Question

briefly explain why zinc and several other divalent metals have hall coefficients opposite in sign to those of monovalent and trivalent metals.

Answer 1

• For most metals, the Hall coefficient is negative, as expected if the charge carriers are electrons. In beryllium, cadmium and tungsten, however, the coefficient is positive. In these metals, the charge carriers are holes, which act like positive charges. In a semiconductor, the Hall coefficient can be positive or negative, depending on whether it is P or N type. An intrinsic semiconductor, with equal numbers of mobile electrons and holes, is predicted to have a zero Hall coefficient.
• The sign of the Hall coefficient indicates the nature of the majority carriers in a material. For all metals, electrons are the majority carriers(I think we can safely say the only carriers) and so the Hall coefficient for all metals is negative(see here, copper has a negative Hall coefficient too). But for semiconductors, sometimes holes(the absence of an electron) are the majority carriers. For these materials, the Hall coefficient is positive.
• There are two essential facts that make a hole a hole: Fact (1) The valence band is almost full of electrons (unlike the conduction band which is almost empty); Fact (2) The dispersion relation near the valence band maximum curves in the opposite direction to a normal electron or a conduction-band electron.