Concentrations of electrons in intrinsic semi-conductor

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SUMMARY

The concentration of electrons in intrinsic semiconductors is described by the formula n ∝ T3/2 exp(Eg/(2kBT)). The variable n represents the electron density, which is proportional to the temperature raised to the power of 3/2 and the exponential term involving the band gap energy (Eg) and temperature (T). This relationship highlights the temperature dependence of the effective density of states at the conduction band edge, confirming that n is not equal to but proportional to the right-hand side of the equation.

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jendrix
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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
 
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jendrix said:
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, [itex]n \propto T^{3/2} \exp(Eg/(2k_BT))[/itex].

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 [itex]m^{-3}[/itex] (or [itex]cm^{-3}[/itex] 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.
 
Last edited:
I see now, thanks :)
 

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