Set of supplementary notes.

108 CHAPTER 8. SEMICONDUCTOR DEVICES
Figure 8.3: Two equivalent ways of representing the energy levels in a p-n junction. (a)
shows the energy levels, and includes the electrostatic potential in the electrochemical potential
µ + eφ(x). In (b) we recognise that the chemical potential is constant, and the effect of
the potential φ is a shift in the energetic position of the energy levels E d (x) = E d − eφ(x),
E a (x) = E a − eφ(x). When the shifted donor or acceptor levels pass through the chemical
potential, these levels are ionised, and the carriers pass from one side of the barrier to the
other, and annahilate. The impurity levels within the depletion region are now charged.
Figure 8.4: (a) Carrier densities and (b) charge densities near the depletion region of a p-n
junction. When the temperature is low, the carrier density changes abruptly at the point where
the chemical potential passes through the donor or acceptor level. Close to the barrier, the
carriers are depleted, and here the system is now physically charged, with a charge density of
+eN d on the n-type side, and −eN a on the p-type side. This dipole layer produces a potential
φ(x) shown in (b). The potential itself self-consistently determines the charge flow and the
width of the depletion region.