The carrier concentration refers to the number of electrons or holes (i.e., positively charged vacancies in the valence band) in a material. In a doped semiconductor, the carrier concentration is determined by the doping concentration, temperature, and other factors.

The relationship between the Fermi level and carrier concentration can be described by the Fermi-Dirac distribution function, which gives the probability of electrons occupying a particular energy level at a given temperature.

However, the relationship between Fermi level and carrier concentration is not linear and can be affected by other factors such as temperature, bandgap energy, and impurity levels.

We have fermi dirac distribution function for electrons in conduction is

We assume that at temperature of interest

where ε = energy of electron

µ = chemical potential

We have density of state for electron at energy ε is

Now, concentration of ε in conduction band is given by

This gives the electron concentration in conduction band of intrinsic semi conductor if chemical potential is known. We can find concentration

The study of Fermi level and carrier concentration is useful in understanding the electrical properties of semiconductors and other materials.

Semiconductors are widely used in electronic devices such as transistors, diodes, solar cells, and LEDs. The properties of these devices depend on the concentration of carriers and the position of the Fermi level within the bandgap of the material.

By studying the Fermi level and carrier concentration, researchers can design and optimize semiconductor devices with specific electrical properties. For example, by controlling the doping concentration and temperature, they can adjust the carrier concentration and the position of the Fermi level to enhance the performance of devices such as solar cells and transistors.

In addition, the study of Fermi level and carrier concentration is also important in understanding the behaviour of materials in different environments. For example, the Fermi level can be affected by external factors such as electric fields, light, and temperature, which can alter the carrier concentration and the electrical properties of the material.

Overall, the study of Fermi level and carrier concentration is essential for the design and optimization of semiconductor devices, as well as for the understanding of the behaviour of materials in different environments.

This note is a part of the Physics Repository.

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