exciton energy (eV) Temperature (K) Remarks

Diamond E

(1S) 0.19 (15) 1S core exciton

0.07 Indirect exciton binding energy

Silicon E(1S) 1.1552 (3) 1.8 Wavelength-modulated absorption

0.01412 4.2 Calculated binding energy

Germanium E(1S) 1S

3/2

) 0.74046 (3) 2.1, 5.1 Optical absorption at 2.1 K and

3/2

1/2

) 0.74158 (3) luminescence at 5.1K

3/2

) 0.00418

3/2

1/2

) 0.00317

Silicon carbide (3C-SiC) E

0.027 2 Wavelength-modulated absorption

Table 4.1-15 Spin–orbit splitting energies of Group IV semiconductors and IV–IV compounds

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

Diamond ∆(Γ



) 0.006 (1) Cyclotron resonance

Silicon ∆

(Γ



) 0.0441 (3) 1.8 Wavelength-modulated absorption

Germanium ∆

to Γ

0.297 10 Electroreﬂectance

to Γ

0.200

Silicon carbide (3C-SiC) ∆

0.010 2 Wavelength-modulated absorption

Table 4.1-16 Effective masses of electrons (in units of the electron mass m

) for Group IV semiconductors and IV–IV compounds

Crystal Quantity Value Temperature (K) Remarks

Diamond m

n, parall

1.4 Field dependence of electron drift velocity

n, perpend

0.36

Silicon m

n, parall

0.9163 (4) 1.26 Cyclotron resonance with uniaxial stress

n, perpend

0.1905 (1)

Part 4 1.1

594 Part 4 Functional Materials

Table 4.1-16 Effective masses of electrons for Group IV semiconductors and IV–IV compounds, cont.

Crystal Quantity Value Temperature (K) Remarks

Germanium m

n, perpend

) 0.0807 (8) 30–100 Cyclotron resonance magnetophonon resonance

0.0823 120

n, parall

) 1.57 (3) 30–100 Cyclotron resonance magnetophonon resonance

1.59 120

(Γ

) 0.0380(5) 30 Piezomagnetoreﬂectance

Gray tin m

n, light

(Γ

) 0.0236 (2) 1.3 Density-of-states mass

n, heavy

) 0.21 4.2

Silicon carbide (3C-SiC) m

n, parall

0.677 (15) 45 Cyclotron resonance

n, perpend

0.247 (11)

Silicon carbide (6H-SiC) m

n, parall

3–6 Cyclotron resonance

n, perpend

0.48 (2)

Table 4.1-17 Effective masses of holes (in units of the electron mass m

) for Group IV semiconductors and IV–IV compounds

Crystal Quantity Value Temperature (K) Field direction Remarks

Diamond m

p, heavy

1.08 Calculated from valence band

p, light

0.36 parameters

spin–orbit split

0.15

p, dens stat

0.75 300 Hall effect

Silicon m

p, heavy

0.537 4.2 Cyclotron resonance

p, light

0.153

spin–orbit split

0.234

p, dens stat

0.591 Density-of-states mass

Germanium m

p, light

0.0438 (3) 4 B parallel to [100] Cyclotron resonance

0.0426 (2) B parallel to [111]

0.0430 (3) B parallel to [110]

p, heavy

0.284 (1) B parallel to [100]

0.376 (1) B parallel to [111]

0.352 (4) B parallel to [110]

spin–orbit split

0.095 (7) 30 Piezomagnetoabsorption

Gray tin m

(Γ

) 0.195 Interband magnetoreﬂection

(Γ

) 0.058

Silicon carbide (3C-SiC) m

0.45 45 High-ﬁeld cyclotron resonance

Silicon carbide (6H-SiC) m

p, parall

1.85 (3) Cyclotron resonance

p, perpend

0.66 (2)

Table 4.1-18 g-factor g

of conduction electrons for Group IV semiconductors

Crystal g

Temperature (K) Remarks

Diamond 2.0030 (3) 140–300 Electron spin resonance

Silicon 1.99893(28) Electron spin resonance

Germanium −3.0(2) 30 Piezomagnetoabsorption

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 595

C. Transport Properties

Tables 4.1-19 – 4.1-21.

Electronic Transport, General Description.

Diamond (C). Owing to the large band gap, most

diamonds are insulators at room temperature, and

Table 4.1-19 Intrinsic carrier concentration n

and electrical conductivity σ

of Group IV semiconductors and IV–IV

compounds

Crystal n

(cm

−3

) σ

(

−1

) T (K) Temperature dependence

Silicon 1.02× 10

3.16× 10

−2

300 Fig. 4.1-31

Germanium 2.33 × 10

2.1×10

−2

300 Figs. 4.1-32 and 4.1-33

3C-SiC Fig. 4.1-34

Si–Ge alloys Composition dependence of intrinsic conductivity: Fig. 4.1-36

Composition dependence of the mobilities: Figs. 4.1-35 and 4.1-37

The intrinsic conductivity of Si up to 1273 K is given by the phenomenological expression log

= 4.247−2.924×10

−1

(σ

in Ω

−1

, T in K).

–1

–2

–3

–1

(10

–3

–1

)

–1

–2

(cm

–1

)

σ (Ω

–1

)

T (K)

1200 800 600 500 400 300

0 1.0 2.0 3.01.5 2.5 3.50.5

Fig. 4.1-31 Si. Conductivity and Hall coefﬁcient vs. re-

ciprocal temperature in the range of intrinsic conduction;

n- and p-type samples with doping concentrations of

1.7×10

−3

and above [1.23]. The different symbols

show results from different samples

so electronic transport is extrinsically determined

and therefore strongly dependent on the impurity

content. Natural (type IIb) and synthetic semicon-

ducting diamonds are always p-type. The electron

mobility can be derived only from photoconductivity

experiments.

–1

–2

–3

–1

(10

–3

–1

)

(Ω

–1

)

T (K)

1000 800 600 500 400 300350 273 250

0.8 1.6 2.4 3.22.0 2.8 3.61.2 4.0

p-type

n-type

Computed

Fig. 4.1-32 Ge. Conductivity vs. reciprocal temperature in

the range of intrinsic conduction [1.24]

Part 4 1.1

596 Part 4 Functional Materials

–1

(10

–3

–1

)

(cm

–3

)

T (K)

0.8 1.6 2.4 3.22.0 2.8 3.61.2 4.0

1000 800 600 500 400 300350 273 250

p-type

n-type

computed

Fig. 4.1-33 Ge. Intrinsic carrier concentration vs. recipro-

cal temperature [1.24]

–1

–2

–3

–4

–5

–6

–1

(Ω

–1

)

0 0.2 0.4 0.6 0.8 1.0

1–x

4×10

1000 500 200 100 70

0 2.5 5.0 7.5 10.0 12.5 15.0

T (K)Carrier concentration (cm

–3

)

–1

(10

–3

–1

)

3C- SiC

Si/C: 0.33

0.37

0.40

Fig. 4.1-34 3C-SiC. Temperature dependence of carrier

concentration for n-type ﬁlms grown by CVD on Si(100)

substrates [1.25]. Solid lines, calculated values. Si/C =

ratio of source gases

3000

2000

1000

H,n

(cm

/V s)

0 0.2 0.4 0.6 0.8 1.0

1–x

Fig. 4.1-35 Si

1−x

. Composition dependence of the

electron Hall mobility at room temperature [1.26]

Fig. 4.1-36 Si

1−x

. Composition dependence of the in-

trinsic conductivity at room temperature [1.26]

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 597

Table 4.1-20 Electron mobilities µ

and hole mobilities µ

of Group IV semiconductors and IV–IV compounds

Crystal µ

(cm

/Vs) µ

(cm

/Vs) T (K) Remarks

Diamond 2000 2100 293 See Figs. 4.1-38 and 4.1-39 for temperature dependence

Silicon 1450 370 300 See Figs. 4.1-40 and 4.1-41 for temperature dependence

2×10

Germanium 3800 1800 300 See Figs. 4.1-33 and 4.1-42 for temperature dependence

Gray tin µ

(Γ

)0.12 × 10

10× 10

100 From Hall and magnetoresistance data, via conductivity

)1.6×10

and Hall coefﬁcient

Silicon carbide (3C-SiC) 510 15–21 296 Epitaxial ﬁlm grown on Si(100)

0 0.2 0.4 0.6 0.8 1.0

2000

1000

H,p

(cm

/V s)

1–x

Fig. 4.1-37 Si

1−x

. Composition dependence of the

hole Hall mobility at room temperature [1.26]

(cm

/V s)

8246

2×10

T (K)

Diamond

(cm

/V s)

8246

4×10

T (K)

Diamond

Fig. 4.1-38 Diamond. Electron mobility vs. temperature.

Open circles, drift mobility data from [1.27]; ﬁlled tri-

angles and ﬁlled circles, Hall mobility data from [1.28]

and [1.29, 30], respectively. Continuous curve, theoretical

drift mobility [1.27]

Fig. 4.1-39 Diamond. Hole mobility vs. temperature.Open

circles, drift mobility data from [1.31]; ﬁlled circles

and ﬁlled triangles, Hall mobility data from [1.29, 30]

and [1.32], respectively. Solid and dashed curves: calcu-

lated drift and Hall mobilities, respectively [1.33]

Part 4 1.1

598 Part 4 Functional Materials

410

(cm

/V s)

–2.42

T (K)

4 × 10

1.3 × 10

10

–3

Fig. 4.1-40 Si. Electron mobility vs. temperature [1.34].

Data points for n

≤ 10

−3

obtained by time-of-

ﬂight technique [1.35]. Other experimental values taken

from [1.36] (4 × 10

−3

) and [1.23] (1.3×10

−3

Continuous line, theoretical lattice mobility, after [1.35].

Dash–dotted line, T

−2.42

dependence of µ

around room

temperature

Silicon (Si). The electronic transport is due exclusively

to electrons in the [100] conduction band minima and

holes in the two uppermost (heavy and light) valence

bands. In samples with impurity concentrations be-

low 10

−3

, the mobilities are determined by pure

lattice scattering down to temperatures of about 10 K

(n-type) or 50 K (p-type), for electrons and holes, respec-

tively. Higher impurity concentrations lead to deviations

from the lattice mobility at corresponding higher tem-

peratures. For electrons, the lattice mobility below

50 K is dominated by deformation-potential coupling

H,p

(cm

/V s)

468

4×10

T (K)

Light-hole band

Total

Heavy-

hole band

Spin-orbit

band

Fig. 4.1-41 Si. (b) Hall hole mobility vs. temperature; cir-

cles from [1.37], solid lines calculated contributions from

the three valence bands

to accoustic phonons. At higher temperatures, interval-

ley scattering between the six equivalent minima of

the conduction band is added to the intravalley pro-

cess, modifying the familiar T

−1.5

dependence of the

acoustic-mode-dominated mobility to T

−2.42

.Attem-

peratures below 100 K, the lattice mobility of holes is

dominated by acoustic scattering, but does not follow

a T

−1.5

law, owing to the nonparabolicity of the va-

lence bands. The proportionality of µ

to T

−2.2

around

room temperature is a consequence of optical-phonon

scattering.

Germanium (Ge). Low-ﬁeld electronic transport is pro-

vided by electrons in the L

minima of the conduction

band and holes near the Γ

point in the valence bands. At

room temperature, the mobility of samples with impurity

concentrations below 10

−3

is limited essentially

by lattice scattering; higher donor or acceptor concen-

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 599

µ (10

/V s)

100

30 40 50 60 80 100 150 200 300

T (K)

Slope = –1.66

Slope = –2.33

Fig. 4.1-42 Ge. Electron and hole mobilities vs. tem-

perature for a constant carrier concentration (high-purity

samples) [1.38]

trations result in an increasing inﬂuence of impurity

scattering. At 77 K, even for doping concentrations be-

low 10

−3

, the mobilities depend on the impurity

Table 4.1-21 Thermal conductivity κ of Group IV semiconductors and IV–IV compounds

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

Diamond C 6–10 293 See Fig. 4.1-43 for temperature dependence

Silicon Si 1.56 300 See Fig. 4.1-44 for temperature dependence

Germanium Ge See Fig. 4.1-46 for temperature dependence

Silicon carbide 3C-SiC

6H-SiC 4.9 300 Perpendicular to c axis; See Fig. 4.1-45 for temperature

dependence

101

T (K)

(W/cm K)

Diamond

Fig. 4.1-43 Diamond. Thermal conductivity vs. tempera-

ture for three type Ia diamonds [1.39]

concentration. Low temperatures and high concentra-

tions lead to the replacement of free-carrier conduction

by impurity conduction.

Gray Tin (α-Sn). In intrinsic samples, light electrons and

holes in the Γ

bands determine the transport properties.

When the Fermi level crosses the energy of the L

min-

ima, heavy electrons have an inﬂuence. This leads,

for example, to a screening enhancement of the light-

electron mobility and, in heavily doped n-type samples,

to a dominant role of the L electrons. Consequently,

Part 4 1.1

600 Part 4 Functional Materials

–1

468

2468 2468

(W/cm K)

T (K)

Fig. 4.1-44 Si. Lattice thermal conductivity vs. tempera-

ture, according to [1.40] (ﬁlled circles), [1.41] (open

circles), and [1.42] (triangles). The curves marked κ

and

2κ

represent the contributions of the longitudinal and

transverse phonons, respectively [1.43]

468

2468 2

–1

4×10

400 500 600 800 1000 1200

0.7

0.6

0.5

0.4

0.3

0.2

0.1

T (K)

–1

(W/cm K)

T (K)

(W/cm K)

a) b)

Fig. 4.1-46a,b Ge. Thermal conductivity vs. temperature. (a) 3–400 K, (b) 400–1200 K. Solid curve in (a) and data

(b) from [1.40]; experimental data in (a) from [1.45]. Dashed line in (b), extrapolated lattice component

468

2468 24

–1

–2

268

T (K)

(W/cm K)

SiC

Fig. 4.1-45 6H-SiC. Thermal conductivity (⊥c axis) vs.

temperature for two different samples [1.44]

Part 4 1.1

Semiconductors 1.1 Group IV Semiconductors and IV–IV Compounds 601

heavily doped n-type samples behave as indirect-gap

semiconductors with an E

of about 0.09 eV.

Silicon–Germanium Alloys (Si

1−x

). The transport

properties have been investigated mostly on single crys-

tals. The mobility is inﬂuenced by alloy scattering,

which makes a contribution µ

alloy

∝ T

0.8

−1

(1−x)

−1

Near the band crossover (x = 0.15), intervalley scatter-

ing has to be taken into account.

D. Electromagnetic and Optical Properties

Tables 4.1-22 – 4.1-25.

Table 4.1-22 High-frequency dielectric constant ε (real part of the complex dielectric constant) of Group IV semicon-

ductors and IV–IV compounds

Crystal ε T (K) Frequency Method

Diamond C 5.70 (5) 300 1–10 kHz Capacitance bridge

Silicon Si 12.1 4.2 750 MHz Capacitance bridge

11.97 300

Germanium Ge 16.5 4.2 750 MHz Capacitance bridge

16.0 4.2 9200 MHz Microwave measurement

16.2 300

15.8 77 1MHz Capacitance bridge

Gray tin α-Sn 24 300 Infrared Infrared reﬂectance measurement

Silicon carbide 3C-SiC 9.52 300 Low frequency Infrared transmission

6.38 High frequency

Silicon carbide 6H-SiC 9.66 300 Low frequency ε

perp

10.03 ε

parall

6.52 300 High frequency ε

perp

6.70 ε

parall

Optical Constants. The real part (ε

) and imaginary part

(ε

) of the dielectric constant at optical frequencies were

measured by spectroscopic ellipsometry. The refractive

index n, the extinction coefﬁcient k, the absorption co-

efﬁcient K, and the reﬂectivity R have been calculated

from ε

and ε

. The frequency dependences of ε

, ε

, n,

and K are shown in Figs. 4.1-48 and 4.1-47.

Diamond. The refractive index n is equal to 3.5at

λ = 177.0 nm. The spectral dependence of the refractive

index n can be approximated by the empirical formula

−1 =aλ



−λ



+bλ



−λ



with the parameters a = 0.3306, b = 4.3356, λ

175.0nm,andλ

= 106.0nm.

Silicon. (See Table 4.1-23).

Germanium. (See Fig. 4.1-48).

Gray Tin (α-Sn). The index of refraction n, extinction

coefﬁcient k, and absorption coefﬁcient K versus pho-

ton energy are shown in Fig. 4.1-47.

Silicon Carbide (SiC).

Part 4 1.1