Page No 510:CONT - Chapter 14 Semiconductors Additional Exercise Solutions class 12 ncert solutions Physics - SaraNextGen [2024-2025]

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On April 24, 2024, 11:35 AM

Question 14.12:

The number of silicon atoms per m³ is 5 × 10²⁸. This is doped simultaneously with 5 × 10²² atoms per m³ of Arsenic and 5 × 10²⁰ per m³ atoms of Indium. Calculate the number of electrons and holes. Given that ni= 1.5 × 10¹⁶ m⁻³. Is the material n-type or p-type?

Answer:

Number of silicon atoms, N = 5 × 10²⁸ atoms/m³

Number of arsenic atoms, n_As = 5 × 10²² atoms/m³

Number of indium atoms, n_In = 5 × 10²⁰ atoms/m³

Number of thermally-generated electrons, ni = 1.5 × 10¹⁶ electrons/m³

Number of electrons, ne = 5 × 10²² − 1.5 × 10¹⁶ ≈ 4.99 × 10²²

Number of holes = nh

In thermal equilibrium, the concentrations of electrons and holes in a semiconductor are related as:

nenh = ni²

Therefore, the number of electrons is approximately 4.99 × 10²² and the number of holes is about 4.51 × 10⁹. Since the number of electrons is more than the number of holes, the material is an n-type semiconductor.

Question 14.13:

In an intrinsic semiconductor the energy gap Egis 1.2 eV. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at 600K and that at 300K? Assume that the temperature dependence of intrinsic carrier concentration niis given by

where n₀ is a constant.

Answer:

Energy gap of the given intrinsic semiconductor, Eg = 1.2 eV

The temperature dependence of the intrinsic carrier-concentration is written as:

Where,

k_B = Boltzmann constant = 8.62 × 10⁻⁵ eV/K

T = Temperature

n₀ = Constant

Initial temperature, T₁ = 300 K

The intrinsic carrier-concentration at this temperature can be written as:

 … (1)

Final temperature, T₂ = 600 K

The intrinsic carrier-concentration at this temperature can be written as:

 … (2)

The ratio between the conductivities at 600 K and at 300 K is equal to the ratio between the respective intrinsic carrier-concentrations at these temperatures.

Therefore, the ratio between the conductivities is 1.09 × 10⁵.