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Picosecond relaxation of photoexcited states in polyacetylene
Synthetic Metals, 17 (1987) 355 360
355
PICOSECOND RELAXATION OF PHOTOEXCITED STATES IN POLYACETYLENE
D. L. WEIDMAN and D. B. FITCHEN Laboratory of Atomic and Solid State Physics and Materials Science Center, Cornell University, Ithaca, NY 14850-2501 (U.S.A.)
ABSTRACT The relaxation behavior of polyacetylene following photoexcitation with tunable picosecond laser pulses is investigated using several time-resolved optical probe techniques. We report here on the picosecond dynamics of the photoinduced bleaching in thin films of (CH)z, and also the corresponding transient changes in reflectance from the surface of thin and thick samples. We focus on the time interval from 1 to 1000 picoseconds after the excitation pulse and examine the kinetics of relaxation and recombination of the photogenerated carriers over the temperature range 5K to 300K, at different excitation wavelengths and in different samples. Our measurements of the changes in transmission and reflectivity confirm that these kinetics differ after a certain time t > to(T) from the initial t -1/2 behavior predicted for the simplest model of a 1D random walk process. They then follow a slower t - a decay to beyond one nanosecond, where the exponent a depends strongly on temperature and weakly on sample preparation. We compare these dynamics to simple models for 1D random walks in the presence of disorder.
There have been several interesting reports at this meeting of time-resolved studies of the production and decay of photoexcitations in polyacetylene. Here we report on some new measurements of photoinduced picosecond transients in the optical transmission and reflection of undoped trans polyacetylene. Our particular interest has to do with the effects of disorder on the dynamics of the photoexcitations. We chose to examine the relaxation behavior in the time interval from 1 to 1000 picoseconds after pulsed photoexcitation since this picosecond behavior is thought to be determined by diffusion of the photogenerated carriers along single chains. (At much longer times, interchain transfer and deep trapping of carriers appear to dominate.) Early measurements 1,2 of the photoinduced transients in the picosecond regime suggested that 0379-6779/87/$3.50
© Elsevier Sequoia/Printed in The Netherlands
356 the photogenerated carriers recombine through a one-dimensional (1D) random walk with a characteristic step time (0.1 ps at 300 K). Thus, in our time interval, these walks should cover distances comparable to the expected scale of intrachain disorder. 3 The experimental method we use is the picosecond pump and probe technique. The transmission version of this method has been used before in earlier studies of polyacetylene. 1-3 We use a thin film sample, of thickness about 1000 ~, such that about half the incident light is transmitted. A pump pulse from a tunable picosecond laser is focussed to a spot of about 25 #m diameter to cause interband photoexcitation of the sample. This same small region of the sample is then probed at a later time by a second pulse at the same or a different wavelength. The transmitted intensity of the probe pulse is measured as a function of the variable time delay, t. The whole process is repeated at a high repetition rate, in the range 1 to 95 MHz in our case, to permit the use of lock-in techniques and signal averaging. In these experiments, the pump and probe pulse were both of 3 ps duration and were both at the same wavelength, in the range 580-660 nm. This technique measures the photoinduced change in transmission which may involve changes in reflection at the surfaces and in the optical thickness of the sample as well as the changes in absorption usually considered. The changes also depend on the relative polarization of the pump and probe beams. This photoinduced anisotropy decays at a different rate from the decay of the photoexcitatlons, l Here we focus on just the decay of the photoexcitations by eliminating the polarization changes by measuring and adding the changes for both relative polarizations. An alternative way of probing these photoexcitat~ons is with the reflection technique. This has the advantage that it can be used on thick as well as thin samples. In particular, it makes it possible to look at photoexcitations in the standard thick film samples of polyacetylene that have been characterized using many different physical techniques. Here one measures transient changes in specular reflection using spatial filtering to discriminate against reflected pump beam light. In Fig. la, we show the picosecond transient changes in transmission and reflection measured for the same thin film sample. In both cases, there is a nearly instantaneous onset of the peak change at zero time delay, followed by a rapid initial decay and then a slower decay over the 1000 ps time range examined. It was shown previously by Shank et al. 2 that the onset in AT occurs in a time less than 0.1 ps. In our case, the response is limited by the 3ps pulse duration. The two curves in Fig. l a are almost exactly complementary and coincide very closely when superimposed. The transient decrease in reflected intensity is comparable in magnitude but somewhat smaller than the increase in transmission. In fact, this indicates that a major part of the transmission change must be due to decreased reflection loss. We have verified that this same time behavior of the decay occurs when the pump and probe wavelengths are varied throughout our laser tuning range. Thus it appears that the time decay of the photoexcltatlon~ can be followed with either transmission or reflection for polyacetylene in this time domain.
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Fig. 1. a) Time behavior of transient changes in transmission and reflection induced and measured with 3 ps pulses at 633 nm in the same thin film sample of tram (CH)= at 77K. b) Log-log plot of the reflectance change shown in (a).
We note in passing that, in contrast to the recent picosecond photoconductivity measurement,4 we are not looking directly at the photoexcitations but rather at the recovery of the ground state properties. The individual laser pulses are here of less than a nanojoule rather than mlcrojoule energy, but they are focused more tightly so that the excitation density is of order 101~ - 1018/cm 3, assuming unit excitation efficiency. Our high repetition rate means that the slow decay channels are saturated and we see only the dynamics of the fast relaxation channels. In Fig. lb, we show the same decay of the transient reflection change on a log-log plot. The straight line fits suggest that this decay can be characterized by a power law behavior. At early times, the decay goes as t -1/2 until some transition time tc (here about 25 ps). At later times, it appears to follow a slower power law decay, t - a , where in this case a ~ 0.30 ± 0.03. A previous study 2 of photolnduced transmission changes using shorter pulses showed that the early time behavior goes like erf(t/r) -1/2. Our results for the initial decay fit on this same curve, although we are unable to follow the decay at shorter times with our 3 ps pulses. Another picosecond study, that by Vardeny et al., 1 noted that this early decay showed a break over to a slower power law decay, but they did not investigate this further. The focus in our present study is on this slower power law decay and its dependence on temperature and sample quality.
358
How can we understand these power law decays? We have considered several simple models for 1D random walks in the presence of disorder. We assume that pairs of carriers are photogenerated at t = 0 with excess kinetic energy, that these carriers thermalize very rapidly, and that they then perform random walks along the chains with a step time T until they recombine by arriving at nearest neighbor sites. If the carriers perform this random walk on an infinite chain with no disorder, then the survival probability after a time t is simply erf(t/r) -~/2, or ~ (t/r) -1/2. Thus the early time behavior in the experiment appears to be characteristic of free diffusion on the chains. The fact that the observed step time r varies with sample temperature from the earliest times implies that the thermalization is very rapid. 2 Now suppose that the random walk is limited to a finite segment of chain. We assume for simplicity that the boundary conditions are perfectly reflecting ends. Then initially the decay goes like t -1/2 for times less than a characteristic time tc that it takes a carrier to traverse the segment. At longer times, the survival probability decays exponentially, since the reflected carriers are more likely to recombine. This behavior does not match the observed decay, even when one convolutes a distribution in lengths for these finite segments. We consider next a model in which the random walk occurs on segments which are weakly connected to each other.
We assume that the carriers can undergo thermally-
activated hopping or tunneling to get from one segment to the next. Numerical simulation shows that we can expect the same initial t -1/2 decay followed by a breakover to a slower power law decay, t - a , after a time tc characteristic of the transit time for a single segment. The magnitude and temperature dependence of a should be strongly dependent on the transmission probability between segments. To test the generality of this power law decay we also looked at a simulation of a somewhat different situation. In this case we assumed a long chain with only weak random site-to-site disorder. We represented this disorder with a small bias potential of random sign at each site on the chain. Random walks in this case also led to a long time decay of the form t - a , with a < 0.5. With these simple model predictions in mind, we explored the picosecond relaxation behavior in reflection for a range of temperature from 5 to 300 K in several different samples of polyacetylene. The decay kinetics were similar to those shown in Fig. 1. The initial decay went as (t/r)-1/2 with r varying from 0.2 ps at 300K to 1.2 ps at 5K. After a time tc which varied from ~ 40 ps at 300K to N 20 ps at 5K, the decay followed a slower power law behavior, t - a . In Fig. 2a, we show the temperature variation of the exponent a for this part of the decay. It shows the qualitative variation one would expect for thermally activated hopping. However, in any photoexcitation experiment, and especially one with focussed laser beams, one must beware of laser heating effects. To investigate this possibility we varied the average power in the beam by an order of magnitude by changing the repetition rate. We see that there does indeed seem to be some laser heating when the average power
359 0o~
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Fig. 2. a) Temperature variation of the exponent a in the power law decay, as measured in reflection for a thin film sample of (CH)= at two different power levels. The curve is the variation obtained from numerical simulation of a 1D random walk in the presence of site-to-site disorder as discussed in the text. (b) Variation of a vs. T for three different samples: "good" quality thick film (A), thin film (0), and "poor" quality thick film (u).
is increased. It is likely that even at our lowest power level there is still some laser heating occurring. In Fig. 2a, we also show a simple model fit to the a vs. T data measured at our lowest power level. The curve is an interpolation based on numerical simulations for the model of 1D random walks in the presence of weak site-to-site disorder. We introduce only two adjustable parameters. The rms magnitude of the site-to-site variation in potential is taken to be 7K, and the effective temperature is taken to be 40 K higher than the nominal sample temperature. This curve approaches the limiting value o~ = 1/2 at high temperatures as expected. Its limiting value at T = OK is very sensitive to the estimate for laser heating. Finally, in Fig. 2b we show a vs. T for three different samples all of the Shiradawa type. One is the "good" thick film sample of Fig. 2a where the Raman profile indicates a significant fraction of long conjugation segments in the sample. The second is the thin film sample of Fig. 1 which has more disorder, based on the Raman profile. The third is a "poor" quality thick film sample, one which has been degraded by exposure to air. All of these samples show remarkably similar decays except for the poor quality sample near room temperature.
In that case, the estimate of a is rough, since the decay is
actually more nearly exponential. This is not inconsistent with the carriers being confined to shorter segments of the polymer. The relative sample independence of the decays at low temperatures and in the better samples suggests that the disorder which determines
360 the picosecond relaxation behavior does not correlate closely with the disorder that is important for the Raman spectral profiles. In conclusion, we have shown that the picosecond decay of photoinduced transients in polyacetylene can be described in terms of 1D random walks in the presence of disorder. This sort of dispersive transport has been discussed in the literature in many different contexts. 5 It will be interesting to see if one can develop a closer connection between the observed decay and microscopic models for the carriers, their diffusive motion, and the traps or disorder involved. ACKNOWLEDGEMENTS This work was supported in part by the National Science Foundation through the Materials Science Center at Cornell. We thank H. W. Gibson and R. Weagley for supplying the thin film samples. REFERENCES 1
Z. Vardeny, J. Strait, D. Moses, T.-C. Chung and A. J. Heeger, Phys. Rev. L e t t , 49 (1982) 1657.
2
C . V . Shank, R. Yen, R. L. Fork, J. Orenstein and G. L. Baker, Phys. Rev. Lett., 49 (1982) 1660.
3
D . L . Weidman, D. B. Fitchen, R. Weagley and H. W. Gibson, to be published.
4 5
D. Moses, M. Sinclair and A. J. Heeger, Synth. Met, 17 (1987) 515 (these Proceedings). See, for instance, S. Alexander et al., Revs. Mod. Phys., 53 (1981) 175, and references therein.
355
PICOSECOND RELAXATION OF PHOTOEXCITED STATES IN POLYACETYLENE
D. L. WEIDMAN and D. B. FITCHEN Laboratory of Atomic and Solid State Physics and Materials Science Center, Cornell University, Ithaca, NY 14850-2501 (U.S.A.)
ABSTRACT The relaxation behavior of polyacetylene following photoexcitation with tunable picosecond laser pulses is investigated using several time-resolved optical probe techniques. We report here on the picosecond dynamics of the photoinduced bleaching in thin films of (CH)z, and also the corresponding transient changes in reflectance from the surface of thin and thick samples. We focus on the time interval from 1 to 1000 picoseconds after the excitation pulse and examine the kinetics of relaxation and recombination of the photogenerated carriers over the temperature range 5K to 300K, at different excitation wavelengths and in different samples. Our measurements of the changes in transmission and reflectivity confirm that these kinetics differ after a certain time t > to(T) from the initial t -1/2 behavior predicted for the simplest model of a 1D random walk process. They then follow a slower t - a decay to beyond one nanosecond, where the exponent a depends strongly on temperature and weakly on sample preparation. We compare these dynamics to simple models for 1D random walks in the presence of disorder.
There have been several interesting reports at this meeting of time-resolved studies of the production and decay of photoexcitations in polyacetylene. Here we report on some new measurements of photoinduced picosecond transients in the optical transmission and reflection of undoped trans polyacetylene. Our particular interest has to do with the effects of disorder on the dynamics of the photoexcitations. We chose to examine the relaxation behavior in the time interval from 1 to 1000 picoseconds after pulsed photoexcitation since this picosecond behavior is thought to be determined by diffusion of the photogenerated carriers along single chains. (At much longer times, interchain transfer and deep trapping of carriers appear to dominate.) Early measurements 1,2 of the photoinduced transients in the picosecond regime suggested that 0379-6779/87/$3.50
© Elsevier Sequoia/Printed in The Netherlands
356 the photogenerated carriers recombine through a one-dimensional (1D) random walk with a characteristic step time (0.1 ps at 300 K). Thus, in our time interval, these walks should cover distances comparable to the expected scale of intrachain disorder. 3 The experimental method we use is the picosecond pump and probe technique. The transmission version of this method has been used before in earlier studies of polyacetylene. 1-3 We use a thin film sample, of thickness about 1000 ~, such that about half the incident light is transmitted. A pump pulse from a tunable picosecond laser is focussed to a spot of about 25 #m diameter to cause interband photoexcitation of the sample. This same small region of the sample is then probed at a later time by a second pulse at the same or a different wavelength. The transmitted intensity of the probe pulse is measured as a function of the variable time delay, t. The whole process is repeated at a high repetition rate, in the range 1 to 95 MHz in our case, to permit the use of lock-in techniques and signal averaging. In these experiments, the pump and probe pulse were both of 3 ps duration and were both at the same wavelength, in the range 580-660 nm. This technique measures the photoinduced change in transmission which may involve changes in reflection at the surfaces and in the optical thickness of the sample as well as the changes in absorption usually considered. The changes also depend on the relative polarization of the pump and probe beams. This photoinduced anisotropy decays at a different rate from the decay of the photoexcitatlons, l Here we focus on just the decay of the photoexcitations by eliminating the polarization changes by measuring and adding the changes for both relative polarizations. An alternative way of probing these photoexcitat~ons is with the reflection technique. This has the advantage that it can be used on thick as well as thin samples. In particular, it makes it possible to look at photoexcitations in the standard thick film samples of polyacetylene that have been characterized using many different physical techniques. Here one measures transient changes in specular reflection using spatial filtering to discriminate against reflected pump beam light. In Fig. la, we show the picosecond transient changes in transmission and reflection measured for the same thin film sample. In both cases, there is a nearly instantaneous onset of the peak change at zero time delay, followed by a rapid initial decay and then a slower decay over the 1000 ps time range examined. It was shown previously by Shank et al. 2 that the onset in AT occurs in a time less than 0.1 ps. In our case, the response is limited by the 3ps pulse duration. The two curves in Fig. l a are almost exactly complementary and coincide very closely when superimposed. The transient decrease in reflected intensity is comparable in magnitude but somewhat smaller than the increase in transmission. In fact, this indicates that a major part of the transmission change must be due to decreased reflection loss. We have verified that this same time behavior of the decay occurs when the pump and probe wavelengths are varied throughout our laser tuning range. Thus it appears that the time decay of the photoexcltatlon~ can be followed with either transmission or reflection for polyacetylene in this time domain.
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Fig. 1. a) Time behavior of transient changes in transmission and reflection induced and measured with 3 ps pulses at 633 nm in the same thin film sample of tram (CH)= at 77K. b) Log-log plot of the reflectance change shown in (a).
We note in passing that, in contrast to the recent picosecond photoconductivity measurement,4 we are not looking directly at the photoexcitations but rather at the recovery of the ground state properties. The individual laser pulses are here of less than a nanojoule rather than mlcrojoule energy, but they are focused more tightly so that the excitation density is of order 101~ - 1018/cm 3, assuming unit excitation efficiency. Our high repetition rate means that the slow decay channels are saturated and we see only the dynamics of the fast relaxation channels. In Fig. lb, we show the same decay of the transient reflection change on a log-log plot. The straight line fits suggest that this decay can be characterized by a power law behavior. At early times, the decay goes as t -1/2 until some transition time tc (here about 25 ps). At later times, it appears to follow a slower power law decay, t - a , where in this case a ~ 0.30 ± 0.03. A previous study 2 of photolnduced transmission changes using shorter pulses showed that the early time behavior goes like erf(t/r) -1/2. Our results for the initial decay fit on this same curve, although we are unable to follow the decay at shorter times with our 3 ps pulses. Another picosecond study, that by Vardeny et al., 1 noted that this early decay showed a break over to a slower power law decay, but they did not investigate this further. The focus in our present study is on this slower power law decay and its dependence on temperature and sample quality.
358
How can we understand these power law decays? We have considered several simple models for 1D random walks in the presence of disorder. We assume that pairs of carriers are photogenerated at t = 0 with excess kinetic energy, that these carriers thermalize very rapidly, and that they then perform random walks along the chains with a step time T until they recombine by arriving at nearest neighbor sites. If the carriers perform this random walk on an infinite chain with no disorder, then the survival probability after a time t is simply erf(t/r) -~/2, or ~ (t/r) -1/2. Thus the early time behavior in the experiment appears to be characteristic of free diffusion on the chains. The fact that the observed step time r varies with sample temperature from the earliest times implies that the thermalization is very rapid. 2 Now suppose that the random walk is limited to a finite segment of chain. We assume for simplicity that the boundary conditions are perfectly reflecting ends. Then initially the decay goes like t -1/2 for times less than a characteristic time tc that it takes a carrier to traverse the segment. At longer times, the survival probability decays exponentially, since the reflected carriers are more likely to recombine. This behavior does not match the observed decay, even when one convolutes a distribution in lengths for these finite segments. We consider next a model in which the random walk occurs on segments which are weakly connected to each other.
We assume that the carriers can undergo thermally-
activated hopping or tunneling to get from one segment to the next. Numerical simulation shows that we can expect the same initial t -1/2 decay followed by a breakover to a slower power law decay, t - a , after a time tc characteristic of the transit time for a single segment. The magnitude and temperature dependence of a should be strongly dependent on the transmission probability between segments. To test the generality of this power law decay we also looked at a simulation of a somewhat different situation. In this case we assumed a long chain with only weak random site-to-site disorder. We represented this disorder with a small bias potential of random sign at each site on the chain. Random walks in this case also led to a long time decay of the form t - a , with a < 0.5. With these simple model predictions in mind, we explored the picosecond relaxation behavior in reflection for a range of temperature from 5 to 300 K in several different samples of polyacetylene. The decay kinetics were similar to those shown in Fig. 1. The initial decay went as (t/r)-1/2 with r varying from 0.2 ps at 300K to 1.2 ps at 5K. After a time tc which varied from ~ 40 ps at 300K to N 20 ps at 5K, the decay followed a slower power law behavior, t - a . In Fig. 2a, we show the temperature variation of the exponent a for this part of the decay. It shows the qualitative variation one would expect for thermally activated hopping. However, in any photoexcitation experiment, and especially one with focussed laser beams, one must beware of laser heating effects. To investigate this possibility we varied the average power in the beam by an order of magnitude by changing the repetition rate. We see that there does indeed seem to be some laser heating when the average power
359 0o~
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200 T (K)
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300
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Fig. 2. a) Temperature variation of the exponent a in the power law decay, as measured in reflection for a thin film sample of (CH)= at two different power levels. The curve is the variation obtained from numerical simulation of a 1D random walk in the presence of site-to-site disorder as discussed in the text. (b) Variation of a vs. T for three different samples: "good" quality thick film (A), thin film (0), and "poor" quality thick film (u).
is increased. It is likely that even at our lowest power level there is still some laser heating occurring. In Fig. 2a, we also show a simple model fit to the a vs. T data measured at our lowest power level. The curve is an interpolation based on numerical simulations for the model of 1D random walks in the presence of weak site-to-site disorder. We introduce only two adjustable parameters. The rms magnitude of the site-to-site variation in potential is taken to be 7K, and the effective temperature is taken to be 40 K higher than the nominal sample temperature. This curve approaches the limiting value o~ = 1/2 at high temperatures as expected. Its limiting value at T = OK is very sensitive to the estimate for laser heating. Finally, in Fig. 2b we show a vs. T for three different samples all of the Shiradawa type. One is the "good" thick film sample of Fig. 2a where the Raman profile indicates a significant fraction of long conjugation segments in the sample. The second is the thin film sample of Fig. 1 which has more disorder, based on the Raman profile. The third is a "poor" quality thick film sample, one which has been degraded by exposure to air. All of these samples show remarkably similar decays except for the poor quality sample near room temperature.
In that case, the estimate of a is rough, since the decay is
actually more nearly exponential. This is not inconsistent with the carriers being confined to shorter segments of the polymer. The relative sample independence of the decays at low temperatures and in the better samples suggests that the disorder which determines
360 the picosecond relaxation behavior does not correlate closely with the disorder that is important for the Raman spectral profiles. In conclusion, we have shown that the picosecond decay of photoinduced transients in polyacetylene can be described in terms of 1D random walks in the presence of disorder. This sort of dispersive transport has been discussed in the literature in many different contexts. 5 It will be interesting to see if one can develop a closer connection between the observed decay and microscopic models for the carriers, their diffusive motion, and the traps or disorder involved. ACKNOWLEDGEMENTS This work was supported in part by the National Science Foundation through the Materials Science Center at Cornell. We thank H. W. Gibson and R. Weagley for supplying the thin film samples. REFERENCES 1
Z. Vardeny, J. Strait, D. Moses, T.-C. Chung and A. J. Heeger, Phys. Rev. L e t t , 49 (1982) 1657.
2
C . V . Shank, R. Yen, R. L. Fork, J. Orenstein and G. L. Baker, Phys. Rev. Lett., 49 (1982) 1660.
3
D . L . Weidman, D. B. Fitchen, R. Weagley and H. W. Gibson, to be published.
4 5
D. Moses, M. Sinclair and A. J. Heeger, Synth. Met, 17 (1987) 515 (these Proceedings). See, for instance, S. Alexander et al., Revs. Mod. Phys., 53 (1981) 175, and references therein.