The conductivity of a semiconductor is given by the relation:
σ = e₀(ncμe- + pvμh+)
nc and pv are the concentrations of the electrons and of the holes, e- and h+ are the mobilities of the electrons and of the holes, defined as u = |u|/|E|, where u is the velocity of a charge in an electric field E, and eâ‚€ is the elementary charge.
a) Show that for an n-doped semiconductor, the conductivity is a minimum when
nc = no((μh+)/μe-)^(1/2), where no is the electron concentration of the intrinsic semiconductor. Here, we suppose that μe- and μh+ do not depend on the concentration of the charge carriers.
b) Give an expression for the minimum conductivity σmin.
c) Determine σmin for doped Si and compare σmin with σin, the conductivity of the intrinsic semiconductor. For Si, we have: no = 1.5 x 10^10 cm^-3, μe- = 1500 cm^2·V^-1·s^-1, μh+ = 500 cm^2·V^-1·s^-1.
