COMSOL 6.3 - Semiconductor Material Properties

These material property groups for all the material models in semiconductors are used by the Semiconductor Module.


	The Property Group, Variable Names, and SI Unit columns are applicable to all materials in the Semiconductor Module. However, the Values and References columns listed in Table 9-23 are specifically for silicon.

Table 9-23: Semiconductor Material Properties (all materials) and Values and REferences for Silicon.
Property Group and Property (all MATERIALS)	Name/Variable (all MATERIALS)	SI unit	Value for Silicon	Reference for Silicon
Basic
Relative permittivity	epsilonr	1	11.7	Ref. 1
Thermal conductivity	k	W/(m·K)	131 W/(m·K)	Ref. 1
Density	rho	kg/m3	2329 kg/m3	Ref. 1
Heat capacity at constant pressure	Cp	J/(kg·K)	700 J/(kg·K)	Ref. 1
Band-Gap Narrowing Models > Jain–Roulston Model
Jain–Roulston coefficient (n-type), A	An_jr	V	3.5·10-8 V	Ref. 12
Jain–Roulston coefficient (n-type), B	Bn_jr	V	0 V	Ref. 12
Jain–Roulston coefficient (n-type), C	Cn_jr	V	0 V	Ref. 12
Jain–Roulston coefficient (p-type), A	Ap_jr	V	3.5·10-8 V	Ref. 12
Jain–Roulston coefficient (p-type), B	Bp_jr	V	0 V	Ref. 12
Jain–Roulston coefficient (p-type), C	Cp_jr	V	0 V	Ref. 12
Band-gap narrowing reference concentration	Nref_jr	1/m3	1 1/cm3	Ref. 12
Conduction band fraction	alpha_jr	1	0.5	Ref. 12
Band-Gap Narrowing Models > Slotboom Model
Band-gap narrowing reference energy	Eref_sb	V	0.00692 V	Ref. 11
Band-gap narrowing reference concentration	Nref_sb	1/m3	1.3·1017 1/cm3	Ref. 11
Conduction band fraction	alpha_sb	1	0.5	Ref. 11
Generation-Recombination > Auger Recombination
Auger recombination factor, electrons	Cn	m6/s	2.8·10-31 cm6/s (valid at 300 K)	Ref. 2
Auger recombination factor, holes	Cp	m6/s	9.9·10-32 cm6/s (valid at 300 K)	Ref. 2
Generation-Recombination > Direct Recombination
Direct recombination factor	C	m3/s	0 m3/s	N/A
Generation-Recombination > Impact Ionization
a factor, electrons, impact ionization	an	1/V	0.426 1/V	Ref. 3
a factor, holes, impact ionization	ap	1/V	0.243 1/V	Ref. 3
b factor, electrons, impact ionization	bn	V/m	4.81·105 V/cm	Ref. 3
b factor, holes, impact ionization	bp	V/m	6.53·105 V/cm	Ref. 3
c factor, electrons, impact ionization	cn	1/KValues	3.05·10-4 1/K	Ref. 3
c factor, holes, impact ionization	cp	1/K	5.35·10-4 1/K	Ref. 3
d factor, electrons, impact ionization	dn	1/K	6.86·10-4 1/K	Ref. 3
d factor, holes, impact ionization	dp	1/K	5.67·10-4 1/K	Ref. 3
Generation-Recombination > Shockley–Read–Hall Recombination
Electron lifetime, SRH	taun	s	10 μs	Ref. 4
Hole lifetime, SRH	taup	s	10 μs	Ref. 4
Mobility Models > Arora Mobility Model
Electron mobility reference	mun0_ref_arora	m2/(V·s)	1252 cm2/(V·s)	Ref. 5
Hole mobility reference	mup0_ref_arora	m2/(V·s)	407 cm2/(V·s)	Ref. 5
Electron mobility reference minimum	mun_min_ref_arora	m2/(V·s)	88 cm2/(V·s)	Ref. 5
Hole mobility reference minimum	mup_min_ref_arora	m2/(V·s)	53.4 cm2/(V·s)	Ref. 5
Electron reference impurity concentration	Nn0_ref_arora	1/m3	1.26·10171/cm3	Ref. 5
Hole reference impurity concentration	Np0_ref_arora	1/m3	2.35·10171/cm3	Ref. 5
Alpha coefficient	alpha0_arora	1	0.88	Ref. 5
Mobility reference minimum exponent	beta1_arora	1	-0.57	Ref. 5
Mobility reference exponent	beta2_arora	1	-2.33	Ref. 5
Impurity concentration reference exponent	beta3_arora	1	2.4	Ref. 5
Alpha coefficient exponent	beta4_arora	m2/(V·s)	-0.146	Ref. 5
Reference temperature	Tref_arora	K	300 K	Ref. 5
Mobility Models > Caughey–Thomas Mobility Model
Electron alpha coefficient	alphan0_ct	1	1.11	Ref. 6
Electron alpha exponent	betan1_ct	1	0.66	Ref. 6
Electron saturation velocity	vn0_ct	m/s	1·107 cm/s	Ref. 6
Electron velocity saturation exponent	betan2_ct	1	-0.87	Ref. 6
Hole alpha coefficient	alphap0_ct	1	1.21	Ref. 6
Hole alpha exponent	betap1_ct		0.17	Ref. 6
Hole saturation velocity	vp0_ct	m/s	8.37·106 cm/s	Ref. 6
Hole velocity saturation exponent	betap2_ct	1	-0.52	Ref. 6
Reference temperature	Tref_ct	K	300 K	Ref. 6
Mobility Models > Fletcher Mobility Model
Fletcher mobility coefficient 1	F1_fl	1/(cm·V·s)	1.04×1021 1/(cm·V·s)	Ref. 7
Fletcher mobility coefficient 2	F2_fl	1/m2	7.45×1013 1/cm2	Ref. 7
Reference temperature	Tref_fl	K	300 K	Ref. 7
Mobility Models > Lombardi Surface Mobility Model
Electron delta coefficient	deltan_ls	V/s	5.82 x 1014 V/s	Ref. 8
Electron mobility reference	mun1_ls	m2/(V·s)	4.75 x 107cm2/(V·s)	Ref. 8
Electron mobility reference	mun2_ls	m2/(V·s)	1.74 x 105 cm2/(V·s)	Ref. 8
Electron alpha coefficient	alphan_ls	1	0.125	Ref. 8
Hole delta coefficient	deltap_ls	V/s	2.05 x 1014 V/s	Ref. 8
Hole mobility reference	mup1_ls	m2/(V·s)	9.93 x 107 cm2/(V·s)	Ref. 8
Hole mobility reference	mup2_ls	m2/(V·s)	8.84 x 105 cm2/(V·s)	Ref. 8
Hole alpha coefficient	alphap_ls	1	0.0317	Ref. 8
Reference temperature	Tref_ls	K	1 K	Ref. 8
Electric field reference	Eref_ls	V/m	1 V/cm	Ref. 8
Doping concentration reference	Nref_ls	1/m3	1 1/cm3	Ref. 8
Mobility Models > Power Law Mobility Model
Electron mobility reference	mun0_pl	m2/(V·s)	1448 cm2/(V·s)	Ref. 5
Hole mobility reference	mup0_pl	m2/(V·s)	473 cm2/(V·s)	Ref. 5
Electron exponent	alphan_pl	1	2.33	Ref. 5
Hole exponent	alphap_pl	1	2.23	Ref. 5
Reference temperature	Tref_pl	K	300 K	Ref. 5
Mobility Models > Klaassen Unified Mobility Model
Reference temperature	T_ref_kl	K	300 K	Ref. 13
Klaassen max electron mobility	mu_e_max_kl	m2/(V·s)	1414.0 cm2/ (V·s)	Ref. 13
Klaassen max hole mobility	mu_h_max_kl	m2/(V·s)	470.5 cm2/(V·s)	Ref. 13
Klaassen min electron mobility	mu_e_min_kl	m2/(V·s)	68.5 cm2/ (V·s)	Ref. 13
Klaassen min hole mobility	mu_h_min_kl	m2/(V·s)	44.9 cm2/(V·s)	Ref. 13
Klaassen lattice mobility electron exponent	theta_e_kl	1	2.285	Ref. 13
Klaassen lattice mobility hole exponent	theta_h_kl	1	2.247	Ref. 13
Klaassen dopant and carrier mobility electron exponent	alpha_e_1_kl	1	0.711	Ref. 13
Klaassen dopant and carrier mobility hole exponent	alpha_h_1_kl	1	0.719	Ref. 13
Klaassen electron reference density	N_ref_e_1_kl	1/m3	9.20e16 1/cm3	Ref. 13
Klaassen hole reference density	N_ref_h_1_kl	1/m3	2.23e17 1/cm3	Ref. 13
Klaassen cluster function donor coefficient	c_D_kl	1	0.21	Ref. 13
Klaassen cluster function acceptor coefficient	c_A_kl	1	0.50	Ref. 13
Klaassen cluster function donor reference density	N_ref_D_kl	1/m3	4.0e20 1/cm3	Ref. 13
Klaassen cluster function acceptor reference density	N_ref_A_kl	1/m3	7.2e20 1/cm3	Ref. 13
Klaassen P parameter BH weight	f_BH_kl	1	3.828	Ref. 13
Klaassen P parameter CW weight	f_CW_kl	1	2.459	Ref. 13
Klaassen P parameter BH prefactor	N_BH_kl	1/m3	1.36e20 1/cm3	Ref. 13
Klaassen P parameter CW prefactor	P_CW_kl	1	3.97e13	Ref. 13
Klaassen 1st s parameter	s_1_kl	1	0.89233	Ref. 13
Klaassen 2nd s parameter	s_2_kl	1	0.41372	Ref. 13
Klaassen 3rd s parameter	s_3_kl	1	0.19778	Ref. 13
Klaassen 4th s parameter	s_4_kl	1	0.28227	Ref. 13
Klaassen 5th s parameter	s_5_kl	1	0.005978	Ref. 13
Klaassen 6th s parameter	s_6_kl	1	1.80618	Ref. 13
Klaassen 7th s parameter	s_7_kl	1	0.72169	Ref. 13
Klaassen 1st r parameter	r_1_kl	1	0.7643	Ref. 13
Klaassen 2nd r parameter	r_2_kl	1	2.2999	Ref. 13
Klaassen 3rd r parameter	r_3_kl	1	6.5502	Ref. 13
Klaassen 4th r parameter	r_4_kl	1	2.3670	Ref. 13
Klaassen 5th r parameter	r_5_kl	1	-0.01552	Ref. 13
Klaassen 6th r parameter	r_6_kl	1	0.6478	Ref. 13
Klaassen electron mobility mass	m_e_kl	kg	me_const	Ref. 13
Klaassen hole mobility mass	m_h_kl	kg	1.258*me_const	Ref. 13
Semiconductor Material
Band gap	Eg0	V	1.12 V (valid at 300 K)	Ref. 1
Effective density of states, conduction band	Nc	1/m3	2.8×1019 1/cm3 ×(T/300 K)3/2	Ref. 1
Effective density of states, valence band	Nv	1/m3	1.04×1019 1/cm3 ×(T/300 K)3/2	Ref. 1
Electron affinity	chi0	V	4.05 V	Ref. 1
Electron mobility	mun	m2/(V·s)	1450 cm2/(V·s)	Ref. 1
Hole mobility	mup	m2/(V·s)	500 cm2/(V·s)	Ref. 1
Semiconductor Material, density-gradient
Electron effective mass, density-gradient	meDG_iso (3-by-3 matrix)	kg	N/A
Hole effective mass, density-gradient	mhDG_iso (3-by-3 matrix)	kg	N/A
Electron effective mass, density-gradient, for penetration depth in barrier	meOx_iso (3-by-3 matrix)	kg	N/A
Hole effective mass, density-gradient, for penetration depth in barrier	mhOG_iso (3-by-3 matrix)	kg	N/A
Electron effective mass, density-gradient, for flux into barrier	meOxStar_iso (3-by-3 matrix)	kg	N/A
Hole effective mass, density-gradient, for flux into barrier	mhOxStar_iso (3-by-3 matrix)	kg	N/A