\begin{figure}[!t]
\centering
{\includegraphics[width=6cm]{./figure/str}
}
\caption{a) The three-dimensional structure of the device which is simulated in Atlas TCAD b) Cross section of the same device as seen from the sides. Different materials and the dimensional parameters are highlighted and drain and source contacts are mentioned. The gate contact is all around the device.}
\label{fig:str}
%\vspace{0.0em}
\end{figure}

We simulated the single electron transistor (SET) based on silicon island and the drain and source contacts made of highly doped silicon (Fig. \ref{fig:str}). The cross section of the island (height into width) is 1x1nm and the length is 2nm. The tunnel junctions are created by the gap between the island and contacts. These gaps provide the confinement in the transport direction and decouple the island from electrodes. The silicon island is warped by the oxide through which gate contact controls the conduction in the island. The device works as the single electron transistor and shows the characteristics of SET such as Coulomb diamonds as shown in results section. We simulated the device in Atlas TCAD using non-equilibrium Green's function (NEGF) formalism in transport direction coupled with Schrodinger equation in transverse direction. The simulator uses mode space technique instead of solving 2d or 3d problem. First solving the Schrodinger equation eigenvalues and eigen vectors are calculated in each slice of device. Then a transport equation is solved for electrons moving in lowest sub-bands which are occupied. This reduces the size of the problem \cite{manual2014silvaco}. But still the simulations are very time consuming and there is a need for an efficient model. From the simulations, we can achieve the transmission spectrum (TS) at equilibrium which is fed to the model to compute the IV characteristics. The IV characteristics are also calculated from the simulations to compare with those from the model.
