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Question 19

The resistivity $$(\rho)$$ of semiconductor varies with temperature. Which of the following curve represents the correct behaviour?

Solution

The fundamental relationship is given by $$\rho = \frac{m}{n e^2 \tau}$$.

In semiconductors, increasing the temperature causes a rapid increase in carrier number density ($$n$$), making $$n \propto T$$.

Since $$\rho \propto \frac{1}{n} \implies \rho \propto \frac{1}{T}$$, the resulting plot forms a rectangular hyperbola.

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