I was asked this question during a viva examination. I tried to give answer through mathematical derivation but I was told to give the answer from intuition.

So why is $n_0 p_0 = n_i^2$, and not $n_0 + p_0 = \text{(some constant)}$

Why is $n_0 + p_0$ not constant ?

  • $\begingroup$ Because it is, in essence, a chemical reaction governed by detailed balance. Just like chemical equilibrium if a reaction is a product, not sum, based reaction constant. $\endgroup$ – Jon Custer May 29 at 11:47
  • $\begingroup$ Maybe it's not the physics answer, but suppose you had $n > 2n_i$. Would you expect to have $p<0$? $\endgroup$ – The Photon May 29 at 17:36

Consider the reaction

$${A <=> B + C}$$

Taking $A$ as the standard state, using the law of mass action or detailed balance from chemistry, the reaction constant is then

$${K = [B][C]}$$

Now, $A$ is a filled state in the valence band. $B$ is an electron in the conduction band and $C$ is a hole in the valence band. As long as there is a path for e-h generation and recombination, the reaction can and will come to equilibrium, and that equilibrium state will obey $np = $ some constant. Adding excess $B$ or $C$ through doping shifts the ratio of $B$ to $C$, but not the overall equilibrium constant.

  • $\begingroup$ What’s does the square bracket notation mean? $\endgroup$ – boyfarrell May 29 at 20:05
  • $\begingroup$ In chemistry those mean concentrations, so map directly to $n$ or $p$. $\endgroup$ – Jon Custer May 29 at 20:54

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