Hall Coefficient Estimator Calculator

The Hall coefficient links the transverse Hall response to current and magnetic field. For a rectangular sample measured with Hall voltage V_H, thickness t, current I, and magnetic flux density B:

• RH = (V_H * t) / (I * B) (units: m^3/C)

For a single dominant carrier type with concentration n:

• RH = +/- 1 / (n * e), where e is the elementary charge.
• Sign is negative for electrons (n-type) and positive for holes (p-type).

If you provide conductivity sigma or resistivity rho, the calculator estimates mobility using: mu = |RH| * sigma with sigma = 1/rho.

1. Select a calculation mode based on what you measured.
2. Enter values with correct units and keep the sign of V_H or RH.
3. Optionally enter uncertainties to estimate sigma(RH) and relative uncertainty.
4. Optionally add resistivity or conductivity to compute mobility.
5. Press Estimate. Results appear above the form.
6. Use Download CSV or Download PDF to export.

1) What the Hall coefficient represents

The Hall coefficient (R_H) is a transport parameter that connects the transverse Hall response to an applied magnetic field and a driven current. In practice, it helps you determine whether electrons or holes dominate conduction and provides a first estimate of carrier concentration.

2) Typical measurement setup and signals

A Hall bar or rectangular sample carries a longitudinal current I while a perpendicular magnetic field B is applied. The Lorentz force pushes carriers sideways, creating a Hall voltage V_H across the width. The polarity of V_H is the key sign indicator.

3) Primary computation used in this tool

This calculator uses R_H = (V_H·t)/(I·B), where t is sample thickness along the field direction. Results are reported in m³/C and cm³/C, so you can compare values across literature, labs, and datasheets without manual conversions.

4) Carrier concentration estimate

For single-carrier transport, the tool estimates n from n = 1/(|e·R_H|). As a quick data reference, many doped semiconductors fall in 10¹⁴–10¹⁹ cm^-3, while metals often exceed 10²² cm^-3. Mixed conduction can deviate from this simple model.

5) Mobility add-on using conductivity or resistivity

If you provide conductivity σ (or resistivity ρ), mobility is estimated by μ = |R_H|·σ with σ = 1/ρ. Reported units include m²/(V·s) and cm²/(V·s), which is common for semiconductor characterization and device modeling.

6) Uncertainty propagation for stronger reporting

Real experiments carry measurement uncertainty from voltage noise, field calibration, current stability, and thickness tolerance. The calculator supports 1σ inputs and propagates them using the standard root-sum-square method on relative terms. This produces σ(R_H) and a relative percent uncertainty.

7) Common error sources and practical checks

Contact misalignment can mix longitudinal voltage into the Hall voltage; reversing B and averaging helps cancel offsets. Ensure B is uniform, avoid thermal gradients, and keep I low enough to reduce self-heating. Verify thickness and geometry because t directly scales R_H.

8) How to interpret results for decisions

Use the sign of R_H to infer dominant carriers, the magnitude to compare doping levels, and the mobility estimate to gauge scattering quality. Exported CSV and PDF reports support lab notebooks, QA documentation, and repeatability studies across samples and temperatures.

1) What does a negative Hall coefficient mean?

A negative R_H typically indicates electrons dominate conduction. The sign comes from the direction of the Hall voltage relative to the applied magnetic field and current, using the common physics sign convention.

2) Why do I need the sample thickness?

Thickness t scales the Hall coefficient through R_H = (V_H·t)/(I·B). If thickness is wrong, R_H and the derived carrier concentration will be proportionally wrong.

3) Can the carrier concentration estimate be inaccurate?

Yes. The simple n = 1/(|e·R_H|) relation assumes a single dominant carrier type and simple band behavior. Two-carrier transport, strong anisotropy, or complex scattering can shift the effective Hall factor.

4) How is mobility calculated in this calculator?

Mobility is estimated by μ = |R_H|·σ, where σ is conductivity. If you enter resistivity ρ, the tool converts it using σ = 1/ρ before calculating mobility.

5) Should I reverse the magnetic field during measurements?

It is strongly recommended. Measuring at +B and −B and averaging the antisymmetric component helps cancel contact misalignment and offset voltages, improving the reliability of V_H and R_H.

6) What units should I use for best accuracy?

Use the units you measured directly, then select matching units in the form. The calculator converts internally to SI (V, T, A, m). This reduces manual conversion mistakes and keeps the sign consistent.

7) Why is the uncertainty section optional?

Not every workflow needs formal uncertainty. When available, entering 1σ uncertainties provides σ(R_H) and relative uncertainty, which improves comparability across runs, instruments, and sample batches.