a |
radius of sphere [m]; multiplier of congruential
random number generator |
A |
complex amplitude |
bx |
orthonormal vector in a Krylov subspace |
B |
complex amplitude |
Bm |
orthonormal basis in m-dimensional Krylov subspace |
c |
offset of a linear congruential random number generator |
c(t) |
complex time dependent scattering amplitude |
C |
capacitance [F] |
C |
capacitance matrix |
Cx |
sub-matrices of the capacitance matrix |
Cij |
capacitance between conductor i and j [F] |
![$C_{\Sigma }$](img6.gif) |
sum of capacitances [F] |
![$C_{\text{eff}}$](img13.gif) |
effective capacitance of a Thévenin equivalent circuit |
d |
diameter or width [m] |
Dpq(X) |
denominator polynomial for Padé approximation of
degree p+q |
![$\delta()$](img14.gif) |
delta-function |
![$\delta_{mn}$](img15.gif) |
Kronecker-delta; is 1 for m=n otherwise 0. |
![$\Delta$](img16.gif) |
difference between two values (
) |
e |
elementary charge
As;
charge of one electron (-e) |
e1 |
unit vector |
E |
energy [J] or [eV] |
E |
error matrix |
Ec |
conduction band edge [eV] |
EC |
Coulomb energy [eV] |
EF |
Fermi energy [eV] |
EF,i |
Fermi energy of intrinsic semiconductor [eV] |
Ef |
energy of a final state (for instance after tunneling) [eV] |
Ei |
energy of an initial state (for instance before tunneling) [eV] |
![$E_{\Sigma}$](img18.gif) |
total energy stored in a system [eV] |
![$\epsilon$](img19.gif) |
dielectric permittivity
![$\epsilon = \epsilon_0 \epsilon_r$](img20.gif) |
![$\epsilon_0$](img21.gif) |
dielectric permittivity of vacuum
As/Vm |
![$\epsilon_r$](img23.gif) |
relative dielectric permittivity [1] |
f |
frequency [1/s] |
f() |
Fermi function |
F |
Helmholtz's free energy [eV] |
![$\Gamma$](img24.gif) |
tunnel rate [1/s] |
![$\Gamma^{(x)}$](img25.gif) |
xth-order co-tunneling rate [1/s] |
![$\Gamma_{ij}$](img26.gif) |
tunnel rate from state j to state i [1/s] |
![$\Gamma(\boldsymbol{S}\vert\boldsymbol{S'})$](img27.gif) |
tunnel rate from state
S' to state
S [1/s] |
h |
Planck constant
Js |
![$\hbar$](img29.gif) |
Js |
H |
Hamilton operator |
Hm |
upper Hessenberg matrix |
I |
electric current [A] |
I |
unit matrix |
Jx |
tunnel junction x |
Ji |
Jordan block |
k |
wave number [1/m] |
kB |
Boltzmann constant
J/K |
Km |
m-dimensional Krylov subspace |
![$\lambda_F$](img32.gif) |
Fermi wavelength [m] |
![$\lambda_i$](img33.gif) |
matrix eigenvalue |
m |
module of a linear congruential random number generator |
me |
electron mass
kg |
me* |
effective electron mass [kg] |
n |
electron concentration; charge carrier concentration
[
] |
![$n_{\text{net}}$](img36.gif) |
net carrier concentration
[
] |
N |
number of electrons; number of nodes |
![$\langle N\rangle$](img38.gif) |
time averaged number of electrons |
Nc |
number of charge-nodes |
Nf |
number of floating-nodes |
Nfm |
number of nodes in a macro-node |
Nm |
number of macro-nodes |
Np |
number of potential-nodes |
Npq(X) |
numerator polynomial for Padé approximation of
degree p+q |
![$\omega_n, \omega_m$](img39.gif) |
eigenvalues [1/s] |
![$\omega_{mn}$](img40.gif) |
difference of two eigenvalues
[1/s] |
![$\omega_x$](img42.gif) |
electron hole excitation energy |
p |
hole concentration [
] |
Pi(t) |
probability of state i |
![$\tilde{P}_i(s)$](img43.gif) |
Laplace transform of Pi(t) |
![$P_{\text{error}}$](img44.gif) |
error probability |
p |
state probability vector |
p(S,t) |
probability density function in state space |
![$\varphi$](img45.gif) |
electrostatic potential [V] |
![$\boldsymbol{\varphi_{p,f}}$](img46.gif) |
potential vector for potential-nodes and floating-nodes |
![$\boldsymbol{\varphi_c}$](img47.gif) |
potential vector for charge-nodes |
![$\varphi_{p,f_{\text{initial}}}$](img48.gif) |
potential of a potential-node or floating-node from which
an electron tunnels |
![$\varphi_{p,f_{\text{final}}}$](img49.gif) |
potential of a potential-node or floating-node to which an
electron tunnels |
![$\psi$](img50.gif) |
wave function |
![$\psi^*$](img51.gif) |
complex conjugate wave function |
![$\psi_n, \psi_m$](img52.gif) |
orthonormal eigenfunctions |
q |
charge [As] |
![$q_{\Sigma}$](img53.gif) |
sum of charges [As] |
![$q_{f\Sigma}$](img54.gif) |
charge of macro-node |
q |
charge vector |
qp,f |
charge vector for potential-nodes and floating-nodes |
qc |
charge vector for charge-nodes |
![$q_{\text{crit}}$](img55.gif) |
critical charge for the Coulomb blockade [As] |
Q0 |
background charge |
r |
magnitude of space vector [m]; random number |
r |
space vector |
rn |
on the interval [0,1] uniformly distributed random number |
![$\tilde{r}_n$](img56.gif) |
integer random number |
RQ |
quantum resistance
![$h/e^2 = \text{25813}\ \mathsf{\Omega}$](img57.gif) |
RT |
tunnel resistance [
] |
Rpq(X) |
rational Padé approximation of order p+q |
![$\rho $](img3.gif) |
spectral radius |
t |
time [s] |
T |
absolute temperature [K] |
|T|2 |
tunnel transmission probability [1] |
![$\tau$](img58.gif) |
duration to the next tunnel event [s] |
![$\bar{\tau}$](img59.gif) |
average duration to the next tunnel event [s] |
![$\theta$](img60.gif) |
angle [rad] |
V |
voltage [V] |
Vb |
bias voltage [V] |
![$V_{\text{in}}$](img61.gif) |
input voltage [V] |
![$V_{\text{out}}$](img62.gif) |
output voltage [V] |
![$V_{\text {th}}$](img63.gif) |
threshold voltage [V] |
![$V_{\text{crit}}$](img64.gif) |
critical voltage for the Coulomb blockade [V] |
V(x) |
one-dimensional potential function |
W |
work done by voltage sources [J] |
x |
x-coordinate [m] |