The role of the dopant in the electronic structure of erbium-doped TiO₂ for quantum emitters

The relentless growth in data storage and the continuous trend of device miniaturization has driven technological progress to approach the quantum limit.^1,2 Quantum information science (QIS), grounded in the principles of quantum mechanics, emerges as a groundbreaking solution for efficient data handling, secure information exchange, and long-distance communication while ensuring data integrity.^3,4 At the heart of quantum technologies lies the manipulation of qubits, the fundamental units of quantum information.^4,5 Quantum coherence plays a crucial role in realizing quantum technologies,⁶ which enables qubits to maintain the superposition of quantum states. However, the challenge lies in preserving coherence, which is limited by the inherent susceptibility to environmental influences. Therefore, ensuring the prolonged persistence of quantum states in superposition (i.e., long coherence time) is essential for successfully implementing quantum information technologies.^5,6

Solid-state spin qubits show significant promise among the candidates for QIS applications, owing to their compatibility with conventional microelectronics.^5,6 Nevertheless, the properties of solid-state spin qubits are linked to their crystal host, necessitating material engineering to enhance the quantum emitter’s properties and mitigate decoherence sources such as charge carriers or phonons. Among potential candidates, rare-earth ions (REIs) in solid-state systems stand out.⁷ In particular, the trivalent erbium ion (Er³⁺) is noteworthy for its optical 4f–4f transition within telecom-C band, aligning with the low-loss transmission in optical fibers, making it an ideal quantum emitter for quantum network systems.^8–13 Selecting the optimal crystal host for REIs in QIS involves considering factors such as low nuclear and electron spin concentrations, nonpolar symmetry, and a large bandgap.^6,13,14 These factors are instrumental in not only enhancing optical transitions but also in mitigating local effects in the vicinity of REIs, thereby addressing coherence issues effectively. Previous studies identified TiO₂ as a promising host for Er₃₊, with the rutile and anatase phases being particularly stable.^15,16 Recent research on Er-doped TiO₂ films and bulk crystals has demonstrated narrow optical inhomogeneous linewidths, underscoring the importance of buffer and capping layers in enhancing optical properties.^15,17 Despite these advancements, further understanding is needed on how Er³⁺ dopants influence the TiO₂ host lattice’s electronic and crystal structure.

This investigation focuses on epitaxial erbium-doped rutile TiO₂ thin films grown on r-plane sapphire substrates, aiming to explore how erbium incorporation affects the material’s optical properties. We employed spectroscopy and diffraction techniques to correlate structural modifications with variations in excited state lifetimes. The selection of sapphire as the substrate was deliberate, as it enables the formation of high-quality single-crystal rutile TiO₂. X-ray diffraction (XRD) confirmed the persistence of single crystallinity despite doping. Variations on the Er³⁺ photoluminescence lifetimes, which set the upper bounds for optical coherence times, were assessed using photoluminescence excitation (PLE) spectroscopy revealing a downward trend with increasing doping. In addition, information on local coordination, lattice distortion, and chemical environment near erbium sites was probed using x-ray absorption spectroscopy (XAS) and extended x-ray absorption fine structure (EXAFS). The analyses indicate that doping increases oxygen vacancy defect density within TiO₂. Furthermore, they suggest that erbium ions are fully coordinated, indicating redistribution of oxygen vacancies away from the Er sites. This increase in additional defect density is likely to limit coherence by introducing alternative decay pathways upon Er³⁺ excitation.

Epitaxial Er:TiO₂ thin films with thicknesses of 65 nm were deposited using a Riber C21 DZ Cluster molecular beam epitaxy (MBE) system. Titanium tetraisopropoxide (TTIP) from Sigma-Aldrich with a purity of 99.999% (trace metal basis) was the titanium precursor as in the TTIP-based MBE of TiO₂ detailed elsewhere.¹⁸ Growths were carried out on an r-plane (102) sapphire substrate at 640 °C temperature, oxygen partial pressure of 7 × 10⁻⁶ Torr, and a TTIP beam-equivalent flux of 3.5 × 10⁻⁶. The growth rate was 32.5 nm per hour. In situ erbium (Er) doping (20, 200, and 500 ppm) using metallic Er was carried out by a high-temperature (860–990 °C) effusion cell.

Single crystal x-ray diffraction characterization was carried out at the 33BM beamline of the Advanced Photon Source (APS) at photon energy of 20 keV. PLE spectroscopy was performed in a custom confocal microscopy setup designed for telecom C-band measurement of thin films, with samples mounted in a cryostat at 3.5 K (s50 Cryostation, Montana Instruments). A tunable 1.5 μm laser illuminated the samples for 1.5 ms using pulses shaped by acousto-optic modulators. Emission from the samples subsequent to excitation was then collected by a Quantum Opus superconducting nanowire single photon detector (SNSPD) for 3 ms collection intervals. Sweeping the excitation laser wavelength resulted in a PLE spectrum and excited state lifetime measurements at each wavelength for each measured sample. Additional information on this experimental setup is given in detail elsewhere.¹² XAS measurements were conducted at O K-edge, Ti L-edge, and Er M₅-edges at the 29ID beamline at the Advanced Photon Source (APS). The beam was directed along surface normal, and the spectra were averaged over the acquired horizontal and vertical polarization to ensure orientation-independent assessment of the local environment. The EXAFS measurements were performed at the 20-BM beamline of the APS. Data collection was conducted in grazing incidence geometry, with an angle of incidence of a few degrees and with linear x-ray polarization in the plane of the film. The sample was rotated about the film surface normal to average in-plane polarizations. The temperature was maintained at 300 K throughout the entire experiment. Since the [101] direction is along the surface normal, separate FEFF8 simulations were carried out with linear polarization along orthogonal in-plane [−101] and [010] directions to obtain theoretical phase shifts and scattering amplitudes.¹⁹ 

Figure 1 shows the single crystal x-ray diffraction spectra, confirming the $(012)Al2O3$ direction normal to the r-plane surface through the specular (0, K, 2K) scan. The film shows a main peak of $(101)TiO2$ film orientation on the r-plane surface consistent with previous literature.^20,21 Positions of the peaks are roughly equivalent with the expected bulk values indicating that the films are relaxed. The lattice parameter approximates that of bulk TiO₂. As was noted in a previous work,²⁰ the matching of the symmetry between the $(012)Al2O3$ and $(101)TiO2$ planes leads to a twinned structure with alternating domains on 10’s of nm length scales. These domains likely lead to a relaxation to the bulk lattice values due to the high-density of domain walls. In addition, all films exhibit a minority (301) orientation, which may result from the high density of twin domains. No systematic behavior with doping was observed, suggesting that the minority (301) orientation is unrelated to doping.

The impact of increasing Er³⁺ dopant density on the rutile TiO₂ host lattice was investigated by optical characterization of the thin film samples performed via time-resolved PLE spectroscopy. Figure 2(a) shows the resulting absorption spectra near 1.5 μm resonance for the series of single crystal erbium-doped rutile TiO₂ films. The ground $(I15/24)$ and excited $(I13/24)$ electronic states of Er³⁺ in rutile fully split into eight (Z₁₋₈) and seven (Y₁₋₇) Kramers’ doublets, respectively [Fig. 2(b)],¹⁵ due to the D_2h point symmetry for Er³⁺ occupying Ti⁴⁺ sites in rutile TiO₂. The growing background toward lower wavelengths stems from the dopant-driven introduction of additional defects and disorder into the lattice, resulting in the available crystal field transitions broadening significantly.²² At high doping levels (such as the 500 ppm sample in this work), the inhomogeneous linewidths are broad enough that individual peaks become more difficult to resolve.

We focus our discussion on the peak highlighted by a vertical dashed line (∼1520 nm), which corresponds to the technologically prescient²² Er³⁺ Z₁ → Y₁ transition in rutile-phase TiO₂.¹⁵ The narrowest observed inhomogeneous linewidth in this set of thin films is ∼50 GHz, found in the sample doped with 20 ppm erbium. The inhomogeneous linewidth increases with higher dopant concentrations, with the broadening of the linewidth attributable to electric fields generated by charged defects near the Er³⁺ sites, including negatively charged point defects resulting from Er³⁺ substituting Ti⁴⁺ sites (i.e., the negative charge upon replacement of Ti⁴⁺ to Er³⁺) and positively charged oxygen vacancy point defects.^17,23–26

The lifetime of the excited state sets an upper limit for the coherence time, and shorter lifetimes may also be an indicator of lower quantum efficiency. Therefore, identifying dopant-driven variation in the excited state lifetime is critical in assessing the material’s quality as a host for quantum processes, given the intentional introduction of dopants, such as Er³⁺, as necessary to facilitate these processes. Understanding the nuances of local electronic and crystal structures is pivotal for comprehending the alterations in the inherent optical properties of Er-doped rutile TiO₂ with varying erbium concentrations.

The photoluminescence lifetimes at the highlighted peak (Table I) exhibit a dopant-driven decreasing trend. This shortening of lifetime is consistent with prior observations in CeO₂ with increasing erbium doping, where the decrease is attributed to the introduction of defects. While the exact nature of these defects remains uncertain, they likely introduce non-radiative or quenching pathways that shorten the photoluminescence lifetimes.²² If the defects were strictly localized to individual Er sites, their interaction would be limited and neither significant linewidth broadening nor a pronounced reduction in lifetime would be expected. However, the impact of these defects is significant, and is emphasized by the decrease in quantum efficiency with higher doping (also presented in Table I), estimated based on the longest observed excited state lifetime of Y₁ → Z₁ for Er-doped rutile TiO₂ in the literature, of 5.25 ± 0.03 ms.¹⁵ The increased linewidth and shorter photoluminescence lifetimes at higher dopant concentrations suggest that the defects surrounding the Er³⁺ sites are not confined to the immediate vicinity but instead form more extended distributions. These extended defects likely modify the local crystal field around the Er ions, thereby influencing the observed optical properties.

To further elucidate these modifications, we employed XAS to investigate erbium-induced changes in the local electronic structure within the crystal lattice. Starting with oxygen spectroscopy, the O K-edge spectra shown in Fig. 3(a) are a result of electronic transitions from O(1s) states to unoccupied O(2p) states. The spectra were acquired simultaneously in both total electron yield (TEY) mode, using the sample photocurrent method, and fluorescence yield (FY) mode, using an energy-discriminating silicon drift diode detector (Vortex) coupled with a multi-channel analyzer (MCA). The TEY and FY spectra are represented by the solid and dashed lines, respectively. The primary distinction between TEY and FY acquisition modes lies in their depth sensitivity, with TEY being more surface-sensitive and FY more bulk-sensitive. TiO₂ consists of a central Ti⁴⁺ ion surrounded by six O²⁻ ions arranged as a distorted TiO₆ octahedron due to the tetragonal symmetry of the crystal structure. This distortion causes the crystal field splitting of the Ti 3d orbitals into lower-energy t_2g states and higher-energy e_g states.^27–29 Geometrically, the e_g orbitals from Ti point toward the O 2p orbitals, while the t_2g lobes point between the O atoms leading to strong hybridization between O(2p) and Ti(3d) orbitals. The significant hybridization leads to two distinguishable pre-peaks at ∼530 and 533 eV labeled as t_2g and e_g, respectively. Moreover, three distinct features at higher energies, with peaks around 539, 542, and 545 eV, denoted as C, D, and E, respectively, correspond to delocalized O(2p)–Ti(4s) and O(2p)–Ti(3d) hybridized states and are a fingerprint of the rutile phase in TiO₂.³⁰ 

Two notable trends emerge from comparing the TEY and FY spectra. First, the intensity ratio of the t_2g and e_g pre-peaks varies with increasing erbium concentration in both TEY and FY spectra, suggesting that these variations are not confined to the surface and exist in the bulk of the film as well. Second, the FY spectra, which provide greater depth sensitivity than TEY, display broader peaks between 538 and 545 eV. This broadening is attributed to contributions from the sapphire substrate.³¹ Due to the strong hybridization between O(2p) and Ti(3d) orbitals, the t_2g and e_g pre-peaks in the O K-edge spectra are expected to be highly sensitive to changes in the electronic structure. Thus, the fitting analysis shown in Fig. 3(b) focused on the two pre-peaks in the TEY spectra to gain insights into the electronic structure of the host lattice. Gaussian functions were fitted to the spectra, revealing two distinct features labeled as A* and B*, adjacent to the main t_2g and e_g peaks, respectively. These adjacent features are ∼1 eV blueshifted from the main peaks and can be attributed to modifications in the electronic structure of the rutile lattice related to oxygen vacancies.³² 

Notably, the A* and B* features are present even in the undoped sample, indicating non-stoichiometric TiO₂. Their area increases with erbium doping, as presented in Table II. Native point defects, such as neutral or charged oxygen vacancies, are common in wide-bandgap metal oxides such as TiO₂.^33,34 The increase in A* and B* areas with doping suggests that erbium introduces new oxygen vacancies into the lattice. Each Er ion is expected to create only half an oxygen vacancy to balance the charge (i.e., one $Ov2+$ vacancy balances the charge of two Er³⁺ ions). Despite this, the substantial increase in A* and B* peak areas implies that defects around different Er sites likely overlap or interact. This overlap leads to significant changes in the XAS spectra, even at low Er concentrations, suggesting that the defects are likely not isolated but form a more extensive network within the material. Moreover, the erbium-driven increase in A* and B* areas is accompanied by a decrease in the t_2g and e_g peak areas, reflecting disruptions in the local electronic structure. The creation of new oxygen vacancies disrupts the strong hybridization between O(2p) and Ti(3d) orbitals, leading to reduced overlap and thus smaller t_2g and e_g peak areas.

Similar to the O K-edge, the Ti L–edge XAS spectra are sensitive to changes in electronic structure due to the hybridization of O(2p) and Ti(3d) orbitals. Therefore, the Ti L–edge was probed using TEY mode to investigate possible dopant-induced modifications in the electronic structure (Fig. 4). The fine structure in the L₃ and L₂ edges results from the breaking of degenerate electronic orbitals by the lattice crystal field, leading to the splitting of 3d states into threefold t_2g and twofold degenerate e_g states. Further distortion from the lattice environment introduces additional splitting, which is pronounced at the L₃-edge. The first two weak pre-edge peaks are attributed to the combined effects of particle–hole coupling and crystal field splitting. These features exhibit low intensity due to partial screening of the core hole by surrounding electrons, which is influenced by the localized electronic environment and transition metal oxidation state, as discussed in previous studies.^35,36 The intense, narrow peak around 458 eV corresponds to the t_2g state, while the e_g states split into two peaks due to the distortion in the TiO₆ octahedra. This distortion leads to an inversion of the relative intensities of the e_g peaks in the XAS spectra for different TiO₂ polymorphs. As a result, the relative intensity ratio of the e_g peaks serves as a distinct fingerprint for identifying TiO₂ polymorphs, and in this case, it is consistent with the rutile phase.²⁸ 

Expected consequences of doping include charge compensation through the formation of additional defects, such as oxygen vacancies and Ti³⁺, as well as distortions of the host lattice.^26,37,38 Prior investigations on Cr-doped rutile TiO₂ highlighted the critical role of oxygen point defects in stabilizing Cr³⁺ ions, particularly through the formation of complex defects involving two Cr atoms and one oxygen vacancy.³⁸ This stabilization is associated with distortions in the crystal lattice due to the elongation of Ti–O bonds, which affect the Ti e_g orbitals. These orbitals are highly sensitive to changes in the local environment because they interact directly with the 2p orbitals of the surrounding O atoms. As the local symmetry and crystal field around the Ti ions change, the energy levels of the e_g orbitals shift accordingly. In our study, the low concentration of Er³⁺ dopant—on the order of hundreds of parts per million (ppm)—makes it challenging to observe significant lattice distortions or prominent features associated with e_g orbital splitting or Ti³⁺-related signals. However, comparisons between undoped and doped samples reveal an overall decrease in spectral intensity with Er doping, suggesting that the dopant induces changes in the local electronic environment around the Ti ions. These changes may arise from slight distortions in the Ti–O coordination environment, which, in turn, alter the crystal field and electronic structure of the Ti sites.

To gain deeper insight into how the dopant affects the formation of additional defects within the host lattice, erbium spectroscopy was performed. The XAS spectrum at the Er M₅-edge (Fig. 5) exhibits three distinct peaks corresponding to 3d → 4f transitions. These transitions, characterized by changes in the total angular momentum quantum number (ΔJ = 0, ±1), are indicative of erbium in the trivalent state.³⁹ 

The local environment around the Er³⁺ sites was further examined using EXAFS at the Er L-edge and Ti K-edge, as shown in Fig. 6. A comparison of the experimental data with FEFF8 simulations is shown in Figs. 6(a) and 6(d), where the Fourier-transformed (FT) XAFS data for the Ti K-edge and Er L₃-edge, respectively, are represented by the solid lines.

These comparisons revealed significant differences, particularly in the FT Er L₃-edge spectra, where a marked shift toward higher distances in the first shell was observed, along with a notable suppression in the higher-R structure. These observations suggest alterations in the local structure around erbium, such as bond length variations or changes in coordination numbers at greater distances. The experimental data, acquired at 300 K, were scaled by a factor of 2 in these two plots to better match with simulations conducted at 0 K.

Figures 6(e) and 6(b) show FT XAFS data and fits for Er L₃-edge and Ti K-edge, respectively. Each polarization contribution was equally weighted (0.5) in the fits to account for in-plane polarization and sample spin, employed during the data acquisition to reduce Bragg peak artifacts in the experiment. The analysis involved simultaneous fitting of data weighted by different k-weights to minimize correlations between coordination number and the Debye–Waller factor (σ²). The small nominal split of 0.04 Å in first shell Ti/Er–O distances cannot be resolved with the limited k-range of the XAFS data (k_max ∼ 10 Å⁻¹) hence the fitted bond length correction was forced to be proportional to the nominal bond lengths. Similarly, coordination numbers of split distances were fitted while maintaining their ratio fixed to nominal values. The FT Er L₃-edge spectrum [Fig. 6(e)] revealed erbium coordinated to oxygen for the first shell (Er–O), with an expanded bond length of 2.20 Å (Table III). This distance is significantly larger than the corresponding Ti–O₍₁₎ bond length of 1.92 Å observed in the Ti K-edge analysis, indicating a local expansion in the lattice around the erbium dopant. In addition, the presence of Ti neighbors at a distance of 3.09 Å in the second shell suggests that Er³⁺ is occupying Ti⁴⁺ lattice sites and is consistent with previous ESR-based investigations on Er-doped rutile TiO₂¹⁵.

The significant local expansion observed around Er aligns with the difference in ionic radii between Er³⁺ and Ti⁴⁺. The theoretical difference in ionic radii is 0.29 Å (0.89–0.605 Å⁴⁰), which closely matches the experimental local expansion of 0.28 Å, as indicated by the difference between the Er–O₍₁₎ bond length (2.20 Å) and the Ti–O₍₁₎ bond length (1.92 Å) presented in Table III. This close agreement between theoretical and experimental values, combined with nominal (N = 2) Er–Ti coordination in the second shell at a bond distance of 3.09 Å, supports the hypothesis that Er³⁺ is substituting at Ti⁴⁺ sites, albeit with significant lattice distortion especially at higher order shells. Interestingly, the amplitude of Ti K-edge XAFS is somewhat reduced in the doped sample, despite the rather low doping level of 500 ppm, indicating that structural distortions around Er ions are extended, affecting a larger % of Ti ions. These results can also be correlated with the overall intensity decreasing in Ti L-edge XAS spectra with doping shown in Fig. 4, as erbium ions appear to cause lattice distortions. The Ti K-edge analysis [Fig. 6(b)] for the undoped sample (blue circles) yielded fitted distances closely resembling the nominal TiO₂ structure. Small differences were observed for the doped sample (red circles), although signatures of increased disorder are present particularly at the longer Ti–Ti correlations (Table III). The same amplitude reduction factor (⁠$S02$⁠) of 0.93 was used for both the Ti K-edge and Er L₃-edge fits to ensure consistency across the analyses.

The substitution of Ti⁴⁺ by Er³⁺ ions raises important questions about the mechanisms of charge compensation that stabilize the dopant within the host structure. The increased area of the A* and B* features in the O K-edge spectra, which are associated with oxygen vacancies, suggests that these vacancies play a key role in compensating for the charge imbalance introduced by Er³⁺ ions, thereby maintaining charge neutrality.^41,42 EXAFS analysis indicates that the first coordination shell of both Er³⁺ and Ti⁴⁺ remains fully occupied by oxygen, as reflected by coordination numbers close to 6 for both species. In particular, the coordination number of Er–O is 6.4 (3) (Table III), while the coordination number for Ti–O is 6.2 (3), supporting full occupation in the first shell. However, the error bars of around 5% in the coordination number allow for the presence of oxygen vacancies in the first Ti–O shell. Thus, while the first shell appears fully occupied within experimental uncertainty, the possibility of oxygen vacancies beyond the first Er–O shell in the lattice cannot be ruled out.

The σ² factors indicate increased disorder beyond the first shell, particularly around the Er³⁺ ions, with a value of 0.0140 (5) Ų for the Er–Ti₍₁₎ distance. In addition, major differences between the data and simulations in the higher shells [Fig. 6(d)] point to erbium-driven structural changes beyond the first coordination shell, which may include oxygen vacancies located farther from the Er³⁺ sites. We were unable to model the Er local structure beyond the Er–Ti₍₁₎ distance. The long-range distortions in the local environment around Er³⁺ ions, extending to at least 4 Å, suggest that these defects are not isolated but cause widespread changes in the lattice. Even at 500 ppm doping levels, these extensive distortions may overlap, affecting a significant amount of Ti atoms, as suggested by the Ti K- and L-edge probes.

Finally, revisiting the PLE discussion, the observed decrease in the photoluminescence lifetime of Er³⁺ can be attributed to the dopant-induced generation of oxygen vacancies. These point defects act as non-radiative recombination centers, enabling energy transfer between Er³⁺ ions and oxygen vacancy defects, which leads to a quenching effect. Consequently, the photoluminescence lifetime decreases due to enhanced non-radiative recombination pathways. Since the photoluminescence lifetime imposes an upper limit on coherence time in quantum systems, the observed reduction in photoluminescence lifetimes indicates a corresponding decrease in coherence times. Other potential sources of non-radiative quenching, such as domain-associated defects or crystal field distortions, may also contribute to this effect and require further investigation to fully elucidate their roles.

In conclusion, our investigation into epitaxial Er-doped rutile TiO₂ thin films reveals significant effects of erbium doping on both structural and electronic properties. XAS analysis at the O K-edge indicates that erbium doping leads to the formation of oxygen vacancies, which alter the electronic structure of the host lattice. EXAFS analysis for the Er L₃-edge spectra indicates that Er³⁺ ions substitute for Ti⁴⁺ ions in the TiO₂ lattice. This substitution results in notable lattice distortions due to the larger ionic radius of Er³⁺ compared to Ti⁴⁺. Coordination number analysis reveals consistent sixfold coordination around erbium, suggesting that neighboring oxygen ions stabilize the local charge environment. However, while our findings indicate significant distortions in higher-order shells, which may be associated with oxygen vacancies displaced from the first shell, further comparative studies are necessary to definitively determine the exact substitution sites. The broadening of the f–f excitation observed in PLE suggests a distribution of crystal fields, indicating structural disorder extending beyond the first coordination shell. This disorder impacts the crystal field sensed by the 4f electrons. The lattice distortions and additional point defects are expected to enhance non-radiative energy transfer, which correlates with the reduced photoluminescence lifetimes observed by PLE. This underscores the complex interplay between dopant-induced structural modifications and optical properties, emphasizing the importance of detailed local electronic and crystal structure investigations for advancing quantum information processing technologies.

This work was supported by Q-NEXT, a U.S. Department of Energy Office of Science National Quantum Information Science Research Centers under Award No. DE-FOA-0002253. The use of the Advanced Photon Source, Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.

The authors have no conflicts to disclose.

J. B. Martins: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). G. Grant: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). D. Haskel: Data curation (equal); Formal analysis (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). G. E. Sterbinsky: Data curation (equal); Investigation (supporting); Methodology (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). I. Masiulionis: Data curation (supporting); Validation (supporting); Visualization (supporting). K. E. Sautter: Conceptualization (equal); Investigation (supporting); Methodology (equal); Visualization (equal). E. Karapetrova: Data curation (equal); Methodology (equal). S. Guha: Funding acquisition (equal); Visualization (equal); Writing – review & editing (equal). J. W. Freeland: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within this article.