The width of the depletion layer is proportional to 1/√Doping.

Explanation:

The depletion layer is a region in a semiconductor device where there are no mobile charge carriers due to the presence of a built-in electric field. It is formed at the junction between two different types of semiconductor materials, such as p-type and n-type.

1. Depletion Layer:
When a p-n junction is formed, the majority carriers from one side (holes in p-type and electrons in n-type) diffuse across the junction and recombine with the majority carriers of the opposite type. This creates a region near the junction with no mobile charge carriers, known as the depletion layer. The width of this region is an important parameter in determining the behavior and characteristics of the p-n junction.

2. Doping:
Doping is the intentional introduction of impurities into a semiconductor to modify its electrical properties. Doping can be done by adding impurities of a different valence to the semiconductor crystal lattice. The concentration of these impurities is referred to as doping concentration.

3. Relationship between Depletion Layer Width and Doping:
The width of the depletion layer is inversely proportional to the square root of the doping concentration. This means that as the doping concentration increases, the width of the depletion layer decreases.

Explanation:
1. The width of the depletion layer is determined by the balance between the diffusion of majority carriers and the electric field created by the ionized donors and acceptors in the depletion region.
2. When the doping concentration is high, there are more ionized donors and acceptors, resulting in a stronger electric field that pushes the majority carriers away from the junction.
3. As a result, the depletion region becomes narrower because the majority carriers are pushed further away from the junction, reducing the width of the region where there are no mobile charge carriers.
4. On the other hand, when the doping concentration is low, there are fewer ionized donors and acceptors, leading to a weaker electric field. This allows the majority carriers to diffuse closer to the junction, increasing the width of the depletion layer.
5. Therefore, the width of the depletion layer is inversely proportional to the square root of the doping concentration, as stated in option C.

A depletion region consists of immobile charge carriers such as positive ions and negative ions. The mobile charge carriers such as free electrons are absent in depletion region. The p-side of the depletion region has negative ions and n-side of the depletion region has positive ions.