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Abstract
The formations of different types of laser-induced periodic surface structures (LIPSS) on the surface of GaP crystals with different laser fluence are researched in experiments. The transition from the high spatial frequency LIPSS (HSFL) to the low spatial frequency LIPSS (LSFL) occurred as the number of the irradiated laser pulse increased. The finite difference time domain method combined with the holographic ablation model is used to simulate the LIPSS formation under the irradiation of multiple pulses. Different types of ripples are predicted by the electromagnetic approach. Results demonstrate that the electromagnetic origins of HSFL and LSFL are due to the interference of incident field and the scattering field under the multi-pulse irradiation.
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1. Introduction
Laser-induced periodic surface structures (LIPSS) are commonly observed on almost all types of solid materials (e.g., semiconductor, dielectric, and metal) [1–10]. According to its period, LIPSS can be divided into high spatial frequency LIPSS (HSFLs, Λ<0.5λ) and low spatial frequency LIPSS (LSFLs, 0.5λ<Λ<λ) [11]. Femtosecond LIPSS has become a universal technique for fabricating functional structures, such as large-area nanograting, colored structure, super-hydrophobicity surface, and optical data storage, because of its potential and flexibility [12–21].
The formation mechanism of LIPSS is an interesting topic. The surface plasmon polariton model considers that the formation of LSFL is due to the modulated energy distribution caused by the interference of the incident laser and the surface plasmon [22–25]. Many other models, such as Sipe’s theory [26] and Coulomb explosion [27], have also been developed to explain ripple formation. However, at present, we do not have a very clear scenario of the physical mechanisms of LIPSS.
The formation of LIPSS is very complex; although the ablation and recombination of the material occurs after electron–phonon relaxation, the spatial characteristics of the final structure have been determined by the extremely short process of laser irradiation [28]. The orientation and periodicity of LIPSS are mainly determined by the laser wavelength and direction of polarization, thereby suggesting that the early stage of the structure formation can be explained by electromagnetic methods. Sipe et al. established efficiency theory by simulating the influence of surface roughness on electromagnetic field 30 years ago; this theory has been widely recognized for its good explanation of LSFLs caused by the uneven energy absorption due to the interference between surface scattered light and incident light [26]. The effect of structural transition has not been fully explored in complex surface morphology. Skolski et al. conducted finite-difference time-domain (FDTD) simulation with an inter-pulse feedback mechanism. the results of the FDTD feedback simulations are compared to observations of LIPSS reported. The simulated results show that the formation of HSFLs and LSFLs can be understood in the frame of an electromagnetic theory [29]. Zhang et al. demonstrated that the FDTD method can be used to study the formation of LIPSS under oblique incidence and arbitrary polarization states. The results show a good agreement with that by the analytical efficacy theory [30]. Florian et al. performed FDTD calculations for a multi-layer system. The simulation result supports that the LSFL with an orientation parallel to the laser polarization is formed at the interface between the laser-induced oxide layer and the substrate [31].
In this paper, we have researched the evolution of LIPSS on the GaP surface with an increasing number of pulses per spot under different laser fluence. The different phenomenon, including the transition from the HSFLs to LSFLs, and the formations of HSFLs and LSFLs are observed on the GaP surface after multi-pulse 800 nm femtosecond laser irradiation. The FDTD is used to simulate the LIPSS formation on the GaP crystal. In addition, the feedback mechanism of LIPSS formation is analyzed by holographic ablation method (HAM). The interaction of electromagnetic waves with rough surfaces and a non-physical ablation threshold is included in the inter-pulse feedback mechanism. The simulation results present the formation of HSFL and LSFL, including the transition from HSFL to LSFL. The good agreement between the experimental and the simulation results demonstrates the origin of LIPSS from the perspective of electromagnetism. Moreover, the enhanced near-field scattering of the laser light was separated from the scattered field. The results demonstrated that the HSFL and LSFL were formed because of the electromagnetic mechanism of local field enhancement and the field interference under multi-pulse irradiation.
2. Experimental
The experimental setup is shown in Fig. 1. The laser source is a Ti-doped sapphire regenerative amplified femtosecond laser with an output pulse width of 50 fs, a central wavelength of 800 nm, and a repetition rate of 1 kHz (Legend Elite, Coherent). In the experiment, A half-wave plate and a Glan polarizer were used to change the laser fluence continuously. A mechanical shutter is used to control the exposure time. Subsequently, the laser beam is focused through a 600 mm lens and incident onto the surface of the GaP crystal. All irradiations were performed in air environment under normal incidence. The sample was mounted on a 3D translation stage controlled by a computer. The sample was stationary during an irradiation. After, the sample was moved by the 3D stage. Every irradiation exposed on a fresh region. After exposure, the sample was cleaned by an ultrasonic cleaner, and the surface morphology was characterized by scanning electron microscopy (SEM).
A single laser pulse will cause an ablation happened on material surface when laser fluence exceed a certain threshold value Fth. This single pulse ablation threshold Fth can be determined from the laser-generated surface modifications processed with different laser fluence. When laser pulse is a Gaussian spatial beam profile, the laser fluence F on the sample surface and the ablation area are related by [32,33]
where S is the crater area, and D is the diameter of laser beam on the surface of sample. The laser fluence F can be obtained from [15,34] where Ep is the single pulse energy. The peak pulse intensity can be calculated by [35] where τp is the width of the laser pulse.3. Results and discussion
3.1 Experimental results
In order to estimate the beam diameter, a graph depicting the squared diameter D2 as a function of the logarithm of the pulse energy Ep is used due to the linear relation between Ep and F. The areas of ablation craters by single laser pulse with different fluence are measured by an optical microscope. According to Eq. (1), the slope of a linear fit yields the Gaussian beam diameter D. A value of D = 50 µm is obtained. With the known beam diameter, the laser fluence F in front of the surface can be calculated from Eq. (2). The graph of the squared diameter D2 of the ablation area versus the laser fluence F is shown in Fig. S1 of Supplement 1. The modification threshold fluence Fth can be obtained by extrapolation of the fits to S = 0 and the value is approximately 1.7 J/cm2.
Figure 2 shows the morphology changes on the GaP surface after the irradiation with the laser fluence of 0.38 J/cm2. First, the ripples are formed on the surface and perpendicular to the laser polarization direction after 600 pulses (Fig. 2(a)). The number of irradiation laser pulses is large because the laser fluence is much smaller than the ablation threshold. When the pulse number is increased to 1000, these ripples are more regular and smoother in the central region of the irradiation area in Fig. 2(b). As the pulse number continues to increase, the HSFLs almost show no changes, and some molten materials begin to appear on the surface in Figs. 2(c)–(d). We measured the width of ten ripples at one point in the center of irradiation area, and calculated the average value as the ripple period at this point. By this method, we measured the periods at 5 points, and took an average as the ripple period. A graph depicting the ripple period as a function of the pulse number is shown in the Fig.S2 of the Supplement 1. The increase of the period of HSFL was observed from 147 nm to 183 nm when the pulse number increases from 600 to 10000.
Fig. 2. SEM images of the surface irradiated by different numbers of laser pulses with laser fluence of 0.38 J/cm2
The change in the surface morphology with laser fluence of 0.9 J/cm2 is shown in Fig. 3. After six pulses of irradiation, randomly distributed short nanoripples appeared on the surface (Fig. 3(a)). The period of the HSFLs reached approximately 183 nm. With 13 pulses, the HSFLs are distributed on the irradiation area, and some LSFLs appeared on the center area. LSFLs began to form on the surface, and the direction is perpendicular to that of laser polarization, The period of the LSFLs is about 650 nm. At this time, the coexistence of LSFLs and HSFLs can be observed (Fig. 3(b)). HSFLs appeared in the region, not completely covered by LSFLs and the periphery of the irradiation area, and showed irregular periodicity. Notably, LSFLs at this time mainly appear in the central region of the irradiation area. With the increase in pulse number, LSFLs became the dominant feature of the surface, but HSFLs still existed on some ridges of LSFLs and did not disappear completely (Fig. 3(d)). The ripple period dependence on pulse number was investigated as shown in Fig. S3 of Supplement 1. The period of HSFL was increased from 183 nm to 230 nm when the pulse number increases from 6 to 16, and the period of LSFL was increased from 650 nm to 730 nm when the pulse number increases from 13 to 40.
Fig. 3. SEM images of the surface irradiated by different numbers of laser pulses with laser fluence of 0.9 J/cm2
Figure 4 shows the evolution of surface morphology at a laser fluence of 1.5 J/cm2. In this case, no ripples can be observed on the surface after the single pulse irradiation (Fig. 4(a)). LSFLs occupied the surface of the material after 4 pulses of laser irradiation (Fig. 4(b)), and the period is approximately 702 nm. After 8 pulses, uniform LSFLs are formed in the center of the ablated area, and HSFL with a period of 167 nm appeared at the periphery area in Fig. 4(c). The reason is that the laser fluence is lower in the edge region far from the ablation center. In the subsequent several pulses, LSFL exhibited no obvious changes in particular (Fig. 4(d)). The relationship of the ripple period dependence on pulse number is shown in Fig. S4 of Supplement 1. The period of LSFL was increased from 702 nm to 740 nm when the pulse number increases from 4 to 20. We also investigated the formation of LSFLs with the irradiation of 10 laser pulses under different laser fluence. The graph depicting the dependence of the LSFL period on the laser fluence is shown in Fig. S5 of Supplement 1. The ripple period grows almost linearly from 700 nm to 778 nm with the increasing laser fluence from 1.35 J/cm2 to 1.95 J/cm2. The linear-increasing trend agrees well with the result in literature [36].
Fig. 4. SEM images of the surface irradiated by different numbers of laser pulses with laser fluence of 1.5 J/cm2.
3.2 FDTD-HAM
Yee, who has the ability to solve Maxwell’s equations numerically, proposed the FDTD method in 1966 [37]. Maxwell’s equations were solved with a set of finite difference equations by FDTD method. It also allows the calculation of electromagnetic fields near micro-nano structures in time and space. Maxwell’s equation is the basis for describing LIPSS electromagnetic origin. To obtain the uneven electric field distribution and energy deposition on the rough surface of the material, we solved the three-dimensional nonlinear Maxwell equation based on FDTD algorithm [30,38]:
where H and E are the magnetic and electric fields, respectively; and D is the electric displacement field. In the simulation, we adopted the spatial step of 5 nm and the time step of 0.037 fs, which satisfied Courant’s condition, thereby ensuring the stability of Yee’s algorithm. µ0 is the vacuum permeability. The electric displacement field can be expressed as follows: where ε0 is the dielectric constant of the vacuum, ω is the angular frequency of light, and εr(ω) is the dielectric function of the crystal. εr(ω) is related to the optical properties of the material and the frequency of the incident laser. Here, we use Drude model to describe the optical properties of the excited GaP, which are expressed by the following formula: where ε(ω) is the dielectric function that changes simultaneously with the angular frequency ω. Under the laser wavelength of 800 nm, νc is the plasma collision frequency, and mopt =0.15 is the optical mass of the carriers. ε=10.2 is the dielectric constant of non-excited GaP crystal. ωp is the plasma frequency; and Nc is the carrier density, which is an important parameter that determines the optical properties of the material.The finite difference time domain holographic ablation model (FDTD-HAM) was used for multi-pulse feedback simulation [29,39]. In this method, the surface is updated by “ablation” after each laser pulse irradiation based on the absorbed energy distribution to account for the inter-pulse feedback mechanism. FDTD-HAM method can be used to simulate the changes in surface morphology after multi-laser pulse irradiations and to explain the electromagnetic origin of LIPSS theoretically. Figure 5 shows the pulse–pulse feedback diagram of the FDTD-HAM simulation. The simulation boundaries are taken as a perfect boundary condition (PBC) boundary in the x and y directions and a perfect boundary condition (PML) boundary in the z direction. A plane wave of 800 nm incidents on the sample surface perpendicularly.
The electric field distribution E(x,y,z) on the sample surface were obtained using FDTD method. The energy distribution A(x,y,z) absorbed by the material was decided by the following equation,
where ε” is the imaginary part of the dielectric constant and can be obtained from Eq. (7) [40]. After calculating the distribution of energy absorbed by the material, the ablation threshold will form an iso-surface A(x,y,z) = Aab in the material, which is indicated as the dash line in Fig. 5(a). The material will be removed when the absorbed energy exceeds the ablation threshold. By removing the part above the iso-surface, the iso-surface becomes a new surface (Fig. 5(b)). The ablation threshold of the material can be determined experimentally, however, which was not suitable for use in FDTD-HAM because the feedback between pulses is only qualitatively included in the FDTD calculation. In a FDTD simulation, the optical parameters, such as the carrier density keep constant during one FDTD-HAM simulation. The dynamics of the carrier, the electron and lattice temperature were not included [29]. Therefore, the ablation threshold obtained in experiment cannot be used in the FDTD-HAM simulation. Different values were selected as ablation threshold for simulation. When the depth of ablation crater simulated by FDTD-HAM method was equal to that of ablation crater obtained in the experiment with the same condition, the parameter was chosen as ablation threshold. Using this method, the ablation threshold was determined to be 0.8 TW/cm3 in simulation. The ablation threshold kept constant in subsequent simulations of different laser fluence to simplify the simulation.3.3 Electric field enhancement
Figure 6 shows the electric field distribution simulated by FDTD when the light incident on the surface with a nanovoid and the radius is 50 nm. The electric field is enhanced along the laser polarization direction when the laser intensity is low, and the material is in the unexcited state (Fig. 6(a)). In contrast, when the material is in the excited state and the dielectric constant is −4.98 + 1.26i, the material exhibits metallic properties. The electric field is enhanced perpendicular to the laser polarization direction (Fig. 6(b)). The energy deposition of the electric field enhancement leads to the removal of material, thereby causing the nanovoid on the surface to grow perpendicular to the laser polarization direction. Nanogroove is formed perpendicular to the direction of laser polarization [22]. We believe that this strong local near-field enhancement is an important reason for the formation of LIPSS. Figure 6(c) shows the intensity distribution around two nanovoids. The interference of the electric fields results in the periodic modulation with laser wavelength periodicity perpendicular to the laser polarization direction. If the distance of the two scattering centers changes, then the coherent superposition of the electric fields is formed with the subwavelength periodicity between the scattering centers (Fig. 6(d)).
Fig. 6. (a) and (b) show the FDTD simulated distribution of energy absorption in a plane with a hemispherical nanovoid, whereas (c) and (d) shows the distribution with two nanovoids separated by 100 nm and 2000nm, respectively. The nanovoid has the radius of 50 nm.
3.4 Simulation of LIPSS formation
To investigate the physics origin of different LIPSS types after the irradiation with different laser fluences, FDTD-HAM multi-pulse feedback simulation was conducted. Figures 7–9 show the evolutions of surface morphology under different laser fluence. A plane wave was used in the simulation, and the size of the square area is 10×10 µm2. Meanwhile, nanovoids with diameter of 80 nm were randomly distributed on the initial surface to indicate the roughness of the surface. The concentration of the inhomogeneities at the surface is defined as C = N πr2/S, where N, r is the number and the radius of the inhomogeneities, respectively; and S is the square area [10]. In this simulation, the concentration of nanovoids is 0.4. The carrier density was calculated by solving Boltzmann’s transport equation [22]. Then, the optical properties of the material used in the simulation can be obtained according to the Eqs. (7) and (8).
Fig. 7. Formation of HSFL simulated by FDTD-HAM method and their Fourier transform spectrum images with laser fluence of 0.38 J/cm2. The black arrow in (a) shows polarization direction. The colorbar in (a)–(d) and (e)–(h) indicate the depth Z(nm) and normalized amplitude respectively.
Fig. 8. Transition from HSFL to LSFL simulated by FDTD-HAM numerical method and their Fourier transform spectrum images with laser fluence of 0.9 J/cm2. The black arrow in (a) shows polarization direction. The colorbar in (a)–(d) and (e)–(h) indicate the depth Z(nm) and normalized amplitude respectively.
Fig. 9. Formation of LSFL simulated by FDTD-HAM numerical method and their Fourier transform spectrum images under laser fluence of 1.5 J/cm2. The black arrow in (a) shows polarization direction. The colorbar in (a)–(d) and (e)–(h) indicate the depth Z(nm) and normalized amplitude respectively.
Figures 7(a)–(d) show the formation of HSFL simulated with the irradiation of the increasing number of laser pulses, and their Fourier transform amplitudes are shown in Figs. 7(e)–(h). The carrier density is approximately 3.1×1027/m3 with laser fluence of 0.38 J/cm2 when the laser pulse irradiates on the surface. The dielectric constant is −1.57 + 1i according to Eq. (7), that is, the surface exhibits a metallic behavior. Random distribution of the nanovoids on the surface works as scattering centers when laser pulse irradiates on the sample. The electric field is enhanced and cause the nanovoids to gradually grow in the direction perpendicular to the laser polarization. After the second pulse irradiation, the formation of irregular nanoripples can be seen on the crystal (Fig. 7(a)). After five laser pulse irradiations, the nanovoids continue to grow and lengthen (Fig. 7(b)). With the increasing number of irradiation laser pulses, the nanovoids continue to grow (Figs. 7(c) and (d)). The trend clearly shows that the strength of type-r feature (HSFL) is enhanced as the number of laser pulse increases. However, the nanoripples are irregular as shown by the FDTD-HAM simulation, which is a certain difference with the experimental results; some studies have shown that the formation of HSFL is very sensitive to the initial surface roughness [14]. In addition, the nanovoids are inhomogeneously distributed on the surface, thereby resulting in several blank areas. A total of 15 laser pulses are not enough to make HSFL cover the surface completely, which is also the reason why the central low-frequency region in the Fourier transform spectrum has a high amplitude. The trend can be concluded in Fig. 7, the gradually growing HSFL can cover the whole surface with more laser pulse irradiations, and these subsequent pulses make HSFLs deeper, thereby resulting in a high breadth depth ratio (Fig. 7(d)). Through the simulation above, it can be concluded that the formation of HSFLs from random rough surfaces is the result of electric field enhancement [19,40].
In order to investigate the effect of the nanovoid size, the simulations have been conducted with the nanovoid diameter D = 40 and 150 nm at the concentration of 0.4. The simulation results are shown in Fig. S6 of Supplement 1. Comparing the Fourier transform spectrum Fig. S6(i)-(l) with (m)-(p) of Supplement 1, the intensity under condition of D = 150 nm is more concentrated towards the center, which indicates the period of HSFL is larger than that of D = 40 nm. Zhang et al. also reported a similar phenomenon that the period of LIPSS would produce a “blue shift” with the decrease of particle size. This is because larger particles tend to scatter electric field energy to the far field, while smaller particles have more obvious enhancement effect in the near field [39]. Therefore, it can be inferred that the relative intensity of electric fields in the near and far field regions is also related to the size of nanovoid on the initial surface, and affects the formation of LIPSS through feedback mechanism.
On the other hand, Fig. S7 of Supplement 1show the effect of different nanovoid densities on the formation of HSFLs. When the inhomogeneity concentration is 0.1, The reduction of scattering center leads to the few HSFLs formed on the surface. It can still be seen from the Fourier transform spectrum that HSFLs has a rather strong amplitude in a wide range. Comparatively, in the case of the inhomogeneity concentration C = 0.6, the intensity is more concentrated on the Fourier spectrum, and HSFLs are more regular. By comparing Fig. S7(p) of Supplement 1 with Fig. 7(h), the peak Fourier transform spectrum is more concentrated. Therefore, we supposed that the concentration of the inhomogeneity has a great effect on the regularity rather than the period of HSFL.
Figure 8 shows the transition from HSFL to LSFL simulated by FDTD-HAM. The carrier concentration is 3.23×1027/m3 with the laser fluence of 0.9 J/cm2, and the dielectric constant is approximately −2.07 + 1.04i. With the increase in pulse number, the change in the surface morphology shows the transition process from HSFL to LSFL. After 8 pulses, the two types of LIPSS co-exist on the surface. The frequency domain shows that the period of HSFLs here is basically the same as that of HSFLs formed under the laser energy fluence of 0.38 J/cm2. In this case, the enhanced ablation effect caused by the increase in laser fluence result in the ablation of the shallow HSFLs, thus presenting deeper surface structures. In the frequency domain, the characteristics of type-r are obviously weakened compared with those in Fig. 7, but not completely disappeared. Because of the weakening of the near-field enhancement effect, the subwavelength periodic energy distribution caused by the coherent superposition of multiple scattered waves emitted from the scattering center gradually dominates at this depth. In addition, the type-r features do not continue to weaken with the increase in the number of pulses nor disappear, which means that HSFLs cannot be completely removed by the ablation effect of pulses under this fluence.
When the laser pulse with fluence of 1.5 J/cm2 irradiates the GaP surface, the carrier density increases to 3.35 ×1027/m3 rapidly. The dielectric constant of the excited crystal is approximately −2.07 + 1.04i, and the surface of the GaP crystal has metallic properties. The ablation effect of single laser pulse becomes more obvious. In Fig. 9, the type-s feature can be recognized after four pulses are applied, as the pulse number continues to increase. Eventually, after the eighth pulse, relatively smooth LSFLs are formed on the surface. Fourier spectrum also shows that the feature of type-r significantly weakened and gradually disappeared after the fourth pulse, which makes us believe that the ablation caused by single pulse is deeper than the surface area and the near-surface area where HSFL exists. The dominant role of the energy distribution driven by surface roughness is no longer obvious in the sub-surface area. The most typical phenomenon is that the intensity distribution of Fourier spectrum rapidly shrinks to |kx/k0|≈1 with the increase in pulse number, which means that the disappearance of HSFLs that correspond to the high-frequency components. Thus, LSFLs appear more smooth with a period little less than the laser. This periodicity is mainly determined by the interference between the scattered far-field and the incident field, which will be discussed in the later section.
3.5 Components of the electric field
The formation of LIPSS is due to the periodic energy modulation caused by coherent superposition between the incident field and the scattered field. To study the interference between scattered waves and incident waves in the far field, the electric field intensity can be decomposed into three different components,
where It is the total electric field intensity; Ir, Is, and Ii are the incident field, scattering field, and interference field, respectively [22]. Figures 10(a) and (c) show the intensity distribution of the interference field and the total electric field caused by a single nanovoid, respectively. Their good consistency in periodicity indicates the decisive role of periodic energy modulation caused by the interference of incident field and scattering field. Figures 10(b) and (d) show the Fourier spectrum of the interference field and scattering field, which further supports the conclusion that it is not scattering field itself that causes the periodic modulation of energy intensity but the interference of incident field and scattering field that plays a major role. At the same time, as mentioned before, the energy distribution caused by such interference is different from the actuating range of the near-field local enhancement of the scattering center, and the resulting periodic energy modulation inside the material surface can be considered one of the important reasons for the formation of LSFLs. However, Gedvilas et al. have reported that ripples do not depend on the laser polarization, but on the beam scanning speed and scanning direction [41,42]. This type of ripples is formed under intensive laser irradiation. The metal absorbs a large amount of laser energy after the laser irradiation, the temperature rises rapidly and the material are superheated and become fluid or even gasified. The eruption material takes most of the periodically distributed energy. The ripples formation is no longer the periodic energy deposition caused by the interaction between scattered light and the incident field, and more consideration should be given to residual thermal effects, surface tension and other hydrodynamic effects [43,44].Fig. 10. Interference electric field intensity (a) and total field intensity (c) caused by a single nanoparticle with the size of 100×100×100 nm3. (b) and (d) shows the Fourier spectrum of interference field and scattering field, respectively. The black arrow in (a) shows polarization direction and the colorbar indicate the normalized amplitude.
4. Conclusion
In this paper, GaP crystals are irradiated by femtosecond laser pulses at 800 nm, and the electromagnetic origin of LIPSS formation and evolution perpendicular to laser polarization direction on GaP crystal surface is studied by FDTD numerical simulation. Experimental results show that different types of LIPSS are formed with different laser fluence. In general, the incident light and scattered light interference and periodic modulation, as well as the near field local enhancement, led to the periodic energy deposition. In addition, the feedback mechanism of LIPSS formation is analyzed by HAM. The formation of different types LIPSS, including the transition from the HSFL to the LSFL, are simulated by the FDTD-HAM method. The good agreement between the experimental and the simulation results demonstrates the origin of LIPSS is related to the near-field enhancement from the perspective of electromagnetism. Moreover, the enhanced near-field scattering of the laser light is separated from the scattered field. The results demonstrated that the HSFL and LSFL were formed because of the electromagnetic mechanism of local field enhancement and the field interference under multi-pulse irradiation.
Funding
National Natural Science Foundation of China (11804227).
Acknowledgments
The authors would like the Shanghai Institute of Technology for their financial support.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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