A.1 List of Symbols

Appendix 1a: Extended List of Symbols

Symbol	Description		MKS Units
a		Acceleration	m/s²
a₀		Bohr radius	m
A		Area	m²
A*		Richardson constant	m/s
A_C		Collector area	m²
A_E		Emitter area	m²
b		Bimolecular recombination constant	m³/s
c		Speed of light in vacuum	m/s
C		Capacitance per unit area	F/m²
C_D		Diffusion capacitance per unit area	F/m²
C_DS		Drain-source capacitance	F
C_FB		Flatband capacitance per unit area of a MOS structure	F/m²
C_G		Gate capacitance	F
C_GS		Gate-source capacitance	F
C_GD		Gate-drain capacitance	F
C_HF		High-frequency capacitance per unit area of a MOS structure	F/m²
C_j		Junction capacitance per unit area	F/m²
C_LF		Low-frequency (quasi-static) capacitance per unit area of a MOS structure	F/m²
C_M		Miller capacitance	F
C_ox		Oxide capacitance per unit area	F/m²
C_s		Semiconductor 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
E₀		Lowest energy in a one-dimensional quantum well	Joule
E_a		Acceptor energy	Joule
E_br		Breakdown field	V/m
E_c		Conduction band energy of a semiconductor	Joule
E_d		Donor energy	Joule
E_F		Fermi energy (thermal equilibrium)	Joule
E_F,n		Fermi energy in an n-type semiconductor	Joule
E_F,p		Fermi energy in a p-type semiconductor	Joule
E_g		Energy bandgap of a semiconductor	Joule
E_i		Intrinsic Fermi energy	Joule
E_n		n^th quantized energy	Joule
E_ph		Photon energy	Joule
E_t		Trap 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_BE(E)		Bose-Einstein distribution function
f_FD(E)		Fermi-Dirac distribution function
f_MB(E)		Maxwell-Boltzmann distribution function
F		Force	Newton
F_n		Quasi-Fermi energy of electrons	Joule
F_p		Quasi-Fermi energy of holes	Joule
gE)		Density of states per unit energy and per unit volume	m^-3J^-1
g(E)		Density of states in the conduction band per unit energy and per unit volume	m^-3J^-1
g(E)		Density of states in the valence band per unit energy and per unit volume	m^-3J^-1
g_d		Output conductance of a MOSFET	S
g_m		Transconductance of a MOSFET	S
G		Carrier generation rate	m^-3s^-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 /2p)	Js
I		Current	A
I_B		Base current of a bipolar transistor	A
I_C		Collector current of a bipolar transistor	A
I_D		Drain current of a MOSFET	A
I_E		Emitter current of a bipolar transistor	A
I_F		Forward active current of a bipolar transistor	A
I_D,sat		Drain current of a MOSFET in saturation	A
I_ph		Photo current	A
I_r		Recombination current	A
I_R		Reverse active current of a bipolar transistor	A
I_s		Saturation current	A
I_sc		Short circuit current of a solar cell	A
J		Current density	A/m²
J_n		Electron current density	A/m²
J_p		Hole current density	A/m²
k		Boltzmann's constant wavenumber	J/K m^-1
l		Mean free path	m
L		Length	m
L_D		Debye length	m
L_n		Electron diffusion length	m
L_p		Hole diffusion length	m
L_x		Hole diffusion length	m
m		Mass	kg
m^*		Effective mass	kg
m_A		Atomic mass	kg
m₀		Free electron mass	kg
m_e^*		Effective mass of electrons	kg
m_h^*		Effective mass of holes	kg
M		Proton mass Multiplication factor	kg
n		Electron density Integer Refractive index Ideality factor	m^-3
n_i		Intrinsic carrier density	m^-3
n(E)		Electron density per unit energy and per unit volume	m^-3
n₀		Electron density in thermal equilibrium	m^-3
n_i		Intrinsic carrier density	m^-3
n_n		Electron density in an n-type semiconductor	m^-3
n_n0		Thermal equilibrium electron density in an n-type semiconductor	m^-3
n_p		Electron density in a p-type semiconductor	m^-3
n_p0		Thermal equilibrium electron density in a p-type semiconductor	m^-3
N		Number of particles Doping density
N_a		Acceptor doping density	m^-3
N_a^-		Ionized acceptor density	m^-3
N_A		Avogadro's number
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_ss		Surface state density	m^-2
N_t		Recombination trap density	m^-2
N_v		Effective density of states in the valence band	m^-3
p		Hole density Particle momentum Pressure	m^-3 kgm/s Nm^-2
p(E)		Hole density per unit energy	m^-3
p₀		Hole density in thermal equilibrium	m^-3
p_n		Hole density in an n-type semiconductor	m^-3
p_n0		Thermal equilibrium hole density in an n-type semiconductor	m^-3
p_p		Hole density in a p-type semiconductor	m^-3
p_p0		Thermal equilibrium hole density in a p-type semiconductor	m^-3
q		electronic charge	C
Q		Heat Charge	Joule C
Q_B		Majority carrier charge density in the base	C/m²
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
Q_inv		Inversion layer charge density per unit area	C/m²
Q_M		Charge density per unit area in a metal	C/m²
Q_n		Charge density per unit area in the depletion layer of an n-type region	C/m²
Q_p		Charge density per unit area in the depletion layer of a p-type region	C/m²
Q_ss		Surface state charge density per unit area	C/m²
r_e		Emitter resistance	Ohm
r_p		Base resistance	Ohm
R		The Rydberg constant Resistance	J Ohm
R_n		Electron recombination rate	m^-3s^-1
R_p		Hole recombination rate	m^-3s^-1
R_s		Sheet resistance	Ohm
s		Spin
S		Entropy	J/K
t		Thickness	m
t_ox		Oxide thickness	m
T		Temperature Kinetic energy	Kelvin Joule
u_w		Spectral density	Jm^-3s^-1
U		Total energy	Joule
U_A		Auger recombination rate	m^-3s^-1
U_b-b		Band-to-band recombination rate	m^-3s^-1
U_n		Net recombination rate of electrons	m^-3s^-1
U_p		Net recombination rate of holes	m^-3s^-1
U_SHR		Shockley-Read-Hall recombination rate	m^-3s^-1
v		Velocity	m/s
v_R		Richardson velocity	m/s
v_sat		Saturation velocity	m/s
v_th		Thermal velocity	m/s
V		Potential energy Volume	Joule m³
V_a		Applied voltage	V
V_A		Early voltage	V
V_br		Breakdown voltage	V
V_B		Base voltage	V
V_BE		Base-emitter voltage	V
V_BC		Base-collector voltage	V
V_C		Collector voltage	V
V_CE		Collector-emitter voltage	V
V_D		Drain voltage	V
V_DS		Drain-source voltage	V
V_DS,sat		Drain-source saturation voltage	V
V_E		Emitter voltage	V
V_FB		Flatband voltage	V
V_G		Gate voltage	V
V_GS		Gate-source voltage	V
V_oc		Open circuit voltage of a solar cell	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
W		Work	Joule
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	Absorption coefficient Transport factor	m^-1
α_F	Forward active transport factor
α_n	Ionization rate coefficient for electrons	m^-1
α_R	Reverse active transport factor
α_T	Base transport factor
β	Current gain
γ	Body effect parameter	V^1/2
γ_E	Emitter efficiency
γ_n	Auger coefficient for electrons	m⁶s^-1
γ_p	Auger coefficient for holes	m⁶s^-1
δ_n	Excess electron density	m^-3
δ_p	Excess hole density	m^-3
δ_R	Depletion layer recombination factor
ΔQ_n,B	Excess electron charge density in the base	C/m²
ε	Dielectric constant	F/m
ε₀	Permittivity of vacuum	F/m
ε_ox	Dielectric constant of the oxide	F/m
ε_s	Dielectric constant of the semiconductor	F/m
ε₀	Permeability of vacuum	H/m
Θ	Tunnel probability
μ	Wavelength	m
μ	Electro-chemical potential	Joule
μ_n	Electron mobility	m²/V-s
μ_p	Hole mobility	m²/V-s
ν	Frequency	Hz
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	Scattering time	s
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	Flux	m^-2s^-1
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
χ	Electron affinity of the semiconductor	V
Ψ	Wavefunction
ω	Radial frequency	rad/s