03-11-2012, 10:41 AM
Electrical Resistivity of Semiconductors
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Apparatus
Four probe assembly with oven, semiconducting sample, current source, voltmeter etc.
Objective:
To study the temperature variation of electrical resistivity of a semiconducting materials
using four-probe technique and determine the bandgap of the semiconductor.
Theory
where r is electrical resistivity of the material. For a long thin wire-like geometry of
uniform cross-section or for a long parellelopiped shaped sample of uniform cross-section,
the resistivity r can be measured by measuring the voltage drop across the sample due to
passage of known ( constant) current through the sample as shown in Fig. 1a . This simple
method has following drawbacks:
· The major problem in such method is error due to contact resistance of measuring
leads.
· The above method cannot be used for materials having random shapes.
· For some type of materials soldering the test leads would be difficult.
· In case of semiconductors, the heating of samples due to soldering results in injection
of impurities into the materials thereby affecting the intrinsic electrical resistivity.
Moreover, certain metallic contacts form schottky barrier on semiconductors.
To overcome first two problems, a collinear equidistant four-probe method is used.
This method provides the measurement of the resistivity of the specimen having wide
variety of shapes but with uniform cross-section. The soldering contacts are replaced by
pressure contacts to eliminate the last problem discussed above.
Experimental Set-up:
The four-probe assembly consists of four spring loaded probes arranged in a line
with equal spacing between adjacent probes. These probes rest on a metal plate on which
thin slices of samples (whose resistivity is to be determined) can be mounted by insulating
their bottom surface using a mica sheet. Black leads are provided for carrying current and
red leads for voltages measurements. The sample, usually, is brittle, hence do not attempt
to mount the sample yourself. This assembly is mounted in a lid of an oven, so that the
four probes and the sample can be kept inside the oven and sample can be heated up to a
temperature of 200° C. The temperature inside the oven can be measured by inserting a
thermometer through a hole in the lid.
The constant current is supplied through probes 1 and 4 by a constant current
source. The value of the current can be read from the LED display on the unit. The digital
voltmeter is used to measure the voltage drop between probes 2 and 3. It uses the same
LED display through a toggle switch. It operates in two modes xl and x10 with maximum
of 199.9 mV and 1.999 V, respectively. Oven can be heated to low (L) or high (H)
temperatures through the electric supply for it.
Procedure:
1. Make the connections as shown in Figure 2.
2. Set some suitable low value of current (2 to 4 mA) from the constant current
source. Note down this reading.
3. Switch the LED display to milli-voltmeter mode. Note the temperature and voltage
between probes 2 and 3 (V1).
4. Switch on the oven supply. Record the voltage between the inner probes as a
function of temperature using the method described in the previous step.
5. Determine the experimental resistivity as a function of temperature using equation
(4) and the measured voltage and current.
6. Express your resistivity data in Ohm-cm unit and temperature in Kelvin(K). Plot
ln® vs. 1000/T(K) and see that it is a straight line. From the slope of the line
(choose only the linear portion of the curve), calculate Eg