SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

98 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

How strongly V(r) couples

the initial and final states

How many final states there

are to scatter into

SCATTERING RATE

Initial electron Final electron

SCATTERING POTENTIAL

V(r)

k k'

+

Figure 3.6: Scattering of an electron initially with momentumkfrom a scattering potential
V(r). The final momentum isk′. The scattering process is assumed to be instantaneous.

•|Mij|^2 : The quantity is called the matrix element of the scattering and is given by

Mij=

∫

ψf∗V(r)ψid^3 r (3.3.8)

The matrix element tells us how the potential couples the initial and the final state. A stronger
coupling causes a higher rate of scattering.

• δ(Ei±ω−Ef):Thisδ-function is simply a representative of energy conservation. The
  process where

Ef=Ei+ω (3.3.9)

is called absorption, while the process

Ef=Ei−ω (3.3.10)