Explanation:

To understand why the width of the depletion layer decreases when the doping levels of the semiconductor are increased, we need to first understand what the depletion layer is and how it is formed.

Depletion Layer:
The depletion layer is a region in a semiconductor device where there are no mobile charge carriers (electrons or holes) due to the combination of p-type and n-type materials. It is formed at the junction between the two types of semiconductor materials.

Formation of Depletion Layer:
When a p-type and an n-type semiconductor are brought together to form a p-n junction, the free electrons from the n-type material diffuse into the p-type material, and the holes from the p-type material diffuse into the n-type material. This diffusion process continues until there is an equal number of electrons and holes on both sides of the junction.

Width of Depletion Layer:
The width of the depletion layer is determined by the concentration of dopants in the p- and n-type regions. When there is a higher concentration of dopants, the width of the depletion layer decreases, and when there is a lower concentration of dopants, the width of the depletion layer increases.

Effect of Increased Doping Levels:
When the doping levels of the semiconductor are increased, it means that there is a higher concentration of dopants in the p- and n-type regions. This higher concentration of dopants results in a higher concentration of charge carriers (electrons or holes) in the semiconductor material.

Impact on Depletion Layer:
The higher concentration of charge carriers leads to a higher rate of diffusion across the junction. As a result, more charge carriers from the n-type material diffuse into the p-type material and vice versa. This increased diffusion rate reduces the width of the depletion layer.

Conclusion:
In summary, when the doping levels of the semiconductor are increased, the width of the depletion layer decreases. This is because the higher concentration of dopants leads to a higher concentration of charge carriers, resulting in an increased rate of diffusion across the junction and a reduction in the width of the depletion layer.