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

CRCR

Coulomb blockade Coulomb Staircase

Thermal smearingCoulomb staircase

V=0

The constant interaction model

Energetic window depending on L Constant Interaction model (C indipendent from N) Constant Interaction model

A simplified and intuitive framework

e/C eq

e/2C 3e/2C 5e/2C R=R 1 +R 2 R 1  T 1 R 2  T 2

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 mm 2R E2E2 E1E1 E F =μ(N) ΔEΔE EVEV EVEV E VB 6H-SiC E CBmax ss E CB  B0   B0 =  m -  s  m (Au)=5.2 eV  s (6H-siC)=3.3eV  B0 =1.9 eV AFM tip R contact e-e-  Thermoionic emission of e - from substrate to nanocluster Δμ μ(N+1) EVEV E VB 6H-SiC E CBmax ss E CB BB   B (R) =  B0 –  (R) AFM tip E vacuum EVEV E VB 6H-SiC E CBmax ss E CB e-e-  Ballistic transport within the nanocluster e-e-  Ohmic contact tip-nanocluster e-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