Question

The resistance of a semiconductor decreases when its temperature increases because:

• A. the number of free charge carriers increases
• B. electron mass decreases
• C. atomic spacing increases
• D. mobility becomes zero

Hint:

Contrast conductors and semiconductors:
In conductors (metals), $n$ is constant, and increasing temperature decreases $\tau$ (more collisions), so resistance increases (positive $\alpha$).
In semiconductors, increasing temperature increases $n$ exponentially, dominating over the change in $\tau$, so resistance decreases (negative $\alpha$).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question is from "Semiconductor Electronics" and "Current Electricity."
It asks for the physical reason behind the characteristic decrease in electrical resistance of a semiconductor with an increase in temperature.

Step 2: Key Formula or Approach:
The resistivity ($\rho$) of a material is given by:
\[ \rho = \frac{m}{n e^2 \tau} \]
where:
$m$ = mass of charge carriers
$n$ = concentration of free charge carriers
$e$ = charge of an electron
$\tau$ = relaxation time (average time between collisions)

Step 3: Detailed Explanation:

• In semiconductors, the energy gap (band gap) between the filled valence band and the empty conduction band is relatively small (typically $\lt 3\text{ eV}$).

• At low temperatures, there is insufficient thermal energy for electrons to cross this gap, meaning the number of free charge carriers in the conduction band is very small, and resistance is high.

• When the temperature of a semiconductor increases, thermal energy is supplied to the lattice.

• This thermal energy breaks covalent bonds, allowing a large number of electrons to transition from the valence band to the conduction band.

• Consequently, the concentration of free charge carriers ($n$) increases exponentially with temperature.

• Although the relaxation time ($\tau$) decreases slightly due to increased thermal vibrations and collisions, the exponential increase in the carrier concentration ($n$) completely dominates.

• As a result, the overall resistivity ($\rho$) decreases significantly, which in turn decreases the electrical resistance ($R = \rho L / A$) of the semiconductor.

• This explains why semiconductors have a negative temperature coefficient of resistance ($\alpha \lt 0$).



Step 4: Final Answer:
The resistance of a semiconductor decreases because the number of free charge carriers increases, which is option (A).