Question

The intrinsic carrier density of a rectangular specimen of Ge is 2.5x10 /m². The length,
width, and height of the specimen are 20 mm, 3 mm, and I mm respectively. Determine
the total current and intrinsic conductivity if a potential difference of 8 V is applied across
the length of the specimen. Given electron and hole mobility as 0.39 m² /Vs and
0.19 m2 /Vs respectively,
(a) 2.78 mA. 2.32 si m
(b) 2.18 mA. 2.02 sim
(C) 2.78 mA. 1.32 sim
(d) 1.78 mA. 1.32 sim​

Answer 1

Given: Intrinsic carrier density of Ge, n_e = n_p = 2.5 x 10^19 /m²

n_e = density if electron

n_p = density of holes

l = 20mm, b = 3mm, h = 1mm, V = 8 volt, µ_e = 0.39 m²/Vs, µ_p = 0.19 m²/Vs

To find: the total current and intrinsic conductivity

Solution:

σ = ( µ_e + µ_p ) x n x e

  = ( 0.39 + 0.19 ) x 2.5 x 10^19 x 1.6 x 10^-19

σ = 2.32 sim

σ = 1/ρ

ρ = 1/σ

R = ρ x l / A

  = 1/σ x l / A

A = b x h = 3 x 1 = 3 mm²

Therefore, R = ( 1 / 2.32 ) x ( 20 / 3 )

Now, V = I x R

I = V / R

I = ( 8 x 2.32 x 3 ) / 20

I = 2.78 mA

Therefore, (A) 2.78 mA, 2.32 sim is correct.