Page 161 - Electrical Properties of Materials

Measurement of semiconductor properties 143

ignored but it acquires special significance at high electric fields. It constitutes
the basis for the operation of a new type of device, which we shall discuss later
among semiconductor devices. You must realize, however, that this is the ex-
ception rather than the rule. The details of the band structure generally do not
matter. For the description and design of the large majority of semiconductor
devices our model is quite adequate.

8.9 Amorphous semiconductors
In this chapter we have considered very pure and regular crystal forms of Ge,
Si, and other semiconductors, and have used simple models based on this
symmetry to derive basic properties like energy gap and conductivity. What
happens if the material is not a single crystal—suppose one evaporates a film
of Si on to a suitable substrate? The film consists of randomly oriented clusters
of crystallites (small crystals). The structure within the crystallites leads to an
energy gap. Remember, in all our three models of band structure (Chapter 7)
band edges form when the electrons’ de Broglie wave interferes with the lattice
spacing. A small array of lattice points gives a less sharp interference pat-
tern, so the band edges are not so well defined. We still get optical absorption
and photoconduction, but with a less sharp spectral variation than shown later
in Fig. 8.18(b). Another effect of small crystallites is that the covalent bonds
break off where the orientation changes, so that there are ‘dangling bonds’,
where the unpaired electrons can act as traps for both itinerant electrons and
holes. Mobility is greatly reduced; and also doping is much less effective, as
the carriers from the dopant are trapped. This effect ties the Fermi level near
the middle of the energy gap, as it is in intrinsic materials and insulators.
If the amorphous layer is formed in a gas discharge containing hydrogen, the
‘dangling bond’ is dramatically reduced. The H atoms neutralize the unpaired
electrons, and the atomic nucleus has a minimal effect on lattice behaviour. In
these circumstances amorphous Si can be doped into both p- and n-type.
Why should we use amorphous semiconductors when we can have them
in superior single crystal form? The reason is purely economical. When we
need them in large areas, as in solar cells (Section 13.2) or in xerographic
applications (Section 10.17), we use the amorphous variety.

8.10 Measurement of semiconductor properties
The main properties to be measured are (i) mobility, (ii) Hall coefficient,
(iii) effective mass, (iv) energy gaps (including the distance of any impurity
layer from the band edge), and (v) carrier lifetime.

8.10.1 Mobility The most direct way of measur-
ing mobility is to measure the drift
This quantity was defined as the carrier drift velocity for unit field,
velocity caused by a known d.c.
μ = v D /E . (8.57) electric field.
Since the electric field is constant in a conductor (and in a semiconductor too),
it can be deduced from measurements of voltage and distance. How can we
measure the drift velocity? Well, in the same way we always measure velocity;
by measuring the time needed to get from point A to C. But can we follow