Regularities and features of two-sided plasma-chemical etching of optical glass parts
Plasma-chemical etching (PCE) of glass has become widespread in the optical industry in the manufacture of diffractive or holographic optical elements (DOE/GOE) . The maximum height of the relief (the depth of the hollows) of the optical parts is 1 to 2 μm. It is believed that the diffractive optical elements need a relief with vertical walls, obtained by anisotropic etching. Nevertheless, the inclined side walls of the relief create additional opportunities for image formation .
The purpose of this work was to determine the technological capabilities of PCE of silicate glasses when plasma contacts with both sides of the workpiece and the ways to improve the corresponding processes.
ANALYSIS OF PCE STAGES
The PCE theory  considers dry etching as a sequence of chemical reactions. The main stages of dry etching are the delivery of working gas molecules to the gas discharge plasma zone, the transfer of working gas molecules in a gas discharge into energetically and chemically active particles, the delivery of such particles to the surface of the processed material, their interaction with the surface of the processed material, as well as the withdrawal of products of interaction from the surface of the processed material.
The efficiency of the delivery of working gas molecules to the gas-discharge plasma zone is influenced by the mutual arrangement of the processed surfaces of the sample and the point of introduction of gases into the working chamber (Fig.). In addition, the delivery of working gas molecules is prevented by narrowed areas in the working chamber, formed by the sample holder, the positioning device and the carrier shelf.
The transition of working gas molecules in a gas discharge into energetically and chemically active particles is caused by the fact that the helical antenna, which is an inductor, triggers an electromagnetic wave along the z axis into the plasma, which decays exponentially. The depth of penetration of the electric field into the plasma is usually characterized by a value that is inverse to the magnitude of the attenuation coefficient of this wave (δ). In turn, the value of δ is determined by the imaginary part of the complex dielectric permittivity of the plasma.
Estimated calculations, the methodology of which is given in the specialized literature , was carried out with reference to the RIE-300 system. It was assumed that the antenna is supplied with a voltage with a frequency of f = 13.56 MHz, SF6 gas is used as the reactive gas, and the pressure in the working chamber is p = 10–100 Pa . According to the results of calculations, the collision frequency of electrons with neutral particles was νm = 1010 s-1, while the circular frequency of the voltage applied to the antenna, ω = 108 s-1. It turns out that νm >> ω, that is, we are dealing with the case of high-pressure plasma. Then, estimating the circular frequency of the plasma oscillations with the value ωpe = 2πfpe = 6 · 1010 Hz, we obtained approximately the depth of penetration of the electric field into the plasma δ = 7 cm. This value is approximately equal to the size (the length L shown in the figure) of the working chamber. The condition δ ≈ L corresponds to a low-density plasma.
In the case of high-pressure and low density plasma, the limiting factor is the minimum current and, correspondingly, the minimum power applied to the antenna for exciting the inductively coupled plasma. For the RIE-300, the maximum power Wmax = 300 W supplied to the antenna is the limit that is also the limiting condition for the transfer of working gas molecules into chemically active particles.
Chemically active particles are fluorine atoms, which are formed under plasma conditions during the decomposition of SF6 molecules into SF5, SF4, SF2, F2 molecules and F atoms , and the fluorine molecules F2 also decay into atoms. The mechanism of delivery of the formed fluorine atoms to the processed surface and the withdrawal of interaction products from it is determined by the ratio between the dimensions of the chamber and the mean free path of the molecules, which depends on the pressure in the vacuum chamber and the components of the gas mixture. Calculation using the recommended formulas  shows that for the above-mentioned range of pressures typical for installations of the type under consideration, the mean free path is λ = 0.05–0.5 mm. This value is much smaller than the dimensions of the chamber, therefore, the delivery of chemically active particles to the surface being treated and the withdrawal of the interaction products take place by the diffusion mechanism.
The interaction of energetically and chemically active particles with the surface of an optical glass involves the removal of the processed material during the chemical reaction with the formation of silicon tetrafluoride:
4F(gas) + SiO2(solid) →
→ SiF4(gas) + O2(gas). (1)
However, optical glass (with the exception of fused quartz) contains in its composition not only silicon dioxide, but also many other compounds, for example, oxides of boron, sodium, potassium, etc. In addition, not only the glass itself is exposed to the action of reactive particles, but also the mask material used to create the desired pattern on the surface to be treated.
The features of PCE of optical glass require experimental studies to establish on their basis factors that limit the productivity of the process and the quality of the treated surface.
METHOD OF EXPERIMENTAL RESEARCH
To carry out experimental studies, a RIE-300 system (Torr International) was used (Fig.).
10Ч10 mm samples for PCE were cut from one group sample made of a photomask preform for 2.5 mm thick integrated circuits with a chromium masking coating. The samples contained a pattern obtained by electron beam lithography – a randomized set of optically transparent (chrome is etched) and opaque (chrome is not etched) sections of equal area.
Each experiment was a technological operation consisting of five steps: the first and fifth steps are oxygen cleaning for 5 minutes; the second and fourth steps are proper PCE with the duration of tpr; The third transition is oxygen cleaning with a duration of tko.
As an output parameter, the productivity of the process was evaluated, which was estimated by the depth of the etched material (silicate glass) determined on a Form Talysurf PGI 420 profilometer with the obtaining of the profile of the sample surface before and after the experiment. The productivity of the process (q, nm/min) was estimated as the quotient of the depth (H, nm) of the glass etched in this experiment and the value of 2tpr, min.
The following experimental factors were considered:
• distance l from the sample to the dielectric window contacting with the spiral antenna of the RIE-300;
• duration of oxygen cleaning tko;
• duration of each of the steps of the PCE tpr (the duration of these two steps is assumed to be equal to each other).
The following ranges of factors were adopted: l = 12–2 mm; tko = 2–6 min; tpr = 5–15 min.
The constant values characterizing the experimental conditions were the power of the electromagnetic wave emitted by the antenna W = 200 W, as well as the gases consumptions. During oxygen cleaning, the oxygen consumption was CO2 = 50 cm3/min, argon consumption was CAr = 50 cm3/min. In the PCE step, the SF6 consumption was CSF6 = 100 cm3/min, oxygen consumption – CO2 = 40 cm3/min, argon consumption – CAr = 35 cm3/min. In the working chamber, the following vacuum pressures were formed: during oxygen cleaning, pko = 65 Pa; during PCE ppr = 57 Pa.
A complete factor experiment 23 was implemented. The coded values of the factors were determined by the formulas:
where: l is the distance from the sample to the dielectric window, mm; tko is the duration of oxygen cleaning, min; tpr is duration of the PCE step, min.
The planning matrix and the results of the experiment are given in the next section.
In the second series of experimental studies, the processed surfaces of the samples were placed at a distance of 6 mm from the window along the center of the antenna spiral and two factors were evaluated for the effect on the PCE process:
• position of the etched surface "up" or "down" relative to the antenna and the etching gas;
• amount of etching gas, which was fixed at two levels, corresponding to an abundant and halved gas supply.
The PCE operation in this series consisted of nine alternating steps: five steps of oxygen cleaning and four steps of the etching lasting 10 min each. Steps of oxygen cleaning were performed with the power of WKO = 200 W supplied to the antenna, and the etching steps – with the power of WPCE = 250 W. Oxygen cleaning was carried out at the following gas flow rates: oxygen – qO2 = 50 cm3/min; argon – qAr = 50 cm3/min. The pressure pko = 62–67 Pa was created.
Steps of the etching were carried out with two variants of gas supply: abundant and reduced. The following gas flow rates corresponded to an abundant supply: argon – qAr = 40 cm3/min; oxygen – qO2 = 35 cm3/min; SF6 – qSF6 = 100 cm3/min. The pressure pPCE = 57–60 Pa was formed. The reduced flow rate corresponded to the gas flow rates: argon – qAr = 20 cm3/min; oxygen – qO2 = 17 cm3/min; SF6 – qSF6 = 50 cm3/min. The pressure pPCE = 28–30 Pa was formed.
The constant composition of the gas mixture was maintained by providing the following relationship between the flow rates of the gases forming the etching mixture: there were 40 parts of argon and 35 parts of oxygen per 100 parts of SF6 gas.
After PCE, the samples were ultrasonically cleaned using the Allstrip solution (OHARA Optical Glass). Then, in the boiling sulfuric acid, the remnants of the chrome mask were removed. The results of profilographic studies are presented in the next section.
In order to identify the processes occurring during the etching of glass under the considered conditions, an optical-microscopic examination of the etched surfaces of the samples was carried out using an optical microscope Axio Imager Vario Z2 manufactured by Carl Zeiss. Samples were also imaged after PCE, ultrasonic washing and acid etching.
RESULTS OF EXPERIMENTAL STUDIES
The planning matrix and the results of the first-stage experiment are shown in Table 1. The results of the profiling of the samples in the second series of experimental studies are presented in Table 2.
Based on the results of the experimental studies given in Table 1, according to standard formulas, the regression coefficients were calculated and the following regression equation was obtained:
q = 8.1 – 1.1x1 + 0.575x2 –
– 0.275x3 – 0.525x1x2 + 0.175x1x3
+ 0.6x2x3 – 0.35x1x2x3 . (3)
The data given in Table 2 show that when the samples are placed by the etching surface "down", the depth of etching of the glass is 5 to 10% greater than in case of the "up" position. And a doubling in the feeding of the etching mixture increases the etching depth by a factor of two. At the same time, the pressure pPCE in the working chamber also doubles.
Optical-microscopic studies have shown that at a depth of etching of h = 2–3 μm, the configuration of some elements of the pattern is distorted. It is noticeable that this distortion is caused by the "undercutting" of the processed material (silicate glass) under the edges of the chromium mask, that is, etching occurs not only in the vertical direction perpendicular to the surface being treated, but also parallel to it, which indicates the isotropic character of the process.
This fact should be taken into account in the development of DOE/GOE: the outlines of the sections forming the "islands" should be expanded by an amount corresponding to the required etching depth.
Optical microscopic studies also showed the presence of substantial re-deposition of the processed material – optical glass in the form of optically transparent "droplets" both on the chromium mask and in glass areas. After removing the chrome mask by acid etching, these "drops" remain only on the glass areas.
DISCUSSION OF RESULTS
OF EXPERIMENTAL STUDIES
Let's analyze the obtained regression coefficients in equation (3).
The value of the coefficient b0 = 8.1 is very close to the value of q = 8.2 nm/min obtained when the experiment was realized at the center of the experimental design, that is, the experimental errors are not large, and all regression coefficients are significant.
The value of the coefficient b1 = –1.1 indicates that the removal rate of the processed material increases as the sample approaches the plasma source (antenna). This can be explained by the uneven distribution of energy in the plasma .
The values of the coefficients b2 = 0.575 and b3 = –0.275 indicate that the rate of removal of the processed material increases with increasing time of oxygen cleaning of the sample between the two steps of the PCE, and decreases with the increase in the duration of the PCE step. The PCE process involves not only the removal of glass under the influence of chemically active particles due to the formation of silicon tetrafluoride according to the reaction (1), but also the appearance of a film on the glass surface as a result of gas-transport polymerization reactions of the following type:
2nSF6 → 3[…—SF4—…]n . (4)
The polymer film, deposited from the SF6 gas, has a loose structure and can be destroyed by oxygen from the gas mixture introduced into the working chamber. Possible reaction of degradation of this polymer:
3…—SF4—…(solid) + 6O2(gas) →
→ 4SO3(gas) + 6F2(gas). (5)
Obviously, an increase in the duration of oxygen cleaning provides a more complete removal of the polymer film, which prevents access to the surface of chemically active particles, and an increase in the duration of the PCE step leads to passivation of the surface.
The coefficient b23 = 0.6 indicates that an increase in the average PCE rate is caused by a simultaneous increase or decrease in the duration of the oxygen cleaning and PCE steps.
Values (taking into account the signs) of the regression coefficients b12, b13 and b123 indicate the intensification of all the processes accompanying the sample processing in a plasma formed by both inert and chemically active gases, when the intensity of the high-frequency electromagnetic field increases.
Estimating the results of this series of experiments in general, it should be pointed out that the achieved capacity of q = 10 nm/min for PCE of silicate glass in the RIE 300 is relatively low, and about five times less than the productivity achieved with the Caroline 15 PE , which is explained by fundamentally different schemes of etching in this equipment. Based on the results of a series of experimental studies, the structure of the PCE operation was developed, consisting of alternating steps of oxygen purification and PCE. Simultaneously, at the step of the PCE, the power supplied to the antenna was increased to 250 W. In this mode, a second series of experiments was implemented, the results of which are presented in Table 2.
A preliminary evaluation of the results presented in Table 2 shows that the PCT rates in the range q = 90–95 nm/min, which are twice as high as the etching performance of the Caroline 15 PE , are achieved.
The presence of re-deposition of the processed material in the form of reverse condensation, as well as of areas covered with green or brown film (CrF3 and CrF4 compounds) indicates a difficulty in withdrawing the products of interaction from the surface being treated, which is due to the diffusion mechanism, that is, the random wandering of interaction products near the surface of the sample, which in such cases is a catalyst for condensation processes. The negative role of this film is that it shields the surface being treated and prevents the penetration of fluorine atoms and ions to it, and thereby slows or completely stops the etching process. Obviously, in our case, the quality of the treated surface is limited by the stage of withdrawal of interaction products from the surface of the processed material.
The results of profilographic studies of the depth of the formed microrelief (Table 2) show that the position of the surface to be treated "down" leads to an increase in productivity by 5–10%. This is explained by the shortening of the path traveled by chemically active particles from their source (Fig.) to the treated surface in comparison with its position "up". Since chemically active particles are delivered by the diffusion mechanism, increasing the distance from the source leads to a decrease in their concentration on the treated surface.
The consumption of gases has a much stronger effect on the efficiency of etching. In the investigated range, an increase in the gas flow rate by a factor of two resulted in a similar increase in the etching rate. Thus, the interaction stage of reactive particles with the surface of the material being processed is a process-limiting process. However, an increase in the gas flow rate leads to an increase in the pressure in the working chamber, which prevents the withdrawal of reaction products from the treated surface.
The etching mode should be selected in such a way that the best quality of the etched surface is achieved at an acceptable etching rate.
Based on the studies carried out, the following conclusions can be drawn regarding the main regularities and features of PCE of silicate glasses in equipment with a planar inductor:
• Analysis of the stage of the transition of working gas molecules into the reactive particles showed that under the conditions under consideration a high-pressure and low-density plasma is formed. Therefore, the limiting factor is the minimum power that should be applied to the antenna for exciting an inductively coupled plasma. It has been experimentally established that for oxygen purification, WKO = 200 W is sufficient, and the PCE process proceeds at a power of WPCE = 250 W.
• Approaching of the workpiece to the plane of the helical antenna, as well as the use of multistage operations, alternating steps of PCT with long oxygen cleaning, contribute to an increase in the productivity of PCT of glass in equipment of the type under consideration.
• It is shown that the delivery of reactive particles to the surface of the processed material is carried out by the diffusion mechanism, and an increase in the flow rate of the gas mixture leads to a proportional increase in the pressure in the working chamber. At gas flows of q = 80–180 cm3/min, the pressure in the working chamber is p = 25–60 Pa.
• It was experimentally established that the rate of etching of silicate glass is directly proportional to the concentration of chemically active particles on the surface being treated and at high concentrations is γ = 90 ± 95 nm/min. This etching rate is quite sufficient for manufacturing details of diffractive optics of optical glass containing a relief of 300–1,500 nm on both sides of the plate.
• Under the conditions considered, the withdrawal of products of the interaction of the gas mixture with the quartz glass and the mask material is difficult, which leads to a re-deposition and formation of haze on the etched surface. Therefore, it is necessary to select the PCE mode by empirical methods, which ensures a balance between the process efficiency (its acceptable value) and the surface quality (achieving its maximum). ■