Carrier concentration and mobility come out of a Hall measurement only if the sample obeys a short list of geometric rules. What van der Pauw requires, when to cut a Hall bar instead, and what the contacts have to do.
A Hall measurement is one of the few characterisations that gives three numbers a semiconductor group genuinely needs from a single experiment: carrier concentration, carrier mobility and resistivity, with carrier type as a sign. It is also one of the few where the sample, not the instrument, is usually what makes the result wrong.
Current is passed through the sample, a magnetic field is applied perpendicular to it, and the transverse voltage that appears is measured. From that voltage and the field comes the sheet carrier density; with a sheet resistance measurement it gives mobility; with a thickness it gives bulk carrier concentration and resistivity.
That chain contains an assumption worth naming. Bulk carrier concentration is calculated from thickness. If the thickness is uncertain by ten per cent, so is the concentration, and no amount of instrument precision recovers it. On a thin film, thickness has to be measured on the actual sample rather than taken from the deposition recipe. The HCS L36 from Linseis takes plug-and-play sample holders for pieces up to 12.5 x 12.5 mm and determines mobility, specific resistance, carrier concentration and the Hall constant; the numbers it reports are only as good as the thickness fed into them.
The van der Pauw arrangement is the usual choice because it works on an arbitrarily shaped piece with four contacts on the edge, which is what a research group actually has. The freedom of shape comes with conditions, each of which fails in a recognisable way.
Low mobility material makes all of this harder, because the Hall voltage is small and the misalignment voltage from imperfectly opposed contacts can be larger than the signal it is buried in. That is where field reversal, current reversal and averaging stop being refinements. The 8400 Series HMS works with both DC and AC magnetic fields and is aimed at that problem, measuring mobility, carrier concentration density and resistivity across a wide range of sample types including low mobility materials.
A Hall bar is a defined rectangular channel with voltage taps at known positions along and across it. It costs a lithography step and buys geometry you know rather than geometry you assume: the current path is confined, the tap separation is defined, and the voltages are read at fixed points instead of derived from a shape.
Cut one when the material is anisotropic, when the film is patterned anyway as part of a device flow, or when a mobility figure will be published and compared with somebody else's. Stay with van der Pauw for routine screening of bulk pieces and unpatterned films, which is most of what a university laboratory does.
The instrument choice follows the same split. The MeasureReady M91 FastHall Measurement Controller uses Lake Shore's patented FastHall technique to shorten the measurement, and the MeasureReady FastHall Station packages the controller, magnet and sample holder as one configured tabletop system, which removes most of the work of bringing a Hall measurement online. For a Bangladeshi group setting this up for the first time, an integrated station has fewer ways to be wired incorrectly than a bench assembled from separate parts. Specifications for the M91 FastHall controller and the 8400 Series HMS set out which sample types each covers.
Where temperature dependence is the point, the measurement moves into a cryostat. The Guarded Insert for PPMS carries van der Pauw and Hall bar samples inside a PPMS with a fully guarded signal path, and used with the M91 it measures resistance from 10 milliohms to 200 gigaohms between 1.9 K and 400 K, with an integrated Cernox sensor reading sample temperature. For wafer scale work, the PS-HM-8425 Hall measurement package for the CRX-VF probe station adds DC Hall measurement as a function of temperature and field, supplied with a switch matrix, current source, voltmeter and a PC running the 8400 Series HMS software, and covering van der Pauw, Hall bar and gated Hall bar measurements.
One last practical point. A Hall measurement and a four point probe measurement are not substitutes: the probe gives sheet resistance and nothing about carriers, while the Hall measurement needs a sheet resistance to produce a mobility. The probe side of that is set out in where four point probe measurements go wrong. If a group is buying one instrument, work out first which of the two questions it is actually asking.