Next: List of Figures Up: Dissertation Grasser Previous: Contents

List of Symbols

$\Delta$ t ... a time step

$\Delta$ x ... a grid point difference

$\beta_{n}^{}$ , $\beta_{p}^{}$ , $\beta_{\nu }^{}$ ... electron, hole, and general exponents in mobility models

$\delta$ ... damping control parameter

$\varepsilon$ ... dielectric constant

$\varepsilon_{\mathrm{r}}^{\mathrm{}}$ ... relative dielectric constant

$\kappa_{L}^{}$ ... lattice heat capacity

$\kappa_{n}^{}$ , $\kappa_{p}^{}$ ... thermal conductivity of electron and hole gas

$\mu_{\nu}^{}$ ... mobility of carrier type $\nu$

$\mu^{\mathrm{L}}_{\nu}$ ... mobility due to lattice scattering

$\mu^{\mathrm{LI}}_{\nu}$ ... mobility due to lattice and impurity scattering

$\mu^{\mathrm{LIS}}_{\nu}$ ... mobility due to lattice, impurity, and surface scattering

$\mu^{\mathrm{LISF}}_{\nu}$ ... mobility including lattice, impurity, surface scattering, and high-field reduction

$\mu^{\mathrm{LIST}}_{\nu}$ ... mobility including lattice, impurity, surface scattering, and high-temperature reduction

$\mu_{n}^{}$ , $\mu_{p}^{}$ ... electron and hole mobilities

$\rho_{L}^{}$ ... lattice mass density

$\tau_{\epsilon,n}^{}$ $\tau_{\epsilon,p}^{}$ $\tau_{\epsilon,\nu}^{}$ ... energy relaxation times for electrons, holes, and general carrier type

$\varphi$ ... node voltage for mixed-mode simulation

$\varphi_{C}^{}$ ... node voltage for mixed-mode simulation applied to a contact

$\varphi_{n}^{}$ , $\varphi_{p}^{}$ ... quasi-Fermi potentials for electrons and holes

$\psi_{C}^{}$ ... contact potential for mixed-mode simulation

$\psi$ ... electrostatic potential

$\psi_{\mathrm{bi}}^{}$ ... Built-In potential

C ... net doping concentration

E ... local electric field

E_b ... local band edge energy for electrons or holes

E_C ... local band edge energy for electrons

E_g ... bandgap energy

E_i ... intrinsic Fermi level

E_V ... local band edge energy for holes

F_n, F_p ... driving force for electrons and holes

I_b^{i, j} ... electron or hole current between the grid points i and j

J_n, J_p ... electron and hole current densities

N_C ... effective density of states for electrons

N_{C, 0} ... effective density of states for electrons evaluated at reference temperature T₀

N_i ... concentration of the i-th active dopand

N_T ... total impurity concentration

N_V ... effective density of states for holes

N_{V, 0} ... effective density of states for holes evaluated at reference temperature T₀

R ... net recombination rate

R^AU ... Auger recombination rate

R^BB ... band to band tunneling recombination rate

R^II ... impact ionization recombination rate

R_i ... net recombination rate of the i-th box

R^SRH ... SRH net recombination rate

R_T ... thermal resistance

S_n, S_p ... electron and hole heat flux density

S_L ... lattice heat flux density

T_C ... contact temperature

T_L ... local lattice temperature

T_n, T_p ... electron and hole temperatures

V_T ... thermal voltage for a certain lattice temperature

V_i ... the box volume of the i-th box

c_L ... specific lattice heat capacity

d ... damping parameter

f_x ... vector function of the equation system

h ... Planck constant

$\hbar$ ... reduced Planck constant

k_B ... Boltzmann constant

m_{n, p} ... absolute electron and hole mass

m_{n, p}^* ... effective electron and hole mass

n ... electron concentration

p ... hole concentration

q ... elementary charge

u_x ... update vector of the equation system

v_{n, 300}, v_{p, 300} ... thermal electron and hole velocities at 300 K

x ... solution vector of the equation system

x^* ... new approach to the solution vector of the equation system

y^ref ... surface reference distance

Next: List of Figures Up: Dissertation Grasser Previous: Contents

Tibor Grasser
1999-05-31

$\Delta$ t	...	a time step
$\Delta$ x	...	a grid point difference
$\beta_{n}^{}$ , $\beta_{p}^{}$ , $\beta_{\nu }^{}$	...	electron, hole, and general exponents in mobility models
$\delta$	...	damping control parameter
$\varepsilon$	...	dielectric constant
$\varepsilon_{\mathrm{r}}^{\mathrm{}}$	...	relative dielectric constant
$\kappa_{L}^{}$	...	lattice heat capacity
$\kappa_{n}^{}$ , $\kappa_{p}^{}$	...	thermal conductivity of electron and hole gas
$\mu_{\nu}^{}$	...	mobility of carrier type $\nu$
$\mu^{\mathrm{L}}_{\nu}$	...	mobility due to lattice scattering
$\mu^{\mathrm{LI}}_{\nu}$	...	mobility due to lattice and impurity scattering
$\mu^{\mathrm{LIS}}_{\nu}$	...	mobility due to lattice, impurity, and surface scattering
$\mu^{\mathrm{LISF}}_{\nu}$	...	mobility including lattice, impurity, surface scattering, and high-field reduction
$\mu^{\mathrm{LIST}}_{\nu}$	...	mobility including lattice, impurity, surface scattering, and high-temperature reduction
$\mu_{n}^{}$ , $\mu_{p}^{}$	...	electron and hole mobilities
$\rho_{L}^{}$	...	lattice mass density
$\tau_{\epsilon,n}^{}$ $\tau_{\epsilon,p}^{}$ $\tau_{\epsilon,\nu}^{}$	...	energy relaxation times for electrons, holes, and general carrier type
$\varphi$	...	node voltage for mixed-mode simulation
$\varphi_{C}^{}$	...	node voltage for mixed-mode simulation applied to a contact
$\varphi_{n}^{}$ , $\varphi_{p}^{}$	...	quasi-Fermi potentials for electrons and holes
$\psi_{C}^{}$	...	contact potential for mixed-mode simulation
$\psi$	...	electrostatic potential
$\psi_{\mathrm{bi}}^{}$	...	Built-In potential
C	...	net doping concentration
E	...	local electric field
E_b	...	local band edge energy for electrons or holes
E_C	...	local band edge energy for electrons
E_g	...	bandgap energy
E_i	...	intrinsic Fermi level
E_V	...	local band edge energy for holes
F_n, F_p	...	driving force for electrons and holes
I_b^{i, j}	...	electron or hole current between the grid points i and j
J_n, J_p	...	electron and hole current densities
N_C	...	effective density of states for electrons
N_{C, 0}	...	effective density of states for electrons evaluated at reference temperature T₀
N_i	...	concentration of the i-th active dopand
N_T	...	total impurity concentration
N_V	...	effective density of states for holes
N_{V, 0}	...	effective density of states for holes evaluated at reference temperature T₀
R	...	net recombination rate
R^AU	...	Auger recombination rate
R^BB	...	band to band tunneling recombination rate
R^II	...	impact ionization recombination rate
R_i	...	net recombination rate of the i-th box
R^SRH	...	SRH net recombination rate
R_T	...	thermal resistance
S_n, S_p	...	electron and hole heat flux density
S_L	...	lattice heat flux density
T_C	...	contact temperature
T_L	...	local lattice temperature
T_n, T_p	...	electron and hole temperatures
V_T	...	thermal voltage for a certain lattice temperature
V_i	...	the box volume of the i-th box
c_L	...	specific lattice heat capacity
d	...	damping parameter
f_x	...	vector function of the equation system
h	...	Planck constant
$\hbar$	...	reduced Planck constant
k_B	...	Boltzmann constant
m_{n, p}	...	absolute electron and hole mass
m_{n, p}^*	...	effective electron and hole mass
n	...	electron concentration
p	...	hole concentration
q	...	elementary charge
u_x	...	update vector of the equation system
v_{n, 300}, v_{p, 300}	...	thermal electron and hole velocities at 300 K
x	...	solution vector of the equation system
x^*	...	new approach to the solution vector of the equation system
y^ref	...	surface reference distance