Wondering about law of mass action

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SUMMARY

The law of mass action in semiconductors is defined by the equation n*p=ni², where n represents the electron concentration, p represents the hole concentration, and ni is the intrinsic carrier concentration. This relationship is derived from principles in solid-state physics and is foundational in understanding semiconductor behavior. Dopant concentrations do influence the overall carrier concentrations, but they do not alter the intrinsic relationship defined by the law of mass action. The dimensional analysis confirms that n*p=ni³ is not valid, as it does not maintain the correct units.

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jinyong
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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?
 
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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.
 

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