1. Introduction

Due to outstanding characteristics such as a high spectral range of transparency, hardness and mechanical stability, sapphire has become a key material in optics, photonics, and electro-optics [1]. Especially in the case of UV applications surface roughness of sapphire optics is an important issue since roughness peaks may cause severe scattering or diffuse reflection where the effect increases with decreasing wavelength [2]. Apart from scattering, roughness also impacts the index of refraction of surfaces where an increase in surface roughness comes along with a decrease in apparent index of refraction [3]. Hence, it has also a certain impact on the performance of optical coatings deposited on surfaces that feature a certain residual roughness. Moreover, roughness and scattering might lower the laser-induced damage threshold of laser optics [4,5]. Thus, super-polishing of sapphire was investigated extensively in the past and quite different methods are applied as summarized in [6]. An appropriate technique for finishing surfaces with lowest residual roughness values is classical chemical mechanical polishing (CMP). Here, the impact or efficiency of different polishing suspensions and further process-related phenomena were studied by several authors [7–11] since CMP is an extraordinary complex process. Depending on the process and eventually assisting techniques, roughness values in the range of some tens of picometers [9,12,13] to some angstroms [14] can be achieved. In addition to CMP, magnetorheological finishing has turned out to be suitable for sapphire surface finishing where the final roughness amounts to some angstroms [15]. A quite young technique is plasma polishing where material removal of sapphire can be obtained by using hydrogenous and thus chemically reacting process gases [16]. However, even though super-polished surfaces generated by applying such techniques feature noteworthy low residual roughness, the effect of scattering may still causes detectable losses of light [17].

Another approach, polishing by direct dielectric barrier discharge (D-DBD) plasmas operated with an inert process gas was presented in previous work [18,19]. It was shown that such treatment, which comes along with plasma-induced surface cleaning, allows a significant increase in laser-induced damage threshold of super-polished sapphire surfaces [20].

However, up to now, merely the proof of principle of inert gas plasma smoothing of optical media was reported where local plasma treatment was applied to fix surface spots and the measured area was merely 2.5 × 10⁻³mm² [19]. Besides a pure reduction in surface roughness, the aspect of large-scale roughness homogeneity is yet of notable interest since roughness may vary significantly over the surface area or cross section of a component [21]. Such variation is equivalent to a local variation in reflection or transmission since both parameters are directly related to surface roughness as for example expressed by the total integrated scatter (TIS) function [2]. However, the aspect of roughness homogeneity over the surface of an optically active surface is neither covered by the pertinent standards nor discussed in literature. Against this background, the impact of D-DBD plasma post-processing on surface roughness homogeneity of large-scale optics surfaces was investigated in the present work.

2. Materials and methods

Investigations were performed on circular plane plates made of sapphire with a diameter of 60 mm polished by classical grinding followed by chemical-mechanical polishing. The initial root mean square roughness (RMS) of these plates after polishing was RMS = 10.7 ± 5.2 angstrom, thus representing a precision polished surface [22].

For plasma post processing, a D-DBD source as introduced in more detail elsewhere [18,19] and schematically shown in Fig. 1(a)) was applied. For efficient ignition at atmospheric pressure, argon was used as process gas where the gas flow was 4 standard liters per minute. The plasma source was operated by high-voltage pulses with a peak-to-valley voltage of 12 kV and a pulse repetition rate of 7 kHz where the distance between the plasma nozzle outlet and the sample surfaces – i.e. the discharge gap thickness – was 7 mm. The electrical power dissipated by the plasma was 1.2 W as calculated by the Electric Current method [23]. Due to the principle of DBD plasmas, the sample surface heating is quite low, i.e. below 100°C [24]. The footprint diameter of the plasma on the sample surface amounts to some few millimeters. In contrast to previous work [19], the samples were thus moved meander-like by an xy-linear stage in order to obtain polishing on the entire surface by overlapping the treatment paths as shown in Fig. 1(b)). The duration of a single treatment cycle was 33 minutes where the plasma dose applied to the sample was approximately 0.84 J/mm². Different numbers of cycles and plasma doses, respectively, were applied to the samples as listed in Table 1.

 

Fig. 1. a) Schematic of the experimental setup used for plasma post-processing including photograph of the used plasma source (inlet); b) visualization of the meander-like treatment path of the plasma footprint on the sample surface.

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Table 1. Sample denomination and particularly applied number of treatment cycles and related parameters

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Before and after plasma post-processing, the RMS surface roughness of the samples was measured via white light interferometry (ADE Phase Shift, model MicroXAM Surface Mapping Microscope) where a 10x objective with an imaging field size of 1.491 × 1.494 mm² and a lateral resolution of 690 nm was used. Since the roughness was thus determined for an area instead of a cross section, it corresponds to the area root mean square roughness Sq according to ISO 25178. Measurements were performed at five different positions: one measuring point on the sample center and four points at the sample edge in a cruciform arrangement as visualized in the inlet in Fig. 3. Each measured roughness value presented hereafter represents the mean value of four single measurements per point. It should be noted that the entire measured area (≈ 11.12 mm²) was about 4,450-times larger than the area measured in previous work (≈ 2.5 × 10⁻³mm²) [19]. Such large-scale measurement was applied in order to gain information on the effect of plasma-induced homogenization of surface roughness.

The RMS roughness value is of specific interest for the characterization of optically active surfaces used for UV or laser optics since it is directly related to diffuse reflection and scattering via the so-called total integrated scatter (TIS), given by

Here, AOI is the angle of incidence of light and λ its wavelength. Multiplying the TIS and the total reflection R_t at any surface gives the percentage of diffuse reflection, R_d = TIS·R_t. [25].

3. Results and discussion

For a first overview, the average values of the RMS roughness of all treated samples before and after plasma treatment were determined as shown in Fig. 2. Here, the general impact of plasma post processing becomes obvious: First, the roughness is notably decreased by a factor of 2.9. Second, the standard deviation is much smaller after plasma treatment; it is reduced by a factor of 8.7.

 

Fig. 2. Comparison of the average values of the mean square roughness RMS before and after plasma treatment including standard deviation resulting from measurement at 15 measuring points on the surface.

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The latter fact demonstrates that the homogeneity in terms of the lateral distribution of roughness values over the plasma post-processed sample surfaces was notably improved. This is also confirmed by (i) the roughness raw values measured at five different positions on the three sapphire samples as shown in Fig. 3 and (ii) the direct comparison of the associated standard deviations of the single samples represented in Fig. 4.

 

Fig. 3. Comparison of the raw values of the mean square roughness RMS of the three samples (S1 to S3) before (a) and after (b) plasma treatment; inlet: definition/visualization of measuring point positions on the circular sample surface.

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Fig. 4. Comparison of the particular standard deviations for the mean square roughness RMS the three samples (S1 to S3) before and after plasma treatment.

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As visualized in Fig. 3(b), quite constant final roughness values of RMS = 3.7 ± 0.3 angstrom are obtained regardless the applied number of plasma treatment cycles. This also applies to the standard deviation and thus the roughness homogeneity as shown in Fig. 4. It thus turns out that the effect of smoothing and homogenization preferentially occurs in the course of the very first cycle. Further cycles – which is equivalent to an extension of the actual treatment duration – do not lead to any mentionable further smoothing.

Such saturation effect was also observed in previous work where the proof of concept of inert gas atmospheric pressure plasma polishing of different optical media including sapphire was presented [19]. Here, saturation of the smoothing effect was observed after some minutes of static and localized plasma treatment as shown in Fig. 5. It should be noted that in this case, the absolute roughness was in the range of some nanometers instead of some angstrom. Since in contrast to the present work, plasma treatment was performed locally on fix surface points with an extension of about 50 × 50 µm², the values were measured using atomic force microscopy (AFM, Nanosurf GmbH, model easyScan2) instead of white light interferometry. Such measurements were performed in air, applying the AFM’s contact mode.

 

Fig. 5. Root mean square roughness RMS vs. plasma treatment duration, visualizing the smoothing saturation effect during inert gas atmospheric plasma post processing of sapphire; AFM data taken from [19].

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As verified by simulations this behavior can be explained by the ignition characteristics of the plasma. Since the sample surface is placed directly within the discharge gap, roughness peaks lead to a local deformation of the electric flux lines. The electric field strength is thus increased at roughness peaks. Locally-selective material removal can then be induced by several mechanisms. First, field emission of electrons and subsequent Coulomb explosion of remaining positive atomic kernels [26], eventually supported by ionization of sapphire material by electron impact [27] may occur. Second, local impact of argon ions from the plasma that are accelerated by the sheath-effect and an accompanying input of kinetic energy [28] can cause material removal. This also applies to the third possible effect, an energy input due to de-excitation of excited plasma species such as metastable argon atoms [29] that are generated by recombination of argon ions with negative charges [30]. These mechanisms fade away with decreasing surface roughness and the accompanying increasing homogeneity of the electric field. Once such saturation is obtained, the adaption of plasma parameters and the electric field strength, respectively, may allow for further smoothing. In the present case, smoothing occurs at an average electric field of E = 84 Vm, i.e. the product of the applied voltage and the discharge gap thickness.

However, roughness – or its homogeneity – over the optically active surface of an optical component is not the only parameter of interest. It should thus additionally be mentioned that the applied plasma post-processing process did not impair the form or accuracy of the plane sapphire surfaces. This was ascertained via auxiliary interferometric measurements of the planeness of the sample surfaces using a commercial interferometer (Zygo Corp., model GPI-XP) where the measured area was 2 × 2 cm². During such measurement, tilt correction was applied. It turned out that neither the planeness was affected nor additional surface errors at higher spatial frequencies, e.g. waviness, were generated. The surface power was 1.931 µm before and 1.926 µm after plasma treatment. The peak-to-valley (PV) value as well as the RMS surface accuracy error also remained almost constant, i.e., PV = 2.784 µm and RMS = 443.79 nm before and PV = 2.723 µm and RMS = 439.66 after plasma post-processing, respectively.

Hence, the observed effect of homogenization is of potential interest for surface finishing of sapphire optics and preferentially for UV applications since it directly results in both a reduction and a homogenization of residual surface scattering. For smooth surfaces as investigated in the present work and assuming normal incidence, Eq. (1), which characterizes scattering, can be simplified and rewritten as

This reduced formula is referred to as the paraxial TIS approximation [31]. Here, it was used for calculating the theoretical TIS ranges occurring between the minimum and maximum roughness values before and after plasma treatment as shown in Fig. 6. The areas displayed here thus represent the possible amount of scattering as a function of wavelength. For better comparability, a common scaling of the y-axis was chosen. The TIS values of post-processed surfaces with adapted scaling are moreover shown in the inset.

 

Fig. 6. Comparison of total integrated scatter (TIS) values calculated for untreated (left) and plasma post-processed (right) sapphire surfaces, defining the possible TIS range.

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Even though the absolute value of TIS is generally extremely low, i.e., in the range of some ppm to some hundreds of ppm, the notable impact of roughness inhomogeneity can clearly be seen as also visualized by the following example: Sapphire windows are classically used as output couplers for excimer laser sources where one of the main applications is excimer laser annealing (ELA) where krypton fluoride (KrF) lasers [32] or xenon chloride (XeCl) lasers [24] are applied. For the first case, where the wavelength amounts to 248 nm, the TIS caused by the roughness of untreated sapphire samples investigated in the present work varies from 3 to 122 ppm – the theoretical scattering inhomogeneity is thus 119 ppm. After plasma post-processing and the accompanying decrease in surface roughness and homogenization in terms of lateral distribution in roughness values, this value range is merely 2 to 7 ppm. Since the scattering inhomogeneity thus amounts to 5 ppm, it is reduced by a factor of about 24.

4. Conclusions

To summarize it can be stated that the used approach – inert gas plasma post-processing using a ‘cold’ direct dielectric barrier discharge at atmospheric pressure – gives rise to two main effects. On the one hand, the surface roughness of precision polished sapphire windows is significantly further reduced to merely a few angstrom. Such general smoothing effect was already observed in previous work where the basic proof of principle of this approach was reported. On the other hand, surface roughness homogeneity is extensively increased; the variation in lateral distribution of roughness values over the sample surfaces is thus reduced without any impairment of the surface shape or form accuracy. Moreover, surface errors at higher spatial frequencies that could be expected due to the treatment strategy do not occur. To our best knowledge, this work thus represents the first study on the improvement of large-scale homogeneity – and not a pure reduction – of surface roughness of sapphire optics. These novel findings show that the basic effect of inert gas plasma post processing features a certain notable potential for surface finishing of precision optics made of sapphire. As a result of such homogenization, the lateral variation of roughness-related essential optical properties such as scattering, reflectance, transmission and even the apparent index of refraction is decreased. This aspect is of specific interest for the realization of UV and laser optics and especially large-scale components where local differences in surface roughness may not only affect pure optical properties, but also cause a reduction in laser-induced damage threshold.