Question

Calculate the intrinsic concentration, intrinsic resistivity, and mean scattering times of electrons and holes in Ge.

Options:
A. 1.45 x 10¹3 cm⁻3, 2.33 Ω·cm, 3.8 x 10⁻14 s
B. 2.8 x 10¹2 cm⁻3, 5.67 Ω·cm, 1.2 x 10⁻13 s
C. 4.21 x 10¹4 cm⁻3, 1.78 Ω·cm, 2.5 x 10⁻15 s
D. 3.6 x 10¹3 cm⁻3, 3.2 Ω·cm, 1.6 x 10⁻14 s

Answer 1

The intrinsic concentration, intrinsic resistivity, and mean scattering times of electrons and holes in Ge can be calculated using specific formulas and given values. The correct options are D: 3.6 x 10¹³ cm⁻³, 3.2 Ω·cm, 1.6 x 10⁻¹⁴ s.

Step-by-step explanation:

To calculate the intrinsic concentration, intrinsic resistivity, and mean scattering times of electrons and holes in Ge, we need to use the formulas:

Intrinsic concentration:

• ni = √(Nc * Nv * exp(-Eg / (2 * k * T)))

where Nc is the effective density of states in the conduction band, Nv is the effective density of states in the valence band, Eg is the band gap energy, k is Boltzmann's constant, and T is the temperature in Kelvin.

Intrinsic resistivity:

• ρ = 1 / (ni * e * μn (*pi* + 1 / *ni*))

where e is the elementary charge, μn is the electron mobility, *pi* is the mean scattering time of holes, and *ni* is the mean scattering time of electrons.

By using the given values for Ge, we can calculate the answers as option D: 3.6 x 10¹³ cm⁻³, 3.2 Ω·cm, 1.6 x 10⁻¹⁴ s.