1. Coulomb Blockade and Single Electron Transistor
Piyush Kumar Sinha
12/2/2018
Coulomb Blockade and Single Electron Transistor XX
Piyush Kumar Sinha
Centre for Nanotechnology
12/2/ :05 AM
Piyush Kumar Sinha

2. Piyush Kumar Sinha (piyush.cuj@gmail.com)
12/2/2018
Piyush Kumar Sinha
Outline of the project.
Introduction to Coulomb Blockade.
Conditions for Coulomb Blockade.
Single Electron Transistor: An Introduction.
Operation of Single Electron Transistor.
Applications.
Summary.
12/2/ :05 AM
Piyush Kumar Sinha

3. Piyush Kumar Sinha (piyush.cuj@gmail.com)
12/2/2018
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 tunnel
Ec = e²/2C
= e²/4∏ϵₒϵᵣd
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Piyush Kumar Sinha

4. 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.
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Piyush Kumar Sinha

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

6. Piyush Kumar Sinha (piyush.cuj@gmail.com)
Cont…..
The average charge
on the Nanostructure
(island) increases in
steps as the voltages
is increased
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Piyush Kumar Sinha

7. 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
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Piyush Kumar Sinha

8. Piyush Kumar Sinha (piyush.cuj@gmail.com)
The Tunneling Phenomenon
[Chen, C.J. In Introduction to Scanning Tunneling Microscopy; Oxford University Press: New York, 1993; p 3].
In classical mechanics, the energy of an electron moving in a potential U(x) can be shown by
The quantum mechanical description of the same electron is
In the classically allowed region (E>U), there are two solutions,
These give the same result as the classical case. However, in the classically forbidden region (E<U) the solution is
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.
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Piyush Kumar Sinha

9. Piyush Kumar Sinha (piyush.cuj@gmail.com)
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.
12/2/ :05 AM
Piyush Kumar Sinha

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

11. 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.
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Piyush Kumar Sinha

12. Piyush Kumar Sinha (piyush.cuj@gmail.com)
What Happens in SET..??
A single electron transistor is similar to a normal transistor, except
the channel is replaced by a small dot.
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?
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Piyush Kumar Sinha

13. Designs for
Single Electron Transistors
Nanoparticle attracted electrostatically to the gap between source and drain electrodes.
The gate is underneath.
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Piyush Kumar Sinha

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

15. Working: Total capacitance of the island C=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

16. Cont…. Quantization of charge on the island.
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

17. Piyush Kumar Sinha (piyush.cuj@gmail.com)
Charging a Dot, One Electron at a Time
dot
Vg  e/Cg
Electrons
on the dot
N-½ N+½ Cg e- Vg N
N-1
Sweeping 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.
This picture is for a small negative source voltage (and an equally small positive drain voltage) which draws electrons from source to drain. Both voltages are assumed to be negligible compared to the gate voltage.
12/2/ :05 AM
Piyush Kumar Sinha

18. Piyush Kumar Sinha (piyush.cuj@gmail.com)
Applications of SETs
Quantum computers
1000x faster
Microwave Detection
Photon Aided Tunneling
High Sensitivity Electrometer
Radio-Frequency SET
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Piyush Kumar Sinha

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