A silicon sample doped n-type at 1018 cm

A silicon sample doped n-type at 10¹⁸ cm^–3 have a resistance of 10 Ω. The sample has an area of 10^–6 cm² and a length of 10 µm. The doping efficiency of the sample is (µ_a = 800 cm²/ V – s)—

Given data,
N_d = 10¹⁸
R = 10 Ω
A = 10^–6 cm²
L = 10 mm = 10 × 10^–4 cm,
µn = 800 cm²/ V–s
% doping efficiency = n₀ N_d × 100 =?

Now, n₀ =	L
	q·µ_n·A·R

=	10 × 10^–4
	1.6 × 10^–19 × 800 × 10^–6 × 10

= 7.81 × 10¹⁷ cm^–3

% doping efficiency =	7.81 × 10¹⁷	× 100 = 78.1%
	1 × 10¹⁸

Hence alternative (B) is the correct choice.