Appendix

PROPERTIES of Ge & Si at 300 К

Properties

Ge

Si

Atoms/cm³

4.42 x Ю²²

5.0 x Ю²²

Atomic weight

72.60

28.09

Breakdown field (V/cm)

~10⁵

~3 x Ю⁵

Crystal structure

Diamond

Diamond

Density (g/cm³)

5.3267

2.328

Dielectric constant

16.0

11.9

Effective density of states in conduction band, N_c (cm'³)

1.04 x Ю¹⁹

2.8 x Ю¹⁹

Effective density of states in valence band, N_v (cm^-3)

6.0 x Ю¹⁸

1.04 x Ю¹⁹

Effective Mass, mVm₀ Electrons

m' = 1.64 m* = 0.082

m* = 0.98 m_t*= 0.19

Effective Mass, mVm₀ Holes

m₍ „* = 0.044

^mh h*⁼ 0-28

m_/ft* = 0.16 ^mh h*⁼ 0-49

Electron affinity, x(V)

4.0

4.05

0.66

1.12

Intrinsic carrier concentration (cm'³)

2.4 x Ю¹³

1.45 x Ю¹⁰

Intrinsic Debye length (mm)

0.68

24

Intrinsic resistivity (П-crn)

47

2.3 x Ю⁵

Lattice constant (A)

5.64613

5.43095

Linear coefficient of thermal expansion, AL/LDT (°C'¹)

5.8 x 10‘⁶

2.6 x 10-⁶

Melting point (°C)

937

1415

Minority carrier lifetime (s)

IQ'³

2.5 x Ю'³

Mobility (drift) (cm²/V-s)

• 3900
• 1900

• 1500
• 450

Optical-phonon energy (eV)

0.037

0.063

Phonon mean free path l₀ (A)

105

76 (electron) 55 (hole)

Specific heat (J/g-°C)

0.31

0.7

Thermal conductivity at 300 К (W/cm-°C)

0.6

1.5

Thermal diffusivity (cm²/s)

0.36

0.9

Vapor pressure (Pa)

1 at 1330°C 10-« at 760°C

1 at 1650°C 10'⁶ at 900°C

Symbol

Unit

Description

m*

Kg

Effective mass

m₀

Kg

Electron rest mass

L

cm or pm

Length

kT

ev

Thermal Energy

к

J/K

Boltzman constant

J

АУст²

Current density

1

A

Current

hv

eV

Photon energy

h

J-s

Planck's constant

f

Hz

Frequency

^e m

V/cm

Maximum field

e

V/cm

Electric field

^Ep

eV

Energy bandgap

Ef

eV

Fermi energy level

E

eV

Energy

D

cm²/s

Diffusion coefficient

C

F

Capacitance

c

cm/s

Speed of light in vacuum

в

Wb/m²

Magnetic induction

a

A

Lattice constant

ф

V

Barrier height or imref

p

Q-cm

resistivity

Up

cm²/V-s

Hole mobility

Pn

cm²A/-s

Electron mobility

Po

H/cm

Permeability in vacuum

T

s

Lifetime or decay time

Quantity

Value

Symbol

Wavelength of 1 eV quantum

1.23977 pm

X

Thermal voltage at 300 К

0.0259 V

kT/q

Thousandth of an inch

25.4 pm

mil

Torr

1 mm Hg

Standard atmosphere

1.01325 x 10⁵ N/m²

Speed of light in vacuum

2.99792 x I0¹⁰cm/s

c

Photon rest mass

1.67264 x 10-²⁷ kg

Mp

Reduced Planck constant

1.05458 x Ю ³⁴ J-s (h/2ir)

Room temperature value of kT

0.0259eV

Micron

10'⁴ cm

pm

Gas constant

1.98719 cal-mol-¹K-¹

R

Gram-mole

6.023 x 10²³ molecules

Electron volt

1.60218 x Ю¹⁹

eV

Electron rest mass

0.91095 x 10-³⁰ kg

m₀

Elementary charge

1.60218 x Ю¹⁹С

q

Calorie

4.184 J

Bohr radius

0.52917 A

^aB

Boltzman constant

1.38066 x 10'²³J/K

к

Avogadro constant

6.02204 x Ю²³ mol'¹

Navo

Atmosphere

760 mmHg

Angstrom unit

1 A= 10^_1 nm

A

w

erf( w)

w

erf(w)

w

erf( w)

w

erf(w)

0.00

0.000 000

0.44

0.466 225

0.88

0.786 687

1.32

0.938 065

0.01

0.011 283

0.45

0.475 482

0.89

0.719 843

1.33

0.940 015

0.02

0.022 565

0.46

0.484 655

0.90

0.796 908

1.34

0.941 914

0.03

0.033 841

0.47

0.493 745

0.91

0.801 883

1.35

0.943 762

0.04

0.045 111

0.48

0.502 750

0.92

0.806 768

1.36

0.945 561

0.05

0.056 372

0.49

0.511 668

0.93

0.811 564

1.37

0.947 312

0.06

0.067 622

0.50

0.520 500

0.94

0.816 271

1.38

0.949 016

0.07

0.078 858

0.51

0.529 244

0.95

0.820 891

1.39

0.950 673

0.08

0.090 078

0.52

0.537 899

0.96

0.825 424

1.40

0.952 285

0.09

0.101 281

0.53

0.546 464

0.97

0.829 870

1.41

0.953 852

0.10

0.112 463

0.54

0.554 939

0.98

0.834 232

1.42

0.955 376

0.11

0.123 623

0.55

0.563 323

0.99

0.838 508

1.43

0.956 857

0.12

0.134 758

0.56

0.571 616

1.00

0.842 701

1.44

0.958 297

0.13

0.145 867

0.57

0.579 816

1.01

0.846 810

1.45

0.959 695

0.14

0.156 947

0.58

0.587 923

1.02

0.850 838

1.46

0.961 054

0.15

0.167 996

0.59

0.595 936

1.03

0.854 784

1.47

0.962 373

0.16

0.179 012

0.60

0.603 856

1.04

0.858 650

1.48

0.963 654

0.17

0.189 992

0.61

0.611 681

1.05

0.862 436

1.49

0.964 898

0.18

0.200 936

0.62

0.619411

1.06

0.866 144

1.50

0.966 105

0.19

0.211 840

0.63

0.627 046

1.07

0.869 773

1.51

0.967 277

0.20

0.222 703

0.64

0.634 586

1.08

0.873 326

1.52

0.968 413

0.21

0.233 522

0.65

0.642 029

1.09

0.876 803

1.53

0.969 516

0.22

0.244 296

0.66

0.649 377

1.10

0.880 205

1.54

0.970 586

0.23

0.255 023

0.67

0.656 628

1.11

0.883 533

1.55

0.971 623

0.24

0.265 700

0.68

0.663 782

1.12

0.886 788

1.56

0.972 628

0.25

0.276 326

0.69

0.670 840

1.13

0.889 971

1.57

0.973 603

0.26

0.286 900

0.70

0.677 801

1.14

0.893 082

1.58

0.974 547

0.27

0.297 418

0.71

0.684 666

1.15

0.896 124

1.59

0.975 462

0.28

0.307 880

0.72

0.691 433

1.16

0.899 096

1.60

0.976 348

0.29

0.318 283

0.73

0.698 104

1.17

0.902 000

1.61

0.977 207

0.30

0.328 627

0.74

0.704 678

1.18

0.904 837

1.62

0.978 038

0.31

0.338 908

0.75

0.711 156

1.19

0.907 608

1.63

0.978 843

0.32

0.349 126

0.76

0.717 537

1.20

0.910 314

1.64

0.979 622

0.33

0.359 279

0.77

0.723 822

1.21

0.912 956

1.65

0.980 376

0.34

0.369 365

0.78

0.730 010

1.22

0.915 534

1.66

0.981 105

0.35

0.379 382

0.79

0.736 103

1.23

0.918 050

1.67

0.981 810

0.36

0.389 330

0.80

0.742 101

1.24

0.920 505

1.68

0.982 493

0.37

0.399 206

0.81

0.748 003

1.25

0.922 900

1.69

0.983 153

0.38

0.409 009

0.82

0.753 811

1.26

0.925 236

1.70

0.983 790

0.39

0.418 739

0.83

0.759 524

1.27

0.927 514

1.71

0.984 407

0.40

0.428 392

0.84

0.765 143

1.28

0.929 734

1.72

0.985 003

0.41

0.437 969

0.85

0.770 668

1.29

0.931 899

1.73

0.985 578

0.42

0.447 468

0.86

0.776 110

1.30

0.934 008

1.74

0.986 135

0.43

0.456 887

0.87

0.781 440

1.31

0.936 063

1.75

0.986 672

w

erf( w)

w

erf(w)

w

erf( w)

w

erf(w)

1.76

0.987 190

2.22

0.998 308

2.67

0.999 841

3.13

0.999 990 42

1.77

0.987 691

2.23

0.998 388

2.68

0.999 849

3.14

0.999 991 03

1.79

0.988 641

2.24

0.998 464

2.69

0.999 858

3.15

0.999 991 60

1.80

0.989 091

2.25

0.998 537

2.70

0.999 866

3.16

0.999 992 14

1.81

0.989 525

2.26

0.998 607

2.71

0.999 873

3.17

0.999 992 64

1.82

0.989 943

2.27

0.998 674

2.72

0.999 880

3.18

0.999 993 11

1.83

0.990 347

2.28

0.998 738

2.73

0.999 887

3.19

0.999 993 56

1.84

0.990 736

2.29

0.998 799

2.74

0.999 893

3.20

0.999 993 97

1.85

0.991 111

2.30

0.998 857

2.75

0.999 899

3.21

0.999 994 36

1.86

0.991 472

2.31

0.998 912

2.76

0.999 905

3.22

0.999 994 73

1.87

0.991 821

2.32

0.998 966

2.77

0.999 910

3.23

0.999 995 07

1.88

0.992 156

2.33

0.999 016

2.78

0.999 916

3.24

0.999 995 40

1.89

0.992 479

2.34

0.999 065

2.79

0.999 920

3.25

0.999 995 70

1.90

0.992 790

2.35

0.999 111

2.80

0.999 925

3.26

0.999 995 98

1.91

0.993 090

2.36

0.999 155

2.81

0.999 929

3.27

0.999 996 24

1.92

0.993 378

2.37

0.999 197

2.82

0.999 933

3.28

0.999 996 49

1.93

0.993 656

2.38

0.999 237

2.83

0.999 937

3.29

0.999 996 72

1.94

0.993 923

2.39

0.999 275

2.85

0.999 944

3.30

0.999 996 94

1.95

0.994 179

2.40

0.999 311

2.86

0.999 948

3.31

0.999 997 15

1.96

0.994 426

2.41

0.999 346

2.87

0.999 951

3.32

0.999 997 34

1.97

0.994 664

2.42

0.999 379

2.88

0.999 954

3.33

0.999 997 51

1.98

0.994 892

2.43

0.999 411

2.89

0.999 956

3.34

0.999 997 68

1.99

0.995 111

2.44

0.999 441

2.90

0.999 959

3.35

0.999 997 838

2.00

0.995 322

2.45

0.999 469

2.91

0.999 961

3.36

0.999 997 983

2.01

0.995 525

2.46

0.999 497

2.92

0.999 964

3.37

0.999 998120

2.02

0.995 719

2.47

0.999 523

2.93

0.999 966

3.38

0.999 998 247

2.03

0.995 906

2.48

0.999 547

2.94

0.999 968

3.39

0.999 998 367

2.04

0.996 086

2.49

0.999 571

2.95

0.999 970

3.40

0.999 998 478

2.05

0.996 258

2.50

0.999 593

2.96

0.999 972

3.41

0.999 998 582

2.06

0.996 423

2.51

0.999 614

2.97

0.999 973

3.42

0.999 998 679

2.07

0.996 582

2.52

0.999 634

2.98

0.999 975

3.43

0.999 998 770

2.08

0.996 734

2.53

0.999 654

2.99

0.999 976

3.44

0.999 998 855

2.09

0.996 880

2.54

0.999 672

3.00

0.999 977 91

3.45

0.999 998 934

2.10

0.997 021

2.55

0.999 689

3.01

0.999 979 26

3.46

0.999 999 008

2.11

0.997 155

2.56

0.999 706

3.02

0.999 980 53

3.47

0.999 999 077

2.12

0.997 284

2.57

0.999 722

3.03

0.999 981 73

3.48

0.999 999 141

2.13

0.997 407

2.58

0.999 736

3.04

0.999 982 86

3.49

0.999 999 201

2.14

0.997 525

2.59

0.999 751

3.05

0.999 983 92

3.50

0.999 999 257

2.15

0.997 639

2.60

0.999 764

3.06

0.999 984 92

3.51

0.999 999 309

2.16

0.997 747

2.61

0.999 777

3.07

0.999 985 86

3.52

0.999 999 358

2.17

0.997 851

2.62

0.999 789

3.08

0.999 986 74

3.53

0.999 999 403

2.18

0.997 951

2.63

0.999 800

3.09

0.999 987 57

3.54

0.999 999 445

2.19

0.998 046

2.64

0.999 811

3.10

0.999 988 35

3.55

0.999 999 485

2.20

0.998 137

2.65

0.999 822

3.11

0.999 989 08

3.56

0.999 999 521

2.21

0.998 224

2.66

0.999 831

3.12

0.999 989 77

3.57

0.999 999 555

w

erf( w)

w

erf(w)

w

erf( w)

w

erf(w)

3.58

0.999 999 587

3.69

0.999 999 820

3.80

0.999 999 923

3.91

0.999 999 968

3.59

0.999 999 617

3.70

0.999 999 833

3.81

0.999 999 929

3.92

0.999 999 970

3.60

0.999 999 644

3.71

0.999 999 845

3.82

0.999 999 934

3.93

0.999 999 973

3.61

0.999 999 670

3.72

0.999 999 857

3.83

0.999 999 939

3.94

0.999 999 975

3.62

0.999 999 694

3.73

0.999 999 867

3.84

0.999 999 944

3.95

0.999 999 977

3.63

0.999 999 716

3.74

0.999 999 877

3.85

0.999 999 948

3.96

0.999 999 979

3.64

0.999 999 736

3.75

0.999 999 886

3.86

0.999 999 952

3.97

0.999 999 980

3.65

0.999 999 756

3.76

0.999 999 895

3.87

0.999 999 956

3.98

0.999 999 982

3.66

0.999 999 773

3.77

0.999 999 903

3.88

0.999 999 959

3.99

0.999 999 983

3.67

0.999 999 790

3.78

0.999 999 910

3.89

0.999 999 962

3.68

0.999 999 805

3.79

0.999 999 917

3.90

0.999 999 965