Master Equation - Based Numerical Simulation in a Single Electron Transistor Using Matlab

Abstract

Recent modern fabrication technology allows us for the fabrication of nanometer-scaled devices, which is possible to observe single electronic or single electron tunneling phenomena (Averin & Likharev, 1991; Likharev, 1988; Likharev, 1999; Hanna et al., 1991; Tucker, 1992). On the other hand, MOSFET (metal-oxide-semiconductor field effect transistor) devices with channel length below 20 nanometer (nm) are no more properly operated because the downscaling of MOS devices causes a large statistical fluctuation of the threshold voltage. A possible approach to overcome this problem is to use the single electron devices for future VLSI (very large scale integrated circuit) (Takahashi et al., 1995; Saitoh et al., 2001). Nanometer scale single electron devices have the following features, i.e., low power consumption and small size. These are key features to realize ultra high density circuits. Single electron circuits with new architecture are also possible because the basic operation of single electron devices is quite different from that of conventional semiconductor devices. There are two major requirements for single electron tunneling phenomena (Coulomb blockade) to occur (Averin & Lhikarev, 1991; Likharev, 1988; Likharev, 1999). Firstly, thermal energy 倦喋劇 must be much smaller than elemental charging energy 結態 に系 ⁄ . This ensures that the transport of charges is in fact governed by the Coulomb charging energy. This condition can be fulfilled either by lowering the temperature or by decreasing the capacitance which means to reduce the island size. Usually, experiments are performed at temperatures of a few mK and for structures with island sizes of a few hundred nanometers. Second requirement is related to tunnel resistance which must exceed the quantum resistance (h ね結態 ⁄ ≈ は.の kΩ). This condition ensures that the wave functions of excess electrons between the barriers are basically localized. On the other word, in the case of lower tunnel resistance, excess charges extend over the barriers so that no single electron tunneling event can be possible. There are several types of circuits where the single electron tunneling phenomena are being explored, such as single electron box (Likharev, 1999), single electron transistor (SET) (Tucker, 1992; Takahashi et al., 1995; Saitoh et al., 2001; Wolf et al., 2010; Sun et al., 2011; Lee et al., 2009), single electron pump (Ono et al., 2003), single electron turnstile (Moraru et al., 2011) and single electron circuits with several junctions (1D and 2D arrays) (Nuryadi et al., 2003; Nuryadi et al., 2005). A double junction system is most important single electron circuit because of a basic component of SET. At small applied voltage, the system remains in the Coulomb blockade state, and no current flows through the double junctions. On the other hand, at higher applied