Page 164 - Electrical Properties of Materials

146 Semiconductors

Voltmeter
leads
Current
Fig. 8.14 leads
The four-point probe. The probes are Probe holder
sharply pointed and held rigidly in a
1 2 3 4 Semiconductor sample
holder which can be pressed with a
known force on to the semiconductor.
A typical spacing is 1 mm between
probes. Table

It is important to realize that in some applications mobility is a function of
field. Since practically everything obeys Ohm’s law at low enough fields we
may define the low field mobility as a constant. For high fields the differential
mobility

dv D
μ diff = (8.60)
dE
is usually the important quantity in device applications.

8.10.2 Hall coefficient

For this measurement four contacts have to be made so as to measure the
voltage at right angles to the current flow. The basic measurement was de-
scribed in Chapter 1. However, geometrical factors also come into this. If
The Hall coefficient [eqn (1.20)] the distance between voltage probes is greater than that between the current
is a measure of the charge density, probes the Hall voltage is reduced. Again, this reduction factor is calculable by
and hence it can be used to relate detailed consideration of the patterns of current flow.
conductivity to mobility.
8.10.3 Effective mass

The standard method of measuring effective mass uses the phenomenon of
These measurements are com- cyclotron resonance absorption discussed in Chapter 1. It is essentially an in-
monly made in the microwave re- teraction of an electromagnetic wave with charge carriers, which leads to an
10
gion (10 Hz) at liquid helium absorption of the wave when the magnetic field causes the electron to vibrate
temperature (about 4 K) or in the at the same frequency as that of the applied electric field. For the resonant ab-
13
infrared (about 10 Hz) at liquid sorption to be noticeable the electron must travel an appreciable part of the
nitrogen temperature (77 K). period without collisions; thus a high-frequency electric field, a high-intensity
magnetic field, and low temperatures are used.
In the apparatus for a microwave measurement, shown diagrammatically in
Fig. 8.15, the sample is enclosed in a waveguide in a Dewar flask filled with
liquid helium, which is placed between the poles of a large electromagnet.
∗
∗ The circulator has the following ma- The microwave signal is fed in through a circulator. Thus the signal entering
gical properties: a signal fed into arm (1) arm (2) is reflected by the reflecting plate at the end of the waveguide having
goes out entirely by arm (2) and a signal passed through the semiconductor in each direction and ends up in the receiver
fed into arm (2) leaves the circulator by
arm (3). connected to arm (3). Employing a wave of fixed frequency and a variable
magnetic field; the effective mass is given [eqn (1.64)] by
B is the magnetic field correspond-
∗
ing to an absorption of signal. m = eB/ω c . (8.61)