The product of the conduction electron concentration and the hole concentration remains independent of the quantity of any doped impurity. In pure germanium, the concentration of conduction electrons is 6 10¹⁹ per cubic metre. After a germanium sample is doped with phosphorus impurity, the conduction electron concentration rises to 2 10²³ per cubic metre. Determine the hole concentration in the doped germanium.

Step-by-step solution

In an intrinsic semiconductor, the concentration of conduction electrons is equal to the concentration of holes, which is the intrinsic carrier concentration n_i . Given n_i = 6 10¹⁹ m ⁻³ . According to the mass action law, the product of electron and hole concentrations remains constant at a given temperature: n_e n_h = n_i^2 After doping, the new electron concentration is n_e = 2 10²³ m ⁻³ . Substituting the values into the mass action law: n_h = n_i^2 n_e = (6 10¹⁹)^2 2 10²³ n_h = 36 10³⁸ 2 10²³ n_h = 18 10¹⁵ =