Phonon‐assisted decay of excitons in anthracene crystals

Abstract

Tho reflection spectra, R ( w ) , are investigated from the (201) face of anthracene single crystals a t low temperatures (4.2 to 60 K). Absence of surface effects makes possible to judge from the reflection curve on the spectral dependence of the decay parameter, y, due to exciton-phonon interaction. The calculation of y ( o ) is made by use of a nomogram graphically representing the functional relation between the values R, o, and y. It is shown that the decay parameter is essentially frequency dependent a t low temperatures. On the basis of the calculated y ( o ) the mean value is estimated of the interaction energy of excitons with acoustic and optical phonons in anthracene crystals. Es werden die Reflexionsspektren, R ( o ) der (20I)-Fliichen von Anthrazen-Einkristallen bei tiefenTemperaturen (4,2 bis 60 K) untersucht. Das Fehlen von Oberflacheneffekten ermoglicht es, aus den Fhflexionskurven auf die spektrale Abhangigkeit des Zerfallsparameters y der Exziton-Phonon-Wechselwirkung zu schliehn. Die Berechnung von y ( o ) wird mittels eines Nornogramms durchgefiihrt, dss die funktionale Beziehung zwischen den Werten R, w und y graphisch darstellt. Es wird gemigt, daI3 der Zerfallsparameter bei tiefen Temperaturen stark frequenzabhiingig ist. Auf der Grundlage der so berechneten y(o)-Werte wird der Mittelwert der Wechselwirkungsenergie der Exzitonen mit akustischen und optischen Phononen in Anthrazenkristallen berechnet.

Some Correlation between Exciton–Phonon Coupling Function and Phonon Damping

“…So, in the case of exciton interaction with LO phonons cpLo may be considered to be constant only if in the frequency range h-'(-SZ + E,) 5 Y 5 K ' E , the damping depends on the frequency as ffo -I/c,f(hv -E , In the case of polaritons as well as in the case of excitons interacting with LA phonons the form of the f (v) dependence for the respective frequency regions is more complicated. Now let us compare our conclusions with experimental data obtained, e.g., in [7] as the result of measuring the reflection spectrum from the (201) face of an anthracene crystal at 4.2 K. As is seen in Fig. 1 damping in the spectral range -0 + E , 5 hv 2 E , is due only to the processes with LO phonon absorption (Q z 45 cm-' is the energy of the anthracene b-band LO phonon).…”

“…A determination of the energy of coupling with phonons is difficult due to 0). [7] problems connected with the separation of the contributions from LO, LA phonons and other processes.…”

“…For phonon annihilation in ( 5 ) the conservation laws are satisfied only for the first term of the sum in which i = 1. Now it is easy to verify that, for instance, in ionic crystals ( 3 ) and (5) for the damping functions of [8] may be obtained substituting the well-known form for the coupling function in (4) or (5) and replacing q (7), respectively, where (8) by the values q+ and qi.+ of (6) and…”

“…In theoretical calculations one or another form of this function can be used depending on the coupling strength, crystal type, and the lattice vibrations with which the excitons interact most intensively [4 to 61. Rather approximately all these functions describe the real character of the exciton-phonon coupling [7]. No first principles calculation of tp(k,p) has yet been done with sufficient accuracy.…”

“…In the final part it is shown how on the basis of such calculations one can determine the cp(q) form by solving the inverse problem. The practicability of the proposed method to determine the coupling function from the damping is demonstrated by comparison with experimental data for the reflection spectra of the anthracene b-band [7].…”