Set of supplementary notes.

104 CHAPTER 7. SEMICONDUCTORS
Figure 7.3: . The left hand figure shows the effect of donor levels at an energy E d = E c − ∆ d .
The chemical potential will shift near the conduction band edge, increasing the electron density
and decreasing the hole density in comparison to the intrinsic case, while the product of the two
is nevertheless constant. The right hand figure shows the corresponding picture for acceptor
levels at an energy E a = E v + ∆ a .
However, in many practical cases, both donor and acceptor states can be assumed to be fully
ionised, so that the resulting carrier concentration in the extrinsic regime is simply given by
the difference N d − N a .
Note that by the law of mass action, np is a constant at fixed temperature, given by
(7.12). Doping with donor or acceptor atoms modifies the chemical potential and thereby
shifts the balance between n and p, but the product remains constant. Even in the presence of
strong donor doping, when the majority of the carriers are electrons, there will still be a small
(minority) population of holes, given by p = n i p i /N d .