Question

The effect of an increase in temperature on the number of electrons in the conduction band (\( n_e \)) and the resistance of a semiconductor will be as follows:

• A. Both \( n_e \) and resistance decrease
• B. Both \( n_e \) and resistance increase
• C. \( n_e \) increases, resistance decreases
• D. \( n_e \) decreases, resistance increases

Hint:

For semiconductors: - Higher temperature → More electrons in conduction band. - More free charge carriers → Lower resistivity → Lower resistance. - This behavior is opposite to metals, where resistance increases with temperature.

Answer 1

The Correct Option is C

Step 1: Understanding the effect of temperature on a semiconductor. - A semiconductor has a band gap between the valence band and conduction band. - At higher temperatures, more electrons get enough thermal energy to jump from the valence band to the conduction band. - This results in an increase in the number of free electrons (\( n_e \)). 
Step 2: Effect on resistance. - The resistance (\( R \)) of a semiconductor is given by: \[ R = \frac{\rho L}{A}, \quad {where } \rho { is the resistivity}. \] - Resistivity (\( \rho \)) is inversely proportional to the number of free charge carriers: \[ \rho \propto \frac{1}{n_e} \] - As \( n_e \) increases with temperature, resistivity decreases, leading to a decrease in resistance. 
Final Answer: \[ \boxed{n_e { increases, resistance decreases}} \]