13 Jul 2026

Hall Effect: Carrier Type, Hall Coefficient, and Carrier Concentration

practical pg-iv cmp semiconductor hall-effect carrier-concentration

Experimental arrangement

Current flows along the semiconductor strip, the magnetic field is perpendicular to it, and the transverse Hall voltage is measured.

Aim

To determine the Hall coefficient and carrier concentration of a semiconductor sample.

Apparatus

Semiconductor Hall sample, electromagnet, constant-current source, microvoltmeter, Gauss meter, and micrometer.

Theory

The current in a semiconductor is carried by drifting electrons or holes. When the specimen is placed in a magnetic field perpendicular to the current, each moving carrier experiences the Lorentz force $q(\mathbf v\times\mathbf B)$. The carriers therefore accumulate on one side of the specimen until the transverse electric force balances the magnetic force:

\[qE_H=qv_dB.\]

This charge separation produces the Hall voltage $V_H$. Reversing the magnetic field or the current reverses the Hall voltage, which is why reversal readings are averaged in practice.

For a specimen of thickness $t$, current $I$, and magnetic field $B$,

\[R_H=\frac{V_Ht}{IB},\qquad n=\frac{1}{eR_H}.\]

The sign of $V_H$ identifies the dominant carrier type, while the magnitude of $R_H$ gives the carrier concentration. For a single carrier type, $n=1/(e

R_H

)$. The Hall angle is obtained from $\tan\theta_H=E_H/E_x$ when the longitudinal field is measured as well.

Observations

Sample thickness $t=0.50\,\text{mm}$; current $I=5\,\text{mA}$.

Magnetic field (T)	Hall voltage (mV)
0.20	1.8
0.30	2.7
0.40	3.6
0.50	4.5

Graph

Hall voltage plotted against magnetic field for constant sample current.

Calculation

For $B=0.40\,\text{T}$ and $V_H=3.6\,\text{mV}$,

\[R_H=\frac{3.6\times10^{-3}\times0.50\times10^{-3}}{5\times10^{-3}\times0.40}=9.00\times10^{-4}\,\text{m}^3\text{C}^{-1}.\]

Thus

\[n=\frac{1}{eR_H}=\frac{1}{(1.602\times10^{-19})(9.00\times10^{-4})}=6.93\times10^{21}\,\text{m}^{-3}.\]

Result

\[\boxed{R_H=9.00\times10^{-4}\,\text{m}^3\text{C}^{-1}},\qquad \boxed{n=6.93\times10^{21}\,\text{m}^{-3}}.\]

Precautions

1. Reverse the magnetic field and average the Hall readings.
2. Keep the sample current constant.
3. Ensure that the magnetic field is perpendicular to the current.

Viva Questions

1. What is the Hall effect? It is the production of a transverse voltage in a current-carrying sample placed in a magnetic field.
2. What determines the sign of Hall voltage? The sign of the dominant charge carriers.
3. Why is a thin sample preferred? It gives a measurable Hall voltage for a given current and field.

Maxima Code

Download the PG-IV Hall-effect calculation.