A pure semiconductor crystal has 8 10²⁸ atoms m ^3 . It is doped by 2 ppm concentration of pentavalent atoms. The number of holes formed in the semiconductor crystal is (Intrinsic carrier concentration, .n_i=1 10¹⁶ ~m ⁻³ ) .

Step-by-step solution

Number of atoms per m ^3 in semiconductor crystal =8 10²⁸ atoms / m ^3 Number of doped atoms =2 ppm =2 atoms out of 10^6 atoms. Numebr of doped atoms in 8 10²⁸ atoms / m ^3 =2 8 10²⁸ 1 10^6 =16 10²² atoms / m ^3 As, each pentavalent impurity atom produces 1 -electron in conduction band, number of conduction electrons =n_e=4 10²² electrons / m ^3 As n_e n_n=n_i^2,= , we have n_n= n_i^2 n_e = (1 10¹⁶ )^2 16 10²² =6.25 10^8 holes / m ^3