In a pure silicon crystal electron-hole concentration is 10¹⁶ per m ^3 at 301 K . Now 10²¹ atoms of phosphorus are added per cubic metre. The new hole concentration in silicon is (in per m ^3 )

Step-by-step solution

Phosphorus doping creates an n-type semiconductor where electrons are majority carriers. Since the donor concentration N_D = 10²¹ m ⁻³ greatly exceeds the intrinsic concentration n_i = 10¹⁶ m ⁻³ , the electron concentration becomes n_e N_D = 10²¹ m ⁻³ . The mass action law n_e n_h = n_i^2 gives the hole concentration: n_h = n_i^2 n_e = (10¹⁶)^2 10²¹ = 10³²⁻²¹ = 10¹¹ m ⁻³ This corresponds to option B .