SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

124 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

Dn Dp μn μp

(cm^2 /s) (cm^2 /s) (cm^2 /V •s) (cm^2 /V •s)

Ge 100 50 3900 1900

Si 35 12.5 1350 480

GaAs 220 10 8500 400

Table 3.4: Low field mobility and diffusion coefficients for several semiconductors at room
temperature. The Einstein relation is satisfied quite well.

This gives

D(1kV/cm−^1 )=

(1. 4 × 104 m/s)(0. 026 × 1. 6 × 10 −^19 J)

(1. 6 × 10 −^19 C)(10^5 V/m−^1 )

=3. 64 × 10 −^3 m^2 /s=36.4cm^2 /s

D(10kV/cm−^1 )=

(7× 104 m/s)(0. 026 × 1. 6 × 10 −^19 J)

(1. 6 × 10 −^19 C)(10^6 Vm−^1 )

=1. 82 × 10 −^3 m^2 /s=18.2cm^2 /s

The diffusion coefficient decreases with the field because of the higher scattering rate at

higher fields.

3.7 CHARGE INJECTION AND QUASI-FERMI LEVELS ............

In semiconductor devices the electron and hole distributions are usually not under equilibrium.
electric fields and optical energy causes electron densities and velocities to be different from the
equilibrium values. If electrons and holes are injected into a semiconductor, either by external
contacts or by optical excitation, the question arises: What kind of distribution function describes
the electron and hole occupation? We know that in equilibrium the electron and hole occupation
is represented by the Fermi function. It is possible to describe the non-equilibrium distribution
by using the concept of quasi-equilibrium

3.7.1 Non-equilibrium Distributions ......................

Under equilibrium conditions, electrons in the conduction band and holes in the valence band
are in equilibrium with each other. Under non-equilibrium conditions it is often reasonable to
assume that electrons are in equilibrium in the conduction band, while holes are in equilibrium
in the valence band. In this case, thequasi-equilibrium electron and holes can be represented by
an electron Fermi functionfe(with electron Fermi level) and a hole Fermi functionfh(with a