Advanced Solid State Physics

Figure 85: STM picture of GaAs doped with Si at Ga-sites.

12.2 Single electron effects

12.2.1 Tunnel Junctions

A tunnel junction looks like in fig. 86 where two metals are separated with an insulating barrier where
a bias voltage is applied. The tunnel junction can be described by a Hamiltonian

H=Hl+Hr+HT

that consists of the HamiltonianHlandHrof the electrons on the left and right side, and of the
tunnelling-Hamiltonian which describes the tunnelling from left to right and contains the height and
width of the barrier. Fermi’s golden rule gives the rate of electrons tunnelling through the barrier

metal insulator metal

eV

Figure 86: Tunnel junction.

Γl→r=

2 π

~

|〈l|HT|r〉|^2 δ(El−Er). (184)

Theδ-function shows you that the energy of the electron has to be the same before and after the
tunnelling. Therefore only electrons in the energy range between the dashed and the solid line can