What it does
The Hall effect is the sideways voltage that appears when a current flows through a conductor in a magnetic field. Its sign tells you whether the charge carriers are electrons (n-type) or holes (p-type), and its size tells you how many there are. Combined with the sheet resistance from a van der Pauw measurement on the same sample, it gives the carriers’ mobility: how easily they move.
This tool takes your raw readings and works out:
- the sheet resistance R_s in ohms per square, solving the van der Pauw equation exactly (the correction factor f matters when R_A and R_B differ);
- the carrier type from the sign of the Hall voltage;
- the sheet carrier density n_s (per cm²) and, if you give the thickness, the bulk density n (per cm³);
- the Hall mobility μ_H in cm²/(V·s);
- the resistivity, conductivity and Hall coefficient;
- a reciprocity check on repeated readings, which flags bad contacts.
How to use it
- Type the film thickness, or leave it blank for a sheet (2D) result.
- Type the van der Pauw resistances R_A and R_B in ohms. Several readings each (current reversed, reciprocal configurations) can be separated by commas; they are averaged and the spread is shown.
- Choose the Hall measurement. One field, +B and −B: give the current, field and the Hall voltage at +B and at −B; the tool takes half the difference, which cancels the offset from misaligned contacts. Field sweep: paste field and Hall voltage pairs (or open a file) and the tool fits a straight line.
- Leave the Hall factor at 1 unless you know it for your material.
- Check the sign convention in the help text matches your wiring.
Worked example
A made-up 500 nm thin film gives R_A readings of 120.4 and 119.6 Ω and R_B readings of 95.2 and 94.8 Ω. The van der Pauw equation gives R_s = 484.94 Ω/□ (f = 0.9953). With 1 mA and 0.5 T, the Hall voltage is −2.10 mV at +B and +1.90 mV at −B, so V_H = −2.00 mV with a 0.1 mV offset removed. The negative sign means electrons: the page shows n-type: 1.56 × 10¹⁴ cm⁻², μ = 82.5 cm²/(V·s). With the thickness, the bulk density is 3.12 × 10¹⁸ cm⁻³ and the resistivity 0.02425 Ω·cm. The readings agree to 0.33 %.
Tips
- Keep contacts small and on the edge; make sure they are ohmic (straight-line current against voltage).
- Use the field sweep to see whether V_H is really linear in B. Curvature suggests two kinds of carriers.
- A large R_A/R_B ratio is allowed, but it often means an odd shape or a bad contact.
FAQ
My carrier type looks wrong. Why? Sign conventions differ between labs and instruments. Check which contact is positive and which way the field points against the convention stated under the Hall inputs.
What is the Hall factor? The ratio of Hall mobility to drift mobility. It depends on how carriers scatter: close to 1 in metals and degenerate semiconductors, up to about 1.9 for impurity scattering.
Can I trust this for a device report? It is a careful calculation for study and lab work. It is no substitute for professional judgement about the sample and the measurement.
Where the numbers come from
- Van der Pauw, L. J. (1958), A method of measuring specific resistivity and Hall effect of discs of arbitrary shape, Philips Research Reports 13, 1 to 9: the equation exp(−πR_A/R_s) + exp(−πR_B/R_s) = 1, solved here by Newton's method.
- Hall coefficient, carrier density and Hall mobility: standard textbook relations (for example Kittel, Introduction to Solid State Physics, and Sze, Physics of Semiconductor Devices). The measurement routine follows common practice described in NIST's public Hall effect pages.
- Checked by fibub against SciPy (brentq on the van der Pauw equation, scipy.constants.e, scipy.stats.linregress). The elementary charge is the exact SI value.
- The example readings are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.