The Fermi potential is a concept used in solid-state physics to describe the energy difference between the Fermi level and the energy level of the intrinsic Fermi level. The Fermi level represents the highest energy level occupied by electrons at absolute zero temperature in a solid, while the intrinsic Fermi level represents the energy level at which the probability of finding an electron is equal to the probability of finding a hole.

The Fermi potential is a function that depends on several factors, which are listed below:

a) Temperature: Temperature plays a crucial role in determining the Fermi potential. As the temperature increases, the energy distribution of electrons also changes. The Fermi potential is directly related to the temperature through the Boltzmann distribution function. Higher temperatures result in a broader distribution of energy levels, leading to a decrease in the Fermi potential.

b) Doping concentration: Doping refers to the intentional introduction of impurities into a semiconductor material to alter its electrical properties. The type and concentration of dopants have a significant impact on the Fermi potential. Doping with donor impurities increases the number of free electrons, shifting the Fermi level closer to the conduction band and reducing the Fermi potential. Conversely, doping with acceptor impurities increases the number of holes, shifting the Fermi level closer to the valence band and increasing the Fermi potential.

c) Difference between Fermi level and intrinsic Fermi level: The Fermi potential is directly related to the difference between the Fermi level and the intrinsic Fermi level. This difference represents the energy required to change the electron concentration in a material. A larger difference indicates a higher potential energy barrier for electron transfer, resulting in a higher Fermi potential.

Overall, the Fermi potential is influenced by temperature, doping concentration, and the difference between the Fermi level and the intrinsic Fermi level. These factors determine the energy distribution and the availability of charge carriers in a material, which in turn affects the electrical properties of semiconductors and other solid-state devices.