SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

3.3. TRANSPORT AND SCATTERING 101

Atomic

displacement

Bandedge

positions

EC

r

EV

LATTICE VIBRATIONS

BANDEDGE VIBRATIONS

Figure 3.8: A schematic showing the effect of atomic displacement due to lattice vibrations on
bandedge energy levels in real space.

each other
Vop=Dou (3.3.15)

whereDo(units are eV/cm) is the optical deformation potential.
In compound semiconductors the two atoms on the basis are different and there is an effective
positive and negative chargee∗on each atom. When optical vibrations take place, the effective
dipole in the unit cell vibrates, causing polarization fields from which the electron scatters. This
scattering, called polar optical phonon scattering, has a scattering potential of the form

Vpo∼e∗u (3.3.16)

Each material has its own effective charge which is related to the ionicity of the material.
By using the Fermi golden rule we can calculate the scattering rates of electrons due to lattice
vibrations. The acoustic acoustic phonon scattering rate for an electron with energyEkto any
other state is given by

Wac(Ek)=

2 πD^2 kBTN(Ek)

ρv^2 s

(3.3.17)

whereN(Ek)is the electron density of states,ρis the density of the semiconductor,vsis the
sound velocity andTis the temperature.
In materials like GaAs, the dominant optical phonon scattering is polar optical phonon scatter-
ing, and the scattering rate is given by (assuming the bandstructure is defined by a non-parabolic