Question

The intrinsic carrier density of a rectangular specimen of Ge is 2.5 10m. 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 m and
0.19 m / P's respectively.
(a) 2.78 mA. 232 sm
(b) 2.18 mA 2.02 sm
(c." HA. .
(d) 1.78 MA 132 sim
B​

Answer 1

Answer:

b is correct answer of this question

Answer 2

Given:

Intrinsic carrier density = n_e = n_p = 2.5 × 10¹⁹ /m²

n_e = density of electron

n_p = density of holes

l = 20 mm

b = 3 mm

h = 1 mm

V = 8 V

μ_e = 0.39 m²/Vs

μ_p = 0.19 m²/Vs

To find:

Determine the total current and intrinsic conductivity if a potential difference of 8 V is applied across the length of the specimen.

Solution:

σ = (μ_e + μ_p) × n × e

n = n_e = n_p

e = 1.6 × 10⁻¹⁹

σ = (0.39 + 0.19) × 2.5 × 10¹⁹ × 1.6 × 10⁻¹⁹

σ = 0.58 × 2.5 × 1.6

σ = 2.32 si/m

σ = 1/ρ

ρ = 1/σ

R = ρ × l/A

R = 1/σ × l/A

A = b × h

A = 3 × 1 = mm²

A = 3 mm²

R = (1/2.32) × (20/3)

V = I × R

I = V/R

I = (8 × 2.32 × 3) / 20

I = 2.78 mA

Therefore option (A) 2.78 mA, 2.32 si/m is correct.