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Variables and Fundamental Constants

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]
$C_{\Sigma }$ sum of capacitances [F]
$C_{\text{eff}}$ effective capacitance of a Thévenin equivalent circuit
d diameter or width [m]
Dpq(X) denominator polynomial for Padé approximation of degree p+q
$\delta()$ delta-function
$\delta_{mn}$ Kronecker-delta; is 1 for m=n otherwise 0.
$\Delta$ difference between two values ( $\Delta E, \Delta t, \ldots$)
e elementary charge $1.602\cdot 10^{-19}$ 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]
$E_{\Sigma}$ total energy stored in a system [eV]
$\epsilon$ dielectric permittivity $\epsilon = \epsilon_0 \epsilon_r$
$\epsilon_0$ dielectric permittivity of vacuum $8.854\cdot 10^{-12}$ As/Vm
$\epsilon_r$ relative dielectric permittivity [1]
f frequency [1/s]
f() Fermi function
F Helmholtz's free energy [eV]
$\Gamma$ tunnel rate [1/s]
$\Gamma^{(x)}$ xth-order co-tunneling rate [1/s]
$\Gamma_{ij}$ tunnel rate from state j to state i [1/s]
$\Gamma(\boldsymbol{S}\vert\boldsymbol{S'})$ tunnel rate from state S' to state S [1/s]
h Planck constant $6.626\cdot 10^{-34}$ Js
$\hbar$ $h/2\pi = 1.055\cdot 10^{-34}$ 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 $1.381\cdot 10^{-23}$ J/K
Km m-dimensional Krylov subspace
$\lambda_F$ Fermi wavelength [m]
$\lambda_i$ matrix eigenvalue
m module of a linear congruential random number generator
me electron mass $9.1\cdot 10^{-31}$ kg
me* effective electron mass [kg]
n electron concentration; charge carrier concentration [ $1/\text{m}^{3}$]
$n_{\text{net}}$ net carrier concentration $n_{\text{net}}=n-p$ [ $1/\text{m}^{3}$]
N number of electrons; number of nodes
$\langle N\rangle$ 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
$\omega_n, \omega_m$ eigenvalues [1/s]
$\omega_{mn}$ difference of two eigenvalues $\omega_m-\omega_n$ [1/s]
$\omega_x$ electron hole excitation energy
p hole concentration [ $1/\text{m}^{3}$]
Pi(t) probability of state i
$\tilde{P}_i(s)$ Laplace transform of Pi(t)
$P_{\text{error}}$ error probability
p state probability vector
p(S,t) probability density function in state space
$\varphi$ electrostatic potential [V]
$\boldsymbol{\varphi_{p,f}}$ potential vector for potential-nodes and floating-nodes
$\boldsymbol{\varphi_c}$ potential vector for charge-nodes
$\varphi_{p,f_{\text{initial}}}$ potential of a potential-node or floating-node from which an electron tunnels
$\varphi_{p,f_{\text{final}}}$ potential of a potential-node or floating-node to which an electron tunnels
$\psi$ wave function
$\psi^*$ complex conjugate wave function
$\psi_n, \psi_m$ orthonormal eigenfunctions
q charge [As]
$q_{\Sigma}$ sum of charges [As]
$q_{f\Sigma}$ charge of macro-node
q charge vector
qp,f charge vector for potential-nodes and floating-nodes
qc charge vector for charge-nodes
$q_{\text{crit}}$ 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
$\tilde{r}_n$ integer random number
RQ quantum resistance $h/e^2 = \text{25813}\ \mathsf{\Omega}$
RT tunnel resistance [ $\mathsf{\Omega}$]
Rpq(X) rational Padé approximation of order p+q
$\rho $ spectral radius
t time [s]
T absolute temperature [K]
|T|2 tunnel transmission probability [1]
$\tau$ duration to the next tunnel event [s]
$\bar{\tau}$ average duration to the next tunnel event [s]
$\theta$ angle [rad]
V voltage [V]
Vb bias voltage [V]
$V_{\text{in}}$ input voltage [V]
$V_{\text{out}}$ output voltage [V]
$V_{\text {th}}$ threshold voltage [V]
$V_{\text{crit}}$ critical voltage for the Coulomb blockade [V]
V(x) one-dimensional potential function
W work done by voltage sources [J]
x x-coordinate [m]

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Next: Graphic Symbols Up: List of Symbols Previous: Units
Christoph Wasshuber