Explain why does conductivity of germanium crystals increases on doping with gallium.

Gallium is a trivalent element while germanium is tetravalent.

On doping germanium with gallium, some of the crystal sites are occupied by gallium atoms. Three electrons of gallium make bonds with germanium while the 4th electron of germanium remains unbounded and thus is free for movement and increases the conductivity of crystal. This place is deficient of electrons and is called electron hole or electron vacancy. The movement of electrons (or electron holes) results in increase in conductivity of germanium.