Determine the proportion of boron impurity required to increase the conductivity of a pure silicon sample by a factor of 100 . Assume that each boron atom contributes one hole, and the concentration of holes in pure silicon at the same temperature is 7 10¹⁵ holes per cubic metre. The density of silicon is 5 10²⁸ atoms per cubic metre.

Step-by-step solution

The conductivity of pure (intrinsic) silicon is given by: _i = n_i e _e + n_i e _h Assuming the mobilities of electrons and holes are approximately equal ( _e _h = ), we get: _i = 2 n_i e When boron (a trivalent impurity) is added, the silicon becomes a p-type semiconductor. The conductivity is predominantly due to holes: _p n_h e _h = N_A e where N_A is the concentration of boron atoms. Given that the conductivity increases by a factor of 100 : _p = 100 _i N_A e = 100 (2 n_i e ) N_A = 200 n_i Substituting the give