Set of supplementary notes.

Chapter 8
Semiconductor devices
We now consider the properties of inhomogeneous systems and devices. In this section we
discuss the general properties of surfaces and interfaces between materials, and then the basic
devices of bulk semiconductor physics. For bulk devices we will use the semiclassical approximation,
treating electrons as classical particles obeying the Hamiltonian 1
H = E n (k) − eφ(r) (8.1)
with the momentum p = h¯k and a spatially varying potential φ(r). The potential will arise
from externally applied fields, from charges induced by doping, and from changes in the material
composition. When we discuss narrow quantum wells, we shall need to modify this
approximation to quantise the levels.
For an isolated solid in equilibrium, the energy difference between the chemical potential
µ the vacuum level is the work function Φ. This is the energy required to remove an electron
from the fermi level and place it in a state of zero kinetic energy in free space.
Two different isolated materials with different work functions will then have different chemical
potentials. If these two materials are placed in contact, their chemical potentials must
equalise, and this is accomplished by electron flow to the more electronegative material; this
material becomes charged, its potential φ changes, and an overall balance will be established.
But in general, there will be as a result internal, inhomogeneous electric fields.
8.1 Metal - semiconductor contact
The figure Fig. 8.1 is a schematic of this process for an ideal metal placed in contact with
a semiconductor. We consider the more interesting case when the chemical potential of the
(doped) semiconductor is above that of the metal.
8.1.1 Rectification by a metal contact
The barrier set up between the metal and insulator inhibits current flow. An electron from
the metal must either tunnel through the barrier (at low temperatures) or may be thermally
1 We shall keep to the convention that e is a positive number, and therefore −eφ is the potential energy of
electrons in an electrostatic potential φ
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