13 Jul 2026

Hall Coefficient of a Semiconductor Sample

practical ug-vi semiconductor hall-effect hall-coefficient

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

When current flows through a semiconductor in a perpendicular magnetic field, a transverse Hall voltage is produced. For sample thickness $t$,

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

The sign of $V_H$ identifies the dominant carrier type.

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 $V_H=3.6\,\text{mV}$,

\[R_H=\frac{3.6\times10^{-3}\times0.50\times10^{-3}}{5\times10^{-3}\times0.40}=2.25\times10^{-3}\,\text{m}^3\text{C}^{-1}.\]

Thus $n=1/(eR_H)=2.78\times10^{21}\,\text{m}^{-3}$.

Result

\[\boxed{R_H=2.25\times10^{-3}\,\text{m}^3\text{C}^{-1}},\qquad \boxed{n=2.78\times10^{21}\,\text{m}^{-3}}.\]

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 Maxima calculation file.