Lesson 5, Part 3: Single electron effects: Coulomb blockade and staircase (Quantum Dots)

Lesson 5, Part 3:

Single electron effects: Coulomb

blockade and staircase (Quantum Dots)

C

R

Coulomb blockade Coulomb Staircase

Thermal smearing

Coulomb staircase

V=0

The constant interaction model

Energetic window depending on L

Constant Interaction model (C indipendent from N)

Constant Interaction model

 

C E Ne

N H

N H

N H

N

l n pot

cin( ) ( ) 2

) (

2

. 





 

N tot

dot E

C N Ne

H N

H

N)  ( )  ( 1)  ² 

 (

C E N e

N N

tot

dot      

 ( ) ( 1) ( ) ²

A simplified and intuitive framework

e/C_eq

e/2C 3e/2C 5e/2C

R=R₁+R₂ R₁ T₁

R₂ T₂

Cotunneling

Application 1: Single Electron Transistor and Memory

0

1

Application 2: NanoSchottky diode

Electronic transport model:

 Thermoionic emission

 Ballistic transport

 Charging Energy (CI)

Au cluster:

3D quantum box

F_m

2R

E₂ E₁

E_F=μ(N)

ΔE

E_V

E_V

E_VB

6H-SiC

E_CBmax

c_s E_CB

F_B0

 F_B0=F_m-c_s F_m(Au)=5.2 eV

c_s(6H-siC)=3.3eV F_B0=1.9 eV AFM tip

R_contact

e^- Thermoionic emission of e^- from substrate to nanocluster

Δμ

μ(N+1)

E_V

E_VB

6H-SiC

E_CBmax c_s

E_CB

F_B

 F_B(R)= F_B0 –(R) AFM tip

E_vacuum

E_V

E_VB

6H-SiC

E_CBmax c_s

E_CB e^-

Ballistic transport within the nanocluster

e^-

Ohmic contact tip-nanocluster e^-

Thermoionic emission of e^- from substrate to nanocluster

Size Effect:

How a bulk (macroscopic) property derives from the

microscopic one

1.85 eV SBH of the macroscopic contact Au/6H-SiC

1 2 3 4 5 6 7

1.3 1.4 1.5 1.6 1.7 1.8

F B

( eV )

2<R> (nm)