Hall effect measurement (van der Pauw) calculator
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KEY POINTS
The Hall coefficient is RH = VH·t/(I·B); carrier concentration is n = 1/(q|RH|) and the sign gives the conductivity type. The van der Pauw method solves exp(−πR_A/Rs) + exp(−πR_B/Rs) = 1 for sheet resistance, and Hall mobility is μH = |RH|/ρ. Unlike a four-point probe, it separates concentration from mobility.
Van der Pauw method: resistivity
Hall effect: carrier concentration and mobility
Enter VH as half the difference between two measurements with the magnetic field reversed, which removes the offset voltage from contact misalignment. 1 T = 10⁴ G (gauss). Thin films and two-dimensional electron gases (HEMTs) are usually evaluated by sheet carrier density ns.
What Hall effect measurements tell you
When a magnetic field is applied perpendicular to a current-carrying semiconductor, the Lorentz force pushes carriers sideways, charge builds up on the sample edges and a voltage appears (the Hall voltage). The Hall voltage is inversely proportional to carrier concentration and reverses sign depending on whether the carriers are electrons or holes, so one measurement gives both conductivity type and carrier concentration. Combined with resistivity, it also gives mobility.
The van der Pauw method measures resistivity and the Hall coefficient on a thin sample of any shape with just four contacts around its edge, and it is the standard way to characterize epitaxial films, compound semiconductors and two-dimensional materials. A four-point probe only measures sheet resistance; Hall measurements separate concentration from mobility.
FAQ
Why reverse the magnetic field?
Taking half the difference between measurements with the field reversed removes the offset voltage caused by misaligned contacts, leaving only the Hall voltage.
What is the Hall factor?
A correction between 1 and about 1.2 that depends on the scattering mechanism. It relates the Hall coefficient to the true carrier concentration.
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Last updated: October 23, 2026