Excitons surface

The optical spectra of strong D-A complexes or radical-ion salts, that is of crystals in which a charge separation already exists in the ground state, are typified by the metallic character of these materials. They will be treated in Chapter 9. 

Molecules which are located at the surface of a crystal are not surrounded on all sides by other molecules as are those in the bulk. Therefore, surface excitons differ from bulk excitons. Due to the smaller number of neighbouring molecules, the shifts and splittings D and I etc. in the equations of Sect. 6.4 are smaller. The electronic terms of surface excitons are thus less shifted relative to those of the free molecules, i.e. the energies of the transitions lie at somewhat higher values than those of the bulk excitons. This is demonstrated in Fig. 6.17 using the example of anthracene. It shows the reflection spectrum from the (001) surface of an anthracene crystal. One can discern resonance and antiresonance lines which belong to the bulk excitons as well as to excitons in the first, second, and third surface lay- 

In the usual crystals, surface excitons are hard to observe. Their absorption is naturally weak compared to that of the bulk and it lies in an energy range in which the bulk also absorbs. They are therefore best observed in reflection. For naphthalene and anthracene, Davydov splittings and solvent shifts are seen in the 0,0 transitions Si So which are about 10-20% smaller than the known bulk transitions in these crystals. See also [39]. 

These surface excitons become important for very thin crystals, which consist to a large extent of surfaces. Here, the somewhat different excitons in the second and third layers from the surface can be more readily identified. Experimental results for ultrathin films are not yet available. 

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The threshold of the photocurrent is at the energy of 1 eV. This value is less than the absorption edge enagy, what proves the existence of deep levels inside the forbidden gap. The absence of the structure at the beginning of the interband transitions excludes the possibility that the photocurrent is due to the surface exciton dissociation. Attempts to observe good photoconduction in ris-(CH) were unsuccessful. The photocunent in cis-(CH)n was three orders of magnitude lower than in trans-(CH) . 

III. Surface-Exciton Photodynamics and Intrinsic Relaxation Mechanisms A. The Optical Response of the Surface Exciton... 

Origins of Broadening of the Surface Exciton Intrinsic Broadening... 

The excitation spectra of surface emission show, besides the a-polarized surface-exciton Davydov component, vibronic surface structures which... 

The collected data on surface excitons and surface phonons are confronted in order to estimate the extent of the weak surface reconstruction of the anthracene crystal. A surface destabilization (relative to the bulk) corresponding to a negative pressure (— 4 kbar) is inferred and thought to lead to angular reconstruction less than or about 10. The observed energy sequence for surface resonances is shown to be compatible only with R 7 van der Waals forces, for both mechanisms proposed. 

III. SURFACE-EXCITON PHOTODYNAMICS AND INTRINSIC RELAXATION MECHANISMS... 

In this theory, the dynamics of the intrinsic-surface-confined excitons account surprisingly well—in a natural way, without introducing ad hoc parameters—for the surface emissive properties, and they allow, a contrario, a very sensitive probing of various types of surface disorders, whether residual, accidental, or induced. The disorder may be thermal, substitutional, chaotic owing to surface chemistry, or mechanical owing to interface compression. It may be analyzed as a specific perturbation of the surface exciton s coherence and of its enhanced emissive properties. 

Excitation spectroscopy Monitoring of the surface emission allows one to discriminate the upper excited surface states and their relaxation dynamics. Problems such as surface reconstruction, or quantum percolation of surface excitons upon thermal and static disorder, are connected with high accuracy to changes of the exciton spectra.61118,119,121... 

In this section we assume the existence of intrinsic surface excitons, and we restrict ourselves to a succinct summary of the basic experimental data, whose detailed and original description has been given elsewhere.1-67 120... 

Before doing so, we summarize the basic experimental features of the surface exciton states. 

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). 

For the b surface exciton, with its dipole contained in the 2D lattice layer, the nonanalytic part of the dispersion has the value (d2/2 0S0)K cos2(K,d). For... 

One of the most obvious perturbations of the surface excitons by the bulk crystal is the short-range coulombic interactions causing surface-exciton transfer to the bulk. We discard these perturbations on the grounds both of theoretical calculations27 and of the experimental observations, which show the presence of a surface exciton (the second subsurface exciton S3 see Fig. 3.2) resolved at about 2cm-1 above the bulk-exciton resonance. 

Here r,(co) shows the effect of the surface reflectivity, which appears as a lorentzian line, centered at the surface resonance, if we neglect the variation of rv(co) with co around the surface resonance ( lOcnU1). The surface excitations are renormalized relative to the bulk-free surface, leading for coupled surface excitons to a frequency shift ds and to a new radiative width rs, both quantities simply related to the complex amplitude of the bulk reflectivity ... 

The emission of the surface exciton, coupled to the bulk polaritons, may also be calculated using the above scheme, which, here also, coincides exactly with the quantuum-mechanical results. Instead of the lorentzian emission (3.20), we obtain an emission proportional to... 

Figure 3.13. Temperature evolution of the parameter re T) of the first-surface exciton (hollow circles). The full circles indicate the values obtained for the bulk exciton (Fig. 2.14). The quasi-coincidence at T 0 is fortuitous, but the surface states appear less broadened than the bulk states in the region 30-50 K, which could correspond to a decay at the surface of the density of interplane phonons coupled to the exciton (see Section III.B).

To summarize, the main conclusions we are able to draw from this investigation of the surface exciton dynamics, for our best crystals at T = 2 K,... 

The only lower states to which the surface exciton can relax are the bulk states. However, we have seen in Section III.A.l that for the surface exciton vectors K 0, the surface-to-bulk coupling is about 2 cm-1 (very small).27 It is possible to calculate the order of magnitude of the probability for the surface exciton to directly relax, by transition to the bulk states and relaxation in the bulk ... 

To explain the observed width, it is necessary to look for strong surface-to-bulk interactions, i.e. large magnitudes of surface-exciton wave vectors. Such states, in our experimental conditions, may arise from virtual interactions with the surface polariton branch, which contains the whole branch of K vectors. We propose the following indirect mechanism for the surface-to-bulk transfer The surface exciton, K = 0, is scattered, with creation of a virtual surface phonon, to a surface polariton (K / 0). For K 0, the dipole sums for the interaction between surface and bulk layers may be very important (a few hundred reciprocal centimeters). Through this interaction the surface exciton penetrates deeply into the bulk, where the energy relaxes by the creation of bulk phonons. The probability of such a process is determined by the diagram... 

Figure 3.15. Diagram of a nonlocal surface-exciton transfer, corresponding to the optical creation of a surface exciton followed by its relaxation to the bulk. The essential virtual stage is the scattering of a surface phonon (K 0) and the creation of a surface polariton with a large wave vector (K 0), producing large interaction energies with the bulk. 21 Then relaxation in the bulk is ultrafast.

Fig. 3.17 shows the b-emission excitation spectrum, with an a-polarized excitation, in the region E°° + 220 cm "1 and above. We observe a strong and broad peak, attributed here to the a surface component, following refs. 117,67. This peak is strongly asymmetric, broadened on the high-energy side. The value of the component indicated on the maximum (25 523 cm 1, at 222 cm 1 above the b component) may be falsified by the asymmetry of the band. (This will be examined in Section III.B.3 below.) We find that the surface-exciton Davydov splitting is quite comparable with its bulk counterpart (222 cm"1 vs 224 cm-1), to the accuracy of our experiments. Furthermore, the two 0-0... 

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