# Probability that energy level is occupied

1. Jun 4, 2009

### unscientific

The probability that an electron is in an excited state is given:

P = e^-(energy difference)/kt

and the probability that an energy level is occupied in semi conductors is:

p = 1/ (e^(E-Ef)kt + 1)

I know both are related to fermi-dirac statistics, which one is the appropraite one to use?

2. Jun 4, 2009

### bartek2009

Both distributions,

FD: p = 1 / (exp[(e - u)/kT] + 1)

and

BE: p = 1 / (exp[(e - u)/kT] - 1)

approach

MB: p = exp[(u - e)/kT]

at high temperatures (i.e. in classical limit).
So it depends on the temperature.

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Last edited by a moderator: Aug 6, 2009
3. Jun 4, 2009

### unscientific

uhh, im afraid i dont get you =x

4. Jun 4, 2009

### bartek2009

FD and BE differ by (+/-)1 factor.
This can be neglected if

exp(e - u) >> 1

which happens in classical regime,
that is at high temperatures
or at low concentrations.

You can try some rough values for semiconductors,
Setting zero at the top of valence band,

Eg ~ 1eV (energy gap)
Ef ~ 0.5eV (midway between val. and cond. band)

so E in cond. band is about 1eV

also kT ~ 0.025eV

so one gets

1/[exp(20) + 1] ~ 1/exp(20) = exp(-20)

since exp(20) is huge.

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Last edited by a moderator: Aug 6, 2009