What does it mean for metal to be p-type or n-type? I understand that semiconductor can be either n-type or p-type (or intrinsic in the absence of doping), but what does it mean for metals to be n-type or p-type? For example, Cu and Ag are a p-type metal, and Zn is an n-type metal. What makes them n-type or p-type?
 A: Metals are not inherently p-type or n-type as dopants.  They are identified as p-type or n-type in a specific material.  You cite nickel oxide in your comment. Presumably if a silver atom replaces a Ni atom in the nickel oxide lattice it behaves in a p-type manner.  This means that it creates an electron state that is closer to the valence band than the conduction band.  Presumably the nickel oxide itself behaves as an insulator with a well defined valence and conduction band.  The impurity creates a localized state within the forbidden band that can easily capture an electron from the valence band thus creating a mobile hole.
I am not that familiar with nickel oxide but I am very familiar with semiconductors, especially Si, GaAs and Ge.  In GaAs, Zn is a good p-type dopant.  It creates an acceptor state only .031 eV from the valence band so Zn being an "n-type metal", as you suggest in your question, is specific to nickel oxide.  Gold in GaAs is an acceptor (p-type) while in  silicon it is more of a troublesome deep acceptor level that acts to trap electrons and enhance recombination.
A semiconductor can be n-type or p-type because it has an abundance of donor or acceptor impurities respectively.  A metal atom can be a donor, an acceptor or a deep level in a specific material structure.
