The enhancement of green upconverted emission from the Er3+/Yb3+ co-doped (Pb,La)(Zr,Ti)O3 ceramic powder under a pumping light with a wavelength of 1480 nm was observed to be greater than 30 times that from the bulk of the same sample. Weak localization of light supported by the spatial profile of scattered light facilitated the three-photon process contributing to stronger green upconverted emission. Significant backward light amplification was also observed and studied in detail. Additionally, the distribution of the localization zones in the sample was investigated using a probing laser beam with a wavelength of 532 nm. The findings in this work could be used in improving the solar cell efficiency, modulating color, and designing smart devices.
© 2016 Optical Society of America
Nowadays, lanthanum-modified lead zirconate titanate ((Pb,La)(Zr,Ti)O3, PLZT) ceramics are one of the most frequently used materials in fundamental research and in various applications owing to a variety of interesting properties observed since their development [1,2]. These materials were recently classified as smart  owing to their excellent ferroelectric, pyroelectric, electrostrictive, and photorefractive properties [1,4,5]. In the last decade, rare-earth (RE) doped PLZT has been widely studied to combine luminescence with other effects. It was also used as one of the most promising materials for developing tunable light sources and multifunctional optical devices [6,7]. For example, IR to visible light upconversion in Er3+doped PLZT ceramics was applied to temperature sensors  and emission at wavelengths of 2.8 and 1.55 μm from Er3+/Yb3+ co-doped PLZT ceramics pumped using a laser diode with a wavelength of 980 nm was achieved . In addition, photochromism and optical amplification were studied in pure and RE doped PLZT ceramics in the past few years [9–11]. From the disordered nature of PLZT ceramics, carriers were found to be captured by traps under excitation by photons, electric field, or heat . Actually, these trapped carriers are responsible for many interesting phenomena [10,12]. We found that they could also lead to weak localization and random laser realization, which is one of the most frequently discussed topics nowadays.
Research activities have recently been focused on random lasers and weak localization of light globally [13–15]. When light propagates through random materials, it can undergo the multiple scattering and interference processes. The most robust among the interference phenomena may be weak localization, which is observable as a cone-shaped enhancement of the backscattered light intensity [16,17]. This phenomenon was studied in some random systems since its first observation in colloidal suspensions [15–18]. The propagation of light in a random system follows the Lévy flight that is proved in Lévy’s glass by Wiersma et al. . In Nd3+ doped PLZT, weak localization of light and random laser properties were found and investigated by our group .
In this work, upconverted light emission was greatly enhanced in powdered samples of Er3+/Yb3+ co-doped PLZT translucent ceramics at shorter wavelengths at the expense of longer wavelengths. Weak light localization was also observed to cause this enhancement.
2. Enhanced emission
Er3+/Yb3+ (3 mol%/5 mol%) co-doped PLZT (10/65/35) translucent ceramics prepared using the hot-press sintering process (refer to [1,2] for details) was ground into powder and then inserted into a fused quartz cuvette. The particle diameters in this powder were measured to be from 6 to 50 μm using a polarizing microscope. Upon illuminating the cuvette with IR light at a wavelength of 1480 nm using a continuous laser diode (Apollo Instrument, Inc. S30-1480-6), strong red and green light emission occurred. The schematic of the experimental setup is shown in Fig. 1(a). A pumping beam with a wavelength of 1480 nm was focused onto the sample using a convergence lens. The spot diameter on the cuvette was 3.0 mm. Emitted light was collected using a lens system and monitored using a UV-visible-NIR spectrometer (Ocean Optics, HR4000CG-UV-NIR). The angles between the axes of the collected emitted light and the pumping beams were 174° [refer to Fig. 1(a)] for a relatively intense scattered light entered the detector and the spectrometer. The inset in Fig. 1(a) is the photograph taken under a pumping intensity of 216.5 mW/mm2. It can be seen that the specimen emits yellowish white light (yellow green and red) at the center with red doughnut-shaped periphery. From the emission spectra measured at three different pumping light powers, four green emission peaks from 526 to 563 nm and two red peaks at 656 and 678 nm were observed, as shown in Fig. 1 (b). This green upconversion light was more intense compared to that in an Er3+ doped LiNbO3 crystal plate . The detailed discussion concerning underlying physics is given in the following section.
To understand the physical processes that cause this intense three-photon process, the relationship between the pumping power and the emission intensity was measured. The linear relationship at wavelengths of 526 and 538 nm is shown in Fig. 2(a). As can be seen, emission intensity Iout is proportional to the nth power of pumping power Ipump (that is Iout∝Ipumpn) . Thus, factor n can be obtained by measuring the slope of the plot after logarithm transition of the axes, the results are 3.09 and 2.96. For other emission peaks, which have the same behavior as the peaks at 526 and 538 nm, the log–log slopes at 550 and 563 nm are 2.86 and 2.91, the log–log slopes at 656 and 678 nm are 2.14 and 2.13, and those at 974 and 986 nm are 2.02 and 2.00, as shown in Figs. 2(b), 2(c), and 2(d), respectively. Factor n indicates the number of photons participates in an emission process . The aforementioned results indicate that the processes contributing to green and red upconverted emissions are mostly three-photon processes, and those contributing to near IR emission are mainly two-photon processes.
For further analysis of the intense green upconversion process, the energy level diagram shown in Fig. 2(e) should be considered. For these upconversion emission bands, similar mechanisms were widely discussed in fluoroindate glasses  and in Y2O3 . The mechanism of transition between the energy levels in our material is expressed as follows:
- (1) For 4I11/2→4I15/2, 4I13/2 level of Er3+ ions were populated owing to ground state absorption (GSA), then excited to 4I9/2 level via excited state absorption (ESA), decays nonradiatively to 4I11/2 level, and returns to 4I15/2 level by emitting light with wavelengths of 974 or 986 nm.
- (2) For 4F9/2→4I15/2, 4I11/2 level of Er3+ ions were excited to 4F9/2 owing to ESA or from 4I13/2 level to 4F9/2 via energy transfer processes (ETU) from Er3+ in 4I11/2 level and Yb3+ in 2F5/2 level, then return to ground level 4I15/2, following by light emission at wavelengths of 656 or 678 nm.
- (3) For 4S3/2→4I15/2, 4I9/2 of Er3+ ions were excited to 2H11/2 level via ESA, relaxes to 4S3/2 level via nonradiative transition, and returns to the ground level by emitting light at wavelengths of 550 and 563 nm.
- (4) For 2H11/2→4I15/2, 4H11/2 level return to 4I15/2 level directly by emitting photons at wavelengths of 526 and 538 nm.
3. Experimental confirmation and theoretical consideration
3.1 Localization measurements
It is interesting to see that the green emission peaks only occurred at a relatively high pumping power. This can be attributed to at least two main reasons. Photons propagating in PLZT ceramic powder with a particle size of the order of micrometers are highly elastically scattered due to inhomogeneity caused by particle boundaries. Consequently, the effective length path of the pumping light greatly increases along with the intensity of light emission. Therefore, the intensity of emission light is stronger compared to that from the material bulk. On the other hand, localization of light plays an important role in the emission enhancement. Because of the intrinsic disordered nature of PLZT ceramics and rich vacancies formed in them , multiple elastic and inelastic scatterings and hence weak localization can occur in the specimen following by the coherent effect and stimulated amplification of light in the region. A similar phenomenon in Nd3+ doped PLZT ceramics was discussed in our previous work .
To verify the first assumption, a straightforward experiment was performed using powder and bulk specimens prepared using the same sample. The upconverted light emission spectra at the same pumping power of 221 mW/mm2 were measured as shown in Fig. 3(a). A great increase in the emitted light intensity from the powdered sample compared to that from the bulk can be seen. In addition, important information can be derived from the emission wavelength dependence of the enhanced ratio. For emission wavelengths of 1007, 679, and 563 nm, the enhancement ratios were 5.4, 12.9, and 30.1 times, respectively. The increase in the enhancement as the wavelengths were decreased was one of the indicators of light localization. As analyzed in , when light localization occurred, photons at longer wavelengths were localized earlier and confined for a longer time within the illuminating zone, and hence they could be converted into photons with shorter wavelengths more probably.
To verify whether weak localization of light occurs in the powdered specimen, we illuminated it using a focused pumping beam and monitored using a microscope in real time. Scattered light was found to distribute in several small areas, and the brightness of each area is different. This is a typical feature of the Lévy flight in a medium that scatters specifically . Along with the central bright spot, the two localized zones can be seen in the microscopic photograph shown in Fig. 3(b). The brightest area in the middle is the center of the illuminated area, and the two additional localized zones are marked using ellipses. The area on the top right of the brightest spot (the region labeled using the red ellipse) is considerably brighter than other areas at the same distances to the illuminated spot. This is regarded as a sign of light localization, and this simple experiment provides a direct evidence of the light localization in our specimen. In addition, the area labeled using the white ellipse is brighter than the areas at the same distances to the illuminated spot that are dark.
Moreover, when weak localization occurs, the backscattered light emission intensity distribution is significantly dependent of the detection angle [17,24]. Therefore, a straightforward experiment for monitoring the spatial profile of backscattered light was performed, as shown in Fig. 3(c). In this experiment, the pumping intensity was fixed at 247 mW/mm2, and the intense green emission peak at a wavelength of 550 nm was measured to study the angular distribution. A diode laser beam with a wavelength of 1480 nm was focused using a lens, reflected by a mirror, and irradiated the specimen. A CCD camera was placed after a 550-nm bandpass filter and after a project screen. The distance between the sample and the CCD camera was 3.00 cm, and the radius of the screen was 1.28 cm. Thus, the angular distribution of the backscattering cone was detected, as shown as Fig. 3(d). As can be seen, the emitted light distributed within a small angle range, and the intensity decreased to a small and relatively stable value when the angle was larger than 0.4 rad. The mean free path could be obtained from the angular distribution. The half-angular width was 0.2 rad, as seen in Fig. 3(d). From the Ioffe-Regal criterion, the angular distribution was given by l ∼λ/θ (where λ is the wavelength, θ is the half peak width, and l is the mean free path) [24–26]. Based on the data shown in Fig. 3(d), the mean free path was calculated to be approximately 1.37 µm. In the experiment, the backscattered light intensity distribution was measured from 0 to 0.43 rad only, another part was added mirror-symmetrically.
3.2 Electrical properties
The enhancement of the light emission from the powdered specimen is greater than 30 times that from the bulk specimen. To find out the reason for this significant enhancement, we studied the undergoing processes near the ceramic surfaces. For the PLZT material, which exhibits significant pyroelectric effect, when the temperature increases/decreases, considerable charge accumulation near the PLZT/air interfaces occurs [shown in Fig. 4(a)], and the refractive index varies significantly [27,28]. Consequently, the abrupt refractive index change leads to intense scattering. The black arrows in Fig. 4(a) illustrate how the light is scattered backwards by the boundary modification. To verify that the pyroelectric effect causes remarkable charge accumulation, a doped PLZT plate, coated with silver paint on a pair of opposite faces as electrodes, was illuminated using strongly absorbed light. A significant photocurrent flowed through the PLZT plate. This unambiguously confirmed the surface charge accumulation and charge carrier transportation (not discussed in this paper). Actually, these charge carriers, especially electrons, can be easily transferred to nearby vacancies and trap there. These trapped carriers can be additional scattering centers . Electron traps are illustrated in Fig. 4(b).
In the past years, photoinduced absorption was observed in pure PLZT ceramics [29,30], revealing polaron involvement in the materials. Although no conclusions are given in the papers, the involvement of energy transfer centers is positive . As depicted in Fig. 4(c), when the PLZT ceramic material is illuminated using near bandgap light, electron hole pairs are generated. There are three kinds of electron traps: shallow trapping (ST), thermally active trapping (TAT), and thermally disconnected trapping (TDT) centers in the PLZT ceramic, along with thermally disconnected hole traps (DHTs). In , we have introduced a calculation method, based on this calculation, when 10 mol% La3+, 3 mol% Er3+, and 5 mol% Yb3+ ions replace Pb2+ ions (the sample used throughout this work), the lowest limit of the vacant site concentration in Er3+/Yb3+ co-doped PLZT is approximately 7.16 × 1020 cm–3. Thus, the average distance between adjacent vacant sites should be shorter than 1.0 nm, which is much shorter than that between Er3+ and Yb3+ ions. Therefore, electron diffusion between adjacent vacant sites is more rapid compared to energy transfer between Er3+ and Yb3+ ions. The existence of vacant sites facilitates the energy transfer process.
In fact, an electron trapped by a vacant site is equivalent to a polaron in nature. The electron is hopping between these vacant sites to assist energy transfer between Er3+ ions . Physically, electron hopping process between vacant sites (equivalent to polaron diffusion) is random in nature, though the range of the step sizes and directions is restricted owing to the fixed lattice of the PLZT ceramics. Thus, the distribution of the trapped carriers (additional scattering centers) is random. It is advantageous that weak localization of light contributed to effective realization of three-photon processes.
3.3 Backward optical amplification
To measure how much light was localized, a probing laser beam at a wavelength of 532 nm was transmitted onto the powdered specimen used throughout the work. The corresponding experimental setup is shown in Fig. 5(a). The pumping laser at a wavelength of 1480 nm was focused on the specimen using a lens. The spot diameter was 4.0 mm that was smaller than that of the pumping beam. The probing laser beam was obliquely incident on the specimen, and then light reflected by the specimen was reflected by a mirror and received by a detector, which was connected to an oscilloscope. Two short-pass filters of wavelengths of 700 and 900 nm were placed in front of the detector. We measured the reflection ratio of the probing laser beam upon illuminating the specimen and found that the reflected beam was amplified considerably. A typical dynamic curve when the pumping laser is turned on (off) is shown in Fig. 5(b). As can be seen, when the pumping laser diode is turned on, the reflected probing intensity increases instantaneously and then fluctuates very quickly. Afterwards, the fluctuation slows over time, and the intensity stabilizes. When the pumping laser is turned off, the reflected probing intensity first decreases to a lower value and then returns to the original value with a damped oscillation. To observe the increasing percentage directly, the intensity was normalized. The periodic features in the rising and dropping processes seem to be originated from interference. The backward gain in percentage was plotted as a function of the pumping power in Fig. 5(c). As expected, as the pumping power was increased, the localization was enhanced, and hence the backward gain was enhanced. Regarding the nature of the backward amplification, it is simply of stimulated emission. Without the pumping light, the incident probing light is reflected by the specimen. When the pumping light is turned on, random lasing and weak localization occur, and the reflected probing light is amplified owing to the stimulated emission.
To study the localization in the ceramics, a simple experiment was performed, the experimental setup was the same as demonstrated in Fig. 5(a), and the results are shown as follows. The pumping spot diameter was 5.0 mm, and its intensity distribution was inhomogeneous. As shown in Fig. 6(a), the yellowish green, grey, and green areas represent a more intense irradiation region, less intense irradiation region, and probing light spot, respectively. In our experiment, the three cases were studied, and the corresponding representative dynamic changes of probing light intensity were monitored using an oscilloscope.
In the first case shown in Fig. 6(b), the probing light spot was almost completely included into the intense irradiation region. The corresponding probing light dynamic change is presented using the blue curve. To explain this phenomenon, the trap-rich nature of PLZT ceramics must be considered. When an intense pumping beam illuminated the specimen, photons could be confined in the pumping illuminated zone for a relatively long time in this area, while photons outside the zone could not penetrate into it easily, and thus the weak localization occurred. Consequently, the probing light intensity was amplified. In the second case [shown in the inset in Fig. 6(c)], the probing light spot was in the dark area. As can be seen in Fig. 6(c), the probing light intensity decreased when the pumping laser was turned on and increased when the pumping laser was turned off. At a small pumping power, the confinement of upconversion photons cannot overcome the scattering loss, and hence the probing intensity decreases when the pumping laser is turned on. In the third case [refer to the inset in Fig. 6(d)], the reflected probing intensity fluctuated, and the average intensity remained the same. The gain owing to the light localization was suppressed by the scattering loss. Regarding the fluctuant character during the turning on/off processes, the fluctuation shown in the backward reflection dynamics becomes clear considering weak localization as coherent backscattering in nature.
As the pumping power was increased, the power of longer waves decreased, while the power of shorter waves increased as shown in Fig. 7(a). This is resulted from the light localization, which partially originated from the temperature change of the specimen. Actually, this photon frequency redistribution can be used in color modulation. When the specimen was pumped using the laser with a wavelength of 1480 nm, it changed color from red to yellowish green as the pumping power was increased. The corresponding emission spectra were measured at different pumping powers. For the six visible emission peaks from 526 to 678 nm shown in Fig. 7(b), when the intensity at each individual emission peak was divided by the total intensity of all the emission peaks in the visible range, the result is shown in Fig. 7(a). These fractional intensities were plotted as functions of the pumping powers. The intensity of the green light increased with the pumping power, while the red light emission decreased. Therefore, color modulation can be realized in the Er3+/Yb3+ co-doped PLZT powder by adjusting the pumping power.
Moreover, intense upconversion emission under a pumping laser beam with a wavelength of 1480 nm can be directly used in improving the efficiency of solar cells. In fact, most of silicon-based solar cells in the market efficiently absorb only light with wavelengths from 300 to 1100 nm. However, using PLZT coating, for example, IR light with a wavelength of approximately 1480 nm can be converted into visible light based on its broad absorption band at 1480 nm. The emission peaks from the Er3+/Yb3+ co-doped PLZT specimen are observed to be mainly distributed in the three regions [Fig. 7(b)], and the light energy in these regions can be absorbed by solar cells well.
In conclusion, excellent three-photon upconversion emission under a pumping diode laser beam with a wavelength of 1480 nm was observed and analyzed in the Er3+/Yb3+ co-doped (Pb,La)(Zr,Ti)O3 ceramic powder. Weak light localization was found to play a significant role in the enhancement of upconversion emission. When the specimen was heated or cooled, charge carriers accumulated on particles because of the quite strong pyroelectric effect. The charge carrier accumulation on the particle surfaces intensifies elastic scattering. On the other hand, the charge carrier accumulation facilitates electron diffusion (polaron transportation) between vacant sites, which enhances inelastic scattering. Therefore, both elastic and inelastic scatterings result in the weak light localization. The weak localization of light was also verified experimentally using the spatial profile of scattered light. The occurrence of the weak localization can be used for explaining the observed accompanying backward amplification. The physical insight into the weak localization should be applicable to similar powdered material systems. All the studied associated effects can be used in designing PLZT powder based smart devices, improving the efficiency of solar cells, and modulating color.
This work was partially supported by the grant of the National Natural Science Foundation of China (NSFC) under project Nos. 11374076 and 11174067.
References and links
1. G. H. Haertling, “Electro-optic ceramics and devices,” in Electronic Ceramics, L. M. Levinson eds. (Marcel Dekker, New York), 371–492 (1987).
2. H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,” Proc. SPIE 5644, 380–394 (2005). [CrossRef]
3. V. K. Wadhawan, P. Pandit, and S. M. Gupta, “PMN-PT based relaxor ferroelectrics as very smart materials,” Mater. Sci. Eng. B 120(1-3), 199–205 (2005). [CrossRef]
4. J. W. Zhang, Y. K. Zou, Q. Chen, R. Zhang, K. K. Li, H. Jiang, P. Huang, and X. Chen, “Optical amplification in Nd3+ doped electro-optic lanthanum lead zirconate titante ceramics,” Appl. Phys. Lett. 89(6), 061113 (2006). [CrossRef]
5. A. S. S. de Camargo, J. F. Possatto, L. A. O. Nunes, É. R. Botero, É. R. M. Andreeta, D. Garcia, and J. A. Eiras, “Infrared to visible frequency upconversion temperature sensor based on Er3+ doped PLZT transparent ceramics,” Solid State Commun. 137(1–2), 1–5 (2006). [CrossRef]
6. J. Le Gouët, L. Morvan, M. Alouini, J. Bourderionnet, D. Dolfi, and J. P. Huignard, “Dual-frequency single-axis laser using a lead lanthanum zirconate tantalate (PLZT) birefringent etalon for millimeter wave generation: beyond the standard limit of tunability,” Opt. Lett. 32(9), 1090–1092 (2007). [CrossRef] [PubMed]
7. H. Zhao, X. Sun, J. W. Zhang, Y. K. Zou, K. K. Li, Y. Wang, H. Jiang, P. L. Huang, and X. Chen, “Lasing action and optical amplification in Nd3+ doped electrooptic lanthanum lead zirconate titanate ceramics,” Opt. Express 19(4), 2965–2971 (2011). [CrossRef] [PubMed]
8. A. S. S. de Camargo, E. R. Botero, É. R. M. Andreeta, D. Garcia, J. A. Eiras, and L. A. O. Nunes, “2.8 and 1.55 mum emission from diode-pumped Er3+-doped and Yb3+ co-doped lead lanthanum zirconate titanate transparent ferroelectric ceramic,” Appl. Phys. Lett. 86(24), 241112 (2005). [CrossRef]
9. C. Xu, J. Zhang, L. Xu, and H. Zhao, “Mechanism of photochromic effect in Pb (Zr, Ti) O3 and (Pb, La)(Zr, Ti) O3 ceramics under violet/infrared light illumination,” J. Appl. Phys. 117(2), 023107 (2015). [CrossRef]
10. Y. Wu, H. Zhao, Y. K. Zou, X. Chen, B. Di Bartolo, and J. W. Zhang, “Optoenergy storage, stimulated processes in optical amplification with electro-optic ceramic gain media of Nd3+ doped lanthanum lead zirconate titanate,” J. Appl. Phys. 110(3), 033106 (2011). [CrossRef]
11. J. Zhang, H. Sun, Y. Zou, X. Chen, B. Di Bartolo, and H. Zhao, “Multifunctional optical device with electrooptic Er3+ and Yb3+ doped lanthanum-modified lead zirconate titanate ceramic gain media,” J. Lightwave Technol. 31(9), 1495–1502 (2013). [CrossRef]
12. W. L. Warren, J. Robertson, D. Dimos, B. A. Tuttle, G. E. Pike, and D. A. Payne, “Pb displacements in Pb(Zr,Ti)O3 perovskites,” Phys. Rev. B Condens. Matter 53(6), 3080–3087 (1996). [CrossRef] [PubMed]
14. L. V. Kuzmin, V. P. Romanov, and L. A. Zubkov, “Coherent backscattering from anisotropic scatterers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(6), 6798–6801 (1996). [CrossRef] [PubMed]
17. M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108(11), 110604 (2012). [CrossRef] [PubMed]
19. L. Xu, H. Zhao, C. Xu, S. Zhang, and J. Zhang, “Optical energy storage and reemission based weak localization of light and accompanying random lasing action in disordered Nd3+ doped (Pb, La)(Zr, Ti)O3 ceramics,” J. Appl. Phys. 116(6), 063104 (2014). [CrossRef]
22. M. A. Hernández-Rodríguez, M. H. Imanieh, L. L. Martin, and I. R. Martin, “Experimental enhancement of the photocurrent in a solar cell using upconversion process in fluoroindate glasses exciting at 1480 nm,” Sol. Energy Mater. Sol. Cells 116, 171–175 (2013). [CrossRef]
23. H. Wang, M. Xing, X. Luo, X. Zhou, Y. Fu, T. Jiang, Y. Peng, Y. Ma, and X. Duan, “Upconversion emission colour modulation of Y2O2S: Yb, Er under 1.55 μm and 980 nm excitation,” J. Alloys Compd. 587, 344–348 (2014). [CrossRef]
26. A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009). [CrossRef]
28. H. Wang, H. Zhao, L. Li, C. Xu, and J. Zhang, “Surface plasmon polariton boosted photorefractive scattering in indium tin oxide coated Fe-doped lithium niobate slabs,” Opt. Commun. 338, 505–510 (2015). [CrossRef]
29. S. Schaab, T. Granzow, Th. Woike, and D. Schaniel, “Light-induced absorption in lead lanthanum zirconate titanate ceramics,” J. Appl. Phys. 105(2), 024103 (2009). [CrossRef]
30. W. L. Warren, C. H. Seager, D. Dimos, and E. J. Friebele, “Optically induced absorption and paramagnetism in lead lanthanum zirconate titanate ceramics,” Appl. Phys. Lett. 61(21), 2530–2532 (1992). [CrossRef]
31. V. I. Arkhipov, E. V. Emelianova, A. Kadashchuk, and H. Bassler, “Hopping model of thermally stimulated photoluminescence in disordered organic materials,” Chem. Phys. 266(1), 97–108 (2001). [CrossRef]