Moving charge accumulates at an edge
Picture a thin conducting strip carrying current from left to right. A perpendicular magnetic field pushes its moving charge sideways. Charge accumulating at an edge builds an electric field of its own. In steady state, the electric and magnetic forces balance across the strip, leaving a Hall voltage between its sides.
Conventional current follows the direction positive charge would travel. Electrons are negative and drift the other way. With a fixed current, field and voltmeter convention, electron-like and hole-like ordinary Hall responses can have opposite signs. A hole is a missing electron in a crystal whose motion behaves as a positive charge.
Sources: [1]
A misplaced probe adds an ordinary voltage drop
A resistive sheet already has a potential gradient along the current. Two probes at the same longitudinal position compare its sides. Move one probe forward and the meter also spans part of that longitudinal drop. This contribution can exceed the small sideways voltage of interest.
Keep the current fixed and reverse only the magnetic field. An ordinary Hall contribution reverses sign. Longitudinal pickup from the same probe positions usually keeps its sign. Half the difference between the readings removes that field-even contribution.
A meter offset or a temperature difference introduces further voltages. Reversing current adds another symmetry test. Counterbalanced repeated sequences and actual timestamps help separate a slow drift. Waiting until the field has settled gives the comparison a definite physical meaning.
The red lead fixes what a positive reading means
Face the sheet with current entering on the left and leaving on the right. Let positive field point toward you. A red lead below and a black lead above read bottom potential minus top potential. Swapping them changes the displayed sign, even though the carriers are unchanged. Every material interpretation needs this wiring convention.
Sources: [3]
Four contacts also determine resistivity
Four small contacts around a uniform sheet can alternate their jobs: two supply current and two sense voltage. Two adjacent configurations yield transfer resistances belonging to those connections. The van der Pauw relation combines them into a sheet resistance belonging to the film. It applies to rectangular, circular and other hole-free shapes under its small-perimeter-contact and uniform-thickness assumptions.
Separate current and voltage connections also reduce the influence of the contacts themselves. Current-carrying leads and interfaces have extra voltage drops. A high-input-resistance voltmeter takes very little current through its probes, so their reading mainly compares the two sheet potentials. The contacts can exchange jobs while preserving this separation.
Sheet resistance is useful for a film. An independent thickness measurement converts it into bulk resistivity. The voltmeter, current readback and field probe each need their own references as well. A further known value withheld from the calibration fit tests whether the scale works at another point.
One slope can combine several populations
For a simple single-carrier model, the Hall coefficient is related to carrier density by . Here is the signed carrier charge. This interpretation also takes the Hall factor to be one. More carriers then need a smaller average drift to carry the same current, changing the Hall voltage.
Electrons and holes can conduct together. Their populations and mobilities both matter: a smaller but more mobile population can dominate the Hall sign. Different mixtures can even share the same low-field slope. Curvature over a wider field range, temperature dependence and additional measurements help distinguish them. A signed transport response becomes a carrier count only with the material assumptions attached.
Sources: [3]