The CMOS technology is at the verge of the miniaturization and it needs to be replaced by the new technologies which should overcome its limitations. One of the most promising technologies is the one based on single electron tunneling phenomenon. If a metallic or semiconducting island is placed between the electrodes separated by the tunnel junctions with very small capacitance, the single electron phenomenon can be observed. When an electron tunnels into the island it raises the electrostatic potential of island stopping the tunneling of the following electrons until external potential is applied. This phenomenon is also known as Coulomb blockade. If the island size is very small (so that the capacitance is very small), tunneling of single electrons can be controlled by the external electrode potentials. Hence the devices based on single electron phenomenon have the attributes of small size and low power consumption.

Over the years, many different schemes for digital logic using single electron transistor have been presented \cite{likharev1987single,tucker1992complementary,fukui1995simple,uchida2003programmable,abutaleb2015new}. In one scheme, the logic states are represented by the single electrons located at tiny metallic electrodes \cite{likharev1987single}. While such a scheme can provide the huge benefits in terms of high speed and very low power consumption, its practical implementation faces serious challenges. Firstly, they should be operated at temperature much less than the critical temperature, otherwise a thermally induced tunneling event can change the entire calculation. Secondly, the output of one logic gate (single electron) should be capable of charging the input of following gates. This requires the stray capacitance of interconnections to be kept negligible and complicated design rules for different number of subsequent gates \cite{tucker1992complementary}. 

Single electron transistors (SET) based on silicon have been previously studied in \cite{zhuang1998silicon,kim2002single,samanta2017single}. In order to operate the transistor at room temperature, the size of the island should be less than 5nm \cite{tanahashi2014peak}. The nano-lithography techniques now a days allow to define such small structures with only a few variations. In this work, we simulate and model the SET based on silicon quantum dot with a size of 1nm. We present two novel contributions in this work. i) We simulate Si based SET, for the first time, using Atlas TCAD \cite{manual2014silvaco} with non-equilibrium Green's function (NEGF) technique. The results are comparable to
the experimental results with similar devices. NEGF formalism is a robust technique for the quantum level simulations. Anantram et. al used NEGF technique to model nanodevices \cite{anantram2008modeling}. The transport through quantum dot weakly coupled with the contacts is studied using NEGF technique in \cite{zimbovskaya2008electron}. ii) We propose transmission spectrum based model for the evaluation of SET characteristics. The proposed model, which is the extended version of \cite{mehdy2016efficient}, uses transmission spectrum to calculate the current. It does not need any complex initial set up and is very efficient, simple, sufficiently accurate and flexible to implement in different conditions. In comparison, Monte Carlo based models \cite{wasshuber1997simon} are accurate but very time consuming. Macromodeling based models \cite{yu1999macromodeling}\cite{ghosh2016modified} are efficient but provide a little physical insights on the device behavior. Analytical models based on physics \cite{lee2002practical} and master equation \cite{miyaji2006compact} solve this problem but they still require a complex procedure to calculate tunnel junction resistances and capacitances \cite{mahapatra2004analytical}. These models require the tunnel junction resistances and capacitances as input while the proposed model requires transmission spectrum as input. The transmission spectrum provides insights on the physics of device especially about the density of states of island which lacks in case of other models. We can easily change the model for the variations in contact coupling, gate coupling and density of state variations due to different fabricated size of island. From the transmission spectrum current is calculated using Landauers formula. The rest of the paper is organized as follows. In section II the explanation of the device and simulations are described. In section III the details of proposed model are given. In section IV the results are discussed and the section V concludes the paper.