Resistivity and Resistance in n-type and p-type Germanium

[CNX]

Resistivity of Ge

I'm doing this lab and haven't taken any SS physics so I'm expected to pick up some of the theory on my own.

I am having trouble explaining the resistance vs temperature curve for n-type and p-type Germanium, i.e. why does resistance increase and then drop from around 290 K to 400 K?

Does the relation between resistivity and resistance, $\rho = R \frac{A}{l}$ still hold for a semiconductor at any temperature?

My intuition wants to say the increased thermal energy of electrons in the conduction band increases resistance from 290 K to the peak, but eventually electrons in the valence band have enough energy to jump the band gap therefore resistance begins to decrease. And I'm not sure about n-type vs p-type here.

 

[NateD]

Yes, the relation between resistivity and resistance still holds for a semiconductor at any temperature. For n-type Germanium, as the temperature increases, more electrons are thermally excited into the conduction band, thus increasing conductivity and reducing resistivity. However, when the temperature reaches a high enough value, the thermal excitation of electrons in the valence band is sufficient to increase the number of charge carriers, which further reduces the resistivity. This explains why the resistivity of n-type Ge decreases with increasing temperature.For p-type Germanium, as the temperature increases, more holes are thermally excited into the conduction band, thus increasing conductivity and reducing resistivity. However, when the temperature reaches a high enough value, the thermal excitation of holes in the valence band is sufficient to increase the number of charge carriers, which further reduces the resistivity. This explains why the resistivity of p-type Ge decreases with increasing temperature.