SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

104 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

Alloy scattering

Alloys are made from combinations of two or more materials. Since atoms on the lattice are
arranged randomly there is random potential fluctuation which causes scattering. The scattering
rate for an alloyAxB 1 −xis found to be

Wtot =

2 π



(

3 π^2

16

V 0

)

Uall^2 N(Ek)

[

x(1−x)^2 +(1−x)x^2

]

a=

3 π^3

8 

V 0 Uall^2 N(Ek)x(1−x) (3.3.22)

HereUallis the potential difference betweenAtype andBtype potentials (see Appendix B),V 0
is the volume of the unit cell in the lattice andN(E)is the density of states without counting
spin degeneracy.
While the phonon and impurity scattering are the dominant scattering processes for most trans-
port problems, electron–electron scattering, electron–hole scattering, and alloy potential scatter-
ing, etc., can also play an important role.

Example 3.1Calculate the ratio of the polar optical phonon emission rate to the

absorption rate for GaAs and GaN at 300K.

The optical phonon energies in GaAs and GaN are 36 meV and 90 meV respectively. If the

electron energies are below these values, there is no phonon emission. The phonon

occupation number in GaAs at 300 K is 0.33 and in GaN is 0.032. Thus above threshold,

the emission to absorption ratios are approximately 4:1 and 32:1 respectively.

3.4 TRANSPORT UNDER AN ELECTRIC FIELD .................

The problem of finding the distribution function of electrons under an electric field is quite
complicated. Two important approaches to understanding transport in semiconductors are the
solution of the transport equation using numerical methods and the Monte Carlo method using
computer simulations. We will summarize the results of such theories by examining the drift
velocity versus electric field relations in semiconductors.

3.4.1 Velocity–electric field relations in semiconductors ............

When an electron distribution is subjected to an electric field, the electrons tend to move in
the field direction (opposite to the fieldEand gain velocity from the field. However, because
of imperfections in the crystal potential, they suffer scattering. A steady state is established
in which the electrons have some net drift velocity in the field direction. The response of the
electrons to the field can be represented by a velocity–field relation. We will briefly discuss the
velocity-field relationships at low electric fields and moderately high electric fields.