Question

Which of the following graph represents the temperature (T) dependence of resistivity (\(ρ\)) of a semiconductor?

• A. A
• B. B
• C. C
• D. D

Hint:

In a semiconductor more carriers are freed as temperature rises, so resistivity falls in a curved, exponential way.

Answer 1

The Correct Option is B

Step 1: Recall the behaviour:
In a metal, resistivity rises with temperature. In a semiconductor, the opposite happens: resistivity falls as temperature rises.

Step 2: Reason:
Heating gives more electrons enough energy to jump from the valence band to the conduction band. The number of free charge carriers grows fast, in an exponential way, so \(\rho \propto e^{E_g/(2k_BT)}\) falls quickly at low T and flattens at high T.

Step 3: Read the graphs:
Graph A is a straight line rising with T (typical of a metal). Graph B is a curve falling steeply and then flattening, as expected. Graph C is a straight falling line. Graph D is a curve that rises.

Step 4: Pick the graph:
Graph B matches the exponential fall. Graph C is also falling, but a straight line would mean a constant rate of fall, which does not match an exponential law. A and D rise, so they are wrong for a semiconductor.

Final Answer:
The curve of resistivity falling non-linearly with temperature is graph B. \[ \boxed{\text{B}} \]