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Abstract
Capacitively coupled atmospheric pressure plasma processing (CCAPPP) has been developed as a sub-aperture figuring tool for high precision fused silica optics, due to deterministic high rate material removal, small tool spot and no induced subsurface damage. In order to carry out an in-depth understanding on the removal and surface morphology formation mechanism of CCAPPP, this study aims to model the plasma discharge process and surface chemical reaction using the multi-physics simulation. The discharge characteristics such as electron density, electron temperature and particle density in the plasma are firstly obtained. Reaction gas components (CF4 and O2) are also added, and the main chemical reactions are analyzed by zero-dimensional modelling. Then the distribution of active atoms (active F atoms, O atoms and CFx molecules) related to the removal process is simulated in the full CCAPPP model. Finally, experiments are carried out to verify the simulation results, indicating that the distribution of active F atoms on the workpiece surface determines the Gaussian removal profile and the ratio of O/CFx is the key factor affecting the surface morphology formation of CCAPPP.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High precision fused silica optics are widely used in high-power laser, telescope and ultraviolet optical systems [1–4]. Various deterministic sub-aperture polishing techniques have been developed to achieve surface finish and form accuracy down to nanometric level, including bonnet polishing (BP) [5,6], magnetorheological finishing (MRF) [7,8], fluid jet polishing (FJP) [9], ion beam figuring (IBF) [10,11], etc.
Among them, atmospheric plasma etching becomes a promising optical figuring tool as it can achieve deterministic high rate material removal, controlled millimeter tool spot and no subsurface damage. The removal principle is that chemically reactive fluorine radicals produced by the plasma react with silica-based materials to form volatile compounds. Jourdain et al. [12] adopted the reactive atom plasma (RAP) process for figuring of large fused silica optics. An inductively coupled type plasma torch with De-Laval nozzle was installed on a surface figuring machine called Helios 1200. A Gaussian removal footprint was generated with nanometric material removal repeatability. An adapted tool-path algorithm was combined with an iterative figuring procedure for the management of heat transfer. More commonly, capacitively coupled plasma is adopted for high precision processing applications. Su et al. [13] investigated capacitively coupled atmospheric pressure plasma processing (CCAPPP) to fabricate large aperture continuous phase structures. Iterative dwell time algorithm was developed for the nonlinear removal rate during fused silica processing. The results indicated that CCAPPP has potentials to fabricate complex structured phase plates down to 0.1 λ (root mean square). Meister and Arnold [14] investigated the thermal issue in the atmospheric plasma jet machining (PJM) of fused silica. A three-dimensional finite elements heat transfer model was established to consider spatio-temporal variations of surface temperature and temperature dependent material removal. The machining convergence was improved by an iterative correction of the targeted material removal according to thermal modelling results. Takino et al. [15] proposed chemical vaporization machining (CVM) with radio frequency plasma with a hemispherical tip electrode in an atmospheric environment. The curvature center of the hemispherical tip was positioned normal to the workpiece surface at the removal point. Experimental studies showed removal profiles were not sensitive to various slope angles over the curved surface, which allowed the fabrication of a highly curved optics under three-axis motion control.
Most of the aforementioned studies focus on surface form figuring using atmospheric plasma processing techniques. The Gaussian removal contour (tool influence function) is obtained experimentally and iterative figuring experiments are necessary to converge the surface error to specification. Also, it is found that the surface morphology is roughened after plasma processing and post smoothing experiment needs to be performed [16–18]. Xin et al. [19,20] investigated experimentally the morphology evolution of ground fused silica after processed by atmospheric plasma. The roughness development mainly resulted from opening and coalescing of the plasma-etched cracks. In microscopic perspective, surface formation and damage removal were resulted from pits growing larger and merging with one another. Arnold et al. [18] found that chemical contaminants on the surface and substrate structural defects introduced into the sub-surface region by grinding and other abrasive techniques were preferably etched by fluorine atoms. Due to the chemical etching mechanism, the surface roughness might increase during processing. However, little research has been carried out on the modelling of atmospheric plasma processing to investigate Gaussian removal characteristics and surface morphology formation, which is of fundamental importance to optimize the process.
In order to carry out an in-depth understanding on the removal and surface morphology formation mechanism of CCAPPP, this study aims to model the plasma discharge process and surface chemical reaction using the multi-physics simulation. The discharge characteristics such as electron density, electron temperature and particle density in the plasma are firstly obtained. Reaction gas components (CF4 and O2) are also added, and the main chemical reactions are analyzed by zero-dimensional modelling. Then the distribution of active atoms related to the removal process is simulated in the full CCAPPP model. Finally, experiments are also carried out to verify the simulation results to investigate the removal contour and surface morphology formation.
2. CCAPPP device and removal characteristics
2.1 CCAPPP device configuration
According to the principle of dielectric barrier discharge (DBD) and CCAPPP, a needle electrode plasma torch as shown in Fig. 1 is designed. A 13.56 MHz radio frequency (RF) power is applied to the central aluminum needle as a positive electrode and the workbench is grounded. Thus the substrate (fused silica) placed on the workbench serves as a dielectric barrier layer. In addition, a ceramic nozzle coaxial with the needle electrode is used to restrain the gas flow. The inner mixed gas, including He, O2, and CF4, can be excited in the RF electromagnetic field. The flow rates of gases are controlled by the multichannel mass flow controller. During the processing, the plasma is generated between the surface of the substrate and the needle electrode, and the high-density active particles directly act on the surface of the substrate.
In order to determine the discharge mode of the needle electrode torch, the voltage and current during plasma discharge are measured by a high-frequency voltage and current probe. And the Lissajous Fig. is calculated, as shown in Fig. 2. The U-I curve of the needle electrode discharge is shown in Fig. 2 (a). It can be seen from Fig. 2 (b) that there are multiple curved steps on both sides of the Lissajous Fig., indicating the pseudo-glow discharge. Therefore, the discharge section of the needle electrode torch is a pseudo glow zone, which is suitable for processing on the surface of the material. The pseudo-glow discharge has good uniformity and the active particle density is high, which is more suitable for processing material surfaces.
2.2 Removal characteristics
The plasma (He and O2) generated by radio frequency power can be regarded as a chemical reactor; the reactant gas (CF4) fed into the reactor is decomposed by the collision of plasma electrons into active species [21]. These reactive radicals (F) which are carried by plasma jet flow, diffuse to the substrate and react with the fused silica surface (SiO2) to accomplish the nanometric removal process. The balanced chemical reaction equation can be described as follows:
Table 1. Atmospheric plasma processing parameters
The fused silica surface morphology before and after CCAPPP is also compared in Fig. 4. The original sample surface was polished and totally transparent, as shown in Fig. 4 (a). It is interesting to note that after the static processing, an opaque annular area was observed, as shown in Fig. 4 (b). The observed outer diameter was 12 mm, which was equivalent to the spot size of the removed profile.
It is clear that the Gaussian removal function of CCAPPP is favorable for error figuring in optic processing. On the other hand, accompanying opaque morphology will reduce the performance of optical components. Therefore, it is very important to analyze the causes of this phenomenon. From the perspective of surface chemical reaction, this study aims to investigate CCAPPP removal function and the formation of the opaque morphology by means of multi-physics modelling.
3. Modelling approach and simulation analysis
3.1 Modelling approach for CCAPPP
This section will focus on the modelling of the discharge process and surface chemical reaction of CCAPPP, in order to investigation the mechanism of material removal and surface formation. The modelling and simulation is performed using the plasma module in the commercial multi-physics simulation software COMSOL. For CCAPPP simulation, four aspects need to be considered, including electron transfer, heavy particles transfer, electrostatic field and plasma chemistry.
By multi-physics modelling, the electron density, electron temperature, and the distribution of various particles in the space can be obtained, and the relationship between the plasma discharge and the surface morphology can be analyzed. Due to the complexity of the device structure and reaction process in the actual processing, the specific simulation process can be decomposed into three steps:
- (1) The establishment and simulation of a simplified two-dimensional needle electrode capacitive coupled discharge model to verify the feasibility of multi-physics simulation;
- (2) Identification of dominant chemical reactions (related to He, CF4 and O2) through zero-dimensional chemical reaction analysis;
- (3) The establishment and simulation of a full two-dimensional CCAPPP model under actual experimental conditions, including two-dimensional needle electrode discharge, primary chemical reactions, as well as flow rate and the spatial distribution of reaction gases.
3.2 Modelling approach for CCAPPP
3.2.1 2D needle electrode discharge model
Although plasma generated in this work is under high pressure (atmospheric pressure), the discharge process is in the pseudo-glow region and continuous (described in section 2.1). Therefore, it can be analyzed by solving continuity equations in COMSOL. COMSOL plasma module can solve drift-diffusion equations of electron density, electron energy density, Poisson equation, the transport equations of particles and the chemical reaction equations. It can simulate either time-dependent or steady state 0D, 1D or 2D model. The output of the model includes electron density and electron temperature distribution, electric field strength and density distribution of all particles. In order to investigate capacitively coupled plasma discharge process of needle electrode and verify the feasibility of simulation, this section first establishes a simplified two-dimensional needle electrode model, as shown in Fig. 5. In this model, it is assumed that there is only a uniform He distribution under atmosphere pressure in the discharge region. The model consists of a needle electrode with a radius of 1.5 mm and a workpiece with a thickness of 3 mm. The distance between the tip of the electrode and the upper surface of the workpiece is 2 mm. The upper surface of the workpiece adopts the wall boundary condition, and there exists charge accumulation; the lower surface of the workpiece is grounded. The surface of the needle electrode is loaded with a 13.56 MHz 1000 V sinusoidal voltage. At the radius of zero (r = 0), an axisymmetric boundary condition is used. On the far right and upper sides, the plasma is in direct contact with the outside atmosphere, thus open boundary conditions are used and no charge is accumulated.
The main particles contained are electrons e, the ground state helium atoms He, the excited state helium atoms He* (He active particles), helium ions He+, excited state He2* molecules and ion He2+. During capacitive coupling discharge, alternating electric fields continually accelerate electrons and transfer energy to electrons. By collision, electrons transfer energy to other heavy particles to ionize and excite, and thus the reaction speed of electrons and other particles is closely related to the temperature of the electrons. Therefore, the density distribution of heavy particles can be solved by solving distribution of the electrons density and temperature. At the same time, the density distribution of heavy particles, especially that on the surface of the workpiece, is closely related to the etching of the surface of the workpiece and the formation of the surface morphology. Therefore, solving the density and temperature distribution of electrons is an important prerequisite for analyzing the removal characteristics and generated surface morphology in CCAPPP process.
The spatial distribution of electron density and electron temperature in He plasma was solved as shown in Fig. 6. It is noted that the density and temperature results are averaged over one RF cycle as the distribution of electron density and temperature is constantly changing in the cycle. It can be seen that the electron density mainly concentrated on the position between the tip of the needle electrode and the ground workpiece, because the electric field is strong and the ionization degree is high. On the other hand, the distribution of electron temperature is much more diffuse.
The radial distribution of all the heavy particles on the surface of the workpiece is shown in Fig. 7 and Fig. 8. It can be seen that the density of various heavy particles (e.g. He* density) follows a Gaussian distribution. Thus, it can be inferred that if the material removal rate is proportional to the plasma density, the removal contour on the workpiece surface will be Gaussian shape.
3.2.2 Chemical reaction model
In CCAPPP, the gases used include He, CF4 and O2. In order to solve the spatial distribution of the reactive particles associated with SiO2 etching, it is necessary to analyze the chemical reactions in the plasma. Therefore, the chemical reactions need to be included in the simulation model. Due to the complexity of chemical reactions in plasma (involving hundreds of ionization, excitation, decomposition, adsorption, recombination, charge exchange, and direct chemical reactions between neutral particles), only the primary reaction process with a high density of products is selected for modelling and simulation calculation. According to a large number of chemical reactions required in He, CF4 and O2 plasma simulations in [84-88], the density of various heavy particles in the steady state is solved by the zero-dimensional model. Figure 9 shows the variation of all heavy particle density over time in the zero-dimensional model. The primary reactions (with higher reaction rate) in the zero-dimensional plasma chemical reaction model are selected for the full model in the following (summarized in Table 2).
Table 2. Reactions, reaction rate constants & reaction energy in He/CF4/O2 plasma
3.2.3 2D full model for CCAPPP
Based on the previous model, this section establishes a full 2D simulation model for CCAPPP, including two-dimensional needle electrode discharge, primary chemical reactions, as well as flow rate and the spatial distribution of reaction gases. In actual processing experiments, the spatial distribution of the components of the reaction gas is not uniform and should be considered. Thus the particle transport and gas flow field are solved first and added into the plasma module as the initial value. The 2D full model for CCAPPP is shown in Fig. 10. On the basis of the 2D needle electrode model, a ceramic nozzle is added. Mass flow boundary conditions are used at the inlet. The exit uses open boundary conditions and the pressure is one atmospheric pressure. In the particle transport, the air inlet will be set according to a mass proportional relationship between He, CF4 and O2. At the right exit, the O2 content is equal to the atmospheric content, while the He and CF4 content are set to be zero. The model used the parameters in Table 1 as other input conditions. The flow rates of He, CF4 and O2 are 337, 48 and 5 sccm, respectively. And the corresponding mass flows are 1.0030×10−6 kg/s, 3.1429×10−6 kg/s and 1.1905×10−7 kg/s, respectively. Thus the total mass flow is 4.2649×10−6 kg/s. Meanwhile, in the fluid field calculation, the average density of the fluid is 0.656 kg/m3.
The flow field distribution of the gas is obtained by solving the Navier-stokes equation, as shown in Fig. 11. The overall gas flow rate is relatively slow, and the maximum is only 0.16 m/s. The Reynolds number of the gas is about 10, which means the gas is in the laminar flow zone. After the gas flowing out of the nozzle, the velocity direction changes to the horizontal direction that is the radial direction of the plasma torch. Out of the nozzle range, the flow field begins to diverge and the flow rate decreases. On the other hand, under the electrode, there is a vortex region with a small flow velocity due to the shielding of the electrode. In this region, the flow rate is less than 0.01 m/s, and the flow field changes gently.
Then the transport process of various gases in steady state can be solved by the Maxwell-Stefan equation, and the spatial distribution of the density of He, CF4 and O2 is obtained. The calculated molar ratio distribution of He, CF4 and O2 gas components is shown in Fig. 12. The proportion of moles of all components flowing into the plasma torch from the inlet to the nozzle is stable. After ejected from the nozzle, the molar ratio of He and CF4 gradually decreases. Unlike He and CF4, the molar ratio of O2 gradually increases after passing through the nozzle region due to the O2 diffusion at the boundary.
Using the molar ratio of the reaction gases obtained (in Fig. 12) as the initial conditions, and adding the primary reaction selected in section 3.2.2, the 2D full model for CCAPPP is simulated.
The electron density, electron temperature, and density distribution of active particles of F, O and CFx (including CF3 and CF2) are obtained. Figure 13 shows the electron density and temperature distributions, and Fig. 14 shows the density distribution of F, O, CF3 and CF2. It can be seen that the distribution range of the active particles is greatly increased relative to the distribution range of electron density, indicating that the active particles have an outward flow tendency as the gas flows. The etching range of the plasma can exceed the limit of the ceramic nozzle, which is consistent with the experimental results. According to the chemical reaction process of SiO2 etching, the active F atom distribution on the substrate surface is an important factor to the removal profile. With different He flow rates, the simulation results show that the molar concentration of surface active F atoms follows Gaussian distribution as shown in Fig. 15. All the fitted Gaussian curves have adjusted R-squared value larger than 0.99.
4. Experimental results and analysis
Experimental processing experiments were also carried out to verify the simulated results. Three He flow rates of 337, 674 and 2021 sccm were used, and other process parameters were kept the same as Table 1. The removal profile was measured by a stylus profilometer (Taylor Hobson PGI 1240) and the surface morphology was observed. The experimental results are listed in Table 3.
Table 3. Experimental results of CCAPPP removal spot under different flow rates of He
4.1 Removal profile
The simulated results (in Fig. 15) show that as the He flow rate increases, the peak value of the active F atom concentration decreases, and FWHM increases. The relationship is in agreement with that of the experimental results (in Table 3). In addition, the simulated molar concentration of surface active F atoms has an FWHM of 4.4, 6 and 8.3 mm respectively, which agrees well with FWHM of 4.7, 6.4 and 7.9 mm of the experimental removal profile obtained in Table 3, when the He flow rate is 337, 674 and 2021 sccm. Therefore, it can be concluded that the Gaussian removal profile of CCAPPP is determined by the distribution of the active F atoms.
4.2 Surface morphology
Different areas were measured by atomic force microscopy (AFM) to quantitatively characterize the roughness. The roughness in opaque areas was 158.2 nm Ra while the roughness in the original surface was 1.6 nm Ra, which means the surface was roughened after CCAPPP. It is also found that the opaque morphology on the processed surface varies with process parameters. When the process parameters of He flow rates of 337, 674, and 2021 sccm were used, the corresponding morphology is shown in Fig. 4 (b), Fig. 16 (a), and Fig. 16 (b), respectively. And the characterized dimension is summarized in Table 3.
It can be seen that as the He flow rate increases, the outer diameter of the opaque area of the removal spot increases and is consistent with the spot width. However, the inner diameter of the opaque area decreases. For example, the opaque morphology changes from the hollow circle (shown in Fig. 4 (b) and Fig. 16 (a)) to the solid circle (shown in Fig. 16 (b)).
Adding O2 in the CF4 plasma can react with CFx radical while too much consumption of CFx can suppress the removal of O when etching SiO2. The ratio of O and CFx affects the etching process of SiO2 [23]. The chemical reaction analysis in section 3.2.2 indicates CF3 and CF2 are two main CFx particles in the plasma and here the sum of CF3 and CF2 is used to represent the overall density distribution of CFx. When the O/CFx ratio is small, the O of SiO2 is not enough to bond with all CFx which leads to C-F barrier layer (C-F polymer) formation on SiO2 surface. Only when the O concentration is high enough, the CFx reaching the SiO2 surface is suppressed to the level (not be able to form C-F barrier layer). As a result, it can be expected that when the C-F barrier layer starts to form, it may cause micromasking effect which varies the etch rate locally and in turn induces surface morphology formation.
According to the density distributions of O, CF3 and CF2 (as shown in Fig. 14), the molar concentration ratio of O/CFx (the sum of CF3 and CF2) can be obtained under different He flow rates. The simulation result is shown in Fig. 17. A threshold line of the O/CFx ratio about 1.37 is drawn. When the He flow rate is 337 and 674 sccm, the O/CFx ratio in the range of about 6.6 and 5.4 mm exceeds the threshold, indicating that rough C-F barrier will not be formed inside this area. The experimental results show the inner diameter of the opaque area is 7 and 5.5 mm in the observed surface morphology (respectively shown in Fig. 4 (b) and Fig. 16 (a)), which matches the simulated O/CFx distribution results. When the He flow rate is increased to 2021 sccm, in the region of 20.5 mm (diameter), the ratio of O/CFx is always below the threshold, indicating that barrier layer will cover the whole removal spot. This corresponds to the solid circle morphology as shown in Fig. 16 (b). In sum, the ratio of O/CFx is considered as the key factor affecting the surface morphology formation of CCAPPP.
5. Conclusions
In order to investigate the removal and surface morphology formation mechanism of CCAPPP, this paper established the model of the gas flow field, particle transport and plasma discharge process. The spatial distribution of the reactant particles in the plasma (active F atoms, O atoms and CFx molecules) were obtained by multi-physics simulation process. The simulation and experimental removal results agreed well with each other. It is concluded that the distribution of active F atoms on the workpiece surface determines the Gaussian removal profile and the ratio of O/CFx is the key factor affecting the surface morphology formation of CCAPPP. Based on the proposed CCAPPP model, the future work will include the removal contour optimization to accommodate multiple spectrum error correction and mitigation of the surface roughening phenomenon.
Funding
National Natural Science Foundation of China (NSFC) (No. 51105112, No. 51175123); National Science and Technology Major Project (2013ZX04001000-205).
Acknowledgments
The authors appreciate Dr. Lei Zhao for academic discussion of the current paper. The authors also would like to sincerely thank the reviewers for their valuable comments on this work.
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