ION AND PLASMA BEAMS IN OPTICAL TECHNOLOGIES

Ion Beam Milling of Precision Optical Surfaces

From the point of view of optical surface shaping ion beam milling is an analog of surface finishing by a small tool. This is one of the methods to correct zonal and local surface errors (zonal and local retouching) used in the fabrication of big dimensional high precise optical surfaces. Usually the retouching is applied to the surfaces pre-polished to an accuracy about (l /4 - l /10)l when the much better accuracy is required - up to (l /20 - l /100)l. Basically these two processes are very similar: the ion beam scans over the surface to be corrected and removes material from the surface by sputtering accordingly to the amplitude of surface error and its distribution over the surface.Let us define the surface error as the massive of known N positive values H(C₁), H(C₂), H(C₃), … , H(C_N), which are the normal deviations of our surface from some reference surface (plane or sphere) in the points of surface with generalized coordinates C₁, C₂, C ₃ , … , C_N accordingly (Fig.1).

Fig.1

Usually we can obtain this massive by analyzing the interferogram of surface. Let the ion source moves along a trajectory S(x), where x is some generalized space coordinate. At first we will discuss the step motion of ion source. It means that the ion source is positioned sequentially at the point S(x₁) of trajectory during the time t₁, then in the point S(x₂) during the time t₂, and so on in M points. So in the position x_m we remove material from the point X_n of the optical surface to depth h_nm = V_nmt_m, where V_nm is the sputtering rate in the point X_n when the ion source is in the position x_m. After the ion source will has passed over the all M points of the trajectory we get the summary sputtered depth of material in point C _m as:

h_n = V_n1t₁ + V_n2t₂ + V_n3t₃ + … + V_nMt_M

Writing the same for other points of surface and equating h_n to H(C _n) we get the system of linear equations describing the process:

V₁₁t₁ + V₁₂t₂ + V₁₃ t₃ + … + V_1mt_m + …. + V_1Mt_M = H(C ₁)

V₂₁t₁ + V₂₂t₂ + V₂₃ t₃ + … + V_2mt_m + …. + V_2Mt_M = H(C ₂)

…………………………………………………………………..

V_n1t₁ + V_n2t₂ + V_n3 t₃ + … + V_nmt_m + …. + V_nMt_M = H(C _n)

……………………………………………………………………

V_N1t₁ + V_N2t₂ + V_N3 t₃ + … + V_Nmt_m + …. + V_NMt_M = H(C _N)

The solution of this system t₁, t₂, t₃, ... , t_m, ..., t_M is the times of positioning of the ion source in the points of its trajectory providing the sputtering of the surface layer with the sputtered depth distribution h(X) corresponding to surface error distribution H(X).

It is easy to show that for continuous motion of the ion source this system of linear equations converts to system of integral equations. The solution of that system is the dependence V(x) – the variable speed of the ion source moving along its trajectory. We did not work with this problem due to the following reasons:

1. The system of integral equations describing this process does not has an analytical solution.
2. These are much easier and cheaper in practice to realize the step motion of ion source with required parameters than continuous moving with variable speed.
3. Linear equations system solution analysis for a many of different process parameters (plane, concave and convex surfaces with different radiuses of curvatures, different parameters of ion beam, different surface error distributions etc.) and experience showed that practically all main goals of ion milling may be reached using the step motion of the ion source with high accuracy (RMS milling error may be no more than a few percents of sputtering depth).

We can see that the column n of matrix | | V_nm| | is the set of values defining the sputtering rates at the points X₁, X₂, … , X_m, … , X_M of surface when the ion source is in the point x_m of its trajectory. So we can introduce the function V(X) that I called as SRDF (Sputtering Rate Distribution Function). Of course this function has to depend on the physical parameters of optical part to be milled, the parameters of the ion beam, and the geometric parameters of process (the distance between the ion source and the optical part, the incident angle of the ion beam on the optical surface, and the position of ion source). These is no problem to figure out this function for simplest cases – plane surface, normal incidence of the ion beam which has no divergence, etc., but very soon we understood that all these simple approximations don’t work in practice. After a number of experiments it has become clear that if we want to reach a good agreement between the theoretical calculations and practical results we must take in account all main parameters of process. The first problem was to create a mathematical model of the ion source. In time we designed and used for ion beam milling a plasma accelerator with close electron drift and extended acceleration zone “Arctur”. We had run a lot of experiments, developed a number of methods and figured out that this ion source may be described for the ion beam milling as a point source generating the flow of ions with energy of 0,5U_A eV (U_A - anode voltage) and with the Gaussian distribution of ion current density over the beam cross-section:

J(r,z) = j⁰(z)exp{ - r² /[(z – H_s)²tg²b]},

where r, z – the axes of cylindrical coordinate system with the beginning in the plane of the ion source output and with z-axis directed along the direction of the ion beam propagation, H_S = 26 mm defines the position of theoretical point ion source, b = 9^o – the ion beam divergence measured on the level of e^-1 of maximum ion beam current j⁰(z).

The next step was the investigation of the sputtering yield angular dependence S(a) for a number of optical materials usually used for the big dimensional optical parts fabrication. We developed a simple technique that allowed us to obtain this dependence for each material with good accuracy in the single run. We got the S(a) data for some flints, crowns, quartz, monocrystal of Ge and polycrystal of ZnSe (see Section "Sputtering parameters of optical materials").

And at last we could to figure out the SDRF. I don’t want to show it here because it is very big formulae and it will take a lot of time and space to explain all it parameters. I just point that this formula takes in account:

1. The material of optical detail and its sputtering yield angular dependence for different energies of ions.
2. The radius of curvature of the milled surface for concave, convex and, of course, plane surfaces.
3. The position of the ion source and the optical surface (the distance between the ion source and the optical surface and the shift of the ion source from the axis of surface).
4. The ion current distribution in the cross section of the ion beam.
5. The divergence of the ion beam.

The separate SDRFs have been got for the detail rotating around its axis of symmetry.

Now we can calculate all elements of the matrix | | V_nm| |for any position of ion source. If we know the matrix | | H_n| | we can write down the system of linear equations.

The next step is to solve the system. We can do it by any known method. But we have one serious limitation for solution: all elements t_m must be non negative. The presence of negative elements in the solution of system means physically that the given problem can’t be solved only by removing material from the surface and that we must deposit additional material on some areas of the optical surface. Because of all elements of matrixes | | V_nm|| and | | H_n| | are principally non negative we will run into this problem very often. We can try to solve it by modification of the ion beam parameters and (or) the parameters of the ion source moving trajectory (these are only two things that we can modify on practice). It has been shown that the most important parameter for the given case is the width of ion current density distribution (width of the beam). It is clear that theoretically the best solution is to use the ion beam with delta-function current distribution. But it is not good to decrease the beam width too much because of the following strong increasing of process time and (or) the power density on the sputtered area of surface. By the way the local overheating and followed by optical part cracking is very serious problem in this kind of treatment, especially for details with big dimensions. We analyzed a big number of solutions obtained for real surfaces with different surface errors. The result was that the optimal effective beam diameter should be about 1/8 – 1/10 of the diameter of surface to be milled or about 1/4 - 1/3 of an error effective dimensions measured in the plane of surface. In practice it means that using the ion beam with the diameter of 30 – 50 mm (depending on the distance from the ion source for the beams with divergence) you can successfully mill the optical surfaces with diameters more than 200 mm – 250 mm.

But the optimization of beam diameter didn’t allow to eliminate completely the presence of negative elements in the solution. We have developed a simple method to optimize the parameters of ion source motion. Here the parameters of ion source trajectory are changing until the solution of system will have only positive elements. And with this solution the RMS deviation of calculated sputtered depth distribution from the profile of surface error usually was not more than a few percents and very often less than one percent. Moreover, in some cases we could concentrate the milling error in defined areas of surface.

We had developed the software TRION1 and used it both for the analysis of ion beam milling and for calculation of real process parameters. This software calculated:

1. Ion source step motion coordinates along the selected trajectory.
2. The depth of surface layer that should be sputtered at the point of intersection of the ion beam axis with the surface (or the sputtering time for the known sputtering rate).
3. The sputtered depth distribution over the surface.
4. The final surface error distribution.
5. The RMS deviation of final surface profile from the reference surface.

Practically the main problem is the monitoring of the sputtered depth at each point of the ion source trajectory. These are two ways:

• To define the sputtering rate in previous test runs for the given parameters of ion source and used optical materials; then to monitor time of sputtering keeping stabilized parameters of the ion source in production run.
• To use in-situ monitoring of the sputtering rate or the sputtered depth.

After a number of attempts of using the simple (at first sight) first way, we have selected the second one by the following reasons:

1. We could not obtain stable results with good accuracy and repeatability.
2. Even if we could stabilize all parameters of the ion beam we cannot be sure that the sputtering yield of our optical material is the constant parameter (see Chapter 3). Beside we cannot monitor and control the sputtering process, so if something will be wrong we won't be able to correct it in-situ and will see it only when the process will be over. In the case of bad results we should start all work from beginning.
3. Using the in-situ monitoring we don’t need expensive stabilized power and gas supplies and don’t need to monitor parameters of the ion beam with high accuracy. It is no matter for us now do the sputtering rate and ion bean parameters vary during the process or they don't. We only need to reach calculated sputtered depth in the given points of surface to be milled. Moreover we can vary ion beam parameters if we like to increase or decrease the sputtering rate by any reasons and we will see results immediately. And it is much more important that using in-situ monitoring of the process we can build the closed loop automatic system of process control.

We can use the following techniques for sputtering rate monitoring based on the measurements of the sputtered particles concentration, which is proportional to the sputtering rate:

1. Method of mass spectrometry. This method is used for plasma etching processes monitoring. I tried to use mass spectrometer (Leybold-Heraeus) but without positive results. Probably the concentration of particles sputtered by narrow ion beam from relatively small area of surface was too small to be registered especially on the background of argon plasma with pressure about 2x10^-2 Pa.
2. Method of optical spectroscopy. In this method the intensity of radiation emitted or absorbed by excited sputtered particles is measured. Again this intensity is connected with the concentration of sputtered particles, but the dependence is very complicated and not investigated well for a lot of materials. Especially we can expect of big problems when working with multicomponent materials like optical glasses are. Method is usually used for quality monitoring of the sputtering (etching) of multilayer structures, when the spectrum of radiation is changed on the boundary of layers made from different materials.
3. Method of quartz resonator. Well known method widely used for monitoring of thin film deposition. It works for any material in any pressure. We had run a lot of experiments and obtained that this method allows to monitor the ion beam sputtering processes by registration of sputtered particles deposited on the quartz crystal surface. Also the methods of calibration have been developed for the different materials and the different shapes of surface to be sputtered. Practically we could monitor the sputtered depth starting from nanometers with the accuracy about ± 3% of the sputtered depth (in depends on monitor resolution).

In my opinion it is absolutely useless to monitor the changing of the surface shape, for example, with the help of interferometry. The first attempts of such measurements were run 30 years ago and without result. It is clear that the surface local heating during the ion beam sputtering will distort the surface and this distortion may be (and usually it is) much more than the surface error to be retouched.

In our ion milling plant an optical part with a diameter up to 500 mm has been installed on rotating holder in vacuum chamber with the diameter 700 mm. The chamber was pumped down by turbomolecular pump. The ion source “Arctur” moved from the center of detail to it periphery with a step at least 1 mm but usually we used steps not less than 10 mm. The ion source regular parameters were the following: the anode voltage U_A = 250 – 300 V, the discharge current J_D = 0.5 – 0.8 A and the cross-section of the beam in the plane of optical surface was approximately 30 mm. The production rate for the equidistant milling of glasses with U_A = 300 V and J_D = 0.6 A could be evaluated by the following formula:

H = 38,2t/r²,

where H is the sputtered depth over detail surface, mm; t – milling time, h; r – radius of surface to be milled, cm.

On Fig.2 you can see the results of zonal ion beam retouching of the plane optical surface with the diameter 218 mm. The run took 80 min with quartz resonator monitoring of the sputtering rate and sputtered depth. The zonal error of the transmitted wave front has been decreased from 1,20ll to 0.08ll and relative contribution of zonal error in total RMS error has been decreased from 0,984 to 0,026. You can see that the profile of surface after ion milling is close enough to the profile calculated by TRION1 software.

Fig.2. 1 - the surface zonal error before ion beam milling, 2 - the surface zonal error after ion beam milling, 3 - expected surface zonal error calculated by TRION1 software.

The next kind of the ion milling we widely used was the equidistant milling. This process was intended for forming the given micro relief on arbitrary shaped optical surface. The relief depths were from tens nanometers to a few microns, the surface quality has been preserved. The optical components with micro relief were used as contact optical devices, for fabrication of optical devices which acting being based on using air gaps between two media (beamsplitters, Fabry-Perot interferometers) as well as to fabricate scales, grids, etc.

The advantages of relief contact optical devices are the following:

• A few times decreasing of labor expences for blocking and deblocking of optical parts, especially with big dimensions;
• Quality of optical contact and optical devices improving. On the base of this method we produced assembled optical devices (3-mirror retro-reflectors with aperture about 100 mm, for example) with the angular accuracy less than 1 arc sec;
• Reliability and stability of optical devices improving because of absence of additional deposited layers between two optical media and physically tight joint of the unit elements.

Basing on obtained results we have developed a few other methods and designs of ion beam milling equipment protected by USSR patents. We planned to continue this work in the following main directions:

• Software improving;
• R&D in the area of ion beams interaction with optical materials (sputtering yields, surface quality, etc.);
• Developing and design of fully automatic ion beam milling system;
• Local errors retouching;
• Ion beam aspherisation of optical elements;
• Ion beam milling of metal mirrors and infrared optical materials;
• Ion beam milling mathematical model and technologies optimization;
• Solving the problem of possible detail overheating due to a long time ion milling.

But to my great regret this work has been stopped due to the known events in the former Soviet Union and following industry stagnation.