How it works
When current I flows in the x-direction and magnetic field B is applied in the z-direction, the Lorentz force qv×B deflects charge carriers in the y-direction. In n-type material, electrons accumulate on one face; in p-type, holes accumulate on the opposite face. This charge buildup creates the Hall electric field EH, which opposes further deflection until equilibrium. The Hall voltage is VH = IB/(nqt), where n is carrier concentration, q = 1.6×10⁻¹⁹ C, and t is the sample thickness. The Hall coefficient RH = 1/nq for n-type and RH = −1/pq for p-type, with the sign indicating carrier type.
Key points to remember
The Hall coefficient RH = 1/nq for electrons and −1/pq for holes — the sign directly identifies majority carrier type, which is a favourite one-mark exam question. Hall voltage VH = IB/nqt, so a thinner sample gives a larger, more measurable VH. Typical Hall voltages in lab experiments range from microvolts to a few millivolts for standard semiconductor strips. Hall effect sensors are used commercially in brushless DC motor position sensing and in magnetic field meters. Carrier mobility can also be extracted as μ = RH × σ, combining Hall measurement with a simple conductivity test.
Exam tip
The examiner always asks you to determine carrier type from the sign of RH and to calculate Hall voltage using VH = IB/nqt — watch the units: B in tesla, t in meters, and n in /m³ not /cm³.