SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

96 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

–k 0 +k

f^0 (k)

=

Σ k = 0

f(k) = f(–k)

Σ f(k) = 0

–k 0 +k

f(k)

(a)

(b)

-field

= 0

Assymetric Function

f^0 (k) f^0 (-k)

f^0 (k)

-Field = 0

Symmetric Function

E

E

E

Figure 3.4: A schematic of the electron momentum distribution function in (a) equilibrium where
f(k)=f(−k)and (b) in the presence of an electric field.

then again moves in space and again scatters. The process is shown schematically in figure 3.5.
The average behavior of the ensemble of electrons will then represent the transport properties of
the electron.

3.3.1 Quantum Mechanics and Scattering of electrons

As noted above in absence of scattering the electron transport is very simple to understand.
However, scattering dominates transport in semiconductor devices. The scattering problem in
solids is treated by using the perturbation theory in quantum mechanics. The electron problem
is formally represented by
HΦ=EΦ (3.3.3)

whereHis the full hamiltonian (potential energy + kinetic energy operator) of the problem and
the electron states are denoted byΦ. This hamiltonian is, in our case, the sum of the hamiltonian