Effective mass of conduction electrons

The first heavy fermion superconductor was discovered in CeCu2Si2 [19]. Common properties in a heavy fermion superconductor are large electronic specific heat coefficient, suggesting that the effective masses of the conduction electrons are 100 times higher than the static mass of an electron, and the unconventional superconductivity is difficult to explain by the BCS theory. It has been believed that the enhancement of the effective masses of conduction electrons in... 

The electronic specific heat coefficient, y, is proportional to the DOSs at the Fermi level. In general, in pure metals, it is of the order of a few mj/ mol K. Simply thinking, the electronic DOSs at the Fermi level is proportional to the effective mass of conduction electrons. The most conspicuous and noticeable systems with respect to their electronic specific heat coefficients are heavy electron systems that include some actinide and cerium compounds to be mentioned later. For example, in the case of a typical heavy electron system CeCug, the electronic specific heat coefficient reaches 1.5 J/mol K, which is more than 1000 times larger than that of a normal metal (Satoh et al., 1989). 

TWg, nif are the effective masses of conduction electrons and electron holes (defined below). Or even ... 

Where b is Planck s constant and m and are the effective masses of the electron and hole which may be larger or smaller than the rest mass of the electron. The effective mass reflects the strength of the interaction between the electron or hole and the periodic lattice and potentials within the crystal stmcture. In an ideal covalent semiconductor, electrons in the conduction band and holes in the valence band may be considered as quasi-free particles. The carriers have high drift mobilities in the range of 10 to 10 cm /(V-s) at room temperature. As shown in Table 4, this is the case for both metallic oxides and covalent semiconductors at room temperature. 

A and B being constants which need not interest us further. (We may assume that A B, which denotes approximate equality of the effective masses of free electrons and holes.) Thus, the electrical conductivity is diffeient in different cross sections parallel to the adsorbing surface (i.e., at different x). Chemisorption, by changing the bending of the bands, may lead to a noticeable change in the electrical conductivity of the subsurface layer of the crystal, which in the case of a sufficiently small crystal may effect the total electrical conductivity of the sample. Even more, so the very type of conductivity in the subsurface layer may change under the influence of chemisorption n conductivity (e < +) may go over into p conductivity (t > +), or vice versa (the so-called inversion of conductivity). 

The energy E will necessarily have this minimum, but its value at this point can be positive or negative only in the latter case will a stable self-trapped particle (i.e. a small polaron) form. This is most likely to occur for large effective mass, and thus for holes in a narrow valence band or for carriers in d-bands. If the polaron is unstable then there is practically no change in the effective mass of an electron or hole in equilibrium in the conduction or valence band. 

In equation 3, ran is the effective mass of the electron, h is the Planck constant divided by 2/rr, and Eg is the band gap. Unlike the free electron mass, the effective mass takes into account the interaction of electrons with the periodic potential of the crystal lattice thus, the effective mass reflects the curvature of the conduction band (5). This curvature of the conduction band with momentum is apparent in Figure 7. Values of effective masses for selected semiconductors are listed in Table I. The different values for the longitudinal and transverse effective masses for the electrons reflect the variation in the curvature of the conduction band minimum with crystal direction. Similarly, the light- and heavy-hole mobilities are due to the different curvatures of the valence band maximum (5, 7). 

Population analysis and site-decomposed DOS indicate that, compared with GaN On, large numbers of extra electrons are introduced into the other sites in the vicinity of the Si-sites. This results in a small effective mass of the electrons introduced in the conduction band. From these findings, we can expect high-conductivity n-type GaN Sic crystals. 

Here nf and nf are the effective masses of the electron and the positive hole created when an electron is excited from the valence band to the conduction band. In bulk CdSe, m Jm and nfjm have been determined to be about 0.12 aud 0.5, respectively. The reduced mass p, = nfgwl l nfg + ml) = 0.091 m is thus much smaller than the mass of an electron. It is seen that the form of equations (3) and (4) is similar to that for a free particle in a sphere but with a uegative sign for the energies of the hole. 

The energy of the conduction electrons is given by h2k2/2 x, where k is the wave vector number and p, is the effective mass of the electron-nucleus. In a real space of Cartesian coordinates k = [kx, ky, fcj, a Fermi sphere can be constructed with radius k = (2 lE )x 2/h. The shape of this sphere is a clearly defined by the electrical properties of the metal. The current density obeys the change in the occupancy of states near the Fermi level, which separates the unfilled orbitals in the metal from the filled ones in the linear momentum space p = hk. 

It is important to note that while the density of states increases mono-tonically with energy [Eq. (7B.5)], as shown in Fig. 7.20a, the probability of occupancy of the higher levels drops rapidly (Fig. 7.20b), such that in the end the filled electron states are all clustered together near the bottom of the conduction band (Fig. 7.20c). Finally, note that for many ceramic materials, the effective masses of the electrons and holes are not known, and the assumption that m — ml — ml is oftentimes made. 

As the effective mass of an electron in silicon is approximately one tenth of the electron rest mass, and as the relative permittivity of silicon is about 10, the energy needed to free the electron is about one hundredth of the band gap, which suggests that the electron should be very easily liberated. Donor energies are often represented by an energy level, the donor level, drawn under the conduction band (Figure 13.9a.ii). 

The results are presented of an investigation of the optical infrared transmission and reflection spectra of the alloy 0.7 InSb-0.3 InAs, doped with tellurium to obtain different electron densities (n). The optical width of the forbidden band (AE) and the optical effective mass of the electrons (mn) were determined from the spectra and their dependence on n studied. It was established that the conduction bands of InSb-InAs solid solutions are nonparabolic. Attempts were made by extrapolation to obtain an estimate of the limiting values of AE and mg in the region of low values of n, and an estimate of the matrix element P was made. It is concluded that there is general agreement between the structure of the energy bands of the semiconductor alloys considered and the Kane model. 

It is of considerable scientific and practical interest to study the physical properties of solid solutions in the quasibinary system InSb-InAs, which have a comparatively narrow forbidden band. The nature of the changes with composition in the optical [1,2] and thermal [3,4] energy gap widths and in the effective mass of the electrons [5,6] have been studied previously. To study these semiconducting alloys furthfer, and particularly to ascertain the structural details of their energy bands, it is desirable to conduct investigations on doped specimens. 

The electrical properties of the homogeneous alloys (Hall effect, conductivity, thermoelectric power) were studied at room temperature on electrically homogeneous samples prepared under identical conditions. The measurements showed that the alloys in systems 1 through 5 have n-type conduction while those in system 6 have p-type conduction. Extrinsic conduction and a high carrier density have been established for the alloys in all the systems. The electrical conductivity and mobility (Fig. 2) decrease monotonically with an increase in the content of A B component in the solution. The thermoelectric power and the effective mass of the electrons have low values and vary little with the composition. 

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