Electrical properties of Silicon (Si)

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 (N_d< 10^-12 cm^-3); time-of-flight technique (Canali et al. [1973]) 2. High purity Si (N_d< 4·10^-13 cm^-3): photo-Hall effect (Norton et al. [1973]) 3. N_d= 1.75·10¹⁶ cm^-3; N_a = 1.48·10¹⁵ cm^-3; Hall effect (Morin and Maita [1954]). 4. N_d= 1.3·10¹⁷ cm^-3; N_a = 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 (N_a = 10¹² cm^-3); time-of-flight technique (Ottaviany et al. [1975]); 2. High purity Si (N_a~10¹⁴ cm^-3); Hall-effect (Logan and Peters [1960]) 3. N_a=2.4·10¹⁶ cm^-3; N_d=2.3·10¹⁵ cm^-3; Hall-effect (Morin and Maita [1954]) 4. N_a=2·10¹⁷ cm^-3; N_d=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

	Field dependences of the electron drift velocity. Solid lines: F\|\|(111). Dashed lines: F\|\|(100). (Jacoboni et al. [1977]).
	Field dependences of the electron drift velocity 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: v_s=v_so·[1+C·exp(T/Ι)]^-1, where v_so=2.4·10⁷cm 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. N_d = 0; 2. N_d = 4·10¹⁸ cm^-3; 3. N_d = 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. N_a = 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

	The dependence of ionization rate α_i for electrons versus 1/F. T = 300 K. (Maes et al. [1990]).
	The dependence of ionization rate β_i for holes versus 1/F. T = 300 K. (Grant [1973]).
	*Breakdown voltage and breakdown field versus doping density for an abrupt p-n* junction.** T = 300 K. (Sze [1981]).
	*Normalized breakdown voltage versus temperature for an abrupt p-n* junction at different doping levels.** (Crowell and Sze [1981]).

Recombination Parameters

	Lifetime τ_p and diffusion length L_p of holes in n-type Si versus donor density. T = 300 K. For 10¹² cm^-3 < N_d ≤ 10¹⁷ cm^-3- from numerous experimental data for good quality industrial produced n-Si. For N_d ≥ 10¹⁷ cm^-3 - (Alamo and Swanson [1987]). L_p (N_a) dependence (dashed line) is calculated as L_p(N_d)=[D_p(N)·τ_p(N)]^1/2, where D_p=(k_B·T/q)·μ_p.
	Lifetime τ_n and diffusion length L_n of electrons in p-type Si versus acceptor density. T = 300 K. For 10¹³ cm^-3 < N_a≤10¹⁶ cm^-3 - from numerous experimental data for good quality industrial produced p-Si. For N_a ≥ 10¹⁶ cm^-3 - (Tyagi and Van Overstraeten [1983]). L_n(N_a) dependence (dashed line) is calculated as L_n(N_a)=[D_n(N)·τ_n(N)]^1/2, where D_n=(k_b·T/q)·μ_n.

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.

Radiative recombination coefficient at 300 K

1.1·10^-14 cm³/s
(Gerlach et al. [1972]).

Auger coefficient at 300 K:

C_n	1.1·10^-30 cm⁶/s
C_p	0.3·10^-30 cm⁶/s
C = C_n + C_p	1.4·10^-30 cm⁶/s

For 180 K ≤ T ≤ 400 K - C≈1.4·10^-30·(T/300)^1/2 (cm⁶/s).

	Field dependences of the electron drift velocity. Solid lines: F\|\|(111). Dashed lines: F\|\|(100). (Jacoboni et al. [1977]).
	Field dependences of the electron drift velocity 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: v_s=v_so·[1+C·exp(T/Ι)]^-1, where v_so=2.4·10⁷cm 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. N_d = 0; 2. N_d = 4·10¹⁸ cm^-3; 3. N_d = 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. N_a = 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]).