# Number of intrinsic charge carriers in semiconductors

On one hand, my book calls both electrons and holes intrinsic charge carriers of a semiconductor, and on the other, it states the relation x = y = n, where x, y and n stand for the number of electrons, holes and intrinsic charge carriers respectively. Shouldn't it be n = x+y instead?

## 1 Answer

Normally what we call the intrinsic charge carrier concentration, that I note $$n_i$$ is the number of charge of any kind (not their) sum. It is a convention to build the theory nothing more. Having defined something like $$n'_i = e + h$$ would have make the equations much more ugly.

This will be of use latter, because even though the semiconductor is not intrinsic the relation

$$e\cdot h = n_i^2$$

will be verified.

Notice that your case verify this.

It is a terrible idea to use the notation $$e, h$$ (especially e) as it will be confused with the charge.

If you are new to semiconductors I recommend you to read the two dedicated chapters of Ashcroft and Mermin. They are clear and give a good baseground.

Best

• Thank you! That explains it all. – Ambica Govind Feb 2 at 13:05
• @ZMeson - and please, please start now with treating electrons and holes as full equals - your life will be much easier. – Jon Custer Feb 2 at 14:56
• @Jon Custer Noted. :) – Ambica Govind Feb 3 at 15:54