Electrical properties of Silicon (Si)

Si - Silicon

Electrical properties

Basic Properties
Mobility and Hall Effect
Transport Properties in High Electric Field
Impact Ionization
Recombination Parameters
Surface Recombination

Basic Properties

Breakdown field ≈3·105V/cm
Mobility electrons ≤1400 cm2 V-1s-1
Mobility holes ≤450 cm2 V-1s-1
Diffusion coefficient electrons ≤36 cm2/s
Diffusion coefficient holes ≤12 cm2/s
Electron thermal velocity 2.3·105m/s
Hole thermal velocity 1.65·105m/s

Mobility and Hall Effect

Electron mobility versus temperature for different doping levels.
1. High purity Si (Nd< 10-12 cm-3); time-of-flight technique (Canali et al. [1973])
2. High purity Si (Nd< 4·10-13 cm-3): photo-Hall effect (Norton et al. [1973])
3. Nd= 1.75·1016 cm-3; Na = 1.48·1015 cm-3; Hall effect (Morin and Maita [1954]).
4. Nd= 1.3·1017 cm-3; Na = 2.2·1015 cm-3; Hall effect (Morin and Maita [1954]).
Electron drift mobility versus donor density at different temperatures
(Li and Thumber [1977]).
Electron drift mobility versus donor density, T=300 K.
(Jacoboni et al. [1977]).
The electron Hall factor versus donor density. 77 and 300 K.
Solid lines show the results of calculations.
Symbols represent experimental data
(Kirnas et al. [1974]).
Resistivity versus impurity concentration for Si at 300 K.
Temperature dependences of hole mobility for different doping levels.
1. High purity Si (Na = 1012 cm-3); time-of-flight technique (Ottaviany et al. [1975]);
2. High purity Si (Na~1014 cm-3); Hall-effect (Logan and Peters [1960])
3. Na=2.4·1016 cm-3; Nd=2.3·1015 cm-3; Hall-effect (Morin and Maita [1954])
4. Na=2·1017 cm-3; Nd=4.9·1015 cm-3; Hall-effect (Morin and Maita [1954])
Hole drift mobility versus acceptor density at different temperatures
(Dorkel and Leturcq [1981]).
Hole drift mobility versus acceptor density. 300 K.
(Jacoboni et al. [1977]).
The hole Hall factor versus acceptor density. 300 K.
(Lin et al. [1981]).

Transport Properties in High Electric Field

Si. Electron drift velocity vs. electric field.
Solid lines: F||(111).
Dashed lines: F||(100).
Jacoboni et al. (1977).
Si. Electron drift velocity vs. electric field at different temperatures.
F||(111).
Jacoboni et al. (1977).
Temperature dependence of the saturation electron drift velocity
(Jacoboni et al. [1977]).
Solid line is calculated according to equation:
vs=vso·[1+C·exp(T/Ι)]-1,
where vso=2.4·107 cm s-1, C=0.8, Ι=600K.
Mean energy of electrons as a function of electronic field F at different donor densities.
F||(111). 300 K.
1. Nd = 0;
2. Nd = 4·1018 cm-3;
3. Nd = 4·1019 cm-3.
(Jacoboni et al. [1977]).
The field dependence of longitudinal electron diffusion coefficient D for 77K and 300 K.
F || (111). Dotted and solid lines show the results of Monte-Carlo simulation.
Symbols represent measured data.
(Canali et al. [1985]).
Field dependences of the hole drift velocity at different temperatures.
F || (100).
(Jacoboni et al. [1977]).
Mean energy of holes as a function of electronic field F.
Na = 0, T=300 K.
(Jacoboni et al. [1977]).
The field dependence of longitudinal hole diffusion coefficient D for 77K and 300 K.
F||(111). Dotted and solid lines show the results of Monte-Carlo simulation.
Symbols represent measured data.
(Canali et al. [1985]).

Impact Ionization

Electron ionization rate αi vs. 1/F.
T = 300 K. (Maes et al. [1990]).
Hole ionization rate βi vs. 1/F.
T = 300 K. (Grant [1973]).
Breakdown voltage and breakdown field vs. doping density for an abrupt p-n junction.
T = 300 K. (Sze [1981]).
Normalized breakdown voltage vs. temperature for an abrupt p-n junction at different doping levels.
(Crowell and Sze [1981]).

Recombination Parameters

Lifetime τp and diffusion length Lp of holes in n-type Si vs. donor density. T = 300 K.
For 1012 cm-3 < Nd ≤ 1017 cm-3- from numerous experimental data for good quality industrial produced n-Si.
For Nd ≥ 1017 cm-3 - (Alamo and Swanson [1987]).
Lp (Na) dependence (dashed line) is calculated as
Lp(Nd)=[Dp(N)·τp(N)]1/2,
where Dp=(kB·T/q)·μp.
Lifetime τn and diffusion length Ln of electrons in p-type Si vs. acceptor density. T = 300 K.
For 1013 cm-3 < Na≤1016 cm-3 - from numerous experimental data for good quality industrial produced p-Si.
For Na ≥ 1016 cm-3 - (Tyagi and Van Overstraeten [1983]). Ln(Na) dependence (dashed line) is calculated as Ln(Na)=[Dn(N)·τn(N)]1/2,
where Dn=(kb·T/q)·μn.

Surface recombination

Surface recombination rate depending on treatment of Si surface lies in the range between 102 ÷(6-8)·104cm/s.
Surface recombination rate on the Si-SiO2 interface can be as small as ≤ 0.5 cm/s.
Si   Remarks Referens
The longest lifetime of holes tp      
Diffusion length Lp = (Dp x tp)1/2      
Surface Recombinaton Velocity      
Radiative recombination coefficient B 1.1 x 10-14 cm3/s   Gerlach et al. (1972)
Auger coefficient Cn 1.1 x 10-30 cm6/s 300 K  
Auger coefficient Cp 0.3 x 10-30 cm6/s 300 K  
Auger coefficient C = Cn + Cp 1.4 x 10-30 cm6/s 300 K  
For 180 K ≤ T ≤ 400 K - C≈1.4·10-30·(T/300)1/2 (cm6/s).