Lake Shore Cryotronics Measure Ready M91 FastHall, User Manual

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FIGURE 1-7
Circular structure
c
L
13
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1.5.6.1.2 Circular Structures
Circular van der Pauw structures (FIGURE 1-7) fare slightly better. Van der Pauw 1
gives a correction factor for circular contacts of
per contact, which results in a correction of

ρ

ρ
= -1% for (c / l) =
1/g
for four contacts.
For the Hall voltage, van der Pauw 1 gives the correction
per contact. At (c / l) = 1/6, this results in a correction of 13% for four contacts.
FIGURE 1-8
Cloverleaf
structure
1.5.6.1.3 Cloverleaf Structures
Van Daal 1 reduced these errors considerably (by a factor of 10 to 20 for resistivity, and
3 to 5 for Hall coefficient) by cutting slots to turn the sample into a cloverleaf
(FIGURE 1-8). The cloverleaf structure is mechanically weaker than the square and
round samples unless it is patterned as a thin film on a thicker substrate. Another
disadvantage is that the active area of the cloverleaf is much smaller than the actual
sample.
FIGURE 1-9
Greek cross
c
a
1.5.6.1.4 Greek Cross Structures
One of the best van der Pauw geometries to minimize finite contact errors is the
Greek cross (FIGURE 1-9). Its advantage over simpler van der Pauw structures is
similar to placing Hall bar contacts at the ends of arms. David and Beuhler
2 analyzed
this structure numerically. They found that the deviation of the actual resistivity
ρ
from the measured value
ρ
m
complied with this equation:
This is a very small error: for c / (c + 2a) = 1/6, where c + 2a corresponds to the total
dimension of the contact arm, the error is about 10
-7
.
Hall coefficient results are substantially better. De Mey
3
has shown that
where µ
H
and µ
Hm
are the actual and measured Hall mobilities, respectively, for c /
(c + 2a) = 1/6, this results in

µ
H
/µ
H
and the error is 0.04%.
1. van Daal, H.J., “Mobility of charge carriers in silicon carbid,” Phillips research reports, Suppl. 3, 1-92
(1965).
2. David, J.M. and Buehler, M.G., “A numerical analysis of various cross sheet resistor test structures”,
Solid State Electron., 20, 539-43 (1977)
3. De Mey, G. “Influence of sample geometry on Hall mobility measurements,” Arch. Electron. Uebertra-
gungstech., 27, 309-13 (1973).