Fermi—Dirac distribution fermions, Pauli principle

Intrinsic Semiconductors. For semiconductors in thermal equiHbrium, (Ai( )), the average number of electrons occupying a state with energy E is governed by the Fermi-Dirac distribution. Because, by the Pauli exclusion principle, at most one electron (fermion) can occupy a state, this average number is also the probabiHty, P E), that this state is occupied (see Fig. 2c). In equation 2, K... 

The results obtained above are of such general importance when applied to the case of electrons (more generally to fermions) that the resulting distribution has its own nomenclature and is referred to as the Fermi-Dirac distribution. To see how eqn (3.122) is applied to determine the average number of particles in a given quantum state when the particles themselves obey the Pauli principle, we consider a particular electronic state with energy e. In this case, the Gibbs sum is of the form... 

Fermi-Dirac distribution - A modification of the Boltzmann distribution which takes into account the Pauli exclusion principle. The number of particles of energy E is proportional to [e > +l] , where p is a normalization constant, k the Boltzmann constant, and T the temperature. The distribution is applicable to a system of fermions. 

In the subsequent chapters in which we will be investigating the thermal, electrical, optical, and magnetic properties of materials, it will be necessary to be able to determine the energy distribution of electrons, holes, photons, and phonons. To do this, we need to introduce some quantum statistical mechanical concepts in order to develop the distribution fimc-tions needed for this purpose. We will develop the Bose-Einstein (B-E) distribution function that applies to all particles except electrons and holes (and other fermions) that obey the Pauli exclusion principle and show how this function becomes the Maxwell-Boltzmann (M-B) distribution in the classical limit. Also, we will show how the Planck distribution results by relaxing the requirement that particles be conserved. Next we develop the Fermi-Dirac (F-D) distribution that applies to electrons and holes and becomes the basis for imderstanding semiconductors and photonic systems. 

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