SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

3.3. TRANSPORT AND SCATTERING 97

Collision

Free flight

Free flight

Collision

Collision

Collision

E

Z = 0 Z

Free flight

CARRIER TRANSPORT IN SEMICONDUCTORS

Figure 3.5: Schematic view of an electron as it moves under an electric field in a semiconductor.
The electron suffers a scattering as it moves. In between scattering the electron moves according
to the “free” electron equation of motion.

of the perfect crystalHoand the energyVcorresponding to the imperfection causing scattering.
Thus
H=Ho+V (3.3.4)
The problem
Hoψ=Eψ (3.3.5)

just gives us the bandstructure of the semiconductor which has been discussed in chapter 2. In
the perturbation theory, we use the approach that the effect of the perturbationV is to cause
scattering of the electron from one perfect crystalline state to another. This theory works well if
the perturbation is small. The effect of the scattering is shown schematically in figure 3.6. The
rate of scattering for an electron initially in stateito a statefin the presence of a perturbation
of the form
V(r, t)=V(r) exp (iωt) (3.3.6)

is given by the Fermi golden rule

Wif=

2 π



|Mij|^2 δ(Ei±ω−Ef) (3.3.7)

where the various quantities in the equation represent the following: