Surface states dielectric function

In particular, the phonon dispersion relations and polarization vectors can be calculated with reasonable accuracy using force-constant models [59] or the embedded atom method [60-62], In recent calculations of Fe-ph and X for surface states, wave functions obtained from the one-electron model potential [63, 64] have been used. For the description of the deformation potential, the screened electron-ion potential as determined by the static dielectric function and the bare pseudopotential is used, Vq z) = f dz e (z,2/ gy)qy), where (jy is the modulus of the phonon momentum wave vector parallel to the surface, and bare Fourier transform parallel to the surface of the bare electron-ion... 

Electroless reactions must be autocatalytic. Some metals are autocatalytic, such as iron, in electroless nickel. The initial deposition site on other surfaces serves as a catalyst, usually palladium on noncatalytic metals or a palladium—tin mixture on dielectrics, which is a good hydrogenation catalyst (20,21). The catalyst is quickly covered by a monolayer of electroless metal film which as a fresh, continuously renewed clean metal surface continues to function as a dehydrogenation catalyst. Silver is a borderline material, being so weakly catalytic that only very thin films form unless the surface is repeatedly cataly2ed newly developed baths are truly autocatalytic (22). In contrast, electroless copper is relatively easy to maintain in an active state commercial film thicknesses vary from <0.25 to 35 p.m or more. 

We must again emphasize, even more strongly than we did at the beginning of this chapter, that surface plasmons and surface phonons are not examples of the failure of the bulk dielectric function to be applicable to small particles. Down to surprisingly small sizes—exactly how small is best stated in specific examples, as in Sections 12.3 and 12.4—the dielectric function of a particle is the same as that of the bulk parent material. But this dielectric function, which is the repository of information about elementary excitations, manifests itself in different ways depending on the size and shape of the system. 

A full set of optical functions consists of reflectivity R and absorption coefficients, p, the imaginary 82 and real 81 parts of the dielectric function 8, the absorption and refraction indices k and n, the product of the integral joint density of states (DOS) function and the transition probability, equal within constant factor to the effective number of valence electrons n E) participating in the transitions to given energy level A the effective dielectric coefficient Sef, and the characteristic electron energy functions for volume (-Imc ) and surface (-Im(l+8) ) losses. 

If the values of the dielectric function of an anisotropic thin film at an isotropic metal surface are large (as in the case of the electronic absorption of the surface states), Eqs. (1.87) can be rewritten as... 

As was shown by Selci et al. [466], the KK method allows the complex dielectric function associated with the semiconductor surface states to be calculated. The surface is treated as an absorbing layer of thickness d < k located between a substrate and an external medium. The differential quantity AR/Rd = (Roi - Rox)/Rox was used as a measure of the surface reflectivity, where Rox is... 

We can also estimate in a first approximation the joint density of states Jcv assuming constant matrix elements within an f-f or d-f transition, respectively. We can describe the imaginary part of the dielectric function in terms of an integration over a surface in the reciprocal space k. For direct optical transitions one finds... 

Earlier observations by Cesario et al. [60] of a decay in fluorescence for arrays of Au nanoparticles spaced above a Ag film by a Si02 layer of increasing thickness, were interpreted as due to the finite vertical extent of the evanescent fields associated with a surface plasmon. In this model the coupling results in an enhanced interaction between individual localized plasmons at individual nanostructures [61] and thus an enhancement in the radiative efficiency increasing the spacer layer thickness moves the nanowires out of the evanescent field of the surface plasmon. A possible physical mechanism for the experimentally observed decay involves nonradiative decay of the excited states. The aluminum oxide deposited in these experiments was likely to be nonstoichio-metric, and defects in the oxide could act as recombination centers. Thicker oxides would result in higher areal densities of defects, and decay in fluorescence. A definitive assignment of the mechanism for the observed fall off of fluorescence would require determination of the complex dielectric function of our oxides (as deposited onto an Ag film), and inclusion in the field-square calculations. Finally it should be noted that at very small thicknesses quenching of the fluorescence is expected [38,62] consistent with observations of an optimum nanowire-substrate spacer thickness. 

Surface stress elasticity Hamiltonian surface optics dielectrics surface trapping states electron and photon transport dynamics work function, etc. 

In the 2- 20 eV range, surface excitations related to the dielectric response function and free carrier density of the surface are observed. Clean-surface loss spectra can include features due to surface phonons, surface plasmons, interband transitions and surface optical phonons in ionic insulators. The probe depth for these phenomena in HREELS is about 10 nm. Transitions between surface states can also be observed in the loss spectrum. Some examples are given in the section related to hydrogen adsorption and surface states below. 

The interpretation of RAS spectra from single-crystal surfaces is not as straightforward as it is for, for example, XPS. This is because the response of the surface depends on the complex dielectric function (a quantity that is difficult to calculate from first principles even for well-characterized materials) for both the bulk of the sample and the surface region. Also, in common with other techniques that are sensitive to surface electronic structure, the existence of intrinsic surface states and surface-modified bulk states compHcates matters. However, absence of a firm theoretical framework for predicting RAS spectra has not necessarily impeded the application of RAS in various fields. An empirical approach, often supported by other techniques that provide information on the electronic transitions responsible for RAS spectral features, can allow surface changes to be studied even without a complete understanding of the RAS spectra. 

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