World Journal of Nano Science and Engineering, 2012, 2, 171-175

http://dx.doi.org/10.4236/wjnse.2012.24022 Published Online December 2012 (http://www.SciRP.org/journal/wjnse)

New Model for Drain and Gate Current of Single-Electron

Transistor at High Temperature

Amine Touati, Samir Chatbouri, Nabil Sghaier, Adel Kalboussi

Laboratory of Microelectronics and Instrumentation, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia

Email: Amine.Touati@istls.rnu.tn

Received May 28, 2012; revised June 6, 2012; accepted July 3, 2012

ABSTRACT

We propose a novel analytical model to describe the drain-source current as well as gate-source of single-electron tran-

sistors (SETs) at high temperature. Our model consists on summing the tunnel current and thermionic contribution. This

model will be compared with another model.

Keywords: Single-Electron Transistor (SET); Master Equation; Orthodox Theory; Tunnel Current; Thermionic Current;

SIMON

1. Introduction

The phenomenal success of semiconductor electronics

during the past three decades was based on the scaling

down of silicon field effect transistors (MOSFET). The

most authoritative industrial forecast, the International

Technology Roadmap for Semiconductors (ITRS) [1]

predicts that this exponential progress of silicon MOS-

FETs and integrated circuits will continue at least for the

next 15 years (“Moore’s Law”) [2]. However, prospects

to continue the Moore law, a very important device: the

single-electron transistor was first suggested in 1985 and

first implemented two years later. This device attracted

much attention because of their nano feature size and less

power consumption. Moreover SETs are suitable for

several applications such as memories, multiple-valued

logic (MVL)… due to the discrete number of electrons in

a coulomb island.

SETs characteristics are very different from those of

MOSFETs. In both of them, electrostatic effects are

dominant, but, due to the existence of Coulomb blockade;

electrons are not so free to move from source to drain,

due to of tunnel junctions. The Coulomb blockade effect:

that is the electrostatic repulsion experienced by an elec-

tron approaching a small negatively charged region, lim-

its the number of electrons in the island. As a result, for

given values of gate and drain voltages, only a range of

charge is possible for tunneling.

Our day extensive research has been conducted on

fabrication, design, and modeling of SET, that has also

been an active area. Monte Carlo simulation has been

widely used to model SETs. SIMON [3] and MOSES [4]

are two most popular SET simulators for circuit analysis

and systems containing more than a few SETs but vali-

dated in ambient temperature range. Several SET ana-

lytical models, each of them based on the orthodox the-

ory, can notably name the models proposed for metallic

SETs by the following:

Uchida et al. [5] proposed an analytical SET model

for resistively symmetric devices (RS = RD) and valid

for DS

VeC

, later Inokawa et al. [6] extended

this model to asymmetric SETs but does not account

for the background charges effect.

Recently a compact analytical model (named MIB) [7]

for SET device, which is applicable for 3

DS

VeC

and wide-range of temperature, and valid for single/

multiple gate symmetric/asymmetric device, is taken

that the only one direction flow to minimize the num-

ber of exponential terms. MIB model can be used for

both digital and analog SET circuit design and for

both pure SET and hybrid CMOS-SET circuit simula-

tion.

CΣ represents the total capacitance of the SET-island:

1SDGG

CCCC C

2

(1)

CG1, CG2, CD and CS represent the capacitances of first

gate, second gate (when exists), tunnel drain and tunnel

source junctions respectively.

Two conditions ensure that the transport of charges

through the metallic island is governed by:

1) Charging the island with an additional charge takes

the time Δt = RTC, which is the RC-time constant of the

quantum dot.

2) The charging energy required to add a single elec-

tron with charge e to the quantum dot is: ΔEC = e²/CΣ.

The system will respect Heisenberg’s uncertainty relation:

C

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