Rigid-band approximation

Fig. 12.5 DOSs (upper panel) and COHPs (lower panel) for a model compound, La2Ca3Ge4. The vertical lines are the Fermi levels for the corresponding x values within a rigid-band approximation.

Figure 6.16 shows recent results of a Jones-type analysis of the stability of Cu-Zn alloys within the rigid-band approximation. This latter approximation assumes that the bands of fee, bcc, and hep copper remain unchanged (or rigid) on alloying, so that the structural energy difference between any two lattices is given by... 

The coherent potential approximation for a disordered alloy (7,2) provides a satisfactory framework for describing the effect of alloying within two extremes on the one hand, the rigid-band approximation, which supposes that band shapes do not alter upon alloying, and on the other hand, the minimum polarity model, which supposes the electron distribution of the elements forming an alloy to be similar to that in free atoms. 

The larger values for x for trans-(-CH = CH-) can be qualitatively understood if one considers the rigid band approximation to be characteristic of cis-(-CH = CH-)n where the soliton pair excitations are confined by the nondegenerate ground state. However, the absolute magnitude of x for trans-(-CH = CH-)n is an order of magnitude smaller than the calculated curves... 

There are several phenomenological models of the electronic structure of such solid solutions based on the rigid band approximation. Such models use either experimental data, e.g., the models of Lesnaya (1981), Zhurakovsky and Nemtchenko (1989), or describe ternary system spectra as a superposition of the valence bands of the starting binary alloys. 

As a small number of electrons are added to the conduction band, polarization of the valence band will occur. Since only a comparatively small number of electrons is in the conduction band, a rigid-band approximation can be made. This implies that remains the same. Assuming for the moment that the interaction is spin independent (which it is not), the lowest-order dressed exciton contribution to the self-energy becomes... 

The most elementary assumption which one can make is that adding A and B does not change n E) at all. This is the rigid band approximation, often used in the interpretation of experimental results. It is, in the present case, equivalent to the slightly more sophisticated model defined by the virtual crystal approximation, in which the Hamiltonian is averaged over the ensemble defined by the above probability distribution, to define a periodic Hamiltonian of the form (46), with... 

The second contribution to the MCD that will be considered is the A term. A terms arise because of the change in the band-shape function f due to the apphed magnetic field. In this context, the rigid-shift approximation (11) is usually applied. By making the rigid-shift approximation it is assumed that the center of the band-shape function moves as u>j changes but that the shape of /otherwise does not change. If this is the case then... 

Fig. 55. Debye temperature, d, and density of states at the Fermi level, N(Ep), for Y(Ni xCox)2B2C and Y(Ni xCux )2B2C as a function of the Co/Cu substitution level x. Symbols results derived from a relativistic band calculations in the atomic sphere approximation. Curves (in lower panel) rigid band model. After Ravindran...

At the time of the Pd/(CH3)2S susceptibility experiment 15) referred to previously, the only conceptual framework available to describe the result was the rigid-band model The adsorbate is supposed to dump some of its electrons into the lowest empty orbitals of the metal (or to pull some from the highest filled ones) without changing the energetic sequence of these orbitals. In other words, the adsorbate adds electrons but no orbitals (or the other way round). It is now known that this is usually a poor approximation 23), and the rigid-band model is no longer used. 

One can see from Fig. 14 that in ternary systems like LiCdi-xIn, the rigid band model is a good approximation for those electronic properties which depend predominantly on... 

The operating mechanism of PLEDs is quite different from conventional p-n junction LEDs. In a PLED, a pure undoped film of luminescent semiconducting polymer is sandwiched between a high work function metal anode and a low work function metal cathode. The charge carrier concentration in such pure semiconducting films is sufficiently low (>=1014-1015 cm-3) that any residual carriers introduced by impurities etc. are swept out by the built-in field that arises from the difference in work functions of the two electrodes. The depletion depth of pristine poly(phenylene vinylene) (PPV) is approximately 250 qm, which is much larger than the thickness of the polymer layer in an LED (typically < 100 nm). Consequently, the electronic structure of the LED can be approximated by the rigid band... 

The electronic properties of inorganic clathrates are often discussed in terms of a rigid band model [63]. According to this approximation electropositive guest atoms donate their valence electrons to the sp bonded framework atoms. Compositions where electronegative guest elements contribute holes to the framework orbitals are known as inverse [64] (cf. Chap. 5). In order to consider clathrates for TE applications it is necessary to optimize their electronic properties thereby maximizing the power factor in Eq. 6.1. From the relationship between the electrical resistivity, p, and cr [32]... 

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