Charge Carriers in the Hall Effect

[transmini]

For a lab I just finished this past week, we were working with the hall effect and finding hall voltages. The metals used were p-germanium and n-germanium semi-conductors. I understand why in n-germanium the hall voltage is positive and p-germanium is negative assuming negative charge carriers for n-type and positive holes as carriers for p-type.

What I don't get is why we are treating positive holes as the carriers. Even though it looks like a positive hole is moving through as a current, the electrons are still what's moving, creating the movement of the holes. So the $\vec{F}=q(\vec{v}\times \vec{B})$ would still be in the same direction as for negative charge carriers, since it is still technically the electrons that are movin, causing the voltages to be the same, since $\vec{v}$ and $\vec{B}$ are in the same direction still and $q$ is still the same sign. Why does the Hall effect behave as if the holes are actually a moving mass instead in p-type, like electrons for n-type?

 

[Chandra Prayaga]

In an n-type semiconductor, the carriers are electrons in the conduction band. In a p-type semiconductor, the carriers are holes, which are vacant states in the valence band. So if you want to describe the motion of the vacant states in terms of motion of electrons, you need to describe the motion of electrons in the valence band. These behave quite differently from electrons in the conduction band. Even though the charge is the same, the mass is not. The effective mass of electrons near the top of the valence band is negative.

 

[sophiecentaur]

Why does the Hall effect behave as if the holes are actually a moving mass instead in p-type, like electrons for n-type?

Perhaps it would be less of problem if you replace "are actually" with "can be treated as". You have to remember that there are no "actually"s and "really"s in Science. It's all models. These models tend to be either slightly dumbed down verbal ones which use familiar terms as metaphors or they are mathematical, which can be scary and even more unfamiliar.
The holes in the Hall effect are what you get (how you can interpret what you get) when an electron moves from a normal atom to an atom of a +type material in the lattice. Semiconductors carry a current because the energy needed for an electron to move from place to place is low enough. This results in the 'observed' effective mass of a hole being different from an electron's mass. Hole 'mass' can be greater or less than that of an electron. It's mentioned at the top of this wiki link.