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APPLICATIONS
3.4.2 Test Procedure
(I
100
80 -
80 -
VGS = ov
0
1
2
3
4
5
6
7
s
fl
1c
VW (Volts)
Figure 3-7. Typlcal Common-Source
FET IV
Characteristics
3.4 RESISTIVITY
MEASUREMENTS
In order to make van der Pauw resistivity
measurements,
four terminals of a sample of arbitrary shape are measured.
A current (from the Model 220) is applied to two terminals,
while the voltage is measured (by the Model 196) across
the two opposite terminals, as shown in Figure 3-9. A total
of eight such measurements on each sample are required,
with each possible terminal and current convention.
The
resulting
voltages are designated VI through
Vs
In order to source current into and measure the voltage
across the sample, specific crosspoints
must be closed.
Table 3-2 summarizes
the crosspoints
to close for each
voltage measurement
on all three samples from the test
configuration
shown in Figure 3-8.
3.4.3 Resistivity
Calculations
Once the eight voltage measurements
are known,
the
resistivity
can be calculated.
Two values of resistivity,
p*
and pB are initially
computed
as follows:
1.1331 fA t, (V, + v, - v, -V,)
1
pa =
I
-
The Model 7072 Semiconductor
Matrix card can be usec
in conjunction
with a Model 220 Current
Source and a
Model 196 DMM to perform resistivity
measurements
on
semiconductors.
Such measurements
can yield such im-
1.1331 fB ts (V, + v, - v, - V,)
portant information
as doping concentration.
pB =
I
3.4.1 Test Configuration
Figure 3-8 shows the basic test configuration
to make
resistivity
measurements
on van der l'auw samples. The
Model 220 sources current through the samples, while the
Model
196 measures the voltage developed
across the
samples. The matrix card, of course, switches the signal
paths as necessary. In order to minimize
sample loading,
which will reduce accuracy, the Model 196 DMM should
be used only on the 3OOmV or 3V ranges. Also, this con-
figuration
is
not
recommended
for
resistance
measurements
above lMn due to the accuracy-degrading
effects of DMM loading.
Where: pA and pB are the resitivities
in O-cm
ts is the sample thickness
in cm
V, through
v, are the voltages measured by the
Model 196
I is the current through
the sample in amperes
fA and fB are geometrical factors based on sample
symmetry
(f, = f, = 1 for perfect symmetry).
Once pA and pB are known,
the average resistivity,
pAvO,
can be determined
as follows:
PA +
Pa
pm0 =
2
3-9
I
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