4.1 Summary of the Equations Describing SET Devices

  The condition to simulate the electron transport as a jump process is
$$\begin{gather}R_T > \frac{h}{e^2} \doteq \text{25813}\ \mathsf{\Omega}.\notag \end{gather}$$
Rate formulas for first and higher order transitions are
$$\begin{gather}\Gamma(\Delta F) =\frac{1}{e^2R_T}\frac{-\Delta F}{1-e^{\frac{\Del... ... \prod_{i=1}^{N-1}\left((2\pi k_BTi)^2+\Delta F_N^2\right). \notag \end{gather}$$
The free energy is given by
$$\begin{align}F=&\frac{1}{2}\begin{bmatrix}\boldsymbol{\varphi_{p,f}}^T&\boldsymb... ...f_{\text{final}}})+ \sum_{i=1}^{N_c} (\Delta E_{Fi}+E_{Ni}).\notag \end{align}$$
The ME and the duration to the next tunnel event for a MC method are
$$\begin{gather}\frac{\partial P_i(t)}{\partial t} = \sum_{j\neq i} \left[\Gamma_{... ...Gamma_{ji}P_i(t)\right]\notag\\ \tau=-\frac{\ln(r)}{\Gamma}.\notag \end{gather}$$