Coulomb Blockade and Single Electron Transistor

1. Coulomb Blockade and Single Electron Transistor Piyush Kumar Sinha Piyush.cuj@gmail.com Centre for Nanotechnology Piyush Kumar Sinha (piyush.cuj@gmail.com)

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

3. Coulomb Blockade Energy required to tunnel Ec = e²/2C = e²/4∏ϵₒϵᵣd 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. Piyush Kumar Sinha (piyush.cuj@gmail.com)

4. Conditions for Coulomb Blockade Piyush Kumar Sinha (piyush.cuj@gmail.com)

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

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

7. An Introduction to Quantum Mechanical Tunneling L L 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 Piyush Kumar Sinha (piyush.cuj@gmail.com)

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

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

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

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

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

13. Designs for Single Electron Transistors Nanoparticle attracted electrostatically to the gap between source and drain electrodes. The gate is underneath. Piyush Kumar Sinha (piyush.cuj@gmail.com)

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

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….

17. e- e- dot Cg Vg Vg  e/Cg Electrons on the dot N-½ N+½ N N-1 Charging a Dot, One Electron at a Time 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+½in that case. The spacing between these half-integer conductance peaks is an integer. Piyush Kumar Sinha (piyush.cuj@gmail.com)

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

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