Anisotropic effective mass

We conclude this subsection with several remarks on the interpretation of the anisotropy of Hc2. The largest in-plane anisotropy reported by Metlushko et al. (1997) coincides with the direction of the nesting vector (0.55,0,0). Another manifestation of strong local anisotropy effects is provided by deviations from the 9 (angular) dependence due to anisotropic effective masses (Fermi velocities)... 

Anisotropic effects of the recorded frequency of cosmic microwave background radiation have been proposed for photon rest mass determination [20]. 

If t Ijh > 1 then the system should form an anisotropic Fermi surface, with a large effective mass perpendicular to the planes. In both directions we should expect the same t (namely Tt ), and the conductivities in the two directions should be ne2xjm1 and ne2xjm2f where m1 and m2 are the effective electron masses. 

The different behavior (direct versus indirect band gap) of Si and Ge with respect to the film orientation can be explained in term of confinement effects on the conduction band minima (CBM) of the two semiconductors.Whereas the six equivalent ellipsoidal CBM of bulk Si occur in the (100) directions about 80% of the way to the zone boundary, in bulk Ge there are eight symmetry-related ellipsoids with long axes along the (111) directions centered on the midpoints of the hexagonal zone faces. Also the different confinement energy shifts with respect to the orientation of the layer can be interpreted in terms of the different highly anisotropic behavior of the effective masses for bulk Ge and Si [170,171]. 

Without loss of generality, we assume a bulk material where the major carriers are electrons with an effective mass inf. In general, the electron masses are anisotropic, and the effective mass is expressed as a symmetric second-rank tensor. The dispersion relation of the electrons is written as... 

In a nanowire system, the quantized subband energy enm and the transport effective mass mzz along the wire axis are the two most important parameters and determine almost all the electronic properties. Due to the anisotropic carriers and the special geometric configuration (circular wire cross section and high aspect ratio of length to diameter), several approximations were used in earlier calculations to derive e m and mzz in bismuth nanowires. In the... 

EPR measurements were first performed on wurtzite GaN in 1993 by Carlos and co-workers [2-4] and on cubic GaN by Fanciulli and co-workers at about the same time [5], The primary resonance in the wurtzite films is slightly anisotropic (gy = 1.9510 and gi = 1.9483) with a width 0.5 mT at 4.2 K and generally acknowledged to be due to a band of delocalised effective mass (EM) donor electrons. The average g value is consistent with the expectations of a 5-band k.p analysis and is also similar to that obtained by Fanciulli [5] for a much broader line (—10 mT) in their conduction electron spin resonance experiments on zincblende films. With this exception all of the work discussed in this Datareview is on the wurtzite phase. 

Most wurtzite-type crystals are direct band-gap materials (2fP-SiC is an exception) and interband transitions can take place between these three Fils and the T7 CB minimum. These materials are anisotropic and this anisotropy reflects on the selection rules for the optical transitions and on the effective masses. The Tg (A) —> T7 (CB) transitions are only allowed for ETc while the two T7 (B. C) —> T7 (CB) transitions are allowed for both polarizations. However, the relative values of the transition matrix elements for the T7 (B, C) —> T7 (CB) transitions can vary with the material. For instance, in w-GaN, the T7 (B) —> T7 (CB) transition is predominantly allowed for ETc while the T7 (C) — I 7 (CB) transition is predominantly allowed for E//c [22]. Table 3.7 gives band structure parameters of representative materials with the wurtzite structure. 

The g-factors of electrons and holes reflect the nature of the conduction and valence bands in much the same way as the effective masses. Thus in AgF, AgCl, and AgBr, free electrons and shallowly trapped electrons whose wavefunctions are made up largely of conduction band functions are expected to be isotropic in nature. A free electron at the bottom of the band will have a single effective mass and g-factor. In contrast, free holes near the L-point and shallowly trapped holes whose wavefunctions are largely valence band functions are expected to show anisotropic behavior. A free hole will have parallel and perpendicular g-factors. The available data on electron and hole masses were given in Table 1 and the data on g-factors are given in Table 9. Thermalized electrons and holes in both modifications of Agl will be at the zone center. The anisotropic nature of the wurtzite crystal structure will be reflected in the effective masses and g-factors. 

Complex, anisotropic spectra were observed in 6H and 4H polytypes doped with Sc [5,8,9]. The g-factors parallel to the crystal axis are smaller than those that are perpendicular to it (see TABLE 2). This anisotropy is opposite to that of the shallow acceptors. Many spectra are observed whose parameters indicate that the Sc-acceptors, like the B-centres, are not effective-mass-like. 

Electron and hole states have been calculated for Si nanowires and quantum dots within the effective mass approximation. In the calculation of the electron states, six anisotropic valleys of bulk Si have been taken into account. It is found that the states depend on the crystallographic direction and on the size of the wires and the dots. These results have been used to calculate electron-hole recombination lifetimes. The magnitudes of the lifetimes are very s ensitive t o t he g eometrical a nd s tructural p arameters o f t he w ires and t he d ots. 11 i s concluded that non-uniformity in the crystallographic direction of Si nanowires and quantum dots causes itself dispersion in the values of the photoluminescence lifetime. 

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