How to Calculate Intrinsic Fermi Energy of Silicon?

[kylie14]

I've tried to look this up online, but I can't find it anywhere. I'm just looking for the intrinsic fermi energy of silicon E_i ?
Can someone maybe direct me towards a website where I could look it up? Either that, or is there a way to calculate it from the energy gap for intrinsic silicon (1.12eV)? I also know the intrinsic carrier concentration n_i (1.5 x10^10 cm^3).
Thanks in advance

 

[phyzguy]

If the Si is undoped (i.e. intrinsic), the Fermi energy is in the middle of the band gap. Then the concentration of electrons and holes is equal. Doping the Si moves the Fermi energy toward either the conduction or valence band, depending on the type of dopant,

 

[kylie14]

Yes, but how to I find out where the what the energy is at the centre of the band gap?
Thanks for your reply

 

[phyzguy]

I don't understand your question. What more do you need to know besides, "in the center of the band gap". There is no absolute reference for potential energy, so the value of the energy relative to the band edges is all you ever need to know.

 

[kylie14]

I needed it because it appeared in an equation I needed to find how far the fermi energy is below the conduction band in n-type silicon.
I've just found another equation though, and you're right. I can find the distance between E_f and E_i, using
E_f - E_i = kT ln(n/n_i)
and then if E_i is in the middle of the band gap then that tells me how far E_f is below the conduction band edge.
Sorry, I'm with it now, thanks for your help.

 

[phyzguy]

Ei is in the middle of the band gap. Since the band gap is 1.12 eV wide, as you said, Ei is 0.56 eV below the conduction band edge (and also 0.56eV above the valence band edge). Suppose you have n = 1E18, and ni = 1.5E10. Then the Fermi level at room temperature is kT log(n/ni) = 0.46 eV above Ei, which puts it 0.10 eV below the conduction band edge. Does this do it?

 

[kylie14]

Yes, I think that's it. Thanks again!

 

[Vokinda]

Please help :
Need expression that relates Ei and Eg both intrinsic and extrinsic case