List of Symbols

$\ensuremath{\mathbf{b}}$	...	right hand side vector
$\ensuremath{\mathbf{b}}_{\mathrm{B}}$	...	part of the right hand side vector containing entries from the boundaries
$\ensuremath{\mathbf{b}}_{\mathrm{S}}$	...	part of the right hand side vector containing entries from the segments
dij	...	distance of grid points i and j
dn	...	width of the space charge region on the n-doped side
dp	...	width of the space charge region on the p-doped side
eb	...	effective barrier height
$\ensuremath{\mathrm{k_{B}}}$	...	Boltzmann constant
l	...	lateral coordinate
m	...	carrier mass
n	...	electron concentration
$\ensuremath{\mathbf{n}}$	...	perpendicular vector
ni	...	intrinsic carrier concentration
ninj	...	injection rate of primary electrons
nsec	...	generation rate of secondary electrons
p	...	hole concentration
psec	...	generation rate of secondary holes
q	...	elementary charge
t	...	time
tn	...	time for simulation step n
$\Delta$tn	...	time step size of step n
$\Delta$$\tilde{t}$	...	estimated time step size
u	...	scalar quantity
v	...	thermionic emission velocity vertical coordinate
w	...	barrier width
x	...	spatial coordinate
$\ensuremath{\mathbf{x}}$	...	vector of unknowns
z	...	spatial coordinate
A*	...	Richardson constant
$\ensuremath{\mathbf{A}}$	...	system matrix
$\ensuremath{\mathbf{A}}_{\mathrm{B}}$	...	part of system matrix containing entries from the boundaries
$\ensuremath{\mathbf{A}}_{\mathrm{S}}$	...	part of system matrix containing entries from the segments
AC	...	alternating current
C	...	integration constant
DC	...	direct current
Dij	...	diffusion constant between grid points i and j
Dn	...	diffusion constant of electrons
Dp	...	diffusion constant of holes
E	...	electric field
E$\perp$	...	electric field perpendicular to interface
$\Delta$EC	...	difference of conduction band edge energies
$\ensuremath{E_{\mathrm{g}}}$	...	band gap energy
Eprim	...	energy of the primary electrons
E$\Delta$t	...	discretization error for step size $\Delta$t
G	...	generation rate
J	...	current density
J$\perp$	...	current density perpendicular to interface
JG	...	current density caused by generation of carriers
Jij	...	current density between grid points i and j
Jinj	...	current density of injected primary electrons
Jninj	...	electron current density caused by injection of electrons
Jpinj	...	hole current density caused by injection of electrons
Ln	...	minority diffusion length of electrons
Lp	...	minority diffusion length of holes
LD	...	Debye length
NA	...	acceptor concentration
NC	...	effective density of states for the conduction band
ND	...	donor concentration
NV	...	effective density of states for the valence band
S$\nu$	...	energy flux density
T	...	temperature
T$\nu$	...	carrier temperature
$\ensuremath{\mathbf{T}}_{\mathrm{B}}$	...	transformation matrix
VS	...	surface band bending
VSCV	...	surface cathodo voltage
VSPV	...	surface photo voltage
$\varepsilon_{\mathrm{0}}^{}$	...	vacuum permittivity
$\varepsilon_{\mathrm{r}}^{}$	...	relative permittivity
$\kappa_{s}^{}$	...	spectral condition number
$\lambda$	...	eigenvalue
$\mu_{\mathrm{l}}^{}$	...	lateral position of the center of the primary electron beam
$\mu_{\mathrm{n}}^{}$	...	mobility of electrons
$\mu_{\mathrm{p}}^{}$	...	mobility of holes
$\mu_{\mathrm{v}}^{}$	...	vertical distance of the center of the primary electron beam from the semiconductor surface
$\xi$	...	spatial coordinate
$\ensuremath{\varphi}$	...	electrostatic potential
$\varphi_{\mathrm{AVC}}^{}$	...	potential measured by the AVC method
$\varphi_{\mathrm{bi}}^{}$	...	built-in potential
$\rho_{\mathrm{dop}}^{}$	...	charge density caused by the doping
$\rho_{\mathrm{inj}}^{}$	...	charge density caused by injection of electrons
$\rho_{\mathrm{inj}}^{0}$	...	charge density caused by injection of electrons for uniform doping
$\sigma_{\mathrm{l}}^{}$	...	lateral standard deviation
$\sigma_{\mathrm{v}}^{}$	...	vertical standard deviation
$\sigma_{S}^{}$	...	surface charge density
$\tau_{n}^{}$	...	minority carrier lifetime of electrons
$\tau_{p}^{}$	...	minority carrier lifetime of holes