Lecture 4 Coulomb blockade

1
Lecture 4 - Coulomb blockade SET
Fulton TA and Dolan GJ, Phys. Rev. Lett. 59
(1987) 109.
2
Circuit for SET transistor 1
V1
When an electron tunnels onto or off the cluster
already containing n excess electrons, the change
in electrostatic energy is
tunnelling junction
C1
R1
VC
Vg
nanocluster
Q
Cg
tunnelling junction
C2
R2
V2
Algebra first calculate charge on middle island
1
Rearrange-
2
3
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
4
Circuit for SET transistor
V1
When an electron tunnels onto or off the cluster
already containing n excess electrons, the change
in electrostatic energy is
tunnelling junction
C1
R1
VC
Vg
nanocluster
Q
Cg
tunnelling junction
C2
R2
V2
The work done by the voltage sources when an
electron tunnels through the jth junction is
5
Circuit for SET transistor
0
tunnelling junction
C1
R1
e-
VC
Vg
nanocluster
Q
Cg
tunnelling junction
C2
R2
V
6
Enthalpy change
7
Coulomb staircase
Electrons fill island until
Tunnelling current
8
Single electron transistor
blockade
9
Experimental Coulomb staircase
Wilkins R et al., Phys. Rev. Lett. 63 (1989) 801.