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In this work we have used in situ reflectance to study structural modifications in silica and quartz irradiated with swift heavy ions. Quantitative analysis of reflectance spectra allowed us to (i) obtain the detailed kinetics of surface modification and (ii) reconstruct the refractive index profiles created in the irradiated materials. We have shown that in situ reflectance yields very accurate results; for instance, track radii and irradiation threshold in silica and quartz obtained from our measurements are similar to those reported in the literature. In particular, reflectance has several advantages over Rutherford Backscattering in the channeling configuration (RBS-C) because it can be measured in situ (allowing recording of detailed kinetics not attainable by RBS-C), requires less sophisticated equipment and, more importantly, can be used with any material whereas RBS-C is restricted to mono-crystalline materials.
© 2016 Optical Society of America
1. Introduction
Irradiation is usually considered detrimental for materials because in many applications it leads to a degradation of physicochemical or mechanical properties [1–3]. However, irradiation effects can be exploited to modify properties of materials at will, improving their performance for certain applications. Examples exist in different fields covering a broad range of materials, methods and phenomena. Namely, semiconductor doping [4,5], waveguide fabrication [6–9], lithography [10,11], etc.
Regarding the ion-induced damage on dielectric materials, it can be produced either by elastic collisions between the incoming ions and the target atoms (i.e., the damage related to the nuclear stopping power, Sn) or initiated through the energy deposited on the electronic system by the incoming particles (i.e., the damage associated with the electronic stopping power, Se). Nuclear damage and amorphization has been extensively studied [12–17] and are reasonably well understood, whereas this is not the case for damage produced in the electronic stopping regime. However, it is becoming increasingly clear that, at least in the case of dielectric materials, the relaxation of the high electronic excitation associated with Se plays an important role in the appearance of damage and the subsequent amorphization induced by the ion-beams [18,19].
Ion irradiation of dielectrics with energies above 0.1 MeV/amu produces high electronic excitation densities, affecting a region (track) of nm dimensions around the ion trajectory usually resulting in permanent modification of the track properties [20–22]. Several models have been used to describe the electronic evolution, subsequent coupling to the lattice and track formation. This includes phenomenological models based on different (often contradictory) concepts [23–30], atomistic models [31–33] and, under development, sophisticated models based on quantum kinetic approaches, semi-classical MonteCarlo and hydrodynamic codes [34–36] (mainly originated in the field of fs laser). Despite the advances achieved in modeling, practical codes able to provide accurate quantitative predictions for practical applications do not exist yet. This makes especially attractive the use of in situ monitoring techniques for fine control of radiation-induced modification of properties.
In this paper we present a methodology based on in situ optical measurements to follow the modification of optical properties upon ion irradiation. We apply it to the modification of silica and quartz; by using both phases of SiO2 we expect to find out similarities and differences of irradiation damage in amorphous and crystalline dielectrics. In addition to the direct monitoring capabilities of the methodology, it provides detailed valuable information for a deep understanding of the refractive index variation as a function of ion fluence. This effect will be discussed from isolated track regime to full track overlapping.
2. Experimental
We carried out irradiation experiments with the 5 MV tandem accelerator in Centro de Micro-Análisis de Materiales (CMAM) [37]. Low OH content (below 10 ppm) silica samples provided by Momentive Ltd and crystalline quartz provided by Crystran were irradiated with Br (5, 10, 15, 25 and 40 MeV) and F (5 MeV) ions in the electronic stopping regime (2−8 keV/nm). Currents in the range 10-15 nA were used in all cases to avoid overheating of the samples.
An optical reflection setup was mounted in the irradiation chamber to perform in situ measurements. It is schematically described in Fig. 1. Two mirrors were used to measure nearly-normal reflectance spectra, which simplifies the ulterior analysis. Samples were illuminated with a halogen lamp and the reflected beam was collected and focused with a 25-mm-diameter, 4-cm-focal-length silica lens (not shown) into a silica optical fiber of 1 mm diameter, located outside of the vacuum chamber. The light was guided to a compact spectrometer, QE6500 (Ocean Optics Inc.), configured with a multichannel array detector for measuring simultaneously the whole spectrum in the range 400-1000 nm with a spectral resolution better than 2 nm. The reflectance spectra were recorded using an integration time of 1 s. Measured spectra were analyzed in the range from 500 to 900 nm to avoid contributions from either the ionoluminescence [38] or the point defects formed during irradiation [39]. This assures that density (and, hence, refractive index) variations as a function of fluence can be followed with great detail.
Fig. 1 Schematic representation of the setup used for in situ reflectance measurements. Samples can be irradiated with swift heavy ions and simultaneously illuminated with white light (blue arrows). Reflected light is collected by an optical fiber and guided to a CCD array spectrometer.
3. Results and discussion
We will focus on reflectance measurements, which provide information on the effective dielectric constant variation in the irradiated region. Some selected reflectance spectra at different fluences of F at 5 MeV (spectra for all other ions are similar) are shown in Fig. 2, for both silica and quartz. Irradiation effects are clearly visible from the beginning of irradiation in isolated track regime. For silica (Fig. 2a), irradiation clearly leads to an overall raise in reflectance. This roughly indicates an increase in density related to compaction. In the case of quartz (Fig. 2(b)), the response to irradiation is just the opposite; i.e., reflectance drops due to sample amorphization. As the irradiation progresses these trends (increase of reflectance for silica and the opposite for quartz) continue until a saturation stage is reached. Finally, for high enough fluences, an interference pattern appears in both materials.
Fig. 2 Reflectance spectra for (a) silica and (b) quartz irradiated with 5 MeV F ions at different fluences. Continuous red lines are the best fit of the experimental data using the multilayer model.
Now we will discuss the physical phenomena related to the described variations of reflectance. Evolution of the irradiated region as a function of fluence (schematically represented in Fig. 3) is approximately the same process for both materials even if the actual variations of density are the opposite. Initially, for very low fluences (< 1011 cm−2, Fig. 3(a)), i.e., the region of isolated tracks, the dependence of density with fluence is approximately linear. Light is reflected mainly at the vaccum-SiO2 interface because the refractive index gradients formed inside the samples (on the the ion-damaged region) are very gradual and, consequently, no interference appears in this regime. For intermediate fluences (1011 – 1014 cm−2) track overlapping becomes significant and this produces the well known Poisson-like variation of the refractive index as a function of the fluence [40]. However, no interference appears yet because the interface between the irradiated and unaffected regions is not sharp enough. Finally, for higher fluences (> 1014 cm−2, Fig. 3(a)), the interface becomes more abrupt, effectively generating a continuous layer with a refractive index markedly different from than of the virgin material. An unambiguous prove of this large refractive index gradient is the appearance of the interference pattern at the end of the irradiation, as a consequence of light reflection at the sample surface and at the interface between the continuous layer formed by irradiation and the substrate.
Fig. 3 Schematic representation of the refractive index variations as a function of fluence for (a) low and (b) high fluences. (c) Multilayer model used to fit the reflectance spectra. In all cases regions 1, 2, and 3 represent the vacuum, the irradiated region and the pristine material, respectively.
So far we have provided a qualitative description of refractive index kinetics but, as we will show now, a quantitative analysis is also possible. In a first approach, we fitted the reflectance spectra using a two-layer model: Vacuum/Irradiated SiO2. In spite of its simplicity, this model is very effective to obtain the values of the refractive index in the surface of the samples because this interface is responsible for most of the reflectance.
Surface refractive index at 633 nm as a function of fluence is depicted in Fig. 4. It should be noted that the wavelength selection is rather arbitrary because the trends are the same for any wavelength in the range 500–900 nm. We have selected 633 nm simply because many refractive index values in the literature are reported for this wavelength. Refractive index kinetics clearly reflects the Poisson-like behavior that we have discussed previously. The only unexpected feature is that in silica (quartz) the refractive index at the higher fluences does not remain at the maximum (minimum) value attained but drops (raises) a little bit. We suspect that this anomaly is related to the mechanical response of the material and are currently investigating this hypothesis [41] but the details are outside the scope of this paper.
Fig. 4 Surface refractive index (at 633 nm) for silica (curves increasing) and quartz (curves decreasing) samples irradiated with various types of swift heavy ions.
Now, it is possible to obtain the track radii at the surface from these curves by fitting them with a Poisson function. More precisely, the normalized variation of the dielectric function, Δεn = |ε – ε0|/ε0, is the quantity that evolves following a Poisson kinetics: Δεn = Δεmax[1−exp(−σϕ)] where ϕ is the fluence, σ = πR2 represents the track cross section and R is the track radius [42]. Typical fits are shown in Fig. 5 for both materials irradiated with F ions at 5 MeV; only a few experimental points are plotted in the figure but the actual fits include many more (usually more than 1000 points for each irradiation). It can be seen that the quality of the fits is very good.
Fig. 5 Normalized variation of the dielectric function for silica and quartz samples irradiated with F ions at 5 MeV. Experimental values were fitted using a modified Poisson law: Δεn = Δεmax[1−exp(−σϕ)], which allowed us to determine first the cross section of the track (σ) and then its radius (σ = πR2).
Figure 6 shows the track radii obtained from the reflectance measurements as a function of the stopping power at the material surface for, all Br and F irradiation experiments. For both ions at 5 MeV we can see a clear indication of the so-called velocity effect [44]. Br ions (slow) give rise to a larger radius than F ions (fast), even if both have roughtly the same energy and electronic stopping power. We made a fit of the data using the model developed by Szenes (R2 = A ln(Se/St); being A a proportionality constant and St the threshold stopping power) [43]. We excluded the point corresponding to Br at 5 MeV from the fit because it is in a different velocity group. The fit yielded threshold values of 1.85 and 2.40 keV/nm for silica and quartz, respectively. Another noticeable effect in Fig. 6 is that the track radii obtained in quartz are consistently lower than their counterparts in silica. This effect is related to the crystalline nature of quartz that provides a seed for the displaced atoms to reorganize [45], significantly reducing the fraction of displaced atoms that remain disordered forming part of the amorphous track. A similar trend can be found on the data sets reported by Kluth and collaborators for silica [46] and quartz [47] and determined by means of small angle x-ray scattering measurements.
Fig. 6 Surface track radii in silica and quartz as a function of the stopping power. Orange continuous lines are a fit of the data using Szenes’ model [43].
On the other hand, it should be noted that the radii obtained for α-quartz by means of Rutherford Backscattering in the channeling configuration (RBS-C) [40] are consistently larger than the ones obtained in this work for the same material and, at the same time, they are very similar to those obtained for silica. For better understanding the reason for this discrepancy it is worth discussing the differences between both techniques. Reflectance is affected by variations in the refractive index and, therefore, it is valid for any type of material as long as the modified phase has enough contrast in the refractive index with respect to the pristine material. RBS-C, on the other hand, is based on the reduction of backscattering produced by the channeling effect and, consequently, it is only valid for single crystals. Hence, if the recrystallization previously described generates a polycrystalline region around the latent track (i.e., halo [40,46]) then RBS-C will “see” the surrounding region as amorphous because the channeling effect is lost. On the contrary, this polycrystalline region will be “invisible” to reflectance measurements because it has the same refractive index than the pristine material. This difference between both techniques might explain the different results yielded by both measurements.
Reflectance data contains information not only from the surface of the sample but also from the inner layers. This is particularly true for large fluences, when the interference pattern appears. Taking this into account we have determined the refractive index (or dielectric constant) profiles formed in the irradiated materials from a fit of the reflectance spectra. For this purpose, we have used a multilayer model based on the matrix formulation of Fresnel equations [48,49]. The procedure for calculating the profiles can be divided in two steps. In the first one, an initial approximation of the total thickness for the damaged material is calculated with a three-layer model: Vacuum/Irradiated SiO2/Virgin SiO2. In this model, the refractive index for the irradiated layer is considered the same as the calculated in the surface of the two-layer model previously described. The calculated thickness is the one for which the theoretical reflectance shows the same number and position (at the same wavelength) of interference’s maxima and minima as the experimental reflectance. Obviously, the amplitude of this theoretical reflectance is much larger than the measured one.
Finally, in the second step, the total thickness of damaged material is divided into a finite number of layers of varying length (Fig. 3(c)); i.e., thicker layers are closer to the surface whereas deeper layers are thinner. We have chosen layers in this way because stepper variations in the refractive index occur mainly at the end of the ion trajectory. Also, the accuracy of the model is improved with a gradual variation of the layer thickness. We tried different configurations for the discretization of the material; e.g., larger changes between each layer thickness or a higher number of layers with constant thickness. However, these configurations lead to unrealistic results. Then, each layer is assigned a variation of the dielectric constant of the material, Δεi, compared to virgin material due to radiation damage. This parameter is fitted with the multilayer model by minimizing the difference (more precisely, the reduced χ2 function [50,51]) between the experimental and calculated reflectance. These fits were initially done for the highest fluence reached at the experiments and the obtained profile was used as the initial approximation for the previous value, and so on.
Figure 7 shows the profiles obtained for silica (Fig. 7(a)) and quartz (Fig. 7(b)) irradiated with F at 5 MeV. The depicted quantity is the normalized variation of the dielectric function. Values at the surface are almost identical to the ones that we obtained with the simple two-layer model. It is worth discussing this result a little further. There are two markedly different processes controlling the reflectance spectra. By far the most important is the refractive index on the surface of the sample because most of the light is reflected at this interface. This reflection is responsible for the average position of the spectrum. Then, reflection in the inner layers modulates this value but without changing the average. For this reason the simple model can give accurate values (but only if it is done for a spectral range, in the case of only one wavelength it is affected by the interference and yields wrong values).
Fig. 7 Effective dielectric function profiles obtained from the fits for (a) silica and (b) quartz samples irradiated with 5 MeV F ions at various fluences. The nuclear stopping power predicted by SRIM-2013 is plotted in orange.
Dielectric function profiles exhibit an interesting behavior, somewhat unexpected for us. There are two clearly defined regions; in the first one, extending from the surface to roughly the ion range, the normalized dielectric function is mostly constant, except for the final 500-700 nm where it decreases monotonically. This region can be clearly ascribed to the electronic contribution of the stopping power. The second region, located in the deepest zone has a Gaussian-like shape and is more pronounced for silica. In principle one may think that it is produced by the nuclear damage, dominant at the end of the trajectory. However, if one compares it with the nuclear stopping power predicted by SRIM-2013 [52,53] (orange lines in Fig. 7) it is clear that this zone is located roughly 700 nm beneath the expected maximum of nuclear damage. Moreover, this effect is consistent for all the analyzed samples, independently of the material and ions used.
The reason for this discrepancy is unclear for us. All of the features (shape and cumulative character) of this final damage peak are indicative of nuclear damage. Maybe it is simply indicative of an error in the SRIM constants or it could be a variation of density related with tensions inside the material. More experiments are needed to elucidate this but by the time being we are inclined to consider this peak a consequence of the nuclear damage.
4. Conclusions
In this work we have studied in real time the modification of the optical properties of silica and quartz irradiated with swift heavy ions. By using an in situ reflectivity setup we obtained detailed information of all the density changes produced in the material as a function of the fluence. Then, by means of a multi-layer model, we determined the refractive index profiles from the initial single track mode to the final (high fluence) continuous layer formation. We have shown that in situ optical monitoring is able to provide information of the variations of density produced by swift heavy ions with a high degree of detail and accuracy, not only at the surface but also for all the track profiles. This provides a unique tool: fast, non destructive and easily controllable with automatic processes. Such technique is interesting for industrial applications and experimental research campaigns.
Acknowledgments
The authors acknowledge the computer resources and technical assistance provided by CESVIMA and funding by Spanish MINECO through projects AIC-A-2011-0718, MAT-2011-28379-C03-02 and MAT-2012-38541, as well as Technofusion project (II)-CM (S2013/MAE-2745). OPR is grateful with Moncloa Campus of International Excellence (UCM-UPM) for the PICATA postdoctoral fellowship.
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