Lecture 4 - Coulomb blockade & SET Fulton TA and Dolan GJ, Phys. Rev. Lett. 59 (1987) 109.

Circuit for SET transistor 1 V1V1 VgVg V2V2 CgCg C1C1 C2C2 R1R1 R2R2 nanocluster tunnelling junction VCVC Q When an electron tunnels onto or off the cluster already containing n excess electrons, the change in electrostatic energy is: Algebra – first calculate charge on middle island: Rearrange- 1 2

Circuit for SET transistor 2 Electrostatic energy Only term that varies as the charge on the cluster varies. Consider process when 1 charge tunnels onto or off the cluster. 3

Circuit for SET transistor V1V1 VgVg V2V2 CgCg C1C1 C2C2 R1R1 R2R2 nanocluster tunnelling junction VCVC Q When an electron tunnels onto or off the cluster already containing n excess electrons, the change in electrostatic energy is: The work done by the voltage sources when an electron tunnels through the j th junction is:

Circuit for SET transistor 0 VgVg V CgCg C1C1 C2C2 R1R1 R2R2 nanocluster tunnelling junction VCVC Q e-e-

Enthalpy change

Coulomb staircase Electrons fill island until Tunnelling current

Single electron transistor blockade

Experimental Coulomb staircase Wilkins R et al., Phys. Rev. Lett. 63 (1989) 801.