Lake Shore Cryotronics Measure Ready M91 FastHall, User Manual

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Geometrical error sources in the Hall bar arrangement are caused by deviations of the
actual measurement geometry from the ideal of a rectangular solid with constant
current density and point-like voltage contacts.
FIGURE 1-12
Hall bar with finite voltage contacts
The first geometrical consideration with the Hall bar is the tendency of the end
contacts to short out the Hall voltage. If the aspect ratio of sample length to width
(l / w = 3), then this error is less than 1%
1 . Therefore, it is important l / w
≥
3.
The finite size of the contacts affects both the current density and electric potential in
their vicinity, and may lead to fairly large errors. The errors are larger for a simple
rectangular Hall bar than for one in which the contacts are placed at the end of arms.
FIGURE 1-13
For a simple rectangle, FIGURE 1-13, the error in the Hall mobility can be
approximated (when µB << 1) by:
2
1. Chwang, R., Smith, B.J. and Crowell, C.R., “Contact size effects on the van der Pauw method for resistiv-
ity and Hall coefficient measurement”, Solid-State Electron. 17 (Dec. 1974) 1217 – 1227.
2. Perloff, D.S., “Four-point probe sheet resistance correction factors for thin rectangular samples”. Solid-
State Electron. 20 (Aug 1977) 681 – 687.