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Optical properties and morphology of thin diindenoperylene films
ARTICLE IN PRESS
Journal of Luminescence 110 (2004) 290–295 www.elsevier.com/locate/jlumin
Optical properties and morphology of thin diindenoperylene films M. Heilig, M. Domhan, H. Port Universita¨t Stuttgart, 3. Physikalisches Institut, Pfaffenwaldring 57, D-70550 Stuttgart, Germany Available online 17 September 2004
Abstract Thin films of diindenoperylene deposited on weakly interacting substrates (quartz) are characterized with scanning probe microscopy techniques at room temperature and by pico-second time-resolved fluorescence spectroscopy between 5 and 300 K. Pronounced T-dependencies of fluorescence spectra and decays are found. The interplay between two fluorescence series in a narrow temperature range ð80 KpTp100 KÞ has been spectrally and temporally resolved. The possible origin of the observed series, competing energy transfer and quenching processes is discussed. r 2004 Elsevier B.V. All rights reserved. PACS: 78.66.Qn; 78.67.n; 78.47.+p; 33.50.Dq Keywords: Organic nanostructures; Diindenoperylene; Thin film; Time-resolved fluorescence spectroscopy
1. Introduction In recent years, large effort has been devoted to the development of organic semiconductor devices like organic thin film chemical sensors, organic light emitting diodes and organic field-effect transistors [1–5]. In parallel with these activities, much progress has been made in the understanding of the underlying physics that controls the Corresponding author. Tel.: +49-711-6855233; fax: +49711-6855281. E-mail address: [email protected] (M. Heilig).
properties of these devices [6]. In comparison with inorganic semiconductors, much less is known about the electronic properties of these materials; even the nature of the semiconductor excitation of organic material remains controversial. To achieve electronic properties comparable to classic inorganic semiconductors, high-quality organic single-crystals appear attractive but are not practicable for commercial application [7]. Therefore organic thin films are more likely to be used. The electronic properties of organic thin films are significantly different from the monomer or bulk-crystal properties, moreover, they depend on
0022-2313/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2004.08.023
ARTICLE IN PRESS M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295
the microscopic film morphology (e.g. grain boundaries, localized defects) [8–10] . High structural order is reported for organic thin films of diindenoperylene (DIP) grown under UHV conditions on different substrates [11,12]. On semiconductor and quartz substrates, the deposited DIP molecules align upright standing to the substrate surface and form densely packed layers. The high structural order on molecular scale favors due to overlapping p-orbitals high lateral transfer processes parallel to the substrate surface. Efficient charge carrier transfer in FET structures with DIP has been demonstrated [13]. To our knowledge, there are no optical investigations on the excited state properties of thin DIP films reported in the literature. The emphasis of our research is to explore the optical properties of thin DIP films in correlation to the film structure by applying several spectroscopic optical methods and different scanning probe microscopy techniques. In this letter, a preliminary account of the work will be given.
291
3. Results and discussion 3.1. Film morphology Information on the morphology was deduced from AFM measurements and concomitant confocal microscopy. In Fig. 1 representative examples at different resolution for a DIP sample with film thickness of 16 nm are given. The film exhibits terrace structures parallel to the substrate surface extending up to several hundreds of nanometers (Fig. 1b). Linescans reveal that the terraces are separated from each other by mono-molecular steps of 1.65 nm (Fig. 1a). These results are in accordance with X-ray data [11,13] and previous AFM investigations of thin DIP films on semiconductor substrates with thick oxide overlayers [12]. The spatially resolved fluorescence intensity in Fig. 1c reflects the structural information obtained by AFM. The optical resolution is approximately 400 nm (diffraction limited) for excitation at 514 nm (19; 400 cm1 ) with intensity of 5 mW at sample position.
2. Experimental
3.2. Fluorescence spectroscopy
Thin DIP films in the thickness range of 8–50 nm were evaporated under UHV conditions onto amorphous quartz substrates. The morphology determination and fluorescence imaging experiments were performed in a home-built scanning probe microscope setup. It combines AFM, confocal fluorescence imaging and optical near-field microscopy (excitation with an Argon ion laser at 514 nm/19; 400 cm1 ). The system is built upon an inverted microscope (Zeiss Axiovert 200 MAT) and additionally provides classical optical microscopy. For temperature-dependent and time-resolved fluorescence measurements we used a frequency doubled active mode locked Nd:YAG laser system (532 nm/18; 800 cm1 ) for photoexcitation and a narrow band detection system with a substractive double monochromator and a cooled fast MCP photomultiplier. Time correlated single photon counting (TCSPC) leads to an overall response time of sub-30 ps. The sample is mounted in a variable temperature helium cryostate ð5 KpTp300 KÞ:
The temperature-dependent steady-state fluorescence spectra (Fig. 2) indicate a complex spectral behavior. With increasing temperature the vibronic structure is gradually smeared out. More pronounced spectral changes were observed above T ¼ 100 K: The detection of time-resolved spectra in selected time windows (fast 0–40 ps, medium 40–4000 ps, slow 4–10 ns) allows to separate spectral sub-components with different temporal and temperature behavior. As a result three line series (S1–S3) can be distinguished (Figs. 3 and 4). In the slow time window (Fig. 3a) a clear doublet splitting of the spectral origin (S2 at 16; 800 cm1 and S3 at 16; 550 cm1 ; resp.) and interchange of the relative intensities is observed between T ¼ 80 and T ¼ 100 K: From comparison of the spectrum at T ¼ 100 K in the slow time window with the corresponding one in the medium time window (Fig. 3b), it is evident that the high-energy doublet component is still present. Actually two complete spectral series
ARTICLE IN PRESS 292
M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295
Fig. 1. AFM topography and characteristic confocal fluorescence image (different sections of the same sample, d ¼ 16 nm on quartz). Left (a): AFM 2 2 mm2 ; center (b): AFM 10 10 mm2 ; right (c): confocal image 10 10 mm2 :
S2 and S3 exist, energetically split by about 250 cm1 and with comparable structure. At higher temperatures 100 KpTp300 K (Fig. 3c) the spectra detected in the slow time window shows the disappearance of the S3 signal and the gradual
transition to a broad, red-shifted and completely unstructured spectrum at room temperature. In the fast time window an additional series S1 can be discriminated already in the spectrum at helium temperature (Fig. 4) with its 0–0-line at
ARTICLE IN PRESS M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
293
(a)
1.0 0.8 0.6 0.4 0.2 0.0
(b)
(c)
Fig. 2. Temperature dependent cw-fluorescence spectra ð5 Kp Tp300 KÞ:
17; 420 cm1 : A clear distinction of the complete S1 spectral component from the other contributions is possible in the high-temperature limit at T ¼ 300 K: Further analysis (see below) of these three series reveals characteristic differences in their natures. S1 is an excitonic level while S2 and S3 are assigned to trap-states of different site energies. This tentative assignment is based on the following observations. Series S1 is the only series observable in the whole temperature range between 5 and 300 K. It exhibits a narrow line width at 5 K (25 cm1 ) and monotonic symmetrical broadening with increasing temperature by about 10 times at 300 K. The broadening shows a T 2 dependence as illustrated in Fig. 5b, which is indicative for weak electron–phonon coupling [14]. In the same temperature range between 5 and 300 K, the fluorescence decay time of S1 increases from sub-30 ps (time-resolu-
Fig. 3. Time-resolved fluorescence spectra: Top (a): 80 KpTp100 K; ‘‘slow’’ time-window; center (b): T ¼ 100 K; ‘‘medium’’ (M) and ‘‘slow’’ (S) time-window; bottom (c): 100 KpTp300 K; ‘‘slow’’ time window.
tion limit of the experiment) to 100 ps. For the 0–0-line position an overall redshift of 120 cm1 is observed (Fig. 5a). Series S2 is shifted to lower energies with respect to S1 (about 630 cm1 at 5 K). This position is not temperature dependent. The S2 fluorescence is long lived with a decay time of 8.8 ns at 5 K comparable to the fluoresence decay time of the molecule in solution (10 ns in trichlorobenzene). Above 80 K both, fluorescence intensity and decay time are reduced drastically with increasing temperature. The S2 signal disappears above 150 K. Series S3 appears only above 80 K in the fluorescence spectra. Its spectral position with origin at 16; 530 cm1 is temperature independent. The measured lifetime at 85 K is 6.4 ns. Above 100 K the decrease of intensity and lifetime is comparable to the behavior of series S2.
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From the present data both population and relaxation pathways of the different levels cannot be identified yet. Obviously, S3 is neither populated directly from S1 nor from S2, otherwise it should be already detectable in low-temperature spectra. The threshold behavior for its appearance can only be explained by the thermally activated crossing of some intermediate energy barrier (against S1, S2 or an additional optically dark state).
4. Conclusion
Fig. 4. Time-resolved fluorescence spectra 5 KpTp300 K; ‘‘fast’’ time window.
UHV-deposited thin films of DIP on quartz have been investigated with respect to morphology and optical emission spectra. The films exhibit homogeneous macroscopic coverage but terracesubstructure on the nanoscale. Three characteristic fluorescence components with clearly different temperature and temporal behavior were observed and separated by time-resolved fluorescence spectroscopy. They are tentatively attributed to an excitonic level S1 and two similar trap states S2 and S3 which exist only in limited temperature ranges (5 KpTp150 K; S2) and (85 KpTp 150 K; S3), respectively. The threshold behavior for the appearance of S3 and the interplay with S2 could not be explained yet. There are no indications for a discrete structural change (phase transition) in the same temperature range. Instead, thermally activated dynamic conformational changes (involving low-frequency modes with intra- or inter-chain coupling, for instance) are quite common in similar densely packed organic film structures [9,15,16]. But also the intrinsic disorder of the film structure could be responsible for the occurrence of separate line series. Therefore experiments are under way to combine the timeresolved fluorescence spectroscopy with high lateral resolution.
Acknowledgements Fig. 5. Temperature dependence of lineposition (above) and linewidth (below) as detected for series S1 in ‘‘fast’’ time window. Experimental data with dotted line as guide to the eye (above) and with fitting curve to a T 2 dependence (below).
The authors are grateful to S. Meyer and J. Pflaum for sample preparation and helpful discussions.
ARTICLE IN PRESS M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295
References [1] L. Torsi, M.C. Tanese, N. Chioffi, L. Sabbatini, P.G. Zambonin, SPIE Int. Soc. Opt. Eng. Proc. 5217 (2003) 167. [2] Z. Shen, P.E. Burrows, V. Bulovic, S.R. Forrest, M.E. Thompson, Science 276 (1997) 2009. [3] K. Ziemelis, Nature 399 (1999) 408. [4] C. Pannemann, T. Diekmann, U. Hilleringmann, Microelectron. Eng. 67 (2003) 845. [5] Y. Inoue, S. Tokito, K. Ito, T. Suzuki, J. Appl. Phys. 95 (2004) 5795. [6] R.H. Friend, et al., Nature 397 (1999) 121. [7] B. Crone, et al., Nature 403 (2000) 521. [8] N. Karl, Organic Electronic Materials, Springer, Berlin, 2001, p. 283.
295
[9] C. Taliani, F. Biscarini, E. Lunedei, P. Mei, M. Muccini, M. Murgia, M. Schneider, G. Lanzani, Int. J. Mod. Phys. B 15 (2001) 3722. [10] P. Mei, M. Murgia, C. Taliani, E. Lunedei, M. Muccini, J. Appl. Phys. 88 (2000) 5158. [11] A.C. Du¨rr, F. Schreiber, M. Mu¨nch, N. Karl, B. Krause, V. Kruppa, H. Dosch, Appl. Phys. Lett. 81 (2002) 2276. [12] A.C. Du¨rr, E. Schreiber, K.A. Ritley, V. Kruppa, J. Krug, H. Dosch, B. Struth, Phys. Rev. Lett. 90 (2003) 016104. [13] M. Mu¨nch, Ph. D. Thesis, Stuttgart University, 2001. [14] V.L. Broude, E.I. Rashba, E.F. Sheka, Spectroscopy of Molecular Excitons, Springer, Berlin, 1985. [15] I. Vragovic, R. Scholz, M. Schreiber, Europhys. Lett. 57 (2002) 288. [16] U. Go´mez, M. Leonhardt, H. Port, H.C. Wolf, Chem. Phys. Lett. 268 (1997) 1.
Journal of Luminescence 110 (2004) 290–295 www.elsevier.com/locate/jlumin
Optical properties and morphology of thin diindenoperylene films M. Heilig, M. Domhan, H. Port Universita¨t Stuttgart, 3. Physikalisches Institut, Pfaffenwaldring 57, D-70550 Stuttgart, Germany Available online 17 September 2004
Abstract Thin films of diindenoperylene deposited on weakly interacting substrates (quartz) are characterized with scanning probe microscopy techniques at room temperature and by pico-second time-resolved fluorescence spectroscopy between 5 and 300 K. Pronounced T-dependencies of fluorescence spectra and decays are found. The interplay between two fluorescence series in a narrow temperature range ð80 KpTp100 KÞ has been spectrally and temporally resolved. The possible origin of the observed series, competing energy transfer and quenching processes is discussed. r 2004 Elsevier B.V. All rights reserved. PACS: 78.66.Qn; 78.67.n; 78.47.+p; 33.50.Dq Keywords: Organic nanostructures; Diindenoperylene; Thin film; Time-resolved fluorescence spectroscopy
1. Introduction In recent years, large effort has been devoted to the development of organic semiconductor devices like organic thin film chemical sensors, organic light emitting diodes and organic field-effect transistors [1–5]. In parallel with these activities, much progress has been made in the understanding of the underlying physics that controls the Corresponding author. Tel.: +49-711-6855233; fax: +49711-6855281. E-mail address: [email protected] (M. Heilig).
properties of these devices [6]. In comparison with inorganic semiconductors, much less is known about the electronic properties of these materials; even the nature of the semiconductor excitation of organic material remains controversial. To achieve electronic properties comparable to classic inorganic semiconductors, high-quality organic single-crystals appear attractive but are not practicable for commercial application [7]. Therefore organic thin films are more likely to be used. The electronic properties of organic thin films are significantly different from the monomer or bulk-crystal properties, moreover, they depend on
0022-2313/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2004.08.023
ARTICLE IN PRESS M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295
the microscopic film morphology (e.g. grain boundaries, localized defects) [8–10] . High structural order is reported for organic thin films of diindenoperylene (DIP) grown under UHV conditions on different substrates [11,12]. On semiconductor and quartz substrates, the deposited DIP molecules align upright standing to the substrate surface and form densely packed layers. The high structural order on molecular scale favors due to overlapping p-orbitals high lateral transfer processes parallel to the substrate surface. Efficient charge carrier transfer in FET structures with DIP has been demonstrated [13]. To our knowledge, there are no optical investigations on the excited state properties of thin DIP films reported in the literature. The emphasis of our research is to explore the optical properties of thin DIP films in correlation to the film structure by applying several spectroscopic optical methods and different scanning probe microscopy techniques. In this letter, a preliminary account of the work will be given.
291
3. Results and discussion 3.1. Film morphology Information on the morphology was deduced from AFM measurements and concomitant confocal microscopy. In Fig. 1 representative examples at different resolution for a DIP sample with film thickness of 16 nm are given. The film exhibits terrace structures parallel to the substrate surface extending up to several hundreds of nanometers (Fig. 1b). Linescans reveal that the terraces are separated from each other by mono-molecular steps of 1.65 nm (Fig. 1a). These results are in accordance with X-ray data [11,13] and previous AFM investigations of thin DIP films on semiconductor substrates with thick oxide overlayers [12]. The spatially resolved fluorescence intensity in Fig. 1c reflects the structural information obtained by AFM. The optical resolution is approximately 400 nm (diffraction limited) for excitation at 514 nm (19; 400 cm1 ) with intensity of 5 mW at sample position.
2. Experimental
3.2. Fluorescence spectroscopy
Thin DIP films in the thickness range of 8–50 nm were evaporated under UHV conditions onto amorphous quartz substrates. The morphology determination and fluorescence imaging experiments were performed in a home-built scanning probe microscope setup. It combines AFM, confocal fluorescence imaging and optical near-field microscopy (excitation with an Argon ion laser at 514 nm/19; 400 cm1 ). The system is built upon an inverted microscope (Zeiss Axiovert 200 MAT) and additionally provides classical optical microscopy. For temperature-dependent and time-resolved fluorescence measurements we used a frequency doubled active mode locked Nd:YAG laser system (532 nm/18; 800 cm1 ) for photoexcitation and a narrow band detection system with a substractive double monochromator and a cooled fast MCP photomultiplier. Time correlated single photon counting (TCSPC) leads to an overall response time of sub-30 ps. The sample is mounted in a variable temperature helium cryostate ð5 KpTp300 KÞ:
The temperature-dependent steady-state fluorescence spectra (Fig. 2) indicate a complex spectral behavior. With increasing temperature the vibronic structure is gradually smeared out. More pronounced spectral changes were observed above T ¼ 100 K: The detection of time-resolved spectra in selected time windows (fast 0–40 ps, medium 40–4000 ps, slow 4–10 ns) allows to separate spectral sub-components with different temporal and temperature behavior. As a result three line series (S1–S3) can be distinguished (Figs. 3 and 4). In the slow time window (Fig. 3a) a clear doublet splitting of the spectral origin (S2 at 16; 800 cm1 and S3 at 16; 550 cm1 ; resp.) and interchange of the relative intensities is observed between T ¼ 80 and T ¼ 100 K: From comparison of the spectrum at T ¼ 100 K in the slow time window with the corresponding one in the medium time window (Fig. 3b), it is evident that the high-energy doublet component is still present. Actually two complete spectral series
ARTICLE IN PRESS 292
M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295
Fig. 1. AFM topography and characteristic confocal fluorescence image (different sections of the same sample, d ¼ 16 nm on quartz). Left (a): AFM 2 2 mm2 ; center (b): AFM 10 10 mm2 ; right (c): confocal image 10 10 mm2 :
S2 and S3 exist, energetically split by about 250 cm1 and with comparable structure. At higher temperatures 100 KpTp300 K (Fig. 3c) the spectra detected in the slow time window shows the disappearance of the S3 signal and the gradual
transition to a broad, red-shifted and completely unstructured spectrum at room temperature. In the fast time window an additional series S1 can be discriminated already in the spectrum at helium temperature (Fig. 4) with its 0–0-line at
ARTICLE IN PRESS M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
293
(a)
1.0 0.8 0.6 0.4 0.2 0.0
(b)
(c)
Fig. 2. Temperature dependent cw-fluorescence spectra ð5 Kp Tp300 KÞ:
17; 420 cm1 : A clear distinction of the complete S1 spectral component from the other contributions is possible in the high-temperature limit at T ¼ 300 K: Further analysis (see below) of these three series reveals characteristic differences in their natures. S1 is an excitonic level while S2 and S3 are assigned to trap-states of different site energies. This tentative assignment is based on the following observations. Series S1 is the only series observable in the whole temperature range between 5 and 300 K. It exhibits a narrow line width at 5 K (25 cm1 ) and monotonic symmetrical broadening with increasing temperature by about 10 times at 300 K. The broadening shows a T 2 dependence as illustrated in Fig. 5b, which is indicative for weak electron–phonon coupling [14]. In the same temperature range between 5 and 300 K, the fluorescence decay time of S1 increases from sub-30 ps (time-resolu-
Fig. 3. Time-resolved fluorescence spectra: Top (a): 80 KpTp100 K; ‘‘slow’’ time-window; center (b): T ¼ 100 K; ‘‘medium’’ (M) and ‘‘slow’’ (S) time-window; bottom (c): 100 KpTp300 K; ‘‘slow’’ time window.
tion limit of the experiment) to 100 ps. For the 0–0-line position an overall redshift of 120 cm1 is observed (Fig. 5a). Series S2 is shifted to lower energies with respect to S1 (about 630 cm1 at 5 K). This position is not temperature dependent. The S2 fluorescence is long lived with a decay time of 8.8 ns at 5 K comparable to the fluoresence decay time of the molecule in solution (10 ns in trichlorobenzene). Above 80 K both, fluorescence intensity and decay time are reduced drastically with increasing temperature. The S2 signal disappears above 150 K. Series S3 appears only above 80 K in the fluorescence spectra. Its spectral position with origin at 16; 530 cm1 is temperature independent. The measured lifetime at 85 K is 6.4 ns. Above 100 K the decrease of intensity and lifetime is comparable to the behavior of series S2.
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From the present data both population and relaxation pathways of the different levels cannot be identified yet. Obviously, S3 is neither populated directly from S1 nor from S2, otherwise it should be already detectable in low-temperature spectra. The threshold behavior for its appearance can only be explained by the thermally activated crossing of some intermediate energy barrier (against S1, S2 or an additional optically dark state).
4. Conclusion
Fig. 4. Time-resolved fluorescence spectra 5 KpTp300 K; ‘‘fast’’ time window.
UHV-deposited thin films of DIP on quartz have been investigated with respect to morphology and optical emission spectra. The films exhibit homogeneous macroscopic coverage but terracesubstructure on the nanoscale. Three characteristic fluorescence components with clearly different temperature and temporal behavior were observed and separated by time-resolved fluorescence spectroscopy. They are tentatively attributed to an excitonic level S1 and two similar trap states S2 and S3 which exist only in limited temperature ranges (5 KpTp150 K; S2) and (85 KpTp 150 K; S3), respectively. The threshold behavior for the appearance of S3 and the interplay with S2 could not be explained yet. There are no indications for a discrete structural change (phase transition) in the same temperature range. Instead, thermally activated dynamic conformational changes (involving low-frequency modes with intra- or inter-chain coupling, for instance) are quite common in similar densely packed organic film structures [9,15,16]. But also the intrinsic disorder of the film structure could be responsible for the occurrence of separate line series. Therefore experiments are under way to combine the timeresolved fluorescence spectroscopy with high lateral resolution.
Acknowledgements Fig. 5. Temperature dependence of lineposition (above) and linewidth (below) as detected for series S1 in ‘‘fast’’ time window. Experimental data with dotted line as guide to the eye (above) and with fitting curve to a T 2 dependence (below).
The authors are grateful to S. Meyer and J. Pflaum for sample preparation and helpful discussions.
ARTICLE IN PRESS M. Heilig et al. / Journal of Luminescence 110 (2004) 290–295
References [1] L. Torsi, M.C. Tanese, N. Chioffi, L. Sabbatini, P.G. Zambonin, SPIE Int. Soc. Opt. Eng. Proc. 5217 (2003) 167. [2] Z. Shen, P.E. Burrows, V. Bulovic, S.R. Forrest, M.E. Thompson, Science 276 (1997) 2009. [3] K. Ziemelis, Nature 399 (1999) 408. [4] C. Pannemann, T. Diekmann, U. Hilleringmann, Microelectron. Eng. 67 (2003) 845. [5] Y. Inoue, S. Tokito, K. Ito, T. Suzuki, J. Appl. Phys. 95 (2004) 5795. [6] R.H. Friend, et al., Nature 397 (1999) 121. [7] B. Crone, et al., Nature 403 (2000) 521. [8] N. Karl, Organic Electronic Materials, Springer, Berlin, 2001, p. 283.
295
[9] C. Taliani, F. Biscarini, E. Lunedei, P. Mei, M. Muccini, M. Murgia, M. Schneider, G. Lanzani, Int. J. Mod. Phys. B 15 (2001) 3722. [10] P. Mei, M. Murgia, C. Taliani, E. Lunedei, M. Muccini, J. Appl. Phys. 88 (2000) 5158. [11] A.C. Du¨rr, F. Schreiber, M. Mu¨nch, N. Karl, B. Krause, V. Kruppa, H. Dosch, Appl. Phys. Lett. 81 (2002) 2276. [12] A.C. Du¨rr, E. Schreiber, K.A. Ritley, V. Kruppa, J. Krug, H. Dosch, B. Struth, Phys. Rev. Lett. 90 (2003) 016104. [13] M. Mu¨nch, Ph. D. Thesis, Stuttgart University, 2001. [14] V.L. Broude, E.I. Rashba, E.F. Sheka, Spectroscopy of Molecular Excitons, Springer, Berlin, 1985. [15] I. Vragovic, R. Scholz, M. Schreiber, Europhys. Lett. 57 (2002) 288. [16] U. Go´mez, M. Leonhardt, H. Port, H.C. Wolf, Chem. Phys. Lett. 268 (1997) 1.