A silicon crystal having a cross-sectional area of 0.001

A silicon crystal having a cross-sectional area of 0.001 cm² and a length of 20 µm is connected to its ends to a 20 V battery. At T = 300 K, we want a current of 100 mA in crystal. The concentration of donor atoms to be added is—

R =		V	=	20V	=	20	= 200 Ω and from relation
		I		100mA		100 × 10^–3

R =		ρl	=	1	·	1
		A		σ		A

or σ =		I	=	2 × 10^–3
		RA		200 × 0.001

= 0.01 (Ω-cm)^–1
and σ = n₀ q. µ_n for S_i, µ_n = 1350
0.01 = n0. (1.6 × 10^–19). 1350

n₀ =	0.01
	1.6 × 10^–19 × 1350

= 4.6 × 10¹³ cm^–3
since n₀ >> n_i (intrinsic concentration)
it means n₀ = N_d
Hence alternative (B) is the correct choice.