# Electrons and Holes in a semiconductor

In an exercise I have an un-doped silicon I find that p=1.80e+11 ,n=6.60e+10 , should the numbers be more close to each other? (for example in GaAs I find 1.10e+14 and 1.60e+14)?? (also p number of holes and n number of electrons)

T=300 Temperature in K Nc=2.8*(10^19) (density of states I guess in English) Nv=1.04*(10^19) Eg=1.12 eV Band Gap

Am I missing something?

• Please provide more information. Undoped means there is no P or N type silicon. How did you get these figures? – Sven B May 24 '18 at 15:26
• Please explain your variables, everyone has different letters for different physical values – laptop2d May 24 '18 at 15:30
• I used the type n=𝑁c exp[Ec-Ef] and p = Nv exp[Ev-Ef] – Stavros Avramidis May 24 '18 at 15:30
• @laptop2d got it – Stavros Avramidis May 24 '18 at 15:37

First, concentrations of electrons and holes must obey the law of mass action (at equilibrium):

$$np=n_i^2$$

Your calculated values clearly violate this for silicon, therefore you can easily tell your calculation is wrong.

It's hard to know what approach an instructor asking this question would want you to follow. If someone asked me to answer this question, I would just write down the answer. If you don't know it off the top of your head, consider what $n_i$ represents. If you still don't know the answer or want to just use some basic equations, continue on.

The problem is easier than you are making it. All semiconductors in equilibrium follow the previous law, and also are charge neutral:

$$n + N_A^- = p + N_D^+$$

In an undoped semiconductor the acceptor and donor concentrations are both zero (by definition) and therefore you are left with:

$$n=p$$

Calculating the actual numbers is left as an exercise for the reader. (Hint: If you need a calculator, it's probably wrong)

• Shouldn't these n=Nc exp[Ec-Ef] and p = Nv exp[Ev-Ef] gave me the correct numbers? – Stavros Avramidis May 24 '18 at 16:12
• @Stavros I don't remember exactly what assumptions go into the derivation of those equations, but they are an approximation. They "should" probably give you the right answer, but clearly they didnt this time (although I didnt check your math) Note that for an intrinsic semiconductor n and p should be exactly the same, not just pretty close. – Matt May 24 '18 at 16:16
• @Stavros Also, how do you know what the Fermi level is? It is not accurate to assume it is at midgap (That can sometimes be a reasonable approximation for Si. This is not one of those cases) – Matt May 24 '18 at 16:18
• It states that Ec - Ef = Egap/2, (also Python did my math) – Stavros Avramidis May 24 '18 at 16:19
• @Stavros Then it is wrong. That is only true if Nc=Nv, which is not the case for Si or any other semiconductor I can think of. – Matt May 24 '18 at 16:20