Mumbai university > FE > SEM 1 > Applied Physics 1

Marks: 3M

Year: May 2014

Fermi level- is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. OR can also be called as last field level.

Fermi energy- The energy associated with Fermi level is called Fermi energy.

Fermi–Dirac distribution function

For a system of identical fermions, the average number of fermions in a single-particle state i is given by a logistic function, the Fermi–Dirac (F–D) distribution, $$\bar{n}_i = \frac{1}{e^{(E_i - μ)/kT} + 1}$$

where k is Boltzmann's constant, T is the absolute temperature,$E_i$ is the energy of the single-particle state i, and μ is the total chemical potential.

At zero temperature, μ is equal to the Fermi energy plus the potential energy per electron. For the case of electrons in a semiconductor, μ, the point of symmetry, is typically called the Fermi level or electrochemical potential.

The F–D distribution is only valid if the number of fermions in the system is large enough so that adding one more fermion to the system has negligible effect on μ. Since the F–D distribution was derived using the Pauli Exclusion Principle, which allows at most one electron

$$0 \lt \bar{n}_i \lt 1$$

to occupy each possible state, a result is that