Crystallization behavior of ion beam sputtered HfO2 thin films and its effect on the laser-induced damage threshold

In this work, we present our results about the thermal crystallization of ion beam sputtered hafnia on 0001 SiO2 substrates and its effect on the laser-induced damage threshold (LIDT). The crystallization process was studied using in-situ X-ray diffractometry. We determined an activation energy for crystallization of 2.6 ± 0.5 eV. It was found that the growth of the crystallites follows a two-dimensional growth mode. This, in combination with the high activation energy, leads to an apparent layer thickness-dependent crystallization temperature. LIDT measurements @355 nm on thermally treated 3 quarter-wave thick hafnia layers show a decrement of the 0% LIDT for 1 h @773 K treatment. Thermal treatment for 5 h leads to a significant increment of the LIDT values.


Introduction
Thin-film interference coatings, like antireflection or high reflectance coatings as well as wavelength and polarization selective coatings, are key elements of optical components as they allow to tune or even radically alter their optical properties [1,2]. Ion beam sputtered (IBS) multilayers represent the current high-end optical coatings in the VIS/NIR range. Compared to other optical coating techniques, the sputtered atoms have high surface mobility due to their high energies (> 10 eV). Consequently, thin films by means of IBS are amorphous and provide the lowest surface roughness and lowest defect concentration for optical applications [3]. Furthermore, light scattering due to the grain boundaries is avoided in the amorphous film structure. Contemporary IBS allows manufacturing high reflective mirror coatings with optical losses below 1 ppm at a wavelength of 643 nm [4]. In laser applications, SiO 2 and HfO 2 are preferred in the multilayer stack as low and high refractive index material, respectively. Besides low optical losses, low absorption in the UV range, HfO 2 exhibits a high laser-induced damage threshold compared to other high index materials [5][6][7].
However, future applications, like new gravitational wave detectors [8,9] or more precise optical clocks [10], require even smaller optical losses. The primary source of the losses in amorphous mirrors is the Brownian motion of the atoms [8,11]. Current possibilities of circumventing the problem of the Brownian losses are by active cooling during operation e.g. [12], which is neither very efficient nor simple or straightforward. Single crystalline coatings instead of amorphous coatings can achieve an inherent reduction of Brownian loss. This was already shown for optical coatings working in the infrared range by applying epitaxial grown GaAs/Al x Ga 1-x As multilayers and a subsequent substrate transfer [13][14][15].
By the fact that no matching substrates exist for the typical coating layers (e.g. HfO 2 /SiO 2 , Ta 2 O 5 /SiO 2 ), this method is not applicable for coatings in the visible range. To enable applications, which requires single crystalline coatings in the visible range, it is essential to gain knowledge on non-epitaxial crystallization to tailor the process.
Thus, the material and its phase transitions have attracted research interest in the past decades since it also promises high-k dielectric for semiconductor applications. A few reports on the crystallization of hafnia on Si substrates exist. These include thermal crystallization of amorphous oxides [16], thermal oxidation of metallic hafnium [17], observation of spontaneous crystallization during atomic layer deposition (ALD) [18,19], the layer thickness [20] or composition dependence of the crystallization temperature [21] and even an attempt to crystallize the hafnia using laser irradiation [22]. Liu et al. investigated the effect of heat treatment on thick IBS hafnia layers deposited on fused silica and single crystalline silicon substrates and reported a stress reduction accompanying the partial crystallization [23]. A recent publication by Abromavicius et al. [24] revealed that crystallization of IBS-HfO 2 can lead to higher LIDT due to stress reduction and/or better thermal management.

Crystallization
The coating was done by reactive IBS from a metallic Hf-target (Plasmaterials with 3 N purity) using a Veeco Spector 1.5 Dual Ion Beam Sputter (DIBS) instrument. The substrates for XRD measurements were epipolished 10 × 10 mm 2 SiO 2 single crystals with 0001 orientation from CrysTec. Prior to coating, the samples were in-situ treated with energetic O 2 ions (1 keV) for 10 min using the second plasma source of the Veeco DIBS machine.
To achieve complete oxidization, the target was flooded with 35 ccm O 2 during the target cleaning and the sputtering sequence. To investigate thickness dependence of the crystallization, we deposited 10, 15, 20, and 50 nm thick HfO 2 layers on the substrate. We determined the sputter rate using an ex-situ profilometer measurement.
The in-situ XRD annealing experiments were carried out using a Bruker D8 Discovery DaVinci diffractometer. The X-ray beam from a standard Cu Kα source (in this experiment λ = 1.5418 Å) is parallelized in the scattering plane by a Goebel mirror and detected by a LynxEye 1D detector. Since polycrystalline films were expected, we selected a grazing incidence geometry, with ω = 2°as an incoming angle. The 2θ range was 28-35°, which contained the expected main peaks of both the cubic and monoclinic HfO 2 [17]. The single crystalline SiO 2 substrates are zero-background substrates for this method, in contrast to the common fused silica.
The in-situ measurements were carried out using an Anton Paar DHS1100 high-temperature stage. We carried out an isochronal annealing sequence to gain an overall view of the transformation with 50 K steps and a holding time of 30 min using a 10 nm thick specimen. Based on this information, we performed isothermal scans with temperatures between 823 and 923 K using the 15 to 50 nm thick samples. The period between each single scan was 6 min. The scans were repeated until no significant change in the XRD pattern was observed in a few subsequent scans. Figure 1 shows the cubic (111) HfO2 peak's proximity in a typical scan (50 nm thick layer, 823 K, 30 min). To integrate the peaks, the background was deduced by a simple linear function approximation, marked by a gray line in Fig. 1. From the peak areas, the transformed fraction f (normalized peak area) was calculated and later fitted as a function of the time t in accordance to the JMAK-equation [25]: with the two fitting parameters: 1 + n' and t c . Hereby the well-known Avrami-exponent containing information on the nucleation and the growth is presented in 1 + n' form. Assuming a constant nucleation rate, the exponent n' is the dimensionality of the growth, e.g. n' = 3 means three dimensional or volumetric growth, while n' = 2 means two dimensional or film like growth. The t c factor is the crystallization time, which can be derived from the N nucleation and G growth rate: Rewriting Eq. (1) into: a linear fit can be performed to determine the parameters t c and n'. This fitting strategy is more sensitive in the detection of changes in the dimensionality. To verify the measurements' consistency, the raw data and the fitting function were also compared with the transformed function vs. time scale (e.g. Eq. 1).
To estimate the activation energies of the crystallization, an Arrhenius-plot was performed according to: where the t c is dependent of the temperature T and the layer thickness d, t 0 , d is a layer thickness dependent prefactor, Q is the layer thickness independent activation energy, and k B is the Boltzmann-constant. Finally, we investigated the sample surfaces in their asdeposited and annealed state using a Veeco Dimension 3100 atomic force microscope (AFM).

Laser-damage testing
For the LIDT measurements, we used P4 polished (rms roughness of about 3 Å, scratch-dig 20-10) fused silica substrates provided by WZW Optics AG. We chose a layer thickness of 3 quarter-wave @355 nm, which ensured an electric field maxima in the layer itself. We produced three sets of specimens; the first set was left in the as-prepared state ("amorphous"), the second one we annealed at 773 K for 1 h ("intermediate"), while the last set was annealed for 5 h at 773 K ("crystalline").
Laser-damage testing was performed using a Litron LPYG-450-100 diode-pumped laser at 355 nm [26]. The repetition rate was 100 Hz, while the pulse duration was 11.6 ns. The effective beam diameter, calculated according to ISO 21254-1:2011 [27], at the surface was 230 μm. The specimens were acclimatized for 24 h before the experiments in the laboratory (20°C temperature, < 50% relative humidity). We carried out S-on-1 measurements with S = 5000. At least 150 sites were irradiated with appropriately chosen laser fluences. We performed the well-known but non-ISO conform test data reduction according to Jensen et al. [28] to improve the data quality in the relevant regime.
We used a scattered light detector to identify the first damage. To verify the detected damage events, a visual inspection through a differential interference contrast microscopy (Leica DM4000 M Led) was performed.
According to the ISO norm 21,254 [27], for each test site, there are three pieces of information: 1.) whether the site is damaged (1/0), 2.) the applied laser fluence Q, and 3.) the number of pulses applied before the damage onset N min . If no damage took place, this value is S. The derived data is the probability of damage by a given combination of Q ± ΔQ fluence interval and N pulse number. A site is considered damaged if The cumulative test method [28] assumes that if an experiment with any fluence of Q' > Q and N min pulses damage would also have been observed.
There are different interpretations of the data. We chose the following two: 1.) the characteristic damage curve or the probability of damage if S pulses are applied at a given fluence 2.) the damage probability as a function of the fluence a given number of pulses.
The specimens used in the laser-damage testing were also checked in ex-situ measurements for their crystallinity using a PanAlytical Empyrean X-ray diffractometer. This system is also equipped with a Cu Kα source. We applied two methods GIXRD at ω = 2°to identify the crystalline phases and X-ray reflectometry (XRR) to determine the density of the layers.

Crystallization
The crystallization was first observed at 973 K for the 10 nm thick films, and the phase was identified to be cubic HfO 2 . After increasing the temperature to 1273 K, a transformation to the stable monoclinic phase took place. We carried out room temperature ex-situ measurements with slow scan speeds for a better signal-tonoise ratio. These scans are shown in Fig. 2.
Since the intensity of the peaks for 10 nm thick layers were not high enough for reliable kinetics experiments, we studied the crystallization kinetics only of the 15-50  Figure 3a shows an example of such kinetics: the development of the cubic (111) peak for the 50 nm thick HfO 2 film annealed at 823 K. In Fig. 3b, the measured and the fitted transferred fraction as a function of time are shown for the 50 nm HfO 2 film. The small insert gives the logarithmic plot in accordance to Eq. (3). The fitting function is in good agreement with the measured data both in the linear and logarithmic scale. The n' exponent, in this case, is 2.15 ± 0.1 for this experiment, and no deviation from this behavior is visible in the early stages. The transformation for the 50 nm film took place at a much lower temperature than for the 10 nm thick film. Table 1 summarizes the crystallization times for the different temperatures and the corresponding dimensionality of the growth n' for the different investigated film thicknesses. For some experiments, the crystallization was too fast. Consequently, only an upper limit of the crystallization time can be given in these cases. We evaluated the exponent n' only where the amount of data could provide a reliable fitting.

Laser-damage testing
To gain information on the crystallinity state of the sample GIXRD was performed on the samples used in the laser damage test. Figure 4 shows the results of these   GIXRD experiment for the 5 h annealed "crystalline" specimen. Fused silica is not an ideal substrate for such investigations since the broad peak centered around 32°c ould belong to either SiO 2 or HfO 2 . Nevertheless, the much sharper c-HfO 2 peak could be separated and characterized (Fig. 4b). Table 2 shows the results of GIXRD and XRR experiments: the ratio of the peak area of the c-HfO2 to the amorphous peak, the Scherrer-size of the crystallites, and the layer density. Figure 5 shows the results of the LIDT experiments using two interpretations. In Fig. 5a, the damage probability (N = 5000) is plotted as a function of the pulse energies for the different specimens. In Fig. 5b, the 5% LIDT is plotted against the number of pulses.
It can clearly be seen from Fig. 5a that the "crystalline" specimen has the highest damage onset, highest 0% LIDT and its 100% LIDT is not worse than that of the "amorphous" specimen. Surprisingly the "intermediate" specimen produced the worst result.
A similar trend can be seen for the 5% LIDT curves. The "crystalline" specimen shows higher laser-damage resistance for all but the lowest number of laser pulses than the "amorphous" one. On the other hand, the "intermediate" specimens show consequently the worst 5% LIDT values. The differences are larger than the expected measurement scatter.

Crystallization
As it can be seen in Table 1, crystallization experiments performed on the 15, 20, and 50 nm thick films provided exponents of about 2, which indicates a two-dimensional growth. This shows that the distances between different nucleation centers are larger than the 50 nm film thickness. This is supported by the findings of the atomic AFM measurements shown in Fig. 6. Figure 6a shows the AFM of the 50 nm HfO 2 coated sample before while Fig.  6b shows a specimen after the thermal treatment. The smooth surface (RMS roughness 0.26 nm) of the as deposited sample changes to structured surface with a RMS roughness of about 0.65 nm. The needlelike and triangular structures with a few hundreds of nanometers lateral dimensions and 5-10 nm height have a mean distance in the micrometer range.
In Fig. 7, all crystallization times are plotted as a function of the inverse temperature. The depicted lines are the fitted Arrhenius-type functions.
The average activation energy turned out to be 2.6 ± 0.5 eV, while the prefactors for the 50, 20, and 15 nm layers are respectively 5.8 × 10 − 14 s, 8.4 × 10 − 14 s, and 1.7 × 10 − 13 s. This ratio of 1:1.5:3 is comparable to the layer thicknesses. Thus, in our experiment, the layer thickness dependence is probably a consequence of the crystallization's two-dimensional nature. For this situation, the nucleation rate per area and not per volume is decisive for the transformation rate. For a thinner film, even for equal volumetric nucleation rate, there is a much-reduced number of nuclei per area.  In general, crystallization is getting easier with an increasing layer thickness, even though our layers are much thicker than the 1.5-5 nm critical thickness reported by Nie et al. [20].
According to Eqs. (1)(2)(3), the transformed volume fraction is dominated by the growth term even for twodimensional growth modes. Short and long-range atomic jumps i.e. diffusion is a thermally activated ratecontrolling process which usually plays a crucial role in crystallite growth. Since hafnia has two sublattices it is interesting whether the cation or the anion jumps are controlling the crystallization.
The activation energy of 2.6 ± 0.5 eV is much higher than the reported experimental activation energy of 1 eV for oxygen self-diffusion in monoclinic hafnia [29]. Some theoretical reports [30,31] assume even lower oxygen activation energies.
We found no report on the self-diffusion of Hf in the different HfO 2 phases. However, ZrO 2 phases have almost identical lattice parameters as the respective HfO 2 phases. Thus, it is often used for comparisons. An experimental series by Swaroop et al. [32] to compare the diffusivity of different cations in yttria-stabilized tetragonal zirconia has shown that Hf′s activation energy is virtually identical to that of the Zr (5.3 eV for lattice and 3.8 eV for grain boundary diffusion).
Computational studies e.g. Refs [33,34] on the Zr selfdiffusion lead to an activation energy well above that of the oxygen's (2.5 eV or higher). During the sintering of ZrO 2 particles, Suárez et al. found that the activation energy of Zr self-diffusion in ZrO 2 is 2.3 eV. Furthermore, they also reported that it is the Zr self-diffusion, which controls the sintering process [35]. Our activation energy of 2.6 ± 0.5 eV is comparable to that of the cation diffusion in ZrO 2 . Therefore, cation atomic jumps could play a more important role in the crystallization of HfO 2 films.

Laser-damage testing
Thermal treatment to cure defects and/or reduce stress levels is a well-known method for improving the laserdamage threshold (e.g. [23,24,36,37]). However, typical annealing treatments stay well below the crystallization limits, as the presence of grain boundaries leads to an increase in the scattered light.
Nevertheless, in the case of hafnia, it is also proven that crystallization [24] is an efficient method of increasing the single layer LIDT and multilayer coatings. Our results for the long annealing times are in qualitative agreement with this finding. We did not observe the very prominent increase of the LIDT as reported in [24], which is not surprising as we annealed at a lower temperature of 500°C instead of the 600 and 700°C marked as the optimal "high-temperature" annealing by Abromavicius et al. Indeed the observed Scherrer-size indicates that HfO 2 crystallites are either very small or they are highly strained [38]. Irrespective of the origin of  the line-broadening, the layers did not reach a relaxed, coarse-grained state. We also found an intermediate decrement of the LIDT values, which is not reported in [24] and worth further investigation. One explanation for the small Scherrersize is high stress, this according to our own experience leads to low LIDT [39]. The other possibility is a high concentration of grain boundaries, which according to Tateno et al. [40] can also be a cause for reduced LIDT. Due to the higher temperatures, no comparable specimen was present in Ref. [24], which could explain why we observed a reduction of the LIDT.

Conclusion
We analyzed the crystallization kinetics of IBS deposited HfO 2 via in-situ XRD. We found that the crystallization for thin films up to 50 nm thickness follows the twodimensional growth mode. The activation energy of the crystallization kinetics is 2.6 ± 0.5 eV which indicates that the displacement of Hf atoms could play a rate controlling role in the crystallization.
We have proven that crystallization leads to a higher LIDT value. However, we also found that a decrement of the laser-damage resistance takes place at an intermediate stage.