Question

A pure silicon semiconductor has a size of 10 mm x 10 mm x 1 mm. There are 5 x 10²⁸ atoms per cubic meter in silicon. It is doped simultaneously with 1 part in one million of arsenic and one part per hundred million of Indium. The number density of intrinsic carriers in pure silicon is 1.5 x 10¹⁶ m³ . The number of electrons, n_e ; and number of hole n_h in semiconductor is

(1) n_e = 5 x 10¹⁵; n_h = 5 x 10⁴

(2) n_e = 5 x 10² ; n_h = 5 x 10¹³

(3) n_e = 5.5 x 10¹⁵; n_h = 4.54 x 10⁴

(4) n_e = 4.95 x 10¹⁵; n_h = 4.54 x 10²

Answer 1

(4) n_e = 4.95 x 10¹⁵; n_h = 4.54 x 10²

Volume of given sample = 100×10^-9m³ = 10^-7m³ 

The extent of doping of assenic is more than that of indium. 

The net extent of doping = (10^-6–10^-8) = 0.99 x 10^-6

The number of electrons in given sample = 4.95 x 1022 x 10^-7 = 4.95 x 10¹⁵ 

The numbe of holes in given sample = 4.54 x 10⁹ x 10^-7 = 4.54 x 10²