Question

Show on a graph, the variation of resistivity with temperature for a typical semiconductor.

Answer 1

Resistivity

1. Resistivity is the resistance of a conductor of unit length and unit area.
2. For a typical semiconductor, the resistivity is defined by the form, $\rho =\frac{m}{{\mathrm{\pi e}}^2\mathrm{\tau }}$, where, n is the number density of electrons, $\tau$ is the relaxation time, m is the mass of the semiconductor, and e is the electronic charge.
3. The above formulae show that the resistivity is inversely proportional to the time in the case of a typical semiconductor. i.e, $\rho \propto \frac{1}{T}$.
4. So, as temperature increases, the resistivity of metal increases, giving it a positive temperature coefficient of resistance.
5. This is because when temperature rises, electrons in the valence band get enough thermal energy to move to the conduction band.
6. As the number of electrons in the conduction band grows, so does conductivity and resistance.
7. Taking $\rho$ as a vertical and t as horizontal. We know, $\rho$ is the function of t.

Therefore, the above graph is represented as R vs $\rho$graph.