Introduction:
In an extrinsic semiconductor, the concentration of minority carriers refers to the number of charge carriers (electrons or holes) that are present in the material but are not the majority carriers. The majority carriers are the charge carriers that are more abundant in the material due to doping. The concentration of minority carriers plays a crucial role in the conductivity and other electrical properties of the semiconductor.

Doping in Extrinsic Semiconductors:
Extrinsic semiconductors are created by intentionally adding impurities to the material to increase its conductivity. This process is called doping. Doping introduces either donor impurities (which provide excess electrons) or acceptor impurities (which create excess holes) into the semiconductor material.

Effect of Doping Concentration:
The concentration of minority carriers in an extrinsic semiconductor is inversely proportional to the doping concentration. This means that as the doping concentration increases, the concentration of minority carriers decreases, and vice versa.

Explanation:
When an extrinsic semiconductor is doped, the majority carrier concentration increases significantly due to the addition of excess electrons or holes. These excess carriers become the majority carriers and dominate the electrical behavior of the material. As a result, the concentration of minority carriers (the carriers that are not the majority) decreases.

Reasoning:
The reason behind this inverse relationship between doping concentration and minority carrier concentration can be explained by considering the Law of Mass Action. According to this law, the product of the majority carrier concentration and the minority carrier concentration in a semiconductor material is constant at a given temperature.

When the doping concentration increases, the majority carrier concentration increases, and as a result, the product of the majority and minority carrier concentrations remains constant. Since the majority carrier concentration dominates the conductivity, the minority carrier concentration decreases to maintain this constant product.

Therefore, the concentration of minority carriers in an extrinsic semiconductor is inversely proportional to the doping concentration. As the doping concentration increases, the concentration of minority carriers decreases, and as the doping concentration decreases, the concentration of minority carriers increases.

Conclusion:
In an extrinsic semiconductor under equilibrium, the concentration of minority carriers is inversely proportional to the doping concentration. This relationship is important to understand the electrical behavior and conductivity of extrinsic semiconductors.