If the forward voltage in a semiconductor is doubled, the width of depletion layer will

Options

A. become half
B. become one fourth
C. remain unchanged
D. become double

Answer

To solve the question regarding the effect of doubling the forward voltage on the width of the depletion layer in a semiconductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the PN Junction Diode**:
- A PN junction diode consists of a P-type semiconductor (which has holes as majority carriers) and an N-type semiconductor (which has electrons as majority carriers).
- When the diode is forward-biased (P side connected to positive voltage and N side connected to negative voltage), the majority carriers (holes and electrons) move towards the junction.

2. **Effect of Forward Bias on Depletion Layer**:
- The depletion layer is the region around the PN junction where charge carriers are depleted. It is formed due to the recombination of holes and electrons at the junction.
- When a forward voltage is applied, it reduces the potential barrier at the junction, allowing more charge carriers to cross the junction.

3. **Doubling the Forward Voltage**:
- If the forward voltage is doubled, the electric field across the depletion layer increases.
- This increased electric field allows more electrons from the N-side to move towards the P-side and more holes from the P-side to move towards the N-side.

4. **Impact on Depletion Width**:
- As more charge carriers cross the junction, the depletion region shrinks.
- The relationship between the width of the depletion layer (W) and the applied voltage (V) can be described as inversely proportional: \( W \propto \frac{1}{\sqrt{V}} \).
- Therefore, if the voltage is doubled (2V), the new width of the depletion layer can be calculated as follows:
\[ W' = \frac{W}{\sqrt{2}} \quad \text{(since voltage is doubled)} \]

5. **Conclusion**:
- Since \( W' \) is inversely proportional to the square root of the voltage, if the forward voltage is doubled, the width of the depletion layer will decrease to half its original width.
- Thus, the final answer is that the width of the depletion layer will become half.

### Final Answer:
The width of the depletion layer will become half if the forward voltage is doubled.