Explain fermi dirac statistic and distribution for semiconductor?

Answer 1

It would be difficult to understand the behavior of electrons without the Fermi Dirac statistics. Why in a metal, electrons can move freely to conduct the electric current and why their contribution in the same metal to the specific heat is negligible, as if their number become for an unknown reason, considerably reduced. We have here a problem of "statistical order" that can be explained only by using the Fermi Dirac statistics (the classical statical mechanics was unable to explain this phenomenon).

Answer 2

The conduction band in a piece of semiconductor consists of mainly available, empty energy levels. When calculating how many electrones will fil these levels and thus be counted in n, contributing to conductivity , we consider two factors : * How many energy levels are there within a given range of energy, in our case the conduction band . * How likely is that each level will be populated by an electron . The likelihood in the second item is given by a probabilty function called the Fermi-Dirac Distribution function . f(E) is the probability that a level with energy E will be occupied by an electron , and the expression is : f(E)= 1/[1 + exp( (E-EF)/(kBT) ) ] where kB is the Boltzmann's constant , 8.62x10-5[eV/K], and T is the Temperature indegrees Kelvin . EFis called the Fermi Energy or Fermi level , it is dermined as the energy point where the probability of occupancy of an electron is exactly 50% 0r 0.5 : f(E)= 1/[1 + exp( (E-EF)/(kBT) ) ] = f(E)= 1/[1 + exp( (EF-EF)/(kBT) ) ] = 1/ [1+ exp(0)] = 1/2

Answer 3

Fermi-Dirac statistics describe the distribution of particles in a system obeying the Pauli Exclusion Principle, such as electrons in a semiconductor. It states that no two indistinguishable fermions can occupy the same quantum state simultaneously. In a semiconductor, electrons fill energy levels up to the Fermi level according to the Fermi-Dirac distribution function, which determines the probability of occupation for each energy level.