# Fermi dirac probability

1. Sep 10, 2016

### falcon555

Hi dear friends
Please reffer to my work , I did part ( a )
Can someone help me to solve part( b )

2. Sep 10, 2016

### rude man

(a) is correctly done.
(b):
My textbook gives the probability distribution for holes as not W(p) as it is for electrons, but as 1 - W(p). Without a believable rationale, but I'm sure it's correct, because later on they use that expression for deriving the totality of free carriers for electrons and for holes and get roughly the same number for each, which has to be correct.

So, bottom line, if you use 1 - W(p) for the holes, and use Wv in lieu of Wc, and proceedig exactly as you did in part (a), you will get your answer. Do that and let us know what you come up with.

3. Sep 11, 2016

### falcon555

If we assume the number of electrons and the holes are the same ,then we suppose to get the same value

Or you mean to say

1 - 3.99 × 10^(-10) = 2.99 × 10^(-10)

4. Sep 11, 2016

### rude man

Right. The answer for (b) is the same as the answer for (a).

But you derived p(Wh) = {1 - exp(WG/kT)}-1 when it should be {1 + exp(WG/kT)}-1 which may be just a typo.
I don't think anyone would say that! (Look at that statement more carefully! )

5. Sep 11, 2016

### falcon555

Ok
It means without any extra calculation we can asume that both the values are the same as a rule of thumb, right?
Because the holes and the electrons are generated in pairs, right?

6. Sep 11, 2016

### rude man

That's what I always suspected, but I decided to make sure by going with the formulas. I wasn't sure if an electron at the very bottom of the conduction band implied a hole at the very top of the valence band until I worked the formulas.

It's certainly true that, in an intrinsic (undoped) semiconductor like Si, a hole is created when and only when an electron is kicked up to the conduction band, and vice-versa.

7. Sep 11, 2016

### falcon555

Thank you very much bro for helping me.
You are great.

Cheers

8. Sep 12, 2016

### rude man

You're very welcome. Educational for me too!
P.S. is that your cat? Lovely boy!