Single Electron Transistor

Seminar 2010 SET

ABSTRACT

Single electron transistor (SET) is a novel idea and has been intensively studied.

This review gives a general picture of SET, such as its mechanism, fabrication,

application and problems faced.

During 1980s, the main discoveries in mesoscopic physics are the

tunneling of single electron and Coulomb blockade phenomena, which make many

scientists predict that if the size of the quantum dots is reduced to several

nanometers, it is highly possible to produce applicable single electron transistor

(SET) which works above liquid nitrogen temperature, and this will bring a

revolution to electronic science. Since then SET has been a hot research area. The

breakthrough of nanotech as well as its successful combination with semiconductor

technologies gives hope to SET, and some think that it will be a mature technique

in the coming decade.

DEPT OF ECE 1 ICET MUVATTUPUZHA

Seminar 2010 SET

1. INTRODUCTION

A conventional field-effect transistor, the kind that makes all modern

electronics work, is a switch that turns on when electrons are added to a

semiconductor and turns off when they are removed. These on and off states give

the ones and zeros that digital computers need for calculation. One then has a

transistor that turns on and off again every time one electron is added to it; we call

it a single electron transistor (SET). Furthermore, the behavior of the device is

entirely quantum mechanical.

Electron transport properties of individual molecules have received

considerable attention over the last several years due to the introduction of single-

electron transistor (SET) devices which allow the experimenter to probe electronic,

vibrational or magnetic excitations in an individual molecule. In a three-terminal

molecular SET the molecule is situated between the source and drain leads with an

insulated gate electrode underneath. Current can flow between the source and drain

leads via a sequential tunneling process through the molecular charge levels, which

the gate electrode is used to tune.


Seminar 2010 SET

2.HISTORY OF SET

The effects of charge quantization were first observed in tunnel

junctions containing metal particles as early as 1968. Later, the idea that the

Coulomb blockade can be overcome with a gate electrode was proposed by a

number of authors, and Kulik and Shekhter developed the theory of Coulomb-

blockade oscillations, the periodic variation of conductance as a function of gate

voltage. Their theory was classical, including charge quantization but not energy

quantization. However, it was not until 1987 that Fulton and Dolan made the first

SET, entirely out of metals , and observed the predicted oscillations. They made a

metal particle connected to two metal leads by tunnel junctions, all on top of an

insulator with a gate electrode underneath. Since then, the capacitances of such

metal SETs have been reduced to produce very precise charge quantization .The

first semiconductor SET was fabricated accidentally in 1989 by Scott-Thomasetal.

In narrow Si field effect transistors. In this case the tunnel barriers were produced

by interface charges.


Seminar 2010 SET

3. SET SCHEMATIC REPRESENTATION

A model of SET is shown in Fig.1,(b) is the simplified model.

Figure(1)

A schematic circuit of SET

The two areas filled with patched pattern are tunneling junctions;

there are some discrete Coulomb islands between them. R1, C1 and R2, C2 are the

resistance and capacitance of the junctions. The junctions form the source and drain

of the transistor, 2 / V voltages are applied to them through conductive wires, the

tunneling current pass through the islands is I. A layer of insulating media separates

the islands from the gate; the capacitance between them is Cg. A voltage of Vg is

applied on the gate and controls the open or close of the SET. Because of its unique

structure, SET has many prospective characteristics such as low power


Seminar 2010 SET

consumption, high sensitivity, high switching speed, high packet density, etc. So

much attention has been attracted on their fabrication and industrial realization.

Fig (2) Schematic diagram of SET


Seminar 2010 SET

4. WORKING OF SET

The single electron transistor is a new type of switching device that uses

controlled electron tunneling to amplify current. Conduction through a molecular

SET only occurs when a molecular electronic level lies between the Fermi energies

of the leads. A bias voltage, V bias, applied between the source and the drain,

changes the electrostatic potential of one of the leads by an energy |eV|. For small

bias voltages, |eV| < Ec + ∆E where Ec is the Coulomb charging energy and ∆E is

the energy difference between consecutive charge states of the molecule being

measured, current cannot flow though the device because the excited molecular

levels are not available to conduct charges between the electrodes. This is known as

the Coulomb blockade regime.

Fig (3) Schematic of a single electron transistor


http://en.wikipedia.org/wiki/File:Set_schematic.svg

Seminar 2010 SET

If bias voltages, |eV| > Ec + ∆E where Ec is the Coulomb charging energy

and ∆E is the energy difference between consecutive charge states of the molecule

being measured, current can flow though the device.

Usually electrons move continuously in the common

transistors, but as the size of the system goes down to nanoscale (for example, the

size of metal atoms can be several nm, and the size of semi-conductive particles

can be several tens nm), the energy of the system is quantumized, that is, the

process of charging and discharging is discontinuous.

The energy for one electron to move into the system is:

EC=e2/2C

where C is the capacitance of this system. This Ec is called Coulomb blockade

energy, which is the repelling energy of the previous electron to the next electron.

For a tiny system, the capacitance C is very small, thus Ec can be very high, and the

electrons cannot move simultaneously, but must pass through one by one. This

phenomenon is called "Coulomb blockade".

If two quantum dots(QD) are joined at a point and form a

channel, it is possible for an electron to pass from one dot over the energy barrier

and move to the other dot, this is called "tunneling phenomenon". In order to

overcome the barrier (Ec), the applied voltage on the quantum dots (V/2) should be

V > e/C

Quantum tunnelling

It refers to the quantum mechanical phenomenon where a particle tunnels through a

barrier that it classically could not surmount because its total mechanical energy is

lower than the potential energy of the barrier. This tunnelling plays an essential role

in several physical phenomena, including radioactive decay and has important

applications to modern devices such as the tunneling diode and the scanning

tunnelling microscope.


Seminar 2010 SET

COULOMB ISLAND

Fig (4) Coulomb Island


Seminar 2010 SET

(a)When a capacitor is charged through a resistor, the charge on the capacitor is

proportional to the applied voltage and shows no sign of quantization.

(b) When a tunnel junction replaces the resistor, a conducting island is formed

between the junction and the capacitor plate. In this case the average charge on the

island increases in steps as the voltage is increased

c) The steps are sharper for more resistive barriers and at lower temperatures.

A signature of this phenomenon is commonly seen at low

temperatures as an absence of current for low bias voltages. As the bias voltage

across the device increases, excited states will provide conduction channels in the

device. As a result, discrete changes in the current through the SET will be obtained

every time a new molecular level falls within the bias window.

The simplest device in which the effect of Coulomb

blockade can be observed is the so-called single electron transistor. It consists of

two tunnel junctions sharing one common electrode with a low self-capacitance,

known as the island. The electrical potential of the island can be tuned by a third

electrode (the gate), capacitively coupled to the island.

In the blocking state no accessible energy levels are within

tunneling range of the electron (red) on the source contact. All energy levels on the

island electrode with lower energies are occupied.

When a positive voltage is applied to the gate electrode the

energy levels of the island electrode are lowered. The electron (green 1.) can tunnel

onto the island (2.), occupying a previously vacant energy level. From there it can

tunnel onto the drain electrode (3.) where it in elastically scatters and reaches the

drain electrode Fermi level (4.).


http://en.wikipedia.org/wiki/Capacitance#Self-capacitance

Seminar 2010 SET

The energy levels of the island electrode are evenly spaced with a

separation of ΔE. ΔE is the energy needed to each subsequent electron to the island,

which acts as a self-capacitance C.

The lower C the bigger ΔE gets. To achieve the Coulomb blockade, three criteria

have to be met:

The bias voltage can't exceed the charging energy divided by the capacitance

Vbias = ;

The thermal energy kBT must be below the charging energy EC = , or else

the electron will be able to pass the QB via thermal excitation;

The bias voltage can't exceed the charging energy divided by the

capacitance Vbias = ;

The thermal energy kBT must be below the charging energy EC = , or else

the electron will be able to pass the QB via thermal excitation.

The single-electron transistor shows that its dc I-V curves may be quite

complex [50]. However, the situation at small source-drain voltage is much

simpler. In fact, Fig. 6c shows that on each period of the Coulomb blockade

oscillations there is one special point Qe = e(n + 1/2), at which the Coulomb

blockade is completely suppressed, and the I-V curve has a finite slope at low

voltages Fig. 6b). Another way to express the same property is to say that the

linear conductance G º dI/dV½V=0 of the transistor as a function of the gate U

voltage exhibits sharp peaks. Theory shows that even if the electron quantization

effects are substantial, the peak position may be found from a very natural

"resonance tunneling" an energy level inside the island (with the account of the


Seminar 2010 SET

gate field potential)should be aligned with the Fermi levels in source and drain,

which coincide at VÆ0. This rule yields a simple equation for the gate voltage

distance between the neighboring Coulomb blockade peaks

If the charging effects dominate (Ec >> Ek) this

relation is reduced,but at strong quantization (Ek >> Ec) the distance between the

Coulomb blockade oscillation peaks, as well as the heiGmax of the peaks, may

vary from level to level.


Seminar 2010 SET

5. FABRICATION OF SET

The fabrication of SET promotes many difficulties. For SET to

be used in a large scale industrially and position. Basically the fabrication methods

can be divided as physical or chemical techniques according to the main

procedures.

The physical methods often utilize the combination of thin film and

lithographic technologies. Devices with carefully tailored geometries and electron

density are got. For example, quantum dots or quasi-zero-dimensional puddles of

electrons with weak coupling to simultaneously patterned electrical leads are

fabricated to form a SET. However, lithographic and materials limitations restrict

the minimum size and composition of such dots (100nm), and studies are typically

limited to sub-Kelvin temperatures.

Another approach is to grow nanostructures chemically. This approach is

prosperous for its low cost and good controllability of the size of Coulomb islands,

and it is possible to be a prospective technique. Though this technique is not mature

industrially, the SET s fabricated in laboratories show fascinating results. Generally

there are three most important steps: first, the fabrication of Coulomb islands as

well as the control of their size and dispersity; second, the formation of tunneling

junctions at the joint of electrodes and Coulomb island; third, the formation of gate

between substrate and Coulomb islands.


Seminar 2010 SET

6. APPLICATIONS

SET has found many applications in many areas. What's most exciting is the

potential to fabricate them in large scale and use them as common units in modern

computer and electronic industry.

SINGLE ELECTRON MEMORY

Scientists have long been endeavored to enhance the capacity of memory

devices. If single electron memory can be realized, the memory capacity is possible

to reach its utmost limit. SET can be used as memory cell since the state of

Coulomb island can be changed by the existence of one electron. Chou and Chan

[5] first pointed out the possibility of using SET as memories in which information

is stored as the presence or absence of a single electron on the cluster. They

fabricated a SET by embedding one or several nano Si powder in a thin insulating

layer of SiO2, then arranging the source and drain as well as gate around this

Coulomb island. The read/write time of Chan's structure is about 20ns, lifetime is

more than 109 cycles, and retention time (during which the electron trapped in the

island will not leak out) can be several days to several weeks. These parameters

would satisfy the standards of computer industry, so SET can be developed to be a

candidate of basic computer units. If a SET stands for one bit, then an array of 4~7

SETs will be substantial to memorize different states. The properties of the memory

unit composed of SETs are far more advantageous than that of CMOS. But the

disadvantage is the practical difficulty in fabrication. When the time comes for the

large scale integration of SETs to form logic gates, the full advantages of single

electron memory will show. This is the threshold of quantum computing.


Seminar 2010 SET

HIGH SENSITIVITY ELECTROMETER

The most advanced practical application currently for SETs is probably the

extremely precise solid-state electrometers (a device used to measure charge). The

SET electrometer is operated by capacitively coupling the external charge source to

be measured to the gate. Changes in the SET source-drain current are then

measured. Since the amplification coefficient is very big, this device can be used to

measure very small change of current. Experiments showed that if there is a charge

change of e/2 on the gate, the current through the Coulomb island is about 109

e/sec. This sensitivity is many orders of magnitude better than common

electrometers made by MOSFIT. SETs have already been used in metrological

applications as well as a tool for imaging localized individual changes in

semiconductors. Recent demonstration of single photon detection and RF

operation of SETs make them exciting for new applications ranging from

astronomy to quantum computer read-out circuitry. The SET electrometer is in

principle not limited to the detection of charge sites on a surface, but can also be

applicable to a wide range of sensitive chemical signal transduction events as well.

For example, the gate can be made coupling with some molecules, thus can

measure other chemical properties during the process.

If the device under test has a large capacitance, it is not advantageous to use

SETs as an electrometer. Since for a typical SET, F CSET m 1 <, the suppression

factor becomes unacceptable when the macroscopic device has a capacitance in the

pF or nF range. Therefore, SET amplifiers are not currently used for measuring real

macroscopic devices. Other low-capacitance electrometers such as a recently

proposed quantum point contact electrometer also suffer from a similar capacitance

mismatch problem. But it is believed that if the capacitance mismatch can be solved

efficiently, SETs may find many new ultralow-noise analog applications.


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MICROWAVE DETECTION

If a SET is attacked black body radiation, the photon-aided tunneling will

affect the charge transfer of the system. Experiments show that the electric

character of the system will be changed even by a tiny amount of radiation. The

sensitivity of this equipment is about 100 times higher than the current best thermal

radiation detector.


Seminar 2010 SET

7. ADVANTAGES AND DISADVANTAGES

ADVATAGES

Small size.

Low energy consumption.

And high sensitivity

DISADVANTAGES

Integration of SETs in a large scale

As has been mention above, to use SETs at room temperature, large

quantities of monodispersed Nan particles less than 10nm in diameter must be

synthesized. it is very hard to fabricate large quantities of SETs by traditional

optical lithography and semiconducting process.

Linking SETs with the outside environment

Practical difficulty in fabrication


Seminar 2010 SET

8. CONCLUSION

Researchers may someday assemble these transistors into

molecular versions of silicon chips, but there are still formidable hurdles to cross.

SETs could be used for memory device, but even the latest SETs suffer from

“offset charges”, which means that the gate voltage needed to achieve maximum

current varies randomly from device to device. Such fluctuations make it

impossible to build complex circuits. The future does look bright for these devices.


Seminar 2010 SET

9. REFERENCE

M. N. Leuenberger and E. R. Mucciolo, Phys. Rev. Lett. 97, 126601 (2009).

C. Romeike, M. R. Wegewijs, and H. Schoeller, Phys. Rev. Lett. 96, 196805

(2008).

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Single Electron Transistor