The intrinsic carrier concentration of a germanium sample is 2.4 ×10^14 / m^3 at 300 K. Its e

step 1 Here the intensive carib concentration for germanium sample is given which is n i is equal 2 .4

The intrinsic carrier concentration of a germanium sample ...

The intrinsic carrier concentration $$ \text { of a germanium sample } $$ is $2.4 \times 10^{14} / \mathrm{m}^{3}$ at $300 \mathrm{~K}$. Its electron and hole mobilities are $0.39$ and $0.19$ $\mathrm{m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}$ respectively. Calculate the conductivity of the sample.

The intrinsic carrier concentration $$
\text { of a germanium sample }
$$
is $2.4 \times 10^{14} / \mathrm{m}^{3}$ at $300 \mathrm{~K}$. Its electron and hole mobilities are $0.39$ and $0.19$ $\mathrm{m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}$ respectively. Calculate the conductivity of the sample.

Key Concepts

Carrier Concentration

Carrier concentration in semiconductors refers to the number of free electrons or holes per unit volume available to conduct electricity. In intrinsic semiconductors, the carrier concentration is primarily determined by the energy bandgap and temperature, as electrons are thermally excited from the valence band to the conduction band, creating equal numbers of electrons and holes. This parameter is critical in defining the electrical properties of the semiconductor.

Electrical Conductivity in Semiconductors

Electrical conductivity in semiconductors is determined by the contribution of both electrons and holes to the current flow. It is calculated as the product of the charge carrier concentration, the elementary charge, and the carrier mobility for both types of carriers. In intrinsic semiconductors, where the concentrations of electrons and holes are equal, the total conductivity is the sum of the conductivities due to each carrier type.

Intrinsic Semiconductor

An intrinsic semiconductor is a pure semiconductor without any significant impurities or dopants. In such materials, the free charge carriers (electrons and holes) are generated solely by thermal excitation across the energy bandgap. The intrinsic nature ensures that the electron concentration is equal to the hole concentration at thermal equilibrium, and their values are highly sensitive to temperature.

Charge Carrier Mobility

Charge carrier mobility refers to the ease with which electrons and holes can move through a semiconductor when an electric field is applied. Mobility is a material-specific property influenced by factors such as lattice imperfections and impurities, and it directly impacts the conductivity of the material. Higher mobility means that carriers can move more quickly, leading to a higher current for the same applied voltage.

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