What this calculator does
Pass a current through a conductor sitting in a magnetic field and a small voltage appears across it, at right angles to both. That transverse voltage is the Hall effect, and measuring it reveals how many charge carriers the material contains and what sign they have.
The sign result is the striking part. In most metals the carriers are electrons and the coefficient is negative, but in some semiconductors it comes out positive, indicating conduction by holes. There was no way to discover that before the Hall measurement existed.
The formula
The Hall coefficient is the measured Hall voltage times the conductor thickness, divided by the current times the magnetic field. Carrier concentration is one over the coefficient times the elementary charge.
| Term | Meaning |
|---|---|
| Hall coefficient (RH) | The transverse voltage per unit current-field product, scaled by thickness. |
| Carrier concentration (n) | The number of mobile charge carriers per cubic metre. |
| Carrier sign | Negative for electron conduction, positive for hole conduction in a semiconductor. |
The inputs explained
| Field | What to enter |
|---|---|
| Hall voltage (VH) (μV) | The measured Hall voltage in microvolts. It is usually very small. |
| Conductor thickness (mm) | The thickness of the sample along the magnetic field direction, in millimetres. |
| Current (I) (A) | The current flowing through the sample, in amperes. |
| Magnetic field (B) (T) | The applied magnetic flux density in tesla. |
When to use it
Characterising a semiconductor
Carrier concentration and type are the two figures that define how a doped sample will behave.
Designing a Hall sensor
A thinner sample with fewer carriers produces a larger Hall voltage for the same field.
Measuring a magnetic field
Running the relationship in reverse with a calibrated sample turns it into a field probe.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What carrier concentration does each Hall voltage imply?
The same sample producing a range of measured Hall voltages.
| Hall voltage | Hall coefficient (RH) | Carrier concentration (n) |
|---|---|---|
| 1 μV | 6.2500e-10 m³/C | 9.9864e+27 /m³ |
| 5 μV | 3.1250e-9 m³/C | 1.9973e+27 /m³ |
| 20 μV | 1.2500e-8 m³/C | 4.9932e+26 /m³ |
| 50 μV | 3.1250e-8 m³/C | 1.9973e+26 /m³ |
Questions
Why does a small Hall voltage mean many carriers?
Because with plenty of carriers available, each one moves slowly to carry the given current. The magnetic deflection depends on carrier speed, so slow carriers pile up less at the edge and produce a smaller transverse voltage.
What does a positive coefficient mean?
That conduction is dominated by holes rather than electrons, which is the signature of a p-type semiconductor. Discovering positive carriers in some materials was one of the early puzzles the Hall effect posed.
Why are Hall voltages so small in metals?
Metals have enormous carrier concentrations, so the drift speed is tiny and the deflection is barely measurable. Semiconductors have far fewer carriers, which is why practical Hall sensors are built from them.
Does sample thickness matter?
Yes, and it works in your favour. A thinner sample concentrates the current and produces a larger Hall voltage for the same field, which is why sensor elements are made as thin films.
For how fast those carriers actually move, see the drift velocity calculator. For the field being measured, see the magnetic field around a wire calculator.