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Abstract
We report a study of the thermally activated processes occurring in Bi-doped GeO2-SiO2 fibers using the demarcation energy concept based on a distribution of the activation energies of a first order physico-chemical reaction. Our attention was paid to the processes of formation of the bismuth-related active centers (BACs) and Bi-centers responsible for the unsaturable loss, as well as to the restoration of the BACs in laser-bleached fibers. The activation energies of these processes were determined analyzing the thermal kinetics of these processes. The formation energies of new BACs and Bi-centers responsible for the unsaturable loss were determined to be around 1.1 eV and higher than 2 eV, respectively. The activation energy of thermal restoration process of the bleached BACs is $\approx$ 0.4 eV. The possible underlying mechanisms of these processes are discussed.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Bismuth-doped fibers have shown great potential for use in different optical devices, and remarkable progress has been achieved in the development of lasers and optical amplifiers for the various bands in the near IR [1–4]. This advance has been made possible due to comprehensive studies of the peculiar optical properties of the bismuth-related active centers (BACs) and improvements on conventional fabrication techniques. Significant attention has mainly been paid to the investigation related to the luminescence features of bismuth-doped glass materials. As a result, recently, a number of novel effects arising in the bismuth-doped fibers were discovered. In particular, one of these effects is the photobleaching, which reveals itself in the decrease of absorption and luminescence intensity caused by the destruction of active centers in optical fibers exposed to laser radiation [5]. The research activities of different scientific groups in this field show that photobleaching significantly depends on the glass matrix, photon energy, type of the BACs, temperature, power radiation etc [6–9]. After that, partial and complete recovery of the bleached BACs initiated by a heating process was demonstrated [10,11]. Thermally initiated formation of the BACs is another exciting effect providing the enhancement of luminescence intensity [12] and optical gain [13] in bismuth-doped fibers. The well-known peculiarity of the Bi-doped fibers is a low BACs concentration due to a strong clustering effect. It was shown that thermal treatment is a reliable approach to increase the BACs content in Bi-doped high-germania fibers without significant deterioration of their gain characteristics. It resulted in the construction of a Bi-doped fiber laser with a shorter cavity. Intensive research of these effects is of interest for both fundamental research and practical applications of this type of fibers. Namely, there is an unsolved fundamental problem concerning the structure of the BACs responsible for the near-IR luminescence and the process of their formation. Long-term stability of the fibers and devices based on such fibers is still a subject of research. The investigation of the above-mentioned novel effects might shed some light on the issues of the BACs structure and their long-term stability, or at least limit the range of possible hypothesizes of the BACs models that would be an undoubted progress in this direction. The mechanisms of most of the mentioned processes occurring in bismuth-doped fibers are not completely studied and require additional research. In this paper, we focus on the kinetics of the thermally activated processes of formation of the BACs and Bi-centers responsible for the unsaturable loss, and the recovery of the bleached BACs. Analysis of the experimental data was performed using the demarcation energy theory in the framework of a variable reaction pathways described in detail in [14] and the approach based on an empirical power-law model [15]. The obtained results allowed us to obtain the main characteristics of these processes.
2. Experimental
Isothermal annealing at various temperatures in the range 450–800 K was performed using a tubular furnace Nakal PT0215 with an isothermal heating zone of 0.4 m. The annealing duration in each experiment was 2.5 hours. The setups for the measurements of the luminescence/absorption characteristics of the bismuth-doped fiber were described in detail in [5,10]. The measurements of the luminescence and transmission spectra were carried out with an HP 70950B spectrum analyzer. A commercial laser diode operating at 1550 nm with output power up to 150 mW was used as an excitation source for the luminescence measurements. We did not take into account the change of luminescence/absorption intensities during the heating process with a rate of 1500 $^{\circ }$C/h because it was negligible. Unlike the luminescence signal measurement, the short length of the isothermal zone did not allow us to investigate segments with a length sufficient for a reliable measurement of the small-signal absorption in the 1650 nm region. That is why the absorption at 925 nm, also belonging to the BACs, was monitored. In general, the research was focused on thermally activated processes based on studying the behavior of luminescence properties during the isothermal annealing process, which we could measure with high accuracy. This became possible since no noticeable temperature quenching of luminescence was observed in the temperature range under study, which was experimentally verified in previous papers [16,17]. The exposure time to the pump radiation in the process of luminescence measuring was chosen as short as possible to avoid the influence of photoinduced effects (for example, photodegradation of active centers) if any were present. It was found that there is a complete agreement between the experimental data in terms of luminescence and absorption characteristics. The behavior of the unsaturable loss during annealing at the same conditions was studied utilizing laser radiation falling into the tail of the band peaked at 925 nm at intensities which are well above the saturation intensity of the BACs. The bismuth concentration in the fiber preform was determined by means of electrothermal atomic absorption spectrometry and inductively coupled plasma atomic emission spectroscopy.
3. Results and discussion
We performed an analysis of the thermal kinetics of growth of the luminescent center content in a pristine and irradiated (with a laser operating at 532 nm with an intensity of $\sim$ 1 MW/cm$^{2}$ during 0.5 h) fibers. The cores of both fibers fabricated by conventional MCVD technique were made of high-germania glass ($\approx$50GeO$_{2}$–50SiO$_{2}$) doped with bismuth. Total Bi concentration was estimated as 200 ppm. It should be noted that BACs with the main luminescence and absorption bands peaked at 1730 nm and 1650 nm, respectively, are predominantly formed in such fibers [18]. In our previous papers [10], it was shown that the thermally activated recovery of the BACs in the bleached fibers is similar to that of point glass defects, in particular, the oxygen-deficient centers. For analysis of the thermal kinetics of formation of the luminescent centers obtained in our experiments, one can apply the approach based on the empirical power-law model describing the thermally activated recovery and bleaching processes of the glass defects [19,20]. We also used this model for the description of the formation process of new BACs during thermal treatment. The change of the luminescence intensity at 1700 nm is assumed to be proportional to the concentration of the BACs. The proposed mechanism for transformation from a precursor of active center (PAC) to a BAC can be the formation of an oxygen-deficient center adjacent to a Bi ion resulting from bond breaking, migration, and structural rearrangement, etc. It is suggested that the transformation goes through a first-order physico-chemical reaction $PAC \xrightarrow {k} BAC$ with an activation energy $E$ and a rate factor $k = k_{0}\,exp(-E/k_{B}T),\;$ where $k_{B}\,=\,8.617 \cdot 10^{-5}$ eV/K is the Boltzmann constant, $k_{0}$ - pre-exponential factor. This suggestion is based on the fact that the growth of the BACs concentration depends on temperature. In glasses, there are reactions with different rates since the activation energy is sensitive to the local environment. That is why there is a distribution of the activation energies $g(E)$ which can be normalized to unity. Here, we used a bell-shaped distribution function centered on $E_{0}$ and of width $\approx$ $3k_{B}T_{0}$ (Eq. (1)).
Figure 1(a) shows the experimentally obtained temporal dependencies of the normalized PAC content at four different temperatures, namely, 673, 723, 773 and 798 K. The described above function $f(t,T)$ with the characteristic parameters ($A$ and $\alpha$) was fitted to the data obtained for each temperature and resulting fit parameters are presenting at the corresponding line. The determined factor $A$ and the exponent coefficient $\alpha$ are plotted against temperature in Fig. 1(b) and Fig. 1(c), correspondingly. The factor $A$ can be expressed in the form:
Fig. 1. a) Temporal evolution of normalized PACs concentration at different temperature of treatment. (symbols - experimental data; lines - fitting). Fitting parameters are shown at the corresponding curve. Factor $A$ (b) and exponent coefficient $\alpha$ (c) as a function of temperature.
where $A_{0}=exp(-\frac {E_{0}}{k_{B}\;T_{0}})$ and $a = \frac {ln(k_{0})}{T_{0}}$. The data in Fig. 1(b) can be well fitted with a straight line indicating the validity of Eq. (3). The graph of $\alpha$ versus temperature is also more or less consistent with the assumption of linear temperature dependence with the constant $T_{0}$ equal to $\approx$ 780 K (Fig. 1(c)). Using the fitting parameters indicated in Fig. 1(b, c), we calculate that $k_{0} \approx {10}^{4}$ s$^{-1}$ and $E_{0}$ =1.14 $\pm$ 0.07 eV.
As the model implies the concentration of the PACs should not depend separately on the reaction time $t$ and temperature $T$. Rather, it should be a function of a specific combination of them which can be expressed as $E_{d}=k_{B}T ln(k_{0}t)$.
Therefore, it is possible to plot the data presented in Fig. 1(a) in terms of $E_{d}$ only. This graph is illustrated in Fig. 2(a). It is necessary to note that for this plot, we used $k_{0} ={10}^{4}$ s$^{-1}$. The dashed curve was obtained by fitting the function $\frac {1}{1+exp(\frac {E_{d}-E_{0}}{k_{B}\;T_{0}})}$ (see Eq. (2)) to the experimental data. The energy $E_{0}$, corresponding to the maximum of the distribution $g(E)$, is 1.11 eV at $T_{0}$ = 780 K. These parameters are in good agreement with the ones derived from data in Fig. 1.
Fig. 2. a) Plot of the normalized $N_{PAC}$ versus the demarcation energy $E_{d}$. The rate factor $k_{0}$ is ${10}^{4}$ s$^{-1}$. The dashed line is fitting curve (Eq. 2); b) The distribution $g(E)$ calculated by differentiation of the line in (a). The range of demarcation energies of the BACs formation process is indicated by symbols (experimental data).
The data in Fig. 2(a) can be used to reconstruct the distribution of the activation energies $g(E)$, which is plotted in Fig. 2(b). It is characterized by a peak at 1.11 eV and its FWHM of 0.25 eV. As can be seen from Fig. 2(b), for $E_{d}$ $\le$ 0.75 eV the overall completion of the physico-chemical reaction of the formation of the BACs is negligible. Considering the mechanism of formation of the bismuth-related active centers in the process of thermal treatment of optical fibers, it should be noted that the energy obtained is rather small compared to the energy of formation of the oxygen vacancies formation, which include the oxygen-deficient centers. From the results of numerous studies, it follows that the activation energy of the oxygen vacancies is more than 2 eV in high-germania glasses. Thus, it becomes evident that the precursors of the bismuth active centers are formed before the fiber is heat treated. From the analysis of the published results on high germanate glasses, it follows that the most likely process with an activation energy of 1.1–1.2 eV occurring in such materials is the diffusion process of oxygen vacancies [21,22]. It should be noted that similar processes take place in bismuth silicate glasses [23] with the similar values of activation energy, which may vary slightly (towards low energies). In particular, in [24], a value of 0.8 eV was obtained when temperature measurements were made in the range 400–500 $^{\circ }$C. It is worth noting that the pre-exponential factor $k_{0}$ for the reaction of the transformation from the PACs to the BACs is $\approx$ 10$^{4}$ ${s}^{-1}$ which is substantially lower than that expected for a pure dissociation mechanism (10$^{9}$– 10$^{12}$ ${s}^{-1}$). It favors a process involving long-distance defect migration with subsequent trapping [24]. The findings in this study strongly support a single diffusion driven reaction, where BACs are formed as complexes of oxygen vacancies and immobile impurities, namely, Bi ions.
It is interesting to compare the data obtained for the formation of new BACs and their restoration after photobleaching, which takes place in a Bi-doped high-germania fiber when visible laser radiation is launched into its core. For this purpose, we conducted a series of experiments on the thermal treatment of bleached bismuth-doped fibers in a way similar to that for the original (pristine) bismuth-doped fibers. As it was mentioned above, the bleaching process of the examined fibers was initiated by exposition to radiation of a laser operating at 532 nm with an intensity of $\sim$ 1 MW/cm$^{2}$ during 0.5 h. The process of the BACs restoration is activated at the lower temperatures than that of new BACs formation, and therefore the thermal treatment of the bleached fibers was performed at 373, 473, 573 and 673 K. This allowed us to separate the process of recovery of the bleached BACs and the above-described process of formation of new BACs because the rate of the later one significantly decreased at these temperatures. The obtained dependence of the normalized precursor concentration for the bleached centers on demarcation energy is presented in Fig. 3.
Fig. 3. Normalized concentration of the precursors for bleached BACs versus the demarcation energy $E_{d}$. (dashed line - fitting curve; symbols - experimental data). The rate factor $k_{0}$ in this case is between ${10}^{0}$ and ${10}^{1}$ s$^{-1}$. Inset: Calculated activation energy distribution function $g(E)$.
It is seen that characteristic energy values are noticeably lower than those of the heat-induced BACs formation process. All data (for different temperatures) also can be fitted by a parameterized function named demarcation energy curve (Eq. (2)). The fitting parameters of $E_{0}$ and $T_{0}$ were 0.44 eV and 900 K, respectively. The calculated distribution function $g(E)$ is shown in Fig. 3(inset). It has a maximum peaked at 0.44 eV and an FWHM of 0.27 eV. One can see that the $g(0)$ in Fig. 3 is different from zero. It is explained either by an inaccuracy of approximation of the experimental data or the presence of a spontaneous recovery process. It is worth noting that the spontaneous recovery process has been found in Bi/Er aluminosilicate fibers after photobleaching [6]. However, our previous results regarding this type of fibers showed that the intensity of this process is negligible at room temperature [11]. Thus, from a comparative analysis of the experimental data for the two observed processes producing the BACs, it can be concluded that these processes have different nature. The low activation energy of 0.44 eV of the restoration process of the BACs probably points to the phenomena related to an electron trap adjacent to the precursor of the BAC being the product of the photobleaching.
We measured the temporal dependences of the unsaturable loss (assigned to Bi-centers) increment during isothermal annealing at various temperatures. Using the same approach as previously, the activation energy distribution function was derived from the obtained results (Fig. 4). In this case, the pre-exponential factor was ${10}^{8}$ s$^{ -1 }$. For the sake of comparison, the activation energy distribution functions for other processes under study are also presented in Fig. 4. It turned out that the activation energy of formation of the Bi-centers is more than 2 eV that is higher than the energies of new BACs formation and the restoration of the BACs bleached by laser radiation. It points out that the precursors for the considered types of centers are different. Taking into account all obtained data it should be noted that activation energies of the formation of the BACs from both considered precursors are noticeably lower than the bond dissociation energy of Bi-O molecule which is $\approx$3.5 eV. It gives a reason to believe that the mechanism of the BACs formation is caused by a physico-chemical reaction resulting in any rearrangement in the environment surrounding a bismuth ion, but not in the breaking of the Bi-O bond. It could be initiated by a chemical process of oxygen vacancy formation, and long-distance defect migration, which takes place in germanate glasses at temperatures 400-600 $^{\circ }$C [24]. Unlike the BAC formation process, it is reasonable to assume that the growth of the Bi-centers responsible for unsaturable loss is due to the reduction of Bi ions because in this case, chemical reactions initiate at higher energies. Nevertheless, a more detailed investigation of the reaction mechanisms, perhaps in combination with a microscopic model of the processes, is beyond the scope of this paper.
Fig. 4. Calculated activation energy distribution $g(E)$ for the studied processes (dashed lines). Experimental data with regard to the unsaturable loss are shown with stars.
4. Conclusion
In summary, using the demarcation energy concept based on the distribution of activation energies of a first-order physico-chemical reaction, the processes of the restoration and formation of the BACs have been studied. Analyis of the thermal kinetics of these processes showed that their activation energies are noticeably different that probably points to the diverse nature of the precursors. Thermal restoration of the BACs bleached by laser irradiation in Bi-doped high-germania glass core fibers is activated at energy of around 0.4 eV. The formation energies of new BACs and Bi-centers responsible for the unsaturable losses after heat treatment are around 1.1 eV and higher than 2 eV, respectively. Taking into account that the pre-exponential factor $k_{0}$, determined with the assumption of a first-order reaction, is several orders of magnitude lower than that expected for a pure dissociation mechanism, one can conclude that diffusion-assisted reaction processes, in particular, migration of an oxygen vacancy in the glass host, are possible mechanisms of the formation of additional BACs. Besides, the obtained data regarding the restoration of the bleached BACs and formation of Bi-centers are consistent with the fact that these processes are possibly a result of electron de-trapping and chemical reduction process, correspondingly. The results presented are of particular importance understanding photo- and thermo-induced processes which could impact long-term stability of these fibers.
Funding
Russian Science Foundation (19-72-10003).
Acknowledgments
The authors are grateful to Dr. S.A. Vasiliev for valuable advice and fruitful discussions and sincere interest in the topic of the research.
Disclosures
The authors declare no conflicts of interest.
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