single electron transistor and coulomb blockade effect

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Coulomb Blockade and Single

Electron Transistor

Piyush Kumar [email protected]

Centre for Nanotechnology

1/29/2012 7:41 AM 1Piyush Kumar Sinha([email protected])



Outline of the project.

Introduction to Coulomb Blockade.

Conditions for Coulomb Blockade.

Single Electron Transistor: An Introduction. Operation of Single Electron Transistor.

Applications.

Summary.

1/29/2012 7:41 AM PiyushKumar Sinha([email protected])

2

PiyushKumar Sinha

([email protected])



Coulomb Blockade

1/29/2012 7:41 AM Piyush Kumar Sinha([email protected])

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Blocking the chargetransport (Tunneling)through the structure.

The increasedresistance at smallbias voltages of anelectronic device

comprising at leastone low capacitancetunnel junction.

Energy required to tunnel

Ec = e²/2C

= e²/4d



Conditions for Coulomb Blockade

Charging energy should be greater than thermal energy (e2/2C>KT)

Low temperature (T 1K)

Conductive island (nanostructure) should be in nanometer range(1-3 nm)

Low capacitance,High Contact Resistance.

Quantum Confinement.


4



Lifting The Blockade:


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If the charging energy is greater than the thermal

energy, Coulomb Blockade takes place.

However, Coulomb Blockade can be lifted if enoughenergy is supplied by applying a bias over the

structure.

For V>e/2c,conductance starts to rise.



Cont..

The average charge

on the Nanostructure

(island) increases insteps as the voltages

is increased

1/29/2012 7:41 AM 6PiyushKumar Sinha([email protected])



An Introduction to Quantum Mechanical

Tunneling

Quantum mechanics allows a small particle, such as an electron, to overcome apotential barrier larger than its kinetic energy.

Tunneling is possible because of the wave-like properties of matter.

Transmission Probability: T 16(1 )e-2L

L L




The Tunneling Phenomenon

In classical mechanics, the energy of an electron moving in a potential U(x) can be shown by p

mU x Ex

2

2 !

The quantum mechanical description of the same electron is ( ) ( ) ( )H x U x E xx] ] ] !

In the classically allowed region (E>U), there are two solutions,

] ]( ) ( ) ,x em E U

ikx! !

s

02

where k J

These give the same result as the classical case. However, in the classically forbidden region (E<U) the solution is

] ] O

O( ) ( ) ,x e

m U Ex! !

02

whereJ

O is a decay constant, so the solution dictates that the wave function decays in the +x direction, and the probability

of finding an electron in the barrier is non-zero.

[Chen, C.J. In Introduction to Scanning Tunneling Microscopy; Oxford University Press: New York, 1993; p 3].




What is a Transistor

A transistor is a solid state semiconductor device

which can be used for numerous purposes including

signal modulation, amplification, voltage

stabilization, and many others.

Transistors act like a variable valve which, based on

its input current (BJT) or input voltage (FET), allow a

precise amount of current to flow through it from

the circuits voltage supply.




Single Electron Transistor

How is it different from a simpletransistor?

what problem does it help to solve?

what is its operation?

How to design a SET?




Introduction to Single Electron

Transistor:

It consists of two tunnels

Junctions sharing one

Common electrode known

as island. A charge can be

induced on island by a third

Electrode (gate) capacitively

coupled to the island.




What Happens in SET..??

A single electron transistoris similar to a normaltransistor, except

1) the channel is replaced by a small dot.

2) the dot is separated from source anddrain by thin insulators.

An electron tunnels in two steps:sourcep dotp drain

The gate voltage Vg is used to control

the charge on the gate-dot capacitor Cg .

How can the charge be controlled withthe precision of a single electron?


12



Nano particle attr acted

electr ostatically to the

ga p between source

and dr ain electr odes.

The gate is under neath.

Designs for

Single Electron Transistors




Operation

The tunnel junction consists of two pieces of metal

separated by a very thin (~1nm) insulator.

The only way for electrons in one of the metal

electrodes to travel to the other electrode is totunnel through the insulator.

Since tunneling is a discrete process, the electric

charge that flows through the tunnel junction flows

in multiples of the charge of electrons e.




Working:

Total capacitance

of the island

C=CS+CD+CG

The electrostatic energy of the

island in this model

E(N,Q G)=(Ne-Q G)2/2C

where N =number of electron on the island,

e =electronic charge and gate charge

Q G=CDVD+CGVG+CSVS



Cont.

Gate charge Q G can be varied by external voltage source in the coulomb blockade regime.

Quantization of charge on the island.

For different gate voltages the island may be occupied by different number of electrons.

The gate voltages can be used to tune the number of electrons on island.

The charge can fluctuate If E(N+1,Q G)=E(N,Q G)

i.e. energy for two successive occupation numbers are degenerate, then coulomb blockade is liftedand charges can be added to or removed from the dot. Conductance of the dot becomes finite.

The gate charge leads to the condition for charge fluctuation Q G=(N+1/2)e



Charging a Dot, One Electron at a Time

Sweeping the gate voltage Vg changes

the charge Q g on the gate-dot

capacitor Cg . To add one electronrequires the voltage (Vg}e/Cg since

Cg=Q g/Vg.

The source-drain conductance G is zero

for most gate voltages, because putting

even one extra electron onto the dot

would cost too much Coulomb energy.

This is called Coulomb blockade.

Electrons can hop onto the dot only at a

gate voltage where the number of

electrons on the dot flip-flops between

N and N+1.Their time-averaged number

is N+½ in that case.

The spacing between these half-integer

conductance peaks is an integer.

dot

(Vg }

e/Cg

Electronson the dot

N-½ N+½

Cg

e- e-

Vg

NN-1




Applications of SETs

Quantum computers

± 1000x faster

Microwave Detection

± Photon Aided Tunneling

High Sensitivity Electrometer

± Radio-Frequency SET




Summary


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single electron transistor and coulomb blockade effect

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