Effective mass of carriers

The Fermi surface topology in refractory carbides has also been studied in detail. The Fermi surface in TiC was first calculated by the linear combination of atomic orbitals (LCAO) method (Em and Switendick, 1965) and then by the KKR method (Schadler, Weinberger, Klima and Neckel, 1984). It was shown that the largest sheets of the Fermi surface are hole-like in character. This contradicts the results of Hall coefficient measurements for TiC (Bittner and Goretzki, 1960 Dubrovskaya, Borukhovich and Nazarova, 1971), which clearly show the electronic character of conductivity. This contradiction was explained by calculations of the effective mass of carriers in TiC and TiN (Zhukov et al 1988a). Despite the hole character of the Fermi surface, effective masses of carriers in TiC along the main directions in the Brillouin zone appear to be positive in most cases, i.e., the electric conductivity of TiC is of electronic character. 

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. 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

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. 

It is of course possible that a carrier in the conduction band or a hole in the valence band will form a spin polaron, giving considerable mass enhancement. The arguments of Chapter 3, Section 4 suggest that the effective mass of a spin polaron will depend little on whether the spins are ordered or disordered (as they are above the Neel temperature TN). This may perhaps be a clue to why the gap is little affected when T passes through TN. If the gap is U —%Bt -f B2 and Bt and B2 are small because of polaron formation and little affected by spin disorder, the insensitivity of the gap to spin disorder is to be expected. 

In relation to this problem is the fact that as the top of a band is approached the effective mass of a carrier changes and the range of allowed k values is small. Thus, the mobility of a carrier either in a narrow band conductor or at the top of an almost filled band must inevitably be small (9). In these cases it is probably not correct to assume the mass of the carrier and an electron to be the same. Under some circumstances the transfer of charge in a narrow band semiconductor is better described as an activated hopping process. 

In addition, the curvature of the Elk plot yields values for m, the effective mass of the electron, which in turn controls the carrier mobility and the... 

Fig. 21. Real part of the conductivity of YbFe4St>i2- The symbols on die left axis represent dc values at different temperatures. Below T (fv 50 K), a narrow peak at zero frequency and a gap-like feature at 18 meV gradually develop. Inset Renormalized band structure calculated from die Anderson lattice Hamiltonian. % and f denote bands of free carriers and localized electrons, respectively. At low temperatures a direct gap A opens. The Fermi level, Ep is near die top of die lower band,, resulting in hole-like character and enhanced effective mass of die quasiparticles (Dordevic et al., 2001).

Ion Scattering Spectroscopy mass, molar mass effective mass of electron concentration of ions or charge carriers concentration of acceptors concentration of donors coordination number of shell j complex refraction index photo ionization cross-section electric charge gas constant... 

Both injection-type and optically pumped nitride-based semiconductor laser structures exhibit fairly high threshold pump levels compared to other III-V or II-VI semiconductors. This is fundamentally due to the specific band structure of the nitrides, i.e. the extremely large effective masses of both electrons and holes. The carrier densities needed to achieve transparency are of the order 2 x 1019 cm 3. 

As a consequence of the wave behaviour of electrons in matter, we replace the variable u by the wave vector k — m u/h, where rn designates the effective mass of the carrier in the crystal, and we translate u into the group velocity... 

Field emission is characterized by its temperature independence. Here meff is the effective mass of the carrier in the dielectric. The essential assumption of the Schottky model is that a carrier can gain sufficient thermal energy to cross the barrier that results from superposition of the external field and image charge potential. Neither tunnelling nor inelastic carrier scattering is taken into account. The following current characteristic is predicted for the Schottky junction ... 

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