A pure silicon crystal at temperature 300 K has electron and hole concentration ( n_i ) 10¹⁶ per m ^3 each and 10²¹ phosphorus atoms ( n_e ) are added per cubic metre. The new hole concentration in silicon crystal is

Step-by-step solution

According to the mass action law for semiconductors: n_e n_h = n_i^2 Given the intrinsic carrier concentration n_i = 10¹⁶ m ⁻³ . Phosphorus is a pentavalent impurity, which acts as a donor. Since the number of donor atoms added is much greater than the intrinsic concentration, the new electron concentration is approximately equal to the donor concentration: n_e N_D = 10²¹ m ⁻³ Substituting the values into the mass action law to find the new hole concentration n_h : n_h = n_i^2 n_e n_h = (10¹⁶)^2 10²¹ n_h = 10³² 10²