Question

A pure siliconn sample has ne = 1.3 x 10¹⁶ m^-3. The material is doped with 

(a) 10¹⁹ atoms m^-3 of phosporous 

(b) 2 x 10¹⁹ atoms m^-3 of boron

one by one. What is ratio of resistivity of doped sample in (a) and (b) due to majority charge carriers? 

Given: 

Mobility of electrons = 0.125 m²V^-1s^-1, Mobility of holes = 0.0426 m²V^-1s^-1 .

(1) 1

(2) 2

(3) 1/2

(4) 2/3

Answer 1

 (4) 2/3

(a) The majority charge carriers are electrons.

n_e = Number of free electrons = 10⁹ m^-3; μ_e = 0.125 m²V^-1 s^-1 , 

\(ρ_e\) = Resistivity of material = \(\frac{1}{n_e eμ_e}\)

(b) The majority charge carriers are holes n_h = Number of holes = 2 x 10¹⁹ m^-3 , μ_n = 0.426 m²V^-1s^-1