Wondering about law of mass action

[jinyong]

I am wondering why the law of mass action in semiconductors is this relation: n*p=ni^2. Any proof of this why is it not n*p=ni^3 or something...Also why doesn't dopants affect this relationship since doesn't dopants increase the overall number of carriers?

 

[Gokul43201]

Does it even make dimensional sense to write n*p=ni^3? You need to learn how the law is derived - you will find it in any solid state electronics text.

And yes, dopant concentrations are considered in arriving at that final result.

 

[charng]

The law of mass action in semiconductors, also known as the law of mass action for charge carriers, is a fundamental concept in semiconductor physics that describes the relationship between the concentration of electrons (n) and holes (p) in a semiconductor material. This law states that the product of the electron and hole concentrations is equal to the square of the intrinsic carrier concentration (ni), which represents the concentration of charge carriers in an undoped or pure semiconductor material.

The reason for this specific relationship is based on the principles of equilibrium in a semiconductor. In an intrinsic semiconductor, the number of electrons is equal to the number of holes, leading to a balanced concentration of both types of carriers. This balance is maintained through the process of electron-hole recombination, where an electron and a hole combine and neutralize each other. In this state of equilibrium, the product of n and p is equal to the square of ni.

As for why this relationship is not n*p=ni^3 or something else, it is due to the specific properties of semiconductors and the way they behave at equilibrium. The concentration of charge carriers in a semiconductor is strongly influenced by factors such as temperature, bandgap energy, and doping. The law of mass action takes into account all of these factors and provides a simple and accurate description of the equilibrium state of a semiconductor material.

Regarding the effect of dopants on this relationship, it is important to note that dopants do not increase the overall number of carriers in a semiconductor. Instead, they introduce impurities into the material that can either donate or accept electrons, leading to an increase or decrease in the concentration of either electrons or holes. However, the overall balance between electrons and holes remains the same, and thus the law of mass action still holds true.

In summary, the law of mass action in semiconductors is a fundamental concept that describes the equilibrium state of charge carriers in a semiconductor material. Its specific relationship of n*p=ni^2 is a result of the properties of semiconductors and the principles of equilibrium. The presence of dopants does not affect this relationship, as they do not alter the overall balance of charge carriers in the material.