Fermi model distribution

One can actually prove a stronger result all nondeterministic LG models that satisfy semi-detailed balance and possess no spurious conservation laws have universal equilibrium solutions whose mean populations are given by the Fermi-Dirac distribution (equation 9.93) [frishc87]. 

The significance of the electrochemical potential is apparent when related to the concepts of the usual stati.stical model of free electrons in a body where there are a large number of quantum states e populated by noninteracting electrons. If the electronic energy is measured from zero for electrons at rest at infinity, the Fermi-Dirac distribution determines the probability P(e) that an electron occupies a state of energy e given by... 

What are surface states In an ideal semiconductor, the electron distribution in the conduction band follows Fermi s distribution law and the assumptions behind the deduction is that the conduction electrons are mobile ( free ). In this model, electrons may come to the surface and overlap or underlap a bit, but there are no traps to spoil the sample distribution. 

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. 

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... 

Wollny M., and Peleg M. (1994). A model of moisture-induced plasticization of crunchy snacks based on Fermi s distribution function. J. Sci. FoodAgri., 64,467-473. 

It is well known that for heavy atoms the effect of the finite nucleus charge distribution has to be taken into account (among other effects) in order to describe the electronic structure of the system correctly (see e.g. (36,37)). As a preliminary step in the search for the effect of the finite nuclei on the properties of molecules the potential energy curve of the Th 73+ has been calculated for point-like and finite nuclei models (Table 5). For finite nuclei the Fermi charge distribution with the standard value of the skin thickness parameter was adopted (t = 2.30 fm) (38,39). 

The two-parameter Fermi model gives a realistic description of the nuclear distribution [38,39], and at the same time provides considerable flexibility in the analysis ... 

Generalizations of the Fermi model to describe deformed nuclei have been applied e.g. in the study of energies for highly charged uranium [44,45]. The nuclear radius parameter c in the Fermi distribution (1) is then replaced by... 

Density of states for an arbitrary metallic solid using the free electron model. The dashed curve is for 7= 0 K, while the dotted curve is for 7> 0 K and employs the Fermi-Dirac distribution given by Equation (11.10). [ P.A. Cox, The Electronic Structure and Chemistry of Solids, 1987, by permission of Oxford University Press.]... 

In the above equations, rip can be identified as the Fermi-Dirac distribution function denoting the average thermal excitation number of the spin-bath. This distribution does not contain any contribution due to the chemical potential, which implies that our stating Hamiltonian Equation 9.1 does not conserve the spin -1/2 particle number. Ideally, the typical system/spin-bath model for dissipation may be considered as an ion in an environment of two-level quantum dots (Bras et al. 2002 Favero et al. 2007 Santori and Yamamoto 2009 Xu and Teichert 2005) with characteristic frequencies governed by the size distributions of the dots. To preclude the possibility of any recurrence and to ensure irreversibility associated with the notion of dissipation, a large number is an essential requirement. 

Equation (1.6) accounts for both the Arrhenius regime and the temperature-independent low-temperature behavior, as described by the fluctuation-induced tunneling conductivity model. Each of the terms in curly brackets include a description of the forward current density component, in the direction of the applied electric field and a backflow current density in the opposite direction. The first term corresponds to the net current in the low-temperature limit, with an abrupt change in the density of states at the Fermi energy, while the other terms are corrections caused by expansion of the Fermi-Dirac distribution to first order in temperature. 

Fowler proposed a theory in 1931 which showed that the photoelectric current variation with light frequency could be accounted for by the effect of temperature on the number of electrons available for emission, in accordance with the distribution law of Sommerfeld s theory of metals. Sommerfeld s theory (1928) had resolved some of the problems surrounding the original models for electrons in metals. In classical Drude theory, a metal had been envisaged as a three-dimensional potential well (or box) containing a gas of freely mobile electrons. This adequately explained their high electrical and thermal conductivities. However, because experimentally it is found that metallic electrons do not show a gaslike heat capacity, the Boltzman distribution law is inappropriate. A Fermi-Dirac distribution function is required, consistent with the need that the electrons obey the Pauli exclusion principle, and this distribution function has the form... 

In order to discuss electron transport properties we need to know about the electronic distribution. This means that, for the case of metals and semimetals, we must have a model for the Fermi surface and for the phonon spectrum. The electronic structure is discussed in Chap. 5. We also need to estimate or determine some characteristic lengths. 

---