Fermi dirac distribution function

At thermal equiUbrium characterized by temperature, T, the distribution of electrons over the allowed band of energies is given by a Fermi-Dirac distribution function ... 

Examination of the Fermi-Dirac distribution function Eq. (2.41) shows that the condition for applicability of the ideal-gas distribution to electron velocities is... 

Overhauser s original derivation of the effect employed the Fermi-Dirac distribution functions for electrons and was an involved calculation. Kittel ISl), Slichter 1S2), and others supplied simple derivations for this effect and Abragam 133) extended it to nonmetallic systems. 

Here u fl" and E " are the periodic part of the Bloch function, energy and Fermi-Dirac distribution functions for the n-th carrier spin subband. In the case of cubic symmetry, the susceptibility tensor is isotropic, Xcj) = Xc ij- It has been checked within the 4 x 4 Luttinger model that the values of 7c, determined from eqs (13) and (12), which do not involve explicitly u and from eqs (14) and (15) in the limit q - 0, are identical (Ferrand et al. 2001). Such a comparison demonstrates that almost 30% of the contribution to 7c originates from interband polarization, i.e. from virtual transitions between heavy and light hole subbands. 

Figure E.10 (a) Bose-Einstein distribution function, (b) Fermi-Dirac distribution function, and (c) filling of levels by fermions at T = 0 and T=T1>0. The dashed line indicates the Fermi energies p.

The probability distribution, F(E), is the Fermi-Dirac distribution function... 

Extension to finite temperature T can be made by using the Fermi-Dirac distribution function for fk in Eq. (82)... 

Modification of this model to get the potential function is obtained considering the Fermi-Dirac distribution function for the electron density and the Boltzmann distribution for the ionic density. This was done by Stewart and Pyatt [58] to get the energy levels and the spectroscopic properties of several atoms under various plasma conditions. Here the electron density was given by... 

The important point is, that the leads are actually in the equilibrium mixed state, the single electron states are populated with probabilities, given by the Fermi-Dirac distribution function. Taking into account all possible single-electron tunneling processes, we obtain the incoming tunneling rate... 

In this regard, the probability of finding an electron in a state with energy E is given by the Fermi-Dirac distribution function, fiE), which is expressed as follows (Figure 1.10) ... 

Before the transfer starts, the energy distribution of electrons takes the form of a Fermi-Dirac distribution function. While the number of electrons is decreasing steadily with time, the distribution of electrons keep the form of a Fermi-Dirac distribution function. This constancy of the distribution is due to the fact that the capture rate of free electrons by the localized states is much faster than the loss of free electrons caused by the transfer when the occupation probability of localized states is not approximately one. Therefore, electrons are considered to be in their quasi-thermal equilibrium condition i.e., the energy distribution of electrons is described by quasi-Fermi energy EF. Then the total density t of electrons captured by the localized states per unit volume can be written as... 

Now the Fermi-Dirac distribution function of Eq. (8.2.2) will be proved. For a system of N particles in equilibrium at a finite temperature T (where N is very large, of the order of Avogadro s number), statistical mechanics suggests that the statistical weight PN(E) for the energy state E is given by... 

Fermi energy — The Fermi energy of a system is the energy at which the Fermi-Dirac distribution function equals one half. In metals the Fermi energy is the boundary between occupied and empty electronic states at absolute temperature T = 0. In the Fermi-Dirac statistics the so-called Fermi function, which describes the occupation fraction as a function of energy, is given by f(E) = —pjrj—> where E is the energy, ft is the - chem-... 

When r > 0 K, the population of the electron energy levels is described by the Fermi-Dirac distribution function (See Section 4.3.3, Eq. 22). At T > 0 K, electrons from the valence band can be thermally excited into the conduction band. As a result, the bottom of the CB becomes partly populated and the top of the VB partly depopulated [Figure 7(b)]. An empty electron level at the top of the valence band is called a (valence-band) hole. The concentration of holes, p, and of electrons, n, can be expressed as a function of the electrochemical potential with Eq. 22. We denote the density of electron levels within IcbT from the top of the VB and the bottom of the CB as the effective density of valence band levels, Avb, and conduction band levels, Nqb, respectively. The electron occupancy of the electron levels at the bottom of the CB is... 

For metal electrodes, the Fermi level is embedded within a broad distribution of closely spaced electronic levels. The Fermi level describes the occupancy of energy levels of a system at equilibrium and can simply be thought of as the chemical potential of electrons in the solid [10]. When employed in the Fermi-Dirac distribution function, Eq. 3 results ... 

The distribution of the electrons among the allowed energy states in the semiconductor crystal at thermal equilibrium is described by the Fermi-Dirac distribution function." It is denoted by ME), which has the form... 

In the case of electrochemical ET, the relevant overlap was between the gaussian density-of-states function of the reacting species in solution and the Fermi-Dirac distribution function of the charge carriers in the electrode (Fig. 4.21). Figure 4B. 1 shows the analogous density-of-states functions for a homogeneous ET reaction. The rate... 

At temperature above T = 0 K the population (F) of the orbitals has a Boltzmann-type distribution which is described by the Fermi-Dirac distribution function ... 

Here o is electrical conductivity, u is thermopower, k is thermal conductivity, t is energy of carrier, p is chemical potential, e is bare charge of electron, and f (e) is Fermi-Dirac distribution function. In deriving eq.(2) we treat the lattice thermal conductivity as a constant. Following we consider the n-type semiconductors, then the change of differential conductivity can be given by ... 

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