Intrasurface relaxation

In Section III.A.l we did not discuss the way the surface emission is excited. The radiative behavior of the surface shows that emission (normal to the surface) is observed as soon as the K = 0 state is prepared. This state may be prepared either by a short ( 0.2ps) resonant pulse, or by relaxation from higher, optically prepared excited states. It is obvious that the quantum yield of the surface emission will critically depend on the excitation, owing to intrasurface relaxation accelerated by various types of fission processes (see Fig. 2.8) and in competition with fast irreversible transfer to the bulk (3.30), which is also a surface relaxation, at least at very low temperatures. Thus, the surface excitation spectra provide key information both on the upper, optically accessible surface states and on the relaxation mechanisms to the emitting surface state K = 0. 

Figure 3.21. Scheme of the expected excitation profile due to the relaxation mechanisms illustrated in Fig. 3.22. We expect A) a Raman peak (quasi-resonant), (B) a dip where the intrasurface relaxation ris is quenched by the relaxation to the bulk rt, and (C) a bump / s competing with rB and overhelmed at higher energies f s. depending on the exact exciton vibration coupling, and different for the modes at 390 and 45 cm. ...

In this subsection we analyze the way the theory in Section III.B.l.b allows us to interpret the structures of the excitation spectra and of the emission spectra. Since the intrasurface relaxation proceeds first by the creation of phonons and of vibrations, we consider one of the resulting modes, of energy hi20, without specifying it, and we call it vibration . 

The position and the width of this dip, at about I Ocm"1 above the Raman peak, indicate the energy gap above which the intrasurface relaxation, assisted by acoustical-phonon creation, competes with the surface-to-bulk relaxation. If we figure 3 to 4cm -1 for the relaxation rate to the bulk (for K 0 wave vectors cf. Section 1II.A.3), we conclude that the intrasurface relaxation, at 10cm 1 above the emitting state, is comparable. This conclusion on the acoustical-phonon relaxation is consistent with the theoretical estimates121127 (cf. Section III.A.4) and the experimental values derived by KK analysis of the bulk reflectivity (Section II.C.3b). 

The model of an isolated layer was refined by introducing substrate effects by coupling the surface 2D excitons to the bulk polaritons with coherent effects modulating the surface emission and incoherent k-dependent effects damping the surface reflectivity and emission, both effects being treated by a KK analysis of the bulk reflectivity. The excitation spectra of the surface emission allowed a detailed analysis of the intrasurface relaxation dominated by resonant Raman scattering, by vibron fission, and by nonlocal transfer of... 

Figure 3.22. Model relaxation of the surface excitons created inside or near the threshold of a two-particle-state continuum (illustrated for the 390-cm 1 mode). After excitation (1) at the energy Ekh + 390 cm. a two-particle state is created (2) by fission. Then the exciton may relax along two competing paths an intrasurface channel (3) leading to emission, and a nonradiative channel (3 ) to the bulk (eventually to its fluorescence), with respective probabilities ris and rB. Therefore, the surface emission efficiency depends on the ratio rjrB, which determines the observed profile. When the excitation occurs at exactly 390 cm 1 above the detection, we observe the very narrow Raman peak.

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