SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

94 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

Ev Ec

Valence band

Perfect structure

ELECTRON ENERGY

DENSITY OF STATES

(a)

Ev Ec

Structure with Defects

ELECTRON ENERGY

DENSITY OF STATES

(b)

Defect levels

}

Conduction band

Valence band Conduction band

No

allowed

states

Figure 3.2: A schematic of the nature of electronic states in solids: (a) for a perfect crystal, (b)
for a crystal with defects.

applied throughμ, the mobility. When the electric field in large the relationship between velocity
and applied field is not so simple and will be discussed later.

3.3 TRANSPORT AND SCATTERING

The problem of transport involves non-equilibrium physics. We need to find the distribution
function for electrons in energy and momentum space under an applied field or under carrier con-
centration gradients. We know that under equilibrium the electron (hole) distribution in energy
(or momentum) is given by the Fermi–Dirac distribution

f(E)=f◦(E)=

1

exp

(

E−EF

kBT

)

+1

E = Ei+

^2 k^2

2 m∗

whereEiis the bandedge.