Lake Shore Cryotronics Measure Ready M91 FastHall, User Manual

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12 CHAPTER 1: Introduction
MeasureReady™ M91 FastHall™ Measurement Controller
1.5.6.1 Structures of van der Pauw Samples and Their Errors
The structure of a practical van der Pauw sample is very similar to the ideal structure
shown in FIGURE 1-5. Over the years, many variations of the structure have been
developed to control and quantify the errors associated with finite contact sizes. We
can summarize some of these effects here.
FIGURE 1-5
Four point contacts
FIGURE 1-6
Square structure
c
L
1.5.6.1.1 Square Structures
The resistivity correction factor

ρ

ρ
for a square van der Pauw structure
(FIGURE 1-6) is roughly proportional to (c / l) for both square and triangular contacts.
With (c / l) = 1/6,

ρ

ρ
is 2% for identical square contacts, and

ρ

ρ
is less than 1% for
identical triangular contacts 1 .
The correction factor

V
H
/V
H
is proportional to (c / l), and is about 15% for triangular
contacts when (c / l) = 1/6. The correction factor also increases by about 3% at this
aspect ratio as the value of µB increases from µB = 0.1 to µB = 0.5.
1. Chwang, R., Smith, B.J., and Crowell, C.R., "Contact size effects in transition-metal doped semiconduc-
tors with application to Cr-doped GaAs", J. Phys. C: Solid State Phys.,13, 2311-23 (1974).