Equilibrium fermi level and carrier concentration

[HenzNett]

Problem statement:
Determine electron and hole concentrations in Si at room temperature given that the Fermi level is 0.20eV above the valence band energy.

So my thoughts on this problem:
First we draw the band diagram, and it's clear that this is P type.
Then, p0 = Nv * exp((Ef - Ev)/KT)
Last step: n0 = ni^2/p0

But the n0 i got is smaller than 1, so I looked it up on the internet and found a similar problem, where instead of using Ef-Ev they used Ef-Ei, so in their equation, p0 = ni*exp((Ei-Ef)/KT)

Which one (if not both) of the equations should I use in this setting?

Thanks.

 

[anathema]

Thank you for sharing your thoughts on this problem. It seems like you have a good understanding of the concept of electron and hole concentrations in semiconductors at room temperature. However, there are a few things that I would like to clarify and suggest for your approach to this problem.

Firstly, you are correct in drawing the band diagram and identifying that this is a p-type semiconductor. This means that the majority carriers are holes and the minority carriers are electrons. The Fermi level being 0.20eV above the valence band energy indicates that there is a higher concentration of holes in the valence band compared to electrons in the conduction band.

Secondly, the equation you have used for calculating the hole concentration, p0, is correct. As you have mentioned, it is based on the principle that the hole concentration is equal to the product of the effective density of states in the valence band (Nv) and the exponential term, which is a function of the difference between the Fermi level and the valence band energy (Ef - Ev) divided by the thermal energy (KT). Therefore, the equation you have used, p0 = Nv * exp((Ef - Ev)/KT), is the correct one to use in this case.

However, for the electron concentration, n0, you have used an equation that is based on the intrinsic carrier concentration, ni, which is not applicable in this case. The intrinsic carrier concentration is the equilibrium concentration of electrons and holes in a pure semiconductor, and it is not relevant in this problem as we are dealing with a doped semiconductor (p-type). Therefore, you should use the equation for the electron concentration, n0 = p0 * exp((Ev - Ef)/KT), where the exponential term is now a function of the difference between the conduction band energy and the Fermi level (Ev - Ef).

In summary, for this problem, you should use the following equations:
- p0 = Nv * exp((Ef - Ev)/KT) to calculate the hole concentration
- n0 = p0 * exp((Ev - Ef)/KT) to calculate the electron concentration

I hope this helps clarify your understanding and approach to this problem. Good luck with your calculations!


(Scientist)