1. Introduction

High power and energy laser systems are critical capabilities in a myriad of burgeoning fields from fusion [1] to materials science under extreme conditions [2] to astrophysics. [3] These systems are often fluence limited due to laser-induced damage in multilayer dielectric coated optical components which occurs primarily in the high refractive index materials such as hafnia. [4] Structural defects including vacancies [5], interstitials [6], nano-crystallites [7] and nano-bubbles [8] as well as chemical defects such as sub-stoichiometric clusters [9] in hafnia are of interest due to their influence on laser-defect interactions and energy deposition in the coating materials. For ns-pulsed UV laser applications, the laser-induced damage in hafnia is believed to be driven by laser-defect coupling which results in an irreversible material modification due to photo-thermal energy conversion and thermal runaway. [4,9–11] Theoretical and experimental results yield anecdotal evidence that these defect induced sub-bandgap electronic states act as potent damage-prone precursors, however little direct evidence exists. [9]

One such sub-bandgap defect in hafnia coatings is related to sub-stoichiometric clusters in the films, which are typically associated with oxygen (O) to hafnium (Hf) ratios less than 2.0. [9,12–15] Exhaustive theoretical and experimental studies have been done to link sub-stoichiometry to damage-prone defect states. [16,17] Such defect states within the band gap can facilitate the intraband electronic transitions and enhance multiphoton absorption leading to laser-induced damage in hafnia films under both ns [8] and sub-picosecond [18] laser exposure at UV and infrared wavelengths, respectively. Theoretical calculations of structural defects in hafnia have helped one to understand possible implications to the optical and electronic bandgap. [19–21] Of particular interest are oxygen-vacancy defects, which have been postulated to play an active role in the trapping of electrons and holes, thus leading to electronic states in the bandgap. [19–21] Experimental investigations utilizing engineered defects show that laser couplings with the sub-bandgap states are responsible for the observed coating laser damage. [9,22–24] For example, a study of engineered hafnium nanoclusters embedded in hafnia films via photothermal heterodyne imaging shows that these metal clusters exhibit absorption leading to damage with ultraviolet light. [23] Another investigation under pulsed UV exposure has noted a significant reduction in laser damage resistance due to process parameter-induced sub-stoichiometric hafnia films. [9,22] However, the studies utilizing engineered defects all have issues associated with the creation of secondary defects while achieving the targeted precursors. These approaches make it difficult to isolate the effect of a specific precursor on optical damage and thus the role of sub-stoichiometry on laser induced damage in dielectric films is still unclear.

In this work we conduct a comprehensive examination of the chemical compositions of dense hafnia films and the correlations to their laser performance under UV ns exposure. The dense films investigated here are produced by a reactive IBS deposition method under different configurations with argon (Ar) being the process gas. The deposition parameters were chosen to optimize the optical performance of dielectric materials. Dense hafnia films have similar physical properties such as the index of refraction and mechanical integrity to those of the bulk counterparts. [8,11] Combining with their environmental stability and low absorption, dense films are usually preferred for applications at harsh environment such as UV laser exposure at ambient conditions. To ensure the uniformity of the film thickness, a sun/planetary rotation is often employed. A schematic of the sun/planetary system used for the present study is displayed in Fig. 1. Ideally, planetary rotation enables a growing film at a given location to experience a lower and higher flux of depositing hafnia adatoms, leading to an averaging effect that results in an excellent uniformity in film thickness across multiple samples being coated simultaneously. [25] This rotation-induced averaging effect also affects the spatial distribution of film stoichiometry and entrapped working gas for samples within a planet. On the other hand, while any optical film produced without planetary rotation does not have the desired thickness uniformity, the resultant films can still yield useful information about the spatial distribution of reflected Ar neutral species and O at the solar surface of the planetary system. To achieve these objectives, our approach is three-fold: i) mapping of the position-dependent stoichiometry from RBS data of the hafnia films produced with- and without the sun/planetary rotation, ii) modeling of the population and energy distribution of Ar reflections at the deposition plane of the IBS planetary by Monte Carlo simulations, [26–30] and iii) measurements of laser-induced damage resistance of the films under UV, ns-laser exposure.

 

Fig. 1. Illustrations of the solar-planetary configuration utilized in the IBS system. (a) The light gray circles represent the sun system and the darker grey circles display the four 200 mm Si wafers used for the analysis of spatial distribution of chemical composition of the hafnia films. R denotes the radial distance from the center of the sun to the center of rotation for the planets. ρ shows the radial distance of a given position on the planet from the planet rotational center. θ and α are the rotational angle of the sun and planet, respectively. The x and y-axis of the sun are denoted by two dotted lines on the sun. (b) Configuration used for the deposition of 2” fused silica substrates for laser damage testing. The black and white circles depict examples of deposition substrates at the edge and center locations on a planet, respectively. The arrows denote the possible rotational direction of the planetary system.

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We find that the energy distribution of reflected Ar neutrals at the surface of the sun and the radial-dependent compositional distribution of entrapped Ar and O in the hafnia films are correlated. Moreover, the stoichiometry of the hafnia films is highly anisotropic with the film towards the edge of the planet being stochiometric but sub-stoichiometric at the center; these stoichiometrically-diverse films also exhibit a large contrast in their laser damage performance. It is hypothesized that the impingement of energetic Ar neutrals causes preferential depletion of oxygen and results in sub-stoichiometric films that are prone to laser-induced damage due to enhanced laser absorption via the sub-bandgap states. This work offers potential mitigation strategies for making dense, stoichiometric and damage resistant dielectric films for UV applications.

2. Experiment

Hafnium oxide films with a half-wave optical thickness for 355-nm light at 45° angle of incidence are produced via IBS in a Veeco Spector-HT system. The deposition is performed in a reactive oxygen environment with a polycrystalline hafnium target and Ar sputtering gas. The principle ion gun extracts the Ar working gas ions at an energy of 1000 eV with a 2 × 10⁻⁴ Torr partial pressure of Ar in the chamber. The oxygen partial pressure is approximately 3.5 × 10⁻⁴ Torr and the base pressure in the chamber is ∼ 5.5 × 10⁻⁴ Torr. All ionic species in the chamber have been neutralized via RF generated electrons, allowing for stable deposition of dielectric materials. [31] In the planetary systems illustrated in Figs. 1(a)-(b), the 200 mm diameter planets rotate independently upon the 700 mm diameter sun via a 39 to 16 sun-to-planet gearing ratio with a sun revolution speed of 24 RPM. Each planet rotates along a radial axis on the sun, which is approximately 180 mm (R) from the center of rotation for the sun.

To obtain the compositional distribution of hafnia films in a planetary as well as to probe the reflected Ar distribution on the solar surface, hafnia films are deposited on four, 200-mm Si wafers in a geometry displayed in Fig. 1(a) with- and without sun/planetary rotation, respectively, using the same gun settings and deposition time. The Si wafers were attached to the four planets of the IBS deposition system and aligned to the four quadrants of the sun. In both cases, the deposited wafers were diced evenly along the centerline to make 10 individual pieces from which the composition of each are analyzed.

To assess the correlation between laser damage resistance and film stoichiometry, hafnia films are deposited in the configuration depicted in Fig. 1(b). All laser damage testing samples are deposited with planetary rotation enabled on 2” round, 10 mm thick UV-grade fused silica obtained from CVI-Melles Griot with a 10/5 scratch/dig surface figure and are ultra-sonically cleaned before deposition. [32,33] As displayed in Fig. 1(b), samples are either populated in the middle (white circles) or the edge of the planet (black circles) which are 70 mm from the center (center to center distance), respectively.

The chemical composition of the hafnia films is characterized by RBS, a well-established technique for thin film chemical analysis [34] that is well suited for the hafnia system. [35] All reported hafnia film compositions were determined by RBS chemical analysis, collected at a scattering angle of approximately 175° with a Si surface barrier detector. The 2 MeV He⁺ ion beam was produced from a 4 MV Dynamitron ion accelerator and the ion scattering energy was calibrated using a gold thin film standard before data collection. Analysis of the RBS data was performed with the aid of the computer simulation program RUMP [36] to determine the O to Hf atomic ratio as well as impurities that may have been entrapped in the film including that of the Ar working gas.

The crystallinity of the two hafnia films (coated at the center and edge location, respectively) used for laser damage testing was determined using glancing incidence x-ray diffraction. A Bruker D8 Discover instrument was used with a Cu source emitting x-rays of 1.5406 Å wavelength. A corundum internal standard and alignment to the zero points for 2-theta, z-height and theta was run prior to data collection. The glancing angle of incidence was 0.45 degrees for this study. This work was done at Eurofins EAG Materials Science LLC in Sunnyvale, CA.

Laser-induced damage testing using a 1-on-1 test protocol is conducted using the third harmonic (355 nm) of a Nd:YAG laser system which is operated in a single-longitudinal mode (Quanta-Ray Model PRO-350-10; Spectra-Physics, Inc., injection seeded) with a pulse duration of 8 ns (FWHM), near Gaussian temporal profile. All tests are performed at 45° angle of incidence using P (in plane) polarization. The near Gaussian laser beam diameter was formatted to 650 µm at 1/e² maximum intensity. Fifty test sites on a rectangular grid were separated by 2 mm to ensure the minimal shot to shot overlap between adjacent laser exposures. A diagnostic reference arm was used to record the laser energy and spatial beam profile at an equivalent sample plane. In situ optical microscopy with approximate resolution of 1 µm was used to acquire images both before and after laser irradiations. More details on the test protocol, beam diagnostics, and data analysis can be found elsewhere [8]. The overall fluence error is ∼10-15% compounded from typical energy meter and beam profile measurement uncertainties.

The surface morphology and damage density after laser exposure are examined using environmental scanning electron microscopy (ESEM) and confocal microscopy. ESEM allows for the imaging of dielectric coatings surfaces without a conductive coating by flowing 0.35 Torr of water vapor over the sample, mitigating and dissipating the occurrence of charging due to the flooded electron beam on the surface. High-resolution confocal images (150× optical magnification) acquired at the center of individual test sites (corresponding to the peak fluence region of the gaussian test beam, 100 × 75 µm²) are processed via thresholding image algorithms to detect and count morphological features (or damage sites) above the background. Damage density (sites per unit area) error is estimated at ± 10% from statistical damage variations at test sites exposed to similar fluences on the same sample.

2.1 Theoretical simulations

Sub-stoichiometry in hafnia films has been linked to in situ and ex situ high energy bombardment with Ar neutral species, which likely arises from energetic Ar⁺ being reflected off the high-Z hafnium target in the sputter deposition process [26,27]. Simulation software packages like the Transport and Range of Ions in Matter, Sputtering Edition (TRIM.SP) have been commonly used to investigate the distribution of sputtered species and working gas reflections for high energy ion-matter interactions [37]. The program relies on Monte Carlo simulation techniques. The Veeco IBS system used in this study employs electron neutralizers, which has been shown to neutralize most species in the chamber leading to stable deposition rates of metal oxides [38,39]. While TRIM.SP is primarily used for quantifying the ion-matter interactions, the code has also been shown to be valid for predicting the interactions between energetic neutral species and matter with high fidelity [26,27,29,30]. The SP edition specifically has been shown to simulate the sputtering rates and yields from monocrystalline and polycrystalline targets accurately at multiple interaction angles, as well as the energetics and angular distributions of the sputtered species and working gas reflections due to inelastic reflections with the target surface. From these angular distributions and the geometry of the chamber, it is possible to project a population and energy distribution of Ar reflections onto the deposition plane of the IBS planetary. For the deposition of hafnia films, the principle Ar energy was 1000 eV and the interaction angle with the hafnium target was 45 degrees for the 10⁶ simulated Ar-Hf target interactions, enhancing the statistical significance of the MC simulations [26,27]. Since the TRIM.SP simulated Ar neutral populations and energetics are projected onto the sun of the IBS system, these results should closely match the chemical analysis results of the hafnia film deposited without the aid of planetary rotation, assuming that the reflected Ar neutrals become entrapped in the growing film with high probability.

As with any simulation method, proper inputs are required to get realistic and relevant results. The three important inputs for TRIM.SP simulations are displacement energy, lattice binding energy and surface binding energy. Displacement energy is the energy that a given recoil requires to overcome the lattice forces and move more than one bond distance unit away from the original position [28]. If the energy of the recoil is less than the displacement energy, the atom returns to the original position and the energy is translated into phonon energy. Displacement energy is typically around 25 eV for metals which is the value used in our simulations, though literature values are largely unknown for most materials [27]. Lattice binding energy is the energy that a target atom loses as it leaves its lattice site and recoils in the target [28]. Lattice binding energy is typically around 2 eV for most materials, and again the analytical values of the lattice binding energy for most material are not known [27]. The last input is the surface binding energy. Surface binding energy is the minimum energy required for a target atom to leave the surface of the target material and is key to sputtering yield and the energetics of reflections [28]. The surface binding energy can be estimated from the heat of sublimation [27,35]. In the current work, the input for the displacement energy, lattice binding energy and the surface binding energy are 25 eV, 3 eV, and 6.287 eV, respectively [27,35,37].

3. Results

The atomic composition of the hafnia films as a function of the radial position in the rotating planet, averaged across the centerline of four 200 mm wafers, is displayed in Fig. 2(a). It is apparent that the O to Hf ratio shows strong dependence on the radial distance from the center of the planet. Namely, while the films have the stoichiometric O to Hf ratio of 2:1 near the edge regions (i.e., radial position of ∼90 mm), the ratio is sub-stoichiometric towards the inner portion and reaches the minimal of 1.7:1 at the center of the planet (radial position of ∼10 mm). Furthermore, the radial dependence of the O to Hf ratio within the planet displays an opposite trend from that of the Ar content in the film, i.e. the O to Hf ratio and the Ar percentages are inversely proportional to each other. This stark contrast is demonstrated in Fig. 2(b). A linear regression fit to this data gives a coefficient of determination of 0.98 showing an apparent causal link between entrapped Ar and stoichiometry (i.e. the O to Hf ratio).

 

Fig. 2. (a) The average radial planetary distribution of O to Hf ratio (square) and entrapped Ar atomic contents (triangle) in the hafnia films. (b) The relationship between the O to Hf ratio and the entrapped Ar content. These parameters are derived from the RBS spectra collected from each film.

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The population and kinetic energy distribution of reflected Ar neutrals from the Hf polycrystalline target are estimated from the TRIM.SP simulations. The projected population along the representative directions, horizontal (x) and vertical (y) on the sun of the IBS system, where the coordinate origin is located at the center of the sun, is shown in Fig. 3(a). The Ar distributions along both axes appear to be roughly isotropic and centered on the radial axis. Furthermore, the simulations also show that the Ar reflection distribution reaches nearly zero along the x-axis at ± 350 mm while the Ar distribution along the y-axis exceeds the bounds of the sun of the ion beam sputtering system. This implies that the population of Ar on the sun is slightly elongated along the y axis, however the distribution along each axis is Gaussian in shape.

 

Fig. 3. TRIM.SP Monte Carlo simulations of the radial distribution of (a) populations and (b) energies of reflected Ar neutrals projected to the solar surface. The black squares correlate to the projection onto the x-axis while the red triangles correspond to the projection onto the y-axis of the sun. (c) A top-down illustration of the configuration of the IBS coating system. (d) The predicted area of the projected reflected Ar neutrals on the solar surface with kinetic energies that are equal or in excess of 370 eV.

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The simulated radial distributions of the energetics along both the x and y directions are shown in Fig. 3(b). It is apparent that the distributions exhibit a large contrast. While the average energy distribution along the y-axis of the sun is notably uniform, the distribution along the x-axis of the sun tells a different story. Along the x-axis the kinetic energy of reflected Ar summits at + 180 target interactions,mm from the sun center which is close to the radial sun position of the planetary centerline. The anisotropy in energy distribution can be attributed to the fact that the 45° target angle is along this axis and thus the high energy, low angle reflected neutrals fall in the positive radial sun space. This phenomenon is a consequence of the difference in atomic mass between the working gas, in this case Ar, and the target, hafnium, leading to ineffective momentum transfer, especially at lower angles of incidence [26,40,41]. A top-down illustration of the IBS system is displayed in Fig. 3(c), showing the angle of the target relative to the ion beam and the distribution/location of the high energy Ar neutral reflections with respect to the sun/planet system (red triangle). From the simulation, the Ar reflections with kinetic energy in excess of 370 eV intersect the sun in an elliptical shape centered at 180 mm from the sun origin as shown in Fig. 3(d).

The amount of Ar entrapped in the hafnia films correlates to the kinetic energy of reflected Ar neutrals at the sun surface. The correlation is demonstrated in Fig. 4(a) where the Ar content along the x-axis in the two stationary planets (red triangles) follows the trends of Ar kinetic energy (black squares) along the same axis. Clearly, the location where the maximum Ar content resides coincides with that of the highest Ar kinetic energy, which is near +180 mm from the sun center. This is approximately the location of the center of the right planet on the sun. Since no measurements of Ar contents are available at the locations other than the planetary, the red traces are incomplete in Fig. 4(a). However, based on the behavior of the measurements, it is believed the missing data would follow the trends displayed in the traces. The strong correlation between the entrapped Ar content and kinetic energy of the reflected Ar neutrals is further demonstrated in Fig. 4(b). It can be seen that the amount of entrapped Ar increases with the Ar kinetic energy up to 300 eV and then levels off at just above 4% until the kinetic energy reaches 370 eV, after which the concentration spikes and levels off again at above 6%. The results suggest that the film composition is significantly affected by the bombardment of high energy of reflected Ar neutrals. Further evidence of this can be found in Fig. 4(c), which displays the remarkably opposing trends of the entrapped Ar neutrals and the oxygen concentration in the film along the x axis. These trends agree with that results summarized in Fig. 2 for the conventional deposition utilizing the averaging effects via planetary rotation, confirming a strong correlation between the entrapped Ar and film oxygen content. There are several data points in Fig. 4(c) with exceedingly high oxygen content along the x axis of the planet. This is mainly caused by the small population of hafnium species intersecting the sun at the high sun angle relative to the target as indicated by Fig. 3(c). The notable hafnium deficiency in the outer region of the sun is typically compensated by planetary rotation during deposition.

 

Fig. 4. (a) A comparison between the simulated energy of reflected Ar neutrals (squares) and the content of entrapped Ar in the hafnia films deposited without planetary rotation (triangles), along the x-axis of the sun. (b) The correlation between the Monte Carlo simulated energies and the content of entrapped Ar. (c) A comparison of the oxygen concentration (blue diamonds) and entrapped Ar content along the x-axis of the sun.

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The atomic composition of the hafnia oxide films produced in the configuration displayed in Fig. 1(b) is consistent with that of the thin films deposited on the 200 mm Si wafer. Namely, the O to Hf ratio for the thin films at the planetary edge (black circles at the edge region of the planet) is nearly stoichiometric at 2 and that at the planetary center (white circles in the center of the planet) is sub-stoichiometric at 1.7. Similarly, the Ar content (in at. %) follows the same trend. That is the stoichiometric and sub-stoichiometric films contain 5.5% and 6.5% of Ar, respectively. Nevertheless, the disparity in O to Hf ratio for these films is most significant. On the other hand, the two films produced at the dissimilar planetary locations exhibit identical structure and are both amorphous. This is confirmed from the GI-XRD spectrum collected from the two films, respectively. As shown in Fig. 5, there is no detectable difference between the spectra and that there are no sharp diffraction peaks. The broad peak at the 31 degree suggest there is small grain within the film with average grain size of 1.4 nm by Scherrer equation. [42]

 

Fig. 5. GI-XRD analysis of the hafnia films deposited near the edge of the planet (black samples) and the samples deposited near the center of the planet (white samples).

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The two stoichiometrically distinct hafnia films at the edge (black) and the center (white), as depicted in Fig. 1(b), respectively, exhibit dissimilar response to the UV ns-laser exposure derived from the 1-on-1 test protocol. The differences are two-fold: i) the laser damage onset (shown in Fig. 6(a)) for the edge films is 2.3 ± 0.2 J/cm² compared to 1.6 ± 0.2 J/cm² for the center films; this variance is nearly 1 J/cm² which is quite significant for laser applications at UV wavelengths; ii) the damage density as a function of fluence of the two films is also distinct, as illustrated in Fig. 6(b). The latter damage metric is estimated based on confocal images of individual test sites, i.e., counting the dark features per unit area from each hafnia film. Representative confocal images are displayed in Figs. 6(c)-(d) which demonstrate a lower damage density (3× or less) for the edge films than that for the center films.

 

Fig. 6. (a) The 1-on-1 UV ns-laser damage probability and (b) damage density as a function of irradiation fluence for a hafnia film deposited near the edge of the planet (square) and the center (triangle), respectively. Representative high-resolution images of the damage morphology observed from the edge and center films, respectively, after similar laser exposures (as noted in each figure with experimental uncertainty of ∼0.5 J/cm²): (c)-(d) confocal microscopy and (e)-(f) ESEM.

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While the damage densities for the two films are notably different, the damage morphologies of the two films are similar. A close-up characterization of the test area using ESEM is displayed in Fig. 6(e)-(f) for the two films tested at 4.9 ± 0.5 J/cm² (edge film) and 5.0 ± 0.5 J/cm² (center film), respectively. The damage morphology in both films are similar, appearing foamy in character likely due to a rapid expansion in entrapped voids and rapid vaporization of the hafnia material due to plasma-induced local heating and absorption [8]. While the damage morphology is similar, the damage densities of the two films at this fluence are significantly different, consistent with that shown in Fig. 6(b). Based on the side-by-side comparison of damage behaviors from two stoichiometrically different films, we hypothesize that the damage precursors are mostly identical in nature but have significantly different densities.

4. Discussion

The main cause of the sub-stoichiometry in the “center” hafnia films is likely the preferential removal of O by the re-sputtering events from the exposure of high energetic reflected Ar neutrals during deposition. [5,43] Upon impingement, the interactions between the bombarded Ar neutrals and Hf or O species at the interface can result in the removal of either Hf or O atoms from the reactively deposited hafnia film. The sputtering efficiency of a species depends strongly on the difference in atomic mass between the bombardment element and depositing species; i.e., the larger the difference, the smaller the sputtering efficiency. Similarly, the removal efficiency depends also on the energy of the impinging reflected Ar neutrals. A simple energy transfer calculation detailed in Rack et al. leads to the conclusion that the energy transfer in the Ar-O interaction are approximately 1.4 times those of the Ar-Hf interaction. [44,45] Thus, the Ar-induced sputtering efficiency of O is much higher than that of hafnium, leading to potential oxygen vacancies on the surface of the film. Since the bombardment coincides with the growth of the film, the oxygen vacancies created by the Ar bombardment are inevitably covered by the hafnia film flux before they can be ameliorated by the backfilled oxygen in the deposition chamber. Nevertheless, the O removal effect will be probabilistic in character and the probability will be greatly enhanced for higher energy and longer exposure of Ar. [45,46]

The extent of O removal is influenced not only by the kinetic energy but also by the exposure time of the reflected Ar neutrals encountered by the rotating substrates within the planetary during deposition. [45] In fact, the amount of O removal and Ar entrapment is mostly affected by the reflected Ar neutrals at kinetic energy greater than 370 eV. The correlation is clearly demonstrated in Figs. 4(a) and (b) and is consistent with previous reports. [5,43] The high energy region is skewed towards the “positive” side of the sun-planet system (Figs. 3(b-(c))) and is centered at 180 nm on the x-axis (Fig. 3(d)), which populates ∼15000 mm² of surface area on the sun and accounts for 5% of angular distance for a single revolution of the sun. The disparity in stoichiometry between the films anchored at different locations (Fig. 1(b)) is attributed to the difference in the exposure time of the film to the energetic region during deposition. To illustrate the difference in exposure time at the high energy region for the two stoichiometrically distinct films, a careful examination of the trajectory of the center point on each film (black vs white) is provided below.

The trace of a given point on the planet during the sun-planetary rotation can be accurately predicted by the following parametric equations:

In our deposition system, for points near the edge region of the planet, the path of a given point would follow a hypocycloid trace during the rotation. Figure 7(a) exemplifies the trajectory of the point on the planet with ρ = 70 mm (which coincide with the center of the black circles displayed in Fig. 1(b)) after 10 sun revolutions. The revolution of 10 is chosen to estimate the average effect as the rotation of the sun-planetary system is non-synchronous. The red ellipse indicates the region on the sun surface where the high energy reflected Ar reflected project. It is apparent that for the given 10 sun revolutions, the center of the black circle encounters the high energetic region approximately four times judging by the number of traces encompassed the red section shown in Fig. 7(b), a closeup look of the region shown in Fig. 7(a). This suggests that films deposited onto the black areas will be exposed to the high energy Ar neutrals approximately four times in the 10 sun revolutions. The points near the center of the planet, i.e. ρ = 0 mm, on the other hand, follow a path of a circle with a radius of 180 mm as displayed in Fig. 7(c). Again, the trajectory encounters the high energetic region (red ellipse in Fig. 7(c)) of reflected Ar neutrals. In contrast to that of the points at the edge location, the center points intercept the high energetic region on every sun revolution, which is three times more frequent than that of the edge films.

 

Fig. 7. (a) Predicted trace of a point with ρ = 70 mm on the planet (or the center of an edge film) after 10 solar revolutions. The red ellipse represents the area where the reflected Ar neutrals with kinetic energy equal or greater than 370 eV intersect the solar surface. (b) A closeup view of the high energy Ar neutral area displaying the total number of times that the center point of the edge film passes through the high energetic region within the 10 solar revolutions. (c) The predicted trace of a point with ρ = 0 mm on the planet (midpoint of the center film) after 10 solar revolutions. (d) A zoomed-in view showing the trace encounters the high energy Ar region for every solar revolution. (e-f) Cartoons depicting sub-stoichiometric defects induced by Ar reflections in hafnia film produced at the center (e) and the edge (f) of the planet. The solid background represents the ideal hafnia and the black dots indicate the sub-stoichiometric clusters induced by the bombardment of energetic Ar reflections.

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The disparity in the encountered frequency to the high energy reflected Ar neutrals region for the films deposited at the two different planetary locations results in a different time of exposure and interaction between the depositing layer and the impinging atoms. Based on results shown in Figs. 7(a-(d)), the time of exposure or the thickness of film interacting with the high energy Ar neutrals during deposition can be estimated. For the edge film, the interaction on average occurs once in every three revolutions. Since the sun system revolves at a speed of 24 RPM, the hafnia film deposited in each solar revolution is about 2.5 Å for the optimal deposition rate of 1 Å/s. As discussed earlier, within one single solar revolution, the intercepted region between the high energy reflected Ar neutrals and growing hafnia film covers approximately 5% of the total angular displacement which is equivalent to 0.125 Å in vertical distance. That is to say that for every 7.5 Å film deposited, 0.125 Å of it is impinged. On the other hand, for the center films, the hafnia is encroached much more often by the high energy Ar atoms. Since the depositing surface encounter the red elliptical region on every rotation, nominally, for each 2.5 Å film deposited, approximately 0.125 Å of it is impacted.

The impingement perturbed regions in the film offers the opportunity for oxygen deficiency leading to a sub-stoichiometric film composition. This is certainly true for those deposited at the planet center where the film is periodically disturbed by the energetic Ar neutrals with a nominal spatial periodicity of 2.5 Å, which is approximately half of the theoretical lattice distance for the monoclinic hafnia, [47] or a single molecular layer of the hafnium-oxygen amorphous network. Within such a short layer thickness, the interaction from the bombardment of Ar neutrals is merely continuous along the penetration depth due to the high probability of incorporation, [48] although the impingement is discrete. The attempt to sputter away oxygen from the film is therefore throughout the entire film growth process which makes the whole film sub-stoichiometric as observed. On the other hand, for the film deposited at the edge region, the story can be quite different. Because the spatial period of the high energy reflected Ar neutral impingement is so much longer than the impingement duration itself (7.5 Å vs 0.125 Å), the film has sufficient time to self-heal the non-stoichiometric defects after their creation, leading to possible sporadic stoichiometric disruption in the growing film, which is on average stoichiometric. Schematic depictions of the outcomes from the two different effects are shown in Figs. 7(e) and (f), respectively. The solid section correlates to ideal, stoichiometric hafnia film while the black dots depict Ar bombardment-induced oxygen deficiency within the film. As displayed, the film grown at the center location contains such defects throughout the film (Fig. 7(e)) and that from the edge location has minimal stoichiometric modified regions (Fig. 7(f)).

The stark disparity in stoichiometry is believed to be responsible for the observed difference in response to UV ns-laser exposure. The degradation in the resistance to laser-induced damage is dominated by the sub-stoichiometric clusters in the film. The existence of the oxygen deficiency creates sub-bandgap states which enhances the laser-defect coupling. The facilitation of energy conversion from photon and phonon lead to irreversible materials modification and damage. Other defects such as crystallinity [7] and inclusions [5,6] may also contribute to laser-induced damage in the films through either similar energy coupling or other pathways, however, they may be mostly active at a relatively high fluence. In the systems that are investigated here, the contribution to the observed difference in laser damage threshold by crystallinity is clearly ruled out. As shown in Fig. 5, there is no detectable difference in crystalline microstructure between the two investigated films. Furthermore, RBS analysis shows no observable impurities other than the entrapped Ar in the subject films. As can be referred from Fig. 1(a), there are slight difference in the entrapped Ar between the films: 5.5% for the edge films and 6.5% for the center films; both in atomic percentage. A previous study has shown that the high content of entrapped Ar can lead to nano-bubbles and create potent laser damage prone precursors upon UV ns-laser exposure. [8] However, since the Ar contents in the two film are well above the solubility limit in the dielectric materials, it is likely that the size and density of the Ar-rich nanobubbles within the films are similar. [49] This means that while nanobubbles are a potent damage prone precursor, it cannot account for the stark differences observed in the damage onset. As a matter of fact, it was reported [8] that the laser damage threshold due to nanobubbles of entrapped Ar in hafnia films at a level of 5.5% or greater is around 2.3 ± 0.2 J/cm², which is much higher than that of the center film in the current study. Therefore, while nanobubbles due to entrapped Ar is clearly a high fluence laser damage precursor, sub-stoichiometric clusters are the low fluence laser damage precursors responsible for the observed threshold difference in hafnia films.

Our results suggest that one plausible path to IBS production of hafnia films with high damage resistance to UV ns-laser irradiation relies on the removal of sub-stoichiometric clusters and maintaining the stoichiometric uniformity in the dielectric films throughout the planetary. Such capability would also enable the manufacturing of large aperture optics for high power and energy laser applications. Since the high energy reflected Ar neutrals are mainly responsible for creating the low-fluence laser damage precursor, tuning the energy distribution profile of the reflected neutrals would be desirable, which could be realized by a different deposition configuration and/or sputtering working gas. Although other process parameters such as oxygen flow rate or deposition rate, to name a couple, can affect the film properties, our results do not support that such modifications of the aforementioned process parameters would be impactful to the film stoichiometric uniformity. Nevertheless, further investigation is needed to develop a viable mitigation strategy for improving film stoichiometry and thus the laser damage resistance.

5. Conclusions

Through a comprehensive investigation by a combination of experimental testing and theoretical simulations, we determine that sub-stoichiometry in hafnia films produced by an IBS method is mainly due to the preferential removal of oxygen by energetic reflected Ar neutrals. The sub-stoichiometry occurs only in those films deposited at the center of the rotating planet while the films at the edge locations of the planet are stoichiometric. The chemical anisotropy is attributed to the large difference in the exposure time to the high energy Ar neutrals between the two films during deposition. The sub-stoichiometric clusters in the center films create sub-bandgap electronic states amplifying the facilitation of laser-defects coupling which leads to film damage at a much lower fluence. The ability of producing films constituting the extreme cases of stoichiometric disruption from the same deposition run offers a non-destructive way for isolating and separating defects in dielectric coatings which will be beneficial for future scientific research. Since non-stoichiometric clusters are inevitable in films synthesized by physical vapor deposition including e-beam evaporation, our results elucidate that sub-stoichiometry plays an important role in laser-defect interactions leading to laser-induced damage in dielectric materials. The results also provide insights into the development of strategies for producing dielectric coatings with improved laser damage resistance for UV and ns-laser applications.