13 Jul 2026

Hall Coefficient, Carrier Type, and Hall Angle of a Semiconductor

practical pg-iii semiconductor hall-effect hall-angle

Aim

To determine the Hall coefficient, identify the type of charge carriers, and calculate the Hall angle of a semiconductor.

Apparatus

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

Experimental arrangement

The specimen carries current along its length, the magnetic field is perpendicular to the specimen, and Hall voltage is measured across its width.

Theory

Moving charge carriers experience the Lorentz force in a magnetic field. In a rectangular sample carrying current along the $x$-direction, the magnetic force pushes carriers towards one side. The resulting transverse electric field grows until the electric and magnetic forces balance. This field produces the Hall voltage $V_H$.

For sample thickness $t$, current $I$, and magnetic field $B$,

\[R_H=\frac{V_Ht}{IB}.\]

The sign of $R_H$ identifies the dominant carriers. If $V_x$ is the longitudinal voltage between contacts separated by $L$, and the Hall contacts are separated by width $w$, the Hall angle is

\[\tan\theta_H=\frac{E_H}{E_x}=\frac{V_H/w}{V_x/L}=\frac{LV_H}{wV_x}.\]

For one dominant carrier type, the concentration is $n=1/(e

R_H

)$.

Observations

Sample thickness $t=0.50$ mm, contact separation $L=10$ mm, width $w=5$ mm, and current $I=5$ mA.

Magnetic field (T)	Hall voltage (mV)	Longitudinal voltage $V_x$ (mV)	Hall angle (degree)
0.20	1.8	180	1.15
0.30	2.7	180	1.72
0.40	3.6	180	2.29
0.50	4.5	180	2.86

Graph

Hall voltage increases linearly with magnetic field when the current is constant.

Calculation

For $B=0.40$ T and $V_H=3.6$ mV,

\[R_H=\frac{(3.6\times10^{-3})(0.50\times10^{-3})}{(5\times10^{-3})(0.40)}=9.00\times10^{-4}\ \mathrm{m^3C^{-1}}.\]

Also,

\[\tan\theta_H=\frac{(10)(3.6)}{(5)(180)}=0.040,\]

so $\theta_H=2.29^\circ$.

Result

\[\boxed{R_H=9.00\times10^{-4}\ \mathrm{m^3C^{-1}}},\qquad \boxed{\theta_H=2.29^\circ}.\]

The positive Hall coefficient indicates a p-type sample.

Viva Questions

1. What causes Hall voltage? The sideways Lorentz force on moving charge carriers.
2. What does the sign of Hall coefficient show? It identifies whether electrons or holes dominate conduction.
3. What is Hall angle? The angle between the total electric field and the longitudinal electric field in a magnetic field.

Maxima Code

Download the PG-III calculation file.