56 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS
Ec
EV
D
ENSITY OF STATES
Pure semiconductors
n = p = ni = pi
- –
++ +
(b)
- – –– ––
(a)
EV EF Ec
Low temperature
ni = pi ~ 0
D
ENSITY OF STATES
(c)
EV EF Ec
High temperature
pi ni
ENERGY
Conduction
band
Valence
band
+ –
+++
Figure 2.17: (a) A schematic showing that electron and hole densities are equal in a pure semi-
conductor. (b) Density of states and Fermi occupation function at low temperatures. (c) Density
of states and Fermi function at high temperatures whenniandpibecome large.
For the valence band we can write a simple expression for a density of states masses , which
includes theHHandLHbands
m∗dos=
(
m∗hh^3 /^2 +m∗h^3 /^2
) 2 / 3
In calculating the position of the Fermi energy, charge density, etc. we need to use the density
of states mass. In pure semiconductors, electrons in the conduction come from the valence band
andn=p=ni=pi,whereniandpiare the intrinsic carrier concentrations. In general the