14
CHAPTER 1:
Introduction
MeasureReady™ M91 FastHall™ Measurement Controller
1.5.6.2 Ideal Measurements of Samples with van der Pauw Structure
This section presents the theory of Hall measurements and resistivity measurements
on ideal van der Pauw samples. Ideal measurements means perfect 2D uniform
samples with four point contacts on the edges, as shown in FIGURE 1-5. The contacts
are numbered in the counterclockwise direction. The voltmeter and current source
used are assumed to be perfect. In section 1.5.6.3 these restrictions will be relaxed
and the measurement in real materials with real instruments will be described.
1.5.6.2.1 Hall Voltage Measurements on van der Pauw Samples
In the ideal van der Pauw structure, to measure Hall voltage, connect the current
source across one diagonal and measure the voltage between the other diagonal
contacts.
V
H
= V
31,42
= V
42,13
1.5.6.2.2 Resistivity Measurements on van der Pauw Samples
The main result of the van der Pauw method is that the resistivity of the sample can
be calculated from two resistance measurements using this equation:
The quantity F is a transcendental function of the two measured resistances (R
12,43
and R
23,14
). Let R
r
be the greater of the ratios R
12,43
/ R
23,14
and R
23,14
/ R
12,43
. The
quantity F can be found by:
In this equation, F=1 when R
r
=1, which occurs with symmetrical samples like circles
or squares when the contacts are equally spaced and symmetrical. The best
measurement accuracy is also obtained when R
r
=1. The MeasureLINK™-MCS
software automatically calculates F and reports the value as the F factor.
1.5.6.3 Calculations for van der Pauw Samples
Section 1.5.6.3.1 and section 1.5.6.3.2 describe the Hall voltage and resistivity
calculations for van der Pauw samples.
1.5.6.3.1 Hall Voltage Calculations for van der Pauw Samples
The Hall voltage is calculated from the current reversed (section 1.5.5.2), field
reversed (section 1.5.5.4), geometry averaged (section 1.5.5.5) voltage. The two
geometries used in the average are the current reversed, field reversed voltage
between contact 4 and 2 with the current applied between contacts 1 and 3 and the
field reversed voltage between contacts 1 and 3 with the current applied between
contact 4 and 2:
This measurement requires six individual measurements of applying a current and
measuring the voltage.
1.5.6.3.2 Resistivity Calculations for van der Pauw Samples
In section 1.5.6.2.2 the resistivity of an ideal van der Pauw structure was defined as
Summary of Contents for Measure Ready M91 FastHall
Page 6: ...MeasureReady M91 FastHall Measurement Controller ...
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Page 64: ...54 cHAPTER 3 Operation MeasureReady M91 FastHall Measurement Controller ...
Page 156: ...146 cHAPTER 4 Computer Interface Operation MeasureReady M91 FastHall Measurement Controller ...
Page 160: ...150 cHAPTER 5 Options and Accessories MeasureReady M91 FastHall Measurement Controller ...
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