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The effect of the substrate on transient photodarkening in stabilized amorphous selenium
Journal of Non-Crystalline Solids 358 (2012) 2389–2392
Contents lists available at SciVerse ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
The effect of the substrate on transient photodarkening in stabilized amorphous selenium S. Abbaszadeh a,⁎, K. Rom b, O. Bubon b, B.A. Weinstein c, K.S. Karim a, J.A. Rowlands b, d, A. Reznik b, d a
University of Waterloo, 200 University Ave. W, Waterloo, ON, Canada, N2L 3G1 Lakehead University, 955 Oliver Road, Thunder Bay, ON, Canada, P7B 5E1 SUNY at Buffalo, 239 Fronczak Hall, Buffalo, NY, , 14260-1500 USA d Thunder Bay Regional Research Institute, 290 Munro Street, Thunder Bay, ON Canada, P7A 7T1 b c
a r t i c l e
i n f o
Article history: Received 2 September 2011 Received in revised form 14 December 2011 Available online 23 January 2012 Keywords: Amorphous selenium (a-Se); Chalcogenide glasses; Photodarkening; Metastable defects; Photo-induced effects
a b s t r a c t The photodarkening (PD) effect has been studied experimentally for amorphous selenium (a-Se) layers with 0.2 wt.% of arsenic (As) deposited on different substrates: glass, indium tin oxide (ITO) coated glass and polyimide-coated ITO glass. It was found that the presence of As qualitatively affects the behavior of PD: while in pure (no As) a-Se the relaxation of the PD is a fast process characterized by a short (~ 10 s) time constant, in As-containing a-Se it has both short (same as in pure a-Se) and comparably long (~ 80 s) components. The interface between a-Se and the substrate affects the PD qualitatively: it influences the magnitude of the effect while not changing the kinetics of the process. The buildup of the PD was more pronounced for the glass substrate (the most rigid) and was least pronounced for the polyimide-coated ITO glass (the most flexible). The difference can be attributed to a different strain at the interface. © 2012 Elsevier B.V. All rights reserved.
1. Introduction It is known that amorphous selenium (a-Se) as many other chalcogenide glasses can undergo photo-induced structural transformation resulting in the red shift in the absorption, or photodarkening (PD). The phenomenological model previously developed by us suggests that PD is caused by photo-induced conversion of some structural units from their ground state configurations into some metastable states that increase the level of disorder, broaden the band tails and hence, increase the absorption [1]. Using a double-well energy configuration, it was shown that the energy barrier between the ground state and a metastable state in pure a-Se was 0.8 eV [2]. A similar activation behavior was observed in photo-induced crystallization (PC) of a-Se studied by Raman spectroscopy [3]. This similarity suggests that the formation kinetics of PD and PC are controlled by the same configurational changes occurring via photo-induced metastable defects. Recently, the photocrystallization studies revealed that the interface between a-Se layer and the substrate significantly influenced the structural stability of a-Se: the onset time of the PC was found to vary for different substrates (glass, polymer encapsulation, and thin blocking/ buffer/indium tin oxide (ITO) layers) [4]. An understanding of the effect of a substrate on photo-induced structural transformation in a-Se is of great practical importance due to the application of a-Se photosensors in optical and radiation
medical imaging. Indeed, structural changes can result in the permanent degradation of a-Se photoconductive properties which has to be prevented. To get a better insight into the effect of the substrate on photoinduced structural transformation, PD was investigated in stabilized a-Se (i.e., doped with 0.2 wt.% of As) deposited on different substrates (with a substrate temperature of 65 °C during deposition) which are used in practical a-Se photosensors, namely glass, (160 nm thick) ITO coated glass and polyimide-coated ITO glass. Our results revealed that the magnitude of the irreversible PD can be reduced by using less rigid substrates (where the glass substrate is the most rigid and the polyimide layer is the least rigid). This can be attributed to the partial strain relaxation at the interface and hence, decrease in the concentration of structural units which are photo-induced to transform from their ground state configuration (which is transparent) to metastable configurations (causing photodarkening). The quantitative analysis of the relaxation of PD show that the double-well model with a single barrier between the ground and metastable states previously used for a pure a-Se layer [2] cannot be applied to stabilized a-Se: the kinetics of relaxation cannot be fitted by single exponential growth. In order to interpret the results, a model with two metastable levels (i.e., with one further structural unit due to the presence of As) is suggested. 2. Experimental details
⁎ Corresponding author. E-mail address: [email protected] (S. Abbaszadeh). 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.12.098
A 16.5 μm thick a-Se stabilized with 0.2% of As was deposited using vacuum evaporation technique in the same run on all three
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S. Abbaszadeh et al. / Journal of Non-Crystalline Solids 358 (2012) 2389–2392
Fig. 1. Structures of the different samples tested. Amorphous selenium was deposited on glass, ITO glass, and a polyimide-coated ITO glass.
different substrates: glass, ITO-coated glass and polyimide-coated ITO glass. ITO glass was chosen as a substrate due to its potential applications in optical imaging. For instance, when a-Se must be biased, an ITO layer coated on a glass plate is typically used as the transparent electrode. Similarly, polyimide-coated ITO glass has its advantages as well. For example, recent studies have found it to provide excellent blocking properties in the case of significant dark current at high fields [5]. Fig. 1 shows the structure of three samples studied in this work. To study the PD of the samples, we used the standard method of observing the changes in transmission as a function of exposure to light. Fig. 2 shows the experimental apparatus that was used to carry out the PD experiment. In this study, two laser beams with wavelengths of 633 nm were used to illuminate the same area of the sample. The less powerful probing beam was used to monitor changes in transmission of light T. It is crucial that the intensity of the probing beam is low enough that it does not contribute to the PD. The more powerful pumping beam, on the contrary, was used to produce PD. The kinetics of the PD were studied by periodically exposing the a-Se to the pumping beam for cycles of 200 s separated by 200 s of rest. During those cycles, the probing beam transmission, T, is continuously monitored and the relative changes compared to the original transmission of light, T/T0, were then calculated. The alternating cycles of pumping and resting were produced using a function generator. Measurements were taken at room temperature and repeated at 35 °C.
3. Results The results of the PD measurements for the three different substrates at room temperature are shown in Fig. 3(A) as a function of T/T0 versus time for four pumping/resting cycles. All samples exhibit only partial recovery during resting cycles, leading to an overall decrease in transmission in subsequent cycles. Therefore, both reversible and irreversible components of PD are present for all substrates. Fig. 3(B) (upper) shows the relaxation of the PD with time during a selected resting cycle (when pumping is switched off) for a-Se deposited on ITO glass. Fig. 4 shows the PD results at 35 °C for the glass substrate and the polyimide-coated substrate, as examples, where full recovery is observed. This agrees with previously reported results, where the irreversible component of the PD disappeared near the glass transition temperature [2]. 4. Discussion Although all samples exhibited partial recovery (see Fig. 3(A)), our experiment showed, however, that the transmission through the polyimide sample decreased the least, followed by the ITO sample and finally the glass sample. Since the magnitude of the irreversible PD effect is proportional to the number of structural units which can be converted into a metastable state and provide the irreversible PD we conclude that this number is the smallest for a-Se interfacing
Fig. 2. Experimental apparatus used to carry out the PD experiment.
S. Abbaszadeh et al. / Journal of Non-Crystalline Solids 358 (2012) 2389–2392
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Fig. 4. Normalized transmission as a function of time for two samples at 35 °C.
model, during relaxation, transitions from metastable configuration back to initial ground state configuration occur through thermal activation over an energy barrier, EB ~ 0.8 eV. As a result, the relaxation of the photodarkening can be fitted by single exponential decay with characteristic time constant τ which relates to the height of the activation energy as: −1
τ ¼ ν 0 expðEB =kB θÞ
Fig. 3. (A) Normalized transmission as a function of time for the three samples at room temperature, (B) The recovery (upper part) and the decay (lower part) of the optical transparency for a resting/pumping cycles at room temperature.
semi-soft material (i.e., polyimide) and the largest for a-Se interfacing rigid substrate (glass) where the strain at the interface is larger. In order to interpret the relaxation kinetics, we first use the single state model [2] previously used to describe PD in pure a-Se. In this
where kB is the Boltzmann constant, θ is the temperature and ν0 is the attempt-to-escape frequency of the order ~10 12 s − 1. However, the single exponential decay fails to fit our experimental results. In contrast, double-exponential decay works much better as it is seen in Fig. 3(B). The characteristic relaxation times τ1 and τ2 derived from fitting resting cycles are 8 s and 85 s, respectively, after averaging over several cycles. The use of two exponentials to fit the data suggests that there may be two metastable states instead of a single in pure a-Se due to the presence of As in studied layers. For all of the substrates, the relaxation time of one of the exponentials, τ1, is in the same range as the relaxation time previously found for the single state model (~ 10 s) [2]. This relaxation time is also similar between the different substrates tested. Conversely, the second relaxation time, however, is significantly longer meaning that the corresponding metastable state relaxes back through larger barrier. It has to be mentioned that the kinetics of the PD during pumping cycles can be modeled by double-exponential decay yielding the same τ1 and τ2 (Fig. 3(B) lower part). The similarity between the time constants extracted from the pumping cycles and the resting cycles suggests that the rate of the conversion from the ground state into the metastable state is much less than 1 s − 1 [2,6]. Since a stretched exponential model was used by Shimakawa et al. [7] to model amorphous chalcogenides, a stretched exponential model was also investigated in this work. The stretched exponential model has the following form: β yðt Þ ¼ y0 þ y1 exp −ðt=τÞ where y0, y1, τ, and β are fitting parameters and β b 1. The stretched exponential results matched well with the double-exponential model and the results are summarized in Table 1. For further comparison, the adjusted coefficient of determination (R 2) is included [8],
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S. Abbaszadeh et al. / Journal of Non-Crystalline Solids 358 (2012) 2389–2392
Table 1 Relaxation parameters for different substrates using different models: single state model (single exponential and stretched exponential) and two state model (double exponential). The goodness of fit is included using R2, where a value closer to unity indicates a better fit. Single exponential τ1 (s) R Glass
Resting Pumping ITO Resting Pumping Polyimide Resting Pumping
34.0 32.2 34.9 27.2 33.5 31.4
2
0.849 0.889 0.809 0.886 0.794 0.873
Double exponential τ1 (s) τ2 (s) R 5.95 5.67 8.48 7.15 6.80 7.00
60.7 76.1 85.1 63.2 75.4 84.1
2
0.882 0.938 0.834 0.920 0.827 0.915
Stretched exponential β
τ (s) R
0.500 0.387 0.452 0.463 0.401 0.411
19.8 24.3 20.4 16.5 16.2 16.0
2
0.880 0.936 0.835 0.918 0.828 0.913
PD. At 35 °C, PD in stabilized a-Se exhibits full recovery, as it was previously found in pure (non-stabilized) a-Se. Acknowledgement We gratefully acknowledge financial support from the Ontario Research Fund-Research Excellence program, the Natural Sciences and Engineering Research Council of Canada, the Canadian Institutes of Health Research, and Teledyne DALSA. As well we are thankful to Prof. S. Baranovskii for the fruitful discussions, Michael M. Adachi for discussions related to the experimental setup, and Nicholas Allec for discussions related to experimental data analysis. References
which indicates the goodness of the fit (where a value closer to unity indicates a better fit). 5. Conclusion It was found that the substrate affects the magnitude of PD significantly in stabilized a-Se: the more rigid the substrate, the stronger is the PD. We conclude that when a-Se is deposited on a rigid substrate, the number of structural units which are photo-induced to transform from their ground states (which are optically transparent) into metastable states (which cause PD) is larger than in the case of a more flexible substrate. The model involving two different kinds of metastable states is used to explain the observed relaxation kinetics of
[1] K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related Materials, Springer, New York, 2011 Ch. 6, Sec. 6.3. [2] A. Reznik, B.J.M. Lui, J.A. Rowlands, S.D. Baranovskii, O. Rubel, V. Lyubin, M. Klebanov, S.O. Kasap, Y. Ohkawa, T. Matsubara, K. Miyakawa, M. Kubota, T. Kawai, J. Appl. Phys. 100 (2006) 113506. [3] R.E. Tallman, A. Reznik, B.A. Weinstein, S.D. Baranovskii, J.A. Rowlands, Appl. Phys. Lett. 93 (2008) 212103. [4] B.A. Weinstein, R.E. Tallman, G.P. Lindberg, J.A. Rowlands, A. Reznik, M. Kubota, K. Tanioka, APS Bull. Amer. Phys. Soc. 56 (2011) Y31. [5] S. Abbaszadeh, N. Allec, K. Wang, K.S. Karim, IEEE Electron Device Lett. 32 (2011) 1263–1265. [6] A. Reznik, S.D. Baranovskii, M. Klebanov, V. Lyubin, O. Rubel, J.A. Rowlands, J. Mater. Sci. - Mater. Electron 20 (2009) S111–S115. [7] K. Shimakawa, N. Nakagawa, T. Itoh, Appl. Phys. Lett. 95 (2009) 051908. [8] J.O. Rawlings, S.G. Pantula, D.A. Dickey, Applied regression analysis: a research tool, Second ed. Springer, New York, 1998.
Contents lists available at SciVerse ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
The effect of the substrate on transient photodarkening in stabilized amorphous selenium S. Abbaszadeh a,⁎, K. Rom b, O. Bubon b, B.A. Weinstein c, K.S. Karim a, J.A. Rowlands b, d, A. Reznik b, d a
University of Waterloo, 200 University Ave. W, Waterloo, ON, Canada, N2L 3G1 Lakehead University, 955 Oliver Road, Thunder Bay, ON, Canada, P7B 5E1 SUNY at Buffalo, 239 Fronczak Hall, Buffalo, NY, , 14260-1500 USA d Thunder Bay Regional Research Institute, 290 Munro Street, Thunder Bay, ON Canada, P7A 7T1 b c
a r t i c l e
i n f o
Article history: Received 2 September 2011 Received in revised form 14 December 2011 Available online 23 January 2012 Keywords: Amorphous selenium (a-Se); Chalcogenide glasses; Photodarkening; Metastable defects; Photo-induced effects
a b s t r a c t The photodarkening (PD) effect has been studied experimentally for amorphous selenium (a-Se) layers with 0.2 wt.% of arsenic (As) deposited on different substrates: glass, indium tin oxide (ITO) coated glass and polyimide-coated ITO glass. It was found that the presence of As qualitatively affects the behavior of PD: while in pure (no As) a-Se the relaxation of the PD is a fast process characterized by a short (~ 10 s) time constant, in As-containing a-Se it has both short (same as in pure a-Se) and comparably long (~ 80 s) components. The interface between a-Se and the substrate affects the PD qualitatively: it influences the magnitude of the effect while not changing the kinetics of the process. The buildup of the PD was more pronounced for the glass substrate (the most rigid) and was least pronounced for the polyimide-coated ITO glass (the most flexible). The difference can be attributed to a different strain at the interface. © 2012 Elsevier B.V. All rights reserved.
1. Introduction It is known that amorphous selenium (a-Se) as many other chalcogenide glasses can undergo photo-induced structural transformation resulting in the red shift in the absorption, or photodarkening (PD). The phenomenological model previously developed by us suggests that PD is caused by photo-induced conversion of some structural units from their ground state configurations into some metastable states that increase the level of disorder, broaden the band tails and hence, increase the absorption [1]. Using a double-well energy configuration, it was shown that the energy barrier between the ground state and a metastable state in pure a-Se was 0.8 eV [2]. A similar activation behavior was observed in photo-induced crystallization (PC) of a-Se studied by Raman spectroscopy [3]. This similarity suggests that the formation kinetics of PD and PC are controlled by the same configurational changes occurring via photo-induced metastable defects. Recently, the photocrystallization studies revealed that the interface between a-Se layer and the substrate significantly influenced the structural stability of a-Se: the onset time of the PC was found to vary for different substrates (glass, polymer encapsulation, and thin blocking/ buffer/indium tin oxide (ITO) layers) [4]. An understanding of the effect of a substrate on photo-induced structural transformation in a-Se is of great practical importance due to the application of a-Se photosensors in optical and radiation
medical imaging. Indeed, structural changes can result in the permanent degradation of a-Se photoconductive properties which has to be prevented. To get a better insight into the effect of the substrate on photoinduced structural transformation, PD was investigated in stabilized a-Se (i.e., doped with 0.2 wt.% of As) deposited on different substrates (with a substrate temperature of 65 °C during deposition) which are used in practical a-Se photosensors, namely glass, (160 nm thick) ITO coated glass and polyimide-coated ITO glass. Our results revealed that the magnitude of the irreversible PD can be reduced by using less rigid substrates (where the glass substrate is the most rigid and the polyimide layer is the least rigid). This can be attributed to the partial strain relaxation at the interface and hence, decrease in the concentration of structural units which are photo-induced to transform from their ground state configuration (which is transparent) to metastable configurations (causing photodarkening). The quantitative analysis of the relaxation of PD show that the double-well model with a single barrier between the ground and metastable states previously used for a pure a-Se layer [2] cannot be applied to stabilized a-Se: the kinetics of relaxation cannot be fitted by single exponential growth. In order to interpret the results, a model with two metastable levels (i.e., with one further structural unit due to the presence of As) is suggested. 2. Experimental details
⁎ Corresponding author. E-mail address: [email protected] (S. Abbaszadeh). 0022-3093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.12.098
A 16.5 μm thick a-Se stabilized with 0.2% of As was deposited using vacuum evaporation technique in the same run on all three
2390
S. Abbaszadeh et al. / Journal of Non-Crystalline Solids 358 (2012) 2389–2392
Fig. 1. Structures of the different samples tested. Amorphous selenium was deposited on glass, ITO glass, and a polyimide-coated ITO glass.
different substrates: glass, ITO-coated glass and polyimide-coated ITO glass. ITO glass was chosen as a substrate due to its potential applications in optical imaging. For instance, when a-Se must be biased, an ITO layer coated on a glass plate is typically used as the transparent electrode. Similarly, polyimide-coated ITO glass has its advantages as well. For example, recent studies have found it to provide excellent blocking properties in the case of significant dark current at high fields [5]. Fig. 1 shows the structure of three samples studied in this work. To study the PD of the samples, we used the standard method of observing the changes in transmission as a function of exposure to light. Fig. 2 shows the experimental apparatus that was used to carry out the PD experiment. In this study, two laser beams with wavelengths of 633 nm were used to illuminate the same area of the sample. The less powerful probing beam was used to monitor changes in transmission of light T. It is crucial that the intensity of the probing beam is low enough that it does not contribute to the PD. The more powerful pumping beam, on the contrary, was used to produce PD. The kinetics of the PD were studied by periodically exposing the a-Se to the pumping beam for cycles of 200 s separated by 200 s of rest. During those cycles, the probing beam transmission, T, is continuously monitored and the relative changes compared to the original transmission of light, T/T0, were then calculated. The alternating cycles of pumping and resting were produced using a function generator. Measurements were taken at room temperature and repeated at 35 °C.
3. Results The results of the PD measurements for the three different substrates at room temperature are shown in Fig. 3(A) as a function of T/T0 versus time for four pumping/resting cycles. All samples exhibit only partial recovery during resting cycles, leading to an overall decrease in transmission in subsequent cycles. Therefore, both reversible and irreversible components of PD are present for all substrates. Fig. 3(B) (upper) shows the relaxation of the PD with time during a selected resting cycle (when pumping is switched off) for a-Se deposited on ITO glass. Fig. 4 shows the PD results at 35 °C for the glass substrate and the polyimide-coated substrate, as examples, where full recovery is observed. This agrees with previously reported results, where the irreversible component of the PD disappeared near the glass transition temperature [2]. 4. Discussion Although all samples exhibited partial recovery (see Fig. 3(A)), our experiment showed, however, that the transmission through the polyimide sample decreased the least, followed by the ITO sample and finally the glass sample. Since the magnitude of the irreversible PD effect is proportional to the number of structural units which can be converted into a metastable state and provide the irreversible PD we conclude that this number is the smallest for a-Se interfacing
Fig. 2. Experimental apparatus used to carry out the PD experiment.
S. Abbaszadeh et al. / Journal of Non-Crystalline Solids 358 (2012) 2389–2392
2391
Fig. 4. Normalized transmission as a function of time for two samples at 35 °C.
model, during relaxation, transitions from metastable configuration back to initial ground state configuration occur through thermal activation over an energy barrier, EB ~ 0.8 eV. As a result, the relaxation of the photodarkening can be fitted by single exponential decay with characteristic time constant τ which relates to the height of the activation energy as: −1
τ ¼ ν 0 expðEB =kB θÞ
Fig. 3. (A) Normalized transmission as a function of time for the three samples at room temperature, (B) The recovery (upper part) and the decay (lower part) of the optical transparency for a resting/pumping cycles at room temperature.
semi-soft material (i.e., polyimide) and the largest for a-Se interfacing rigid substrate (glass) where the strain at the interface is larger. In order to interpret the relaxation kinetics, we first use the single state model [2] previously used to describe PD in pure a-Se. In this
where kB is the Boltzmann constant, θ is the temperature and ν0 is the attempt-to-escape frequency of the order ~10 12 s − 1. However, the single exponential decay fails to fit our experimental results. In contrast, double-exponential decay works much better as it is seen in Fig. 3(B). The characteristic relaxation times τ1 and τ2 derived from fitting resting cycles are 8 s and 85 s, respectively, after averaging over several cycles. The use of two exponentials to fit the data suggests that there may be two metastable states instead of a single in pure a-Se due to the presence of As in studied layers. For all of the substrates, the relaxation time of one of the exponentials, τ1, is in the same range as the relaxation time previously found for the single state model (~ 10 s) [2]. This relaxation time is also similar between the different substrates tested. Conversely, the second relaxation time, however, is significantly longer meaning that the corresponding metastable state relaxes back through larger barrier. It has to be mentioned that the kinetics of the PD during pumping cycles can be modeled by double-exponential decay yielding the same τ1 and τ2 (Fig. 3(B) lower part). The similarity between the time constants extracted from the pumping cycles and the resting cycles suggests that the rate of the conversion from the ground state into the metastable state is much less than 1 s − 1 [2,6]. Since a stretched exponential model was used by Shimakawa et al. [7] to model amorphous chalcogenides, a stretched exponential model was also investigated in this work. The stretched exponential model has the following form: β yðt Þ ¼ y0 þ y1 exp −ðt=τÞ where y0, y1, τ, and β are fitting parameters and β b 1. The stretched exponential results matched well with the double-exponential model and the results are summarized in Table 1. For further comparison, the adjusted coefficient of determination (R 2) is included [8],
2392
S. Abbaszadeh et al. / Journal of Non-Crystalline Solids 358 (2012) 2389–2392
Table 1 Relaxation parameters for different substrates using different models: single state model (single exponential and stretched exponential) and two state model (double exponential). The goodness of fit is included using R2, where a value closer to unity indicates a better fit. Single exponential τ1 (s) R Glass
Resting Pumping ITO Resting Pumping Polyimide Resting Pumping
34.0 32.2 34.9 27.2 33.5 31.4
2
0.849 0.889 0.809 0.886 0.794 0.873
Double exponential τ1 (s) τ2 (s) R 5.95 5.67 8.48 7.15 6.80 7.00
60.7 76.1 85.1 63.2 75.4 84.1
2
0.882 0.938 0.834 0.920 0.827 0.915
Stretched exponential β
τ (s) R
0.500 0.387 0.452 0.463 0.401 0.411
19.8 24.3 20.4 16.5 16.2 16.0
2
0.880 0.936 0.835 0.918 0.828 0.913
PD. At 35 °C, PD in stabilized a-Se exhibits full recovery, as it was previously found in pure (non-stabilized) a-Se. Acknowledgement We gratefully acknowledge financial support from the Ontario Research Fund-Research Excellence program, the Natural Sciences and Engineering Research Council of Canada, the Canadian Institutes of Health Research, and Teledyne DALSA. As well we are thankful to Prof. S. Baranovskii for the fruitful discussions, Michael M. Adachi for discussions related to the experimental setup, and Nicholas Allec for discussions related to experimental data analysis. References
which indicates the goodness of the fit (where a value closer to unity indicates a better fit). 5. Conclusion It was found that the substrate affects the magnitude of PD significantly in stabilized a-Se: the more rigid the substrate, the stronger is the PD. We conclude that when a-Se is deposited on a rigid substrate, the number of structural units which are photo-induced to transform from their ground states (which are optically transparent) into metastable states (which cause PD) is larger than in the case of a more flexible substrate. The model involving two different kinds of metastable states is used to explain the observed relaxation kinetics of
[1] K. Tanaka, K. Shimakawa, Amorphous Chalcogenide Semiconductors and Related Materials, Springer, New York, 2011 Ch. 6, Sec. 6.3. [2] A. Reznik, B.J.M. Lui, J.A. Rowlands, S.D. Baranovskii, O. Rubel, V. Lyubin, M. Klebanov, S.O. Kasap, Y. Ohkawa, T. Matsubara, K. Miyakawa, M. Kubota, T. Kawai, J. Appl. Phys. 100 (2006) 113506. [3] R.E. Tallman, A. Reznik, B.A. Weinstein, S.D. Baranovskii, J.A. Rowlands, Appl. Phys. Lett. 93 (2008) 212103. [4] B.A. Weinstein, R.E. Tallman, G.P. Lindberg, J.A. Rowlands, A. Reznik, M. Kubota, K. Tanioka, APS Bull. Amer. Phys. Soc. 56 (2011) Y31. [5] S. Abbaszadeh, N. Allec, K. Wang, K.S. Karim, IEEE Electron Device Lett. 32 (2011) 1263–1265. [6] A. Reznik, S.D. Baranovskii, M. Klebanov, V. Lyubin, O. Rubel, J.A. Rowlands, J. Mater. Sci. - Mater. Electron 20 (2009) S111–S115. [7] K. Shimakawa, N. Nakagawa, T. Itoh, Appl. Phys. Lett. 95 (2009) 051908. [8] J.O. Rawlings, S.G. Pantula, D.A. Dickey, Applied regression analysis: a research tool, Second ed. Springer, New York, 1998.