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

(N/A) When germanium is doped with gallium,some of the lattice positions of germanium are occupied by gallium atoms. Gallium has only $3$ valence electrons,which are used to form covalent bonds with neighboring germanium atoms. Consequently,for every gallium atom,a vacancy or 'hole' is created at the site where the $4^{th}$ electron is missing. These holes are responsible for electrical conduction. Under the influence of an electric field,electrons from neighboring atoms move to fill these holes,effectively causing the holes to move towards the negatively charged plate,while electrons move towards the positively charged plate,thus increasing the conductivity.