A.1 List of Symbols

Appendix 1: List of Symbols

Symbol	Description	MKS Units
A	Area	m²
c	Speed of light in vacuum	m/s
C	Capacitance per unit area	F/m²
C_FB	Flatband capacitance per unit area of a MOS structure	F/m²
C_j	Junction capacitance per unit area	F/m²
C_ox	Oxide capacitance per unit area	F/m²
D_n	Electron diffusion constant	m²/s
D_p	Hole diffusion constant	m²/s
E	Energy	Joule
E	Electric field	V/m
E_a	Acceptor energy	Joule
E_c	Conduction band energy of a semiconductor	Joule
E_d	Donor energy	Joule
E_F	Fermi energy (thermal equilibrium)	Joule
E_g	Energy bandgap of a semiconductor	Joule
E_i	Intrinsic Fermi energy	Joule
E_v	Valence band energy of a semiconductor	Joule
E_vacuum	Electron energy in vacumm	Joule
f(E)	Distribution function (probability density function)
F_n	Quasi-Fermi energy of electrons	Joule
F_p	Quasi-Fermi energy of holes	Joule
g_c(E)	Density of states in the conduction band per unit energy and per unit volume	m^-3J^-1
g_v(E)	Density of states in the valence band per unit energy and per unit volume	m^-3J^-1
G_n	Electron generation rate	m^-3s^-1
G_p	Hole generation rate	m^-3s^-1
h	Plank's constant	Js
	Reduced Plank's (= h /2π)	Js
I	Current	A
J	Current density	A/m²
J_n	Electron current density	A/m²
J_p	Hole current density	A/m²
k	Boltzmann's constant	J/K
l	Mean free path	m
L	Length	m
L_n	Electron diffusion length	m
L_p	Hole diffusion length	m
m	Mass	kg
m₀	Free electron mass	kg
m_e^*	Effective mass of electrons	kg
m_h^*	Effective mass of holes	kg
n	Electron density	m^-3
n_i	Intrinsic carrier density	m^-3
n(E)	Electron density per unit energy and per unit volume	m^-3J^-1
n₀	Electron density in thermal equilibrium	m^-3
n_i	Intrinsic carrier density	m^-3
N	Doping density	m^-3<
N_a	Acceptor doping density	m^-3
N_a^-	Ionized acceptor density	m^-3
N_B	Base doping density	m^-3
N_c	Effective density of states in the conduction band	m^-3
N_C	Collector doping density	m^-3
N_d	Donor doping density	m^-3
N_d⁺	Ionized donor density	m^-3
N_E	Emitter doping density	m^-3
N_v	Effective density of states in the valence band	m^-3
p	Hole density	m^-3
p(E)	Hole density per unit energy	m^-3J^-1
p₀	Hole density in thermal equilibrium	m^-3
p_n	Hole density in an n-type semiconductor	m^-3
q	electronic charge	C
Q	Charge	C
Q_d	Charge density per unit area in the depletion layer of an MOS structure	C/m²
Q_d,T	Charge density per unit area at threshold in the depletion layer of an MOS structure	C/m²
Q_i	Interface charge density per unit area	C/m²
R	Resistance	Ohm
R_n	Electron recombination rate	m^-3s^-1
R_p	Hole recombination rate	m^-3s^-1
t	Thickness	m
t_ox	Oxide thickness	m
T	Temperature	Kelvin
U_n	Net recombination rate of electrons	m^-3s^-1
U_p	Net recombination rate of holes	m^-3s^-1
v	Velocity	m/s
v_th	Thermal velocity	m/s
V_a	Applied voltage	V
V_B	Base voltage	V
V_C	Collector voltage	V
V_D	Drain voltage	V
V_E	Emitter voltage	V
V_FB	Flatband voltage	V
V_G	Gate voltage	V
V_t	Thermal voltage	V
V_T	Threshold voltage of an MOS structure	V
w	Depletion layer width	m
w_B	Base width	m
w_C	Collector width	m
w_E	Emitter width	m
w_n	Width of an n-type region	m
w_p	Width of a p-type region	m
x	Position	m
x_d	Depletion layer width in an MOS structure	m
x_d,T	Depletion layer width in an MOS structure at threshold	m
x_j	Junction depth	m
x_n	Depletion layer width in an n-type semiconductor	m
x_p	Depletion layer width in a p-type semiconductor	m

α	Transport factor
β	Current gain
γ	Body effect parameter	V^1/2
γ_E	Emitter efficiency
δ_n	Excess electron density	m^-3
<δ_p	Excess hole density	m^-3
ΔQ_n,B	Excess electron charge density in the base	C/m²
ε_ox	Dielectric constant of the oxide	F/m
e_s	Dielectric constant of the semiconductor	F/m
μ_n	Electron mobility	m²/V-s
μ_p	Hole mobility	m²/V-s
ρ	Charge density per unit volume Resistivity	C/m³ Ωm
ρ_ox	Charge density per unit volume in the oxide	C/m³
σ	Conductivity	Ω^-1m^-1
τ_n	Electron lifetime	s
τ_p	Hole lifetime	s
φ	Potential	V
φ_B	Barrier height	V
φ_F	Bulk potential	V
φ_i	Built-in potential of a p-n diode or Schottky diode	V
φ_s	Potential at the semiconductor surface	V
Φ_M	Workfunction of the metal	V
Φ_MS	Workfunction difference between the metal and the semiconductor	V
Φ_S	Workfunction of the semiconductor	V
Φ	Electron affinity of the semiconductor	V