Sheet resistance looks like the easiest measurement in the laboratory until two operators get different numbers from the same wafer. Geometry factors, probe spacing, contact behaviour, film thickness and temperature explain nearly all of it.
Two students measure the same indium tin oxide coated glass on the same afternoon and report sheet resistances that differ by a fifth. Neither did anything obviously wrong. One measured near the edge, one measured in the middle, one used a higher current, and the air conditioning went off between the two sessions. All four of those matter, and none of them is visible in the number that gets written in the logbook.
The reason for four probes rather than two is specific and narrow. Current is forced through the outer pair and voltage is read across the inner pair by a high impedance input, so essentially no current flows through the voltage contacts. Whatever resistance sits at those contacts, and in their leads, drops no voltage and therefore does not appear in the reading. That is the whole benefit, and it is a real one: on a low resistance film, contact and lead resistance can be larger than the film itself.
Everything else survives. The four contact arrangement does nothing about the geometry of the current spreading, the proximity of an edge, the thickness of the layer, a contact that is not ohmic, mechanical damage from the tips, illumination on a photoconductive sample, or temperature. Those are the error sources, and they are the rest of this article.
The raw quantity a four point probe gives you is a ratio of measured voltage to forced current. Turning that into sheet resistance or resistivity requires a geometric factor, and which factor applies depends on the sample.
The failure is not usually arithmetic. It is that the thin sheet factor gets applied to a sample that is not a thin sheet, because it is built into the meter and nobody changed it. If your coupon is a few millimetres across and the probe spacing is one millimetre, the infinite sheet assumption is wrong and the error is not small. Read the correction factor off the table for your actual geometry and record which one you used alongside the result.
Current injected at the outer probes spreads out into the sample and returns. If a boundary sits within that spreading region, the current is confined, the measured voltage rises, and the sheet resistance comes out too high. As a working rule, keep the distance from the probe array to any edge at least several times the probe spacing, and prefer a sample whose smallest lateral dimension is an order of magnitude larger than the probe span. Where the sample is genuinely small, use a closer probe spacing rather than accepting an edge correction you cannot verify.
Probe spacing also has to suit the uniformity you are trying to resolve. A wide spacing averages over a larger area and is more forgiving of local defects; a close spacing resolves variation but is more sensitive to a single bad contact. If the point of the measurement is uniformity mapping across a wafer, fix the spacing, fix the load, and move the sample rather than changing probes between points.
Rotating the probe head through ninety degrees and repeating the measurement is the cheapest anisotropy check available. If the two readings differ by more than the repeat scatter, either the film is anisotropic or the geometry correction is wrong, and both are worth knowing before publication.
The thin sheet result assumes the layer thickness is small compared with the probe spacing, so the current flows essentially in two dimensions. That is comfortably satisfied by a deposited film and a millimetre probe spacing. It is not satisfied by a sintered pellet, a bulk crystal or a thick coating, where the current spreads in three dimensions and the bulk formula with the probe spacing in it applies instead.
There is a second, quieter trap on films. Sheet resistance is a complete answer in itself for a conductive coating: it is what a circuit designer or a solar cell engineer wants. Resistivity is sheet resistance multiplied by thickness, and the thickness has to come from somewhere else, usually ellipsometry, a masked step or a cross section. Any error in that thickness lands directly in the resistivity. If you have not measured the thickness on the same sample, quote sheet resistance and stop, rather than converting with a nominal value from the deposition recipe.
A conductive film on a conductive substrate is not measurable this way at all, because the current finds the substrate. Measure the film on an insulating witness coupon deposited in the same run.
Tungsten carbide or osmium tips pressed onto a surface make a contact whose behaviour depends on the material. On a metal or a degenerate semiconductor the contact is ohmic and the measurement is straightforward. On a lightly doped semiconductor, a wide band gap oxide or a polymer conductor, the contact can rectify, and the reading then depends on the current you chose.
A calibrated reference sample of known sheet resistance, measured at the start of every session, catches tip wear, a failing test unit and an operator error in one step. It is the single most useful accessory on the bench and the one most often left out of the order.
Semiconductor resistivity is strongly temperature dependent, and so, to a smaller degree, is that of metals. A laboratory in Dhaka that sits at twenty two degrees with the air conditioning running and drifts into the thirties when it fails is a laboratory where sheet resistance changes through the afternoon. That is not an instrument fault. It means every recorded measurement needs a recorded temperature, and comparisons between samples measured on different days are only meaningful with it. A thermally stabilised stage removes the argument entirely for anyone doing systematic work.
Photoconductive materials respond to room light. Silicon, many oxides and most organic semiconductors will read differently under the bench fluorescent than in the dark. A light shroud over the probe station is inexpensive and settles the question. For samples that are both light and moisture sensitive, an enclosed shroud with a dry purge does the same job for humidity, which matters through the monsoon in any laboratory without tight humidity control.
Finally, write down more than the answer. A sheet resistance is reproducible only if the record includes the probe spacing, the correction factor used, the current, the load setting, the number of points averaged, the sample temperature and whether the shroud was down. Six numbers and a note take a minute. Reconstructing them a year later takes a re-measurement.