Coulomb Blockade and Single Electron Transistor

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Coulomb Blockade and Single Electron Transistor

Piyush Kumar SinhaPiyush.cuj@gmail.com

Centre for Nanotechnology

04/19/2023 09:01 PM 2

Outline of the project.

• Introduction to Coulomb Blockade.• Conditions for Coulomb Blockade.• Single Electron Transistor: An Introduction.• Operation of Single Electron Transistor.• Applications.• Summary.

Piyush Kumar Sinha (piyush.cuj@gmail.com)

Piyush Kumar Sinha (piyush.cuj@gmail.com)

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Coulomb Blockade• Blocking the charge

transport (Tunneling) through the structure.

• The increased resistance at small bias voltages of an electronic device comprising at least one low capacitance tunnel junction.

Energy required to tunnelEc = e²/2C

= e²/4∏ϵₒϵᵣd

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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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.

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Lifting The Blockade:

If the charging energy is greater than the thermal energy, Coulomb Blockade takes place.

However, Coulomb Blockade can be lifted if enough energy is supplied by applying a bias over the structure.

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

04/19/2023 09:01 PM 6

Cont…..

• The average charge on the Nanostructure (island) increases in steps as the voltages is increased

Piyush Kumar Sinha (piyush.cuj@gmail.com)

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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An Introduction to Quantum Mechanical Tunneling

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

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

Transmission Probability: T ≈ 16ε(1 – ε)e-2κL

L L

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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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 Uikx

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where k

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

( ) ( ) ,x e

m U Ex 0

2 where

k 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].

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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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 circuit’s voltage supply.

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Single Electron Transistor

How is it different from a simple transistor?

what problem does it help to solve?

what is its operation?

How to design a SET?

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Introduction to Single Electron Transistor:

It consists of two tunnelsJunctions sharing oneCommon electrode knownas island. A charge can beinduced on island by a third Electrode (gate) capacitivelycoupled to the island.

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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What Happens in SET..??

A single electron transistor is similar to a normal transistor, except

1) the channel is replaced by a small dot.

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

An electron tunnels in two steps: source dot drain

• The gate voltage Vg is used to control the charge on the gate-dot capacitor Cg .

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

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Nanoparticle attracted electrostatically to the gap between source and drain electrodes.The gate is underneath.

Designs for Single Electron Transistors

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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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 to tunnel 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 capacitanceof the islandC=CS+CD+CG

The electrostatic energy of the island in this model E(N,QG)=(Ne-QG)2/2C where N =number of electron on the island, e =electronic charge and gate charge QG=CDVD+CGVG+CSVS

Cont….

Gate charge QG 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,QG)=E(N,QG) i.e. energy for two successive occupation numbers are degenerate, then coulomb blockade is lifted and 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 QG=(N+1/2)e

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Charging a Dot, One Electron at a TimeSweeping the gate voltage Vg changes the charge Qg on the gate-dot capacitor Cg . To add one electron requires the voltage Vg e/Cg since Cg=Qg/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

Electrons on the dot

N-½ N+½

Cg

e- e-

Vg

NN-1

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Applications of SETs

• Quantum computers– 1000x faster

• Microwave Detection– Photon Aided Tunneling

• High Sensitivity Electrometer– Radio-Frequency SET

04/19/2023 09:01 PM Piyush Kumar Sinha (piyush.cuj@gmail.com)

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Summary