Hall Voltage Calculator

Compute Hall voltage, Hall coefficient, carrier concentration and mobility and identify semiconductor type (n/p) from current, magnetic field and sample geometry.

Select material and type; preset carrier concentrations based on typical doping [citations:7,9].
mA
Typical range 1–30 mA .
T
1 T = 10 kG; up to 1 T typical .
µm
Ω·cm
Required for mobility calculation.
n‑Ge: 10mA, 0.5T p‑Ge: 10mA, 0.5T n‑Si: 5mA, 1T, 200µm n‑GaAs: 1mA, 0.2T
Calculating...

Understanding the Hall Effect

Discovered by Edwin Hall in 1879, the Hall effect is the production of a transverse voltage across a current‑carrying conductor placed in a perpendicular magnetic field. It is a fundamental tool for semiconductor characterization .

Governing equations (single carrier type, non‑degenerate):

  • Hall voltage: VH = (I·B)/(q·n·d) (with sign: negative for electrons, positive for holes)
  • Hall coefficient: RH = VH·d/(I·B) = 1/(q·n) (for one type)
  • Carrier concentration: n = 1/(q·|RH|)
  • Hall mobility: μH = |RH|·σ = |RH|/ρ (σ = conductivity)

Sign of Hall Voltage and Carrier Type

For n‑type (electrons), the Lorentz force deflects electrons to one side, making that side negative; the Hall voltage is negative (for a defined coordinate system). For p‑type (holes), the voltage is positive. This calculator uses the standard convention: B along +z, I along +x, VH measured along +y .

Applications of Hall measurements:

  • Determination of carrier type (n or p) .
  • Measurement of carrier concentration and mobility .
  • Magnetic field sensing (Hall sensors) .
  • Characterization of doping uniformity and quality.

Two‑Carrier and Mixed Conduction

When both electrons and holes contribute, the Hall coefficient becomes RH = (pμp² - nμn²) / [q(pμp + nμn)²]. This can lead to sign reversal with temperature or doping. The single‑carrier approximation used here is valid when one type dominates (e.g., extrinsic semiconductor) .

Practical Measurement Guidelines

  • Van der Pauw method: For arbitrary shapes, use four contacts and permute current/voltage to extract RH and resistivity .
  • Offset compensation: Measure VH with +B and –B; average to remove thermoelectric offsets: VH = (V(+B) – V(–B))/2 .
  • Sample geometry: Thickness d must be uniform; width w does not enter VH formula because Hall field builds up across the width, but voltage is measured across that width.

? About This Tool

Developed by GetZenQuery Semiconductor Characterization Group — experts in Hall effect and transport measurements. The models are validated against published experimental data and academic lab manuals .

  • Melissinos, A. C. (1966). Experiments in Modern Physics. Academic Press. [Google Scholar]
  • Sze, S. M., & Ng, K. K. (2007). Physics of Semiconductor Devices (3rd ed.). Wiley. [Wiley]
  • Leybold Heraeus, "Hall Effect of n‑Germanium" experiment guide . [Leybold]
  • MDPI Instruments (2025). "Software Tool for Hall Parameter Evaluation" . [MDPI]

Questions? Contact [email protected].

Frequently Asked Questions

The Lorentz force acts on moving charges. For electrons (negative), the force direction is opposite to that for holes (positive). Consequently, electrons and holes accumulate on opposite sides, giving opposite polarity of VH .

Hall mobility μH = RH·σ includes a scattering factor r (typically 1–2). Drift mobility μ (used in conductivity) is lower: μ = μH/r. Our calculator uses the simplified relation assuming r=1, common in introductory contexts .

As temperature increases, carrier concentration n may rise (intrinsic regime) and mobility decreases due to phonon scattering. This changes RH and VH. At high T, mixed conduction can cause RH to change sign in p‑type materials if μe > μh .

Yes, but the carrier concentration in metals is much higher (≈10²² cm⁻³), yielding very small Hall voltages (µV). The formulas still hold, but sensitivity is lower. Our material presets focus on semiconductors.

This offset (mismatch voltage) arises from contact misalignment: the two Hall contacts are not exactly equipotential along the sample. It can be nulled by a potentiometer or subtracted by measuring with both field polarities .