SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

2.4. OCCUPATION OF STATES: DISTRIBUTION FUNCTION 41

+ + + +

+ + + +

+ + + +

Electron in a periodic potential

Bloch theorem: ψ = ukeik•r

Equation of motion

dk

dt = Fext

Electron behaves as if it is in free space, but

with a different effective mass

E versus k relation effective mass

h

Figure 2.7: Electrons in a periodic potential can be treated as if they are in free space except that
their energy–momentum relation is modified because of the potential. Near the bandedges the
electrons respond to the outside world as if they have an effective massm∗. The effective mass
can have apositiveornegativevalue.

2.4 OCCUPATION OF STATES:

DISTRIBUTION FUNCTION

Bandstructure calculations give us the allowed energies for the electron. How will the particles
distribute among the allowed states? To answer this question we need to use quantum statistical
physics. According to quantum mechanics particles (this term includes classical particles and
classical waves which are represented by particles) have an intrinsic angular momentum called