Concentrations of electrons in intrinsic semi-conductor

[jendrix]

Hi, I've just started using the formula for the abovie which is given as:

n t^3/2 exp(Eg/2kBT)

however instead of n= I think the sign is n is proportional, like this ∞

I was wondering which would be correct?

Thanks

 

[uart]

Hi, I've just started using the formula for the abovie which is given as:

n t^3/2 exp(Eg/2kBT)

however instead of n= I think the sign is n is proportional, like this ∞

I was wondering which would be correct?

Thanks

Yes it's definitely proportional to, not equals. That is, $n \propto T^{3/2} \exp(Eg/(2k_BT))$.

You can "see" this easily enough by looking at the dimensions (units) of each side of the equation. The term "n" is a density, and therefore $m^{-3}$ (or $cm^{-3}$ etc), whereas the unit on the RHS is T^1.5.

The "T^(3/2)" factor is merely the temperature dependent part of the equation for the "effective density of states referred to the conduction band edge", if you want to google that.

 

[jendrix]

I see now, thanks :)