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methods. Despite the knowledge of its health risks, hydrofluoric acid( HF) is still applied for experiments [ 5 – 7 ]. However, meanwhile potassium hydroxide( KOH) solution replaces the highly toxic HF, even though KOH is still very corrosive [ 3, 8, 9 ]. The etching process leads to a crack expansion which requires precise control to accurately correlate removal and damage depth [ 10 ].
A number of researchers have been investigated the surface effects that are affected by chemical etching. The focus is currently still on wet chemical etching, where efforts are being made to understand the etching effect and create models based on specific processes, e. g., hydrofluoric-based etching. This resulted in several publications over the last years on the topic of modelling mainly the isotropy of etching processes. Such models are based on finite elements approaches. In 1990, Katardjiev et al. used numerical analysis to investigate the development of semiconductors surface during the growth and removal [ 11 ]. They applied the Huygens principle of wavefront propagation, which states that every point on a wavefront is the starting point of a new wave. These elementary waves overlap to form a new wavefront. Almost 30 years later, this approach was applied to describe the expanding of scratches during wet chemical etching of fused silica with a finite element model [ 12 ]. Lui et al. investigated the hydrofluoric acid-based etching effect on surface defects of FS optics [ 6 ]. They performed finite difference time domain( FDTD) simulations and proposed a local-curvature-dependent model to explain etching rates on rough surfaces [ 6 ]. In a comparison of wet chemical etching and dry etching by medium pressure plasma process, Krishna et al. concluded that overall both processes are isotropic, while the kind of attacks differ [ 13 ]. With the applied dry etching process in medium-pressure setting, the first removal can be seen at the peaks which as a result decrease, while chemical wet etching causes a uniform enlargement of the holes, laterally and in depth [ 13 ]. The influence of an atmospheric pressure plasma jet to FS having selective indentation defects, created using a Vickers test indenter was investigated by Jiao et al. [ 14 ]. Based on the simulation results of the 3D-level-set method, the research group was able to confirm the isotropic etching process of FS, which, however, also exhibits anisotropic properties at the crack edges [ 14 ]. These studies focus mainly on defect models or measured individual defects and their progress at shallow etching depths.
As an alternative, the application of the atmospheric plasma jet( PJ) provides a controlled, local etching process with almost less health risks. PJ technology has been established for more than two decades, mainly applied for form generation and figure error correction of freeform optics [ 15 – 18 ]. In this paper, we present a study on the SSD preparation in fused silica surfaces employing plasma jet etching. A simplified mathematical approach has been developed to model the isotropic etch front evolution. SSD morphology has been investigated on indentation-induced cracks, single scratch-generated defects and SSD caused by mechanical grinding. A comparison with experimental etch front determination is made, resulting in the evaluation of the lateral distribution of an isotropic etch factor. With the help of this factor the distribution of SSD depths can be determined.
2 Experimental
Targeted material removal was obtained by dry chemical etching applying an atmospheric pressure PJ. Since the process details have already been described in numerous publications [ 16, 17, 19 ], only a few main facts will be given. The PJ source is based on a coaxial conductor system where the main process gases helium( He), oxygen( O 2), and tetrafluoromethane( CF 4) are supplied through the inner conductor. Nitrogen( N 2), affecting as shield gas, is supplied peripherally. The plasma discharge is ignited at the nozzle by excitation with microwave energy( MW, f 2.48 GHz). The generated PJ interacts with the sample surface converting SiO 2 into gaseous products SiF 4 and O 2 which causes the material removal. The PJ source operates in a conventional CNC motion system. Etching is performed stepwise where the etching depth varies for the different types of defects. Using this method, it is possible to successively expose cracks reaching into the material. Smaller etching depth increments provide more detailed information about the etching mechanism, while larger increments enable deeper etching to be achieved more quickly.
3 Material and methods
Etching experiments have been performed on fused silica samples of size 40 40 10 mm( Corning Inc.). In order to generate defined SSD characteristics, two different methods were used. Static indentations by a Vickers tip, schematically shown in Figure 1A and a scratch test device applying a Rockwell-Diamond tip given in Figure 1B were employed to imitate an abrasive grain moving over the sample surface. Mechanical preparation of the samples was done by University of Applied Sciences in Jena.
In order to prove the developed method for SSD depth determination, it was finally applied to a mechanically ground and polished sample( diameter: 50 mm / thickness: 8.3 mm) provided by Layertec GmbH.
3.1 Surface topography measurements
After each plasma jet etching step, the surface topography was measured using white light interferometer( WLI, NPflex, Bruker Corp.). For cases where WLI was not applicable due to strong surface gradients leading to data dropout, a confocal microscope( lsurf explore, NanoFocus AG) was employed. The confocal microscope provided more information about the shape, especially of deep indentations with steep sidewalls. The field of view was 231 173 lm 2 for WLI measurements and 320 320 lm 2 for the confocal microscope, respectively. In preliminary tests the correspondence of the results obtained from both measurement devices was proven.
3.2 Etch front calculation method
To model the local removal during plasma treatment assuming isotropic etching, the etch front was simulated starting at a measured surface topography described by