Hall Coefficient Calculator
Enter the Hall voltage, sample thickness, drive current, and applied magnetic field to instantly compute the Hall coefficient. The calculator also derives carrier concentration, Hall mobility, electrical conductivity, resistivity, and Hall angle so you get the full picture of a material's charge transport in one place.
What is the Hall effect?
When a current-carrying conductor or semiconductor is placed in a magnetic field perpendicular to the current direction, a transverse voltage builds up across the material. This phenomenon is the Hall effect, discovered by Edwin Hall in 1879. The mechanism is the Lorentz force: the magnetic field deflects moving charge carriers sideways until the resulting electric field exactly balances the magnetic force. The polarity of that transverse voltage (the Hall voltage) reveals whether the dominant carriers are negative electrons or positive holes.
Hall coefficient formula and what it tells you
The Hall coefficient is defined as RH = VH * t / (I * B), where VH is the Hall voltage, t is the sample thickness along the field direction, I is the drive current, and B is the magnetic flux density. Its sign reveals carrier type: a negative RH confirms electron conduction (n-type), a positive RH confirms hole conduction (p-type). From RH you can derive the carrier concentration as n = 1 / (|RH| * e), where e is the elementary charge (1.602 * 10^-19 C). When you also know the electrical conductivity sigma, the Hall mobility follows directly: mu = |RH| * sigma. A high mobility material sustains faster charge transport with less scattering, which is why Hall measurements are a standard quality check in semiconductor manufacturing.
How to perform a Hall measurement
A standard Hall bar sample is a thin rectangular slab with current contacts at each end and voltage contacts on the long sides. You apply a fixed current along the bar, sweep or fix the magnetic field perpendicular to the sample plane, and measure the transverse (Hall) voltage between the side contacts. For a reliable result the current contacts should be far from the voltage taps to avoid geometric errors, and the measurement is often repeated at reversed field and reversed current to cancel offset voltages. The van der Pauw method allows similar measurements on arbitrarily shaped samples by placing contacts at the perimeter, making it popular for thin films and wafers. Temperature control matters because carrier concentration and mobility both change with temperature: room-temperature values are the standard reference point.
Hall angle and the Hall mobility in context
The Hall angle theta_H = arctan(mu * B) is the angle between the net current flow and the applied electric field under the magnetic field. In metals the Hall angle is tiny (fractions of a degree at typical lab fields) because the high carrier concentration gives a large conductivity and only a small deflection. In high-mobility semiconductors such as indium arsenide or gallium arsenide, the Hall angle can reach several degrees or more, making Hall sensors based on those materials very sensitive. Materials with electron mobility above 1000 cm2/(V*s) are preferred for Hall sensor applications, with InAs and GaN high-electron-mobility transistors (HEMTs) among the leading candidates.
Typical Hall coefficient values for common materials
| Material | RH (m3/C) | Carrier type | Carrier concentration (cm-3) | Typical application |
|---|---|---|---|---|
| Copper (Cu) | -5.5e-11 | n-type | 8.5e22 | Interconnects, wiring |
| Silver (Ag) | -8.9e-11 | n-type | 5.9e22 | Contacts, mirrors |
| Gold (Au) | -7.2e-11 | n-type | 5.9e22 | Contacts, bonding wire |
| Aluminum (Al) | -3.5e-11 | n-type | 1.8e23 | Packaging, interconnects |
| Silicon (Si, n-type) | -~1e-2 | n-type | ~1e15 | MOSFETs, diodes |
| Silicon (Si, p-type) | +~1e-2 | p-type | ~1e15 | MOSFETs, diodes |
| Germanium (n-type) | -~1e-2 | n-type | ~1e13 | Detectors, transistors |
| GaAs (n-type) | -~1e-3 | n-type | ~1e16 | HEMTs, LEDs, solar cells |
| InAs (n-type) | -~1e-3 | n-type | ~1e16 | Hall sensors, IR detectors |
Values at room temperature (~300 K). Carrier concentrations and mobilities vary with doping and temperature.
Frequently asked questions
What is the Hall coefficient and what are its units?
The Hall coefficient (RH) quantifies how strongly a material develops a transverse voltage per unit of drive current and magnetic field per unit thickness. In SI units it is measured in cubic metres per coulomb (m3/C). Older literature often uses cm3/C, which is 10^6 times larger. A negative value indicates electrons carry the current; a positive value indicates holes.
How do I identify whether a semiconductor is n-type or p-type from the Hall measurement?
The sign of the Hall coefficient directly tells you the carrier type. If you apply current in the x-direction and a magnetic field in the z-direction, electrons are deflected in the negative y-direction (by the Lorentz force), producing a negative Hall voltage and a negative RH. Holes are deflected in the opposite sense, giving a positive RH. This is one of the most reliable ways to confirm whether a semiconductor is n-type or p-type without destroying the sample.
Can I use this calculator for metals as well as semiconductors?
Yes. The Hall coefficient formula is the same for metals and semiconductors. For metals the carrier concentration is very high (around 10^22 to 10^23 cm-3), so RH is extremely small - typically on the order of 10^-10 m3/C. In semiconductors the carrier concentration is much lower (10^13 to 10^18 cm-3 for typical doping levels) and RH is correspondingly larger. The carrier type derived from the sign is valid for both material classes.
What factors can cause inaccurate Hall measurements?
Common sources of error include geometric misalignment of the voltage contacts (which mixes the longitudinal and Hall voltages), surface leakage currents, ohmic heating if the current is too high, and contact resistance asymmetry. Reversing both the current and the magnetic field and averaging the four resulting voltages largely cancels offset errors and thermoelectric contributions. For thin-film or irregular samples the van der Pauw geometry with contacts at the perimeter is more reliable than a standard Hall bar.
Why is carrier mobility important and how is it related to the Hall coefficient?
Carrier mobility (mu) measures how quickly a charge carrier moves through a material in response to an electric field. Higher mobility means lower resistance for a given carrier density, which translates to faster switching in transistors and lower loss in conductors. Hall measurements give you both the carrier density and, when combined with conductivity, the mobility without needing to know the sample geometry precisely. The relationship is mu = |RH| * sigma, where sigma is the electrical conductivity.
What is the difference between Hall mobility and drift mobility?
Drift mobility is defined as the average carrier velocity per unit electric field (mu = v_d / E). Hall mobility is defined as mu_H = |RH| * sigma. In the simplest free-electron model the two are identical, but when scattering mechanisms are energy-dependent (as they usually are in real semiconductors) a correction factor called the Hall scattering factor r_H = mu_H / mu_drift arises. For many practical purposes r_H is close to 1, so Hall mobility is a good approximation to drift mobility.