Exciton surface monolayer

For a coherent interpretation of the reported experimental data, we need a model of surface excitons, the structures I, II, and III being attributed to excitons confined, respectively, in the first, the second, and the third surface monolayer (see Fig. 3.5). The rapid decay of the van der Waals forces along the c axis explains the very fast transition, in a few molecular layers, from surface to bulk spectroscopy (the other two faces of the anthracene crystal do not show surface-confined excitons). 

In this section we analyze the surface investigation of molecular crystals by the technique of UV spectroscopy, in the linear-response limit of Section I, which allows a selective and sharp definition of the surface excited states as 2D excitons confined in the first monolayer of intrinsic surfaces (surface and subsurfaces) of a molecular crystal of layered structure. The (001) face of the anthracene crystal is the typical sample investigated in this chapter. 

To first order, we consider the molecular structure of the surface layers to be identical to that of the bulk layers. Consequently, all the characteristics corresponding to short-range intralayer interactions (e.g. Davydov splitting, vibrational frequencies, excitonic band structure, vibronic relaxations are similar for bulk and surface layers). In fact, we shall see that even slight changes may be detected. They will be analyzed in Section III.C, devoted to surface reconstruction. Therefore, our crystal model consists of (a,b) monolayers translated in energy relative to the bulk excitation by 206, 10, and 2cm-1 for the first three layers, as indicated in Fig. 3.5. No other changes are considered in this first-order crystal model. 

Presented experimental data reveal that for CdSe/ZnS quantum dots with two ZnS monolayers values follow a monotonous function drastically decaying with the QD core diameter. From the physico-chemical point of view, we conjecture that upon interaction of P with QD surface, the electron wave function may be locally modified (via inductive and/or mesomeric effects [9]) forming a surface local state capable to trap the electron of the photogenerated exciton (Fig. 2A). Thus, we will consider the behaviour of the electron wave function at the interface to the functional pyridyl group of the attached porphyrin. The single-carrier envelope wave functions y/a in a spherical core/shell QD are determined by the Schrodinger equation... 

After these remarks let us return again to the first monolayer of the anthracene crystal. Note, first of all, that the width of the exciton band in this crystal for wavevectors directed along the C -axis (i.e., along the normal to the (a, b) plane) is very small ( 5 cm-1) in comparison with bandwidth of excitons with wavevectors parallel to the (a, b) plane and it is very small in comparison with the blue-shift of the exciton level in the outermost monolayer. For this reason, first of all, the mobility of excitons located in monolayers in the direction towards the surface is rather small. On the other hand, as the energy of he exciton located at the outermost monolayer is larger than the energy of the exciton in the bulk the interaction of bulk excitons with the surface is repulsive. We have here a type of dead layer for the bulk exciton. Qualitatively this picture helps explain why the experimental observation of photoluminescence of excitons located at the outermost monolayer of the anthracene crystal was possible. 

Let us consider now the conditions under which the dependencies of the type displayed in Figs. 9.4 and 9.5 can be realized. Note, first of all, that in layered crystals which we discuss now, the width of an exciton band A for wavevectors directed along the normal to the (a, b) plane is rather small and in this consideration can be neglected. For this reason Figs. 9.4 and 9.5 determine the minimum energy of an exciton in a monolayer of a crystal as a function of its distance to the surface.54 However, the large homogeneous width 7 of the lowest exciton transition can destroy this picture of spectra. The picture will survive only for such layered crystals like the anthracene crystal in which the inequalities... 

In this subsection we go back to more detail than in Section 9.1 discussion of excitations in first monolayers of organic crystals of anthracene family (naphthalene, tetracene and so on). As we explained the spectrum of this states depends on the distance to surface of crystal. For this reason these excitons are called site shift surface excitons (SSSE) what is reflected in title of this subsection. 

We emphasize first of all that the disorder in the subsurface region, i.e. in the region of localization of the surface exciton, may result from its own internal disorder or may be caused by other, external reasons (e.g. by absorbed molecules). The microscopic surface states under consideration are strongly affected by both types of disorder. This circumstance should be borne in mind even in the cases when SSSE are treated in isotopically disordered crystalline solutions. In such states, which interact weakly with internal crystal monolayers, the effect of internal and external disorder can result in equally serious consequences. We will now make some qualitative remarks on the Anderson localization of surface excitons. As before let us assume a molecular crystal, ignore the exciton-phonon interaction, but take into account, for instance, the diagonal disorder (i.e. the random energy distribution of molecular excitations). 

The exciton effects observed in absorption spectra of porphyrin monolayers are often different from those in stacked or lateral fibrous assemblies. One usually finds exclusively long-wavelength shifts of the Soret bands or no effect at all. Porphyrins either lie parallel to each other on the subphase (no shift) or are oriented in a slipped stack-of-cards configuration tilted by 10-20° angles against the subphase surfaces, which produce file observed 20-100 nm red shifts (Fig. 6.8.2). 

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