Is there twice the amount of current in semiconductors than that in conductors (at same temp.)?

Question

In semiconductors unlike conductors where $e^-$ move from lower quantum states to higher quantum states in conduction band, electrons move from Valence Band to CB and create 'holes'. These holes add on to the current and as a result in semiconductor we have twice the current than that in conductors at same temp?

Answer 1

You need to distinguish between the ideas of current and charge carrier density. It's the charge carrier density that is doubled for intrinsic semiconductors.

Suppose we have a current flowing through some material:

If we take some imaginary surface in our conductor, shown here by the dashed line, then the current is the amount of charge crossing this surface per unit time. Suppose we have a current $I$, and our charges have the electron charge $e$, then the number of charges crossing the surface per second is just:

$$ N = \frac{I}{e} \tag{1} $$

If the charge carrier density, i.e. the number of charge carriers per unit volume in our conductor, is $\rho$ and they move with a velocity $v$ (i.e. the drift velocity) then the number crossing our surface (with area $S$) in the conductor is just:

$$ N = \rho v A \tag{2} $$

and we can combine equations (1) and (2) to give us an equation that links the current, charge carrier density and charge carrier velocity:

$$ \rho v A = \frac{I}{e} $$

In an intrinsic semiconductor every electron that is excited to the conduction band produces two charge carriers, so the carrier density is not simply the electron density but the sum of the electron and hole density (though note that electrons and holes n=don't necessarily have the same mobility). That means for a given current the carrier velocity will be lower than it would be if only one type of carrier were present. Or similarly that for a given carrier velocity the current will be higher.

But note that the carrier density in an intrinsic semiconductor is much smaller than in a typical metallic conductor, even given the doubling of the density.

A footnote: I've used the description intrinsic semiconductor because in doped semiconductors only one type of carrier is mobile. In N type semiconductors the holes are pinned to gap states and are immobile, while in P type semiconductors the electrons are pinned to gap states and immobile. Only in intrinsic semiconductors to we get equal numbers of mobile electrons and holes.