Method and Apparatus for Ion Deposition and Etching

The accompanying drawings, which are incorporated into and form a part of the specification, illustrate several embodiments of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings:

FIG. 1 shows a prior art stationary deposition mask;

FIG. 2 shows a prior art rotating deposition mask;

FIG. 3 illustrates a system for performing the method of the invention;

FIGS. 4A-D show beam profiles and spatial frequency components for two ion beams.

FIG. 5 illustrates a coating on an object to be ion beam etched in accordance with the invention; and

FIGS. 6A-C graphically show coating transmission consistency across a relatively broad optical spectrum for different coating thicknesses in the FIG. 5 object.

Reference is now made to FIG. 3, which illustrates a system suitable for carrying out the method of the invention. As seen therein, an object 10 having a surface 12, beam source 14, an ion source grid 16, and an interferometer or other surface determining or monitoring instrument 18 such as a phase measuring interferometer or heterodyne interferometer are positioned within a vacuum chamber (not shown). A computer 20 is operatively connected to an apparatus 22 for controlling the position of object 10. Beam source 14 and ion source grid 16 are also under the control of computer 20 as is monitoring instrument 18. Ion source 14 is preferably a Kaufman ion source such as disclosed in a publication, Fundamentals of Ion-Source Operation by Harold R. Kaufman, Library of Congress Catalog Card Number 84-71750, although other sources may be used, including electron cyclotron resonance (ECR) and microwave plasma ion sources. Kaufman sources are well known and produce high current, low energy broad ion beams containing nearly monoenergetic ions so that ion beam sputtering therewith is essentially a linear process. The removal profile of the beam from source 14 is essentially the same regardless of where on the surface 12 of object 10 beam 24 is directed. Thus, sputtering yield remains constant. Beam source 14 and/or object 10 is translatable so that in operation the beam 24 remains normal, or at another selected angle, to surface 12 or to a reference plane or surface. The beam profile 24 does not change appreciably and its current energy distribution remains substantially constant during operation. Beam source 14 may additionally comprise a sputter magnetron or other device for ion assisted or other deposition.

In accordance with the invention, an algorithm compares a desired predetermined surface topography with the existing surface topography of surface 12 on object 10 and utilizing image restoration, controls beam 24 to provide deposition, such as ion assisted deposition, upon or to ion etch surface 12 to produce the predetermined surface topography. The predetermined topography may be symmetric or non-symmetric and ion assisted deposition may be also used to figure surface. The surface to be etched can be that of a coating.

By using several ion beam removal profiles, it is possible to cover the entire spatial frequency range as shown in FIGS. 4A-4D. Here, the nulls in the spatial frequency components of the broad beam can be chosen to fall on non-null components of a narrower beam. The use of both beams then covers the whole spatial frequency range of interest. The broad beams usually run higher current than the narrower beams. Higher beam current translates directly to faster material removal. The tradeoff is then to use the broadest available profiles as much as possible before using the narrower beams, provided that the spatial frequency range of the object figure error is properly covered.

The different beam profiles can be obtained by using different ion sources, varying the grid operation, masking fixed beam profiles, or altering the operating environment. If multiple ion sources are used, all sources can be operating simultaneously on different parts of the optic. This reduces the elapsed time for figuring while still obtaining the correct figure. The order of application of the different removal profiles is not significant because the material removal is linear and invariant with respect to space, ion dose, and time.

In many cases, the ion beam dwell time array exhibits regions in which little time is spent by the ion source, while other regions have a much larger time spent on them. The use of a single fixed array of ion sources achieves some speed-up in elapsed time, particularly if each source is on for about the same amount of time as the whole array moves across the optic (for uniform removal or deposition). The entire array should remain fixed for the dwell time specified by the largest element in the dwell time array corresponding to the position of each source in the array. In this case, it is better to have several completely separate arrays of sources, some of which dwell on the regions requiring the most material removal (a smaller total area), with the other arrays working on larger total areas where smaller dwell times are required. Practicing the invention thereby makes optimum use of the available ion current to get the shortest elapsed figuring time.

In practicing the invention, ion etching and ion depositing beam figuring is controlled using deconvolution for nearly flat optics, and matrix computations for optical and other elements having large surface slopes and high curvatures. The model for figuring computation begins with the superposition integral, ##EQU1## where h(x,.alpha.,y,.beta.) is the impulse response or point-spread function for the system model. In this case, the impulse is located at point (.alpha.,.beta.). The function f(x,y) is the original surface profile or existing topography of the optic or other element, and the function d(x,y) is the desired surface profile or predetermined surface topography. The function t(.alpha.,.beta.) is the time that the ion beam dwells on the element at point (.alpha.,.beta.). The function h(x,.alpha.,y,.beta.) is the material removal profile for the ion beam.

The material removal profile described as h(x,.alpha.,y,.beta.) is spatially variant. The shape of the removal profile can change depending on where the ion beam is pointed. If the removal profile is found not to change with position, then the removal profile is said to be position invariant or spatially invariant. The removal function may also have additional parameters related to dynamically changing the mechanical and electromagnetic configuration of the ion source.

For surfaces containing no large slop changes, the removal or deposition profile is spatially invariant for the ion sources used in practicing the invention. Surfaces having significant curvature will induce spatially variant removal or deposition profiles.

Figuring can also be performed by depositing material using a single deposition source or a plurality of deposition sources. In this case, the removal function is replaced with an addition function which satisfies the same constraints as the removal function. Those skilled in the art will understand that the calculations of the control parameters using additive techniques, e.g., ion deposition, are the same as the calculations of the control parameters for material removal, e.g., ion etching.

All of the functions but t(.alpha.,.beta.) are known or measurable. To perform surface figuring, the function t(.alpha.,.beta.) must be calculated. Because surface figuring in accordance with the preferred embodiment of the invention is under digital control, metrology and instrumentation, the integrals of equation 1 are replaced with summations and the domain is discrete. For the spatially invariant case, the superposition summation reduces to the definition of the discrete convolution. ##EQU2## Equation 2 can be solved using matrix techniques. However, using orthogonal transforms is easier and provides insight into the success or failure of the figuring operation.

An orthogonal transform such as the Fourier, Hadamard, Hartley, Cosine, and the like, has the property of diagonalizing a circulant (one dimensional) or block-circulant (two dimensional) matrix. This means that the solution to equation 2 in terms of t(.alpha.,.beta.) can be obtained using algebraic techniques, provided that the removal or addition profile is spatially invariant. This procedure is described hereinbelow.

Let be an orthogonal transform. Taking the transform of both sides of equation 2 gives

where F is the transform of f(x,y)(F(u,v)= {f(x,y)}), D is the transform of D(x,y), the coordinates (u,v) are the conjugate coordinates to the spatial coordinates (x,y), etc. Equation 3 can be rearranged to form ##EQU3## where .gamma. is a multi-variate function used to control the division when H(u,v) approaches zero or when F-D becomes noisy. When .gamma.=1, equation 4 is called an inverse filter. When .gamma. is a function of the signal-to-noise ratio at the transform coordinate (u,v), equation 4 is a Least Squares or Wiener filter. The function .gamma. can be optimized to produce a time dwell array t(x,y)= .sup.-1 {F(u,v)} which has optimal or special properties when applied as the time dwell array for an ion beam figuring operation.

Filters constructed using equation 4 are called restoration, deblurring or deconvolution filters and are used extensively in image processing and system controls.

Once all of the functions in equation 2 are known, the residuals arising from the ion figuring process can be calculated by forming

for different conditions applied with .gamma.. E(u,v) is the error between the desired surface and what can actually be achieved with a well characterized ion figuring process. In accordance with the invention, by looking at e(x,y)= .sup.-1 {E(u,v)}, one can evaluate the prospects for a successful figuring operation before any work is actually done. This step provides for the rejection of those optical or other elements which have surfaces that are economically or otherwise unsuitable for ion beam figuring by removal or deposition.

For the case where the ion beam removal or deposition function is spatially variant, the time dwell array, calculated using matrix methods, is represented by

where r is a vector formed by stacking the rows of f(x,y)-d(x,y), t is formed by stacking the rows of t(x,y), and H is formed by stacking partitions formed by stacking the rows of the point-spread function h(x,.alpha.,y,.beta.) for each (.alpha.,.beta.). The matrix H is the spatially varying point-spread function (PSF) matrix. The time array is recovered by forming

where H.sup.-1 is the inverse of the matrix H. When the point-spread function is spatially invariant, H can be diagonalized by an orthogonal transform as described previously.

The matrix H is somewhat ill-conditioned, meaning that small amounts of noise or error present in the matrix coefficients will have a large effect on the coefficients in the inverse matrix. To help alleviate this problem, the inverse matrix can be calculated using Singular Value Decomposition (SVD) or Q-R or other decompositions where unstable vectors are removed from the inverse calculation. This produces an approximation to the solution, but one that has higher tolerance to noise. Iterative constrained conjugate gradient optimization can also be used to perform the calculation for the inverse PSF matrix.

The use of the constraints or vector removal corresponds to the use of .gamma..noteq.1 in equation 4. An estimate of the residuals after figuring with a well characterized ion beam figuring process can be found by forming

where H.sup.-1 is the calculated inverse point-spread matrix. The error vector can then be unstacked to form an error image which can be inspected for figurability just as in the spatially invariant case.

Edge effects are produced with conventional figuring techniques due to the inherent properties of polishing tools. For efficient material removal, a tool should be fairly stiff. As the tool moves so that part of it extends beyond the edge of the element being figured, pressure increases on the part of the surface in contact with the tool and the removal profile distorts. Surface material within the radius of the tool is improperly figured, thereby causing an edge effect. Although many attempts have been made to solve this problem in conventional grinding or milling, the effect remains. Similar problems exist in all types of surface contact tools and devices for material removal.

In ion beam figuring, removal and deposition profiles do not depend on mechanical supports and the ion beam profile remains the same whether or not an object to be figured is in place. Thus, optics and other elements having essentially no edge effects can be produced. Because the beam dwell array value at a given point depends on the condition of the surface in a region around that point, the size of the region being about the same size as the spatial extent of the removal or addition function, the dwell array value depends in part on a condition which does not exist, since it is off the edge of the object. In practicing the invention, the image of the object provided by the metrology is treated as a small piece of an infinite surface. Using this model, the measured surface map of the object is imagined to be an apertured rendition of the surface map of a much larger object extending far beyond the field of view of the metrological instrumentation. Data is constructed to fill in those parts of the surface map which would correspond to those parts of the larger object obscured by the aperture. Hence the image restoration or matrix solutions see a modified object with no abrupt edge and compute the correct dwell array for the original object. The constructed data must have the same properties in terms of surface structure as the original object because there should be a match of the real data with the nonphysical data at the edge of the physical object.

Construction of data beyond the edge of the physical object is achieved with Band Limited Surface Extrapolation (BLSE) using orthogonal transforms. Original data is filtered to provide a smoothed result with some data outside the original data. The original data is then re-inserted into the resultant image. These steps are repeated a number of iterations to build up data outside the original data area, limited in frequency content by the filter which provides the band limits.

The building up of the off-edge data can be very slow. The rate of construction of data is partially determined by the band limit filter. Since ideal filters introduce "ringing" artifacts into the image, variable order filters, such as Butterworth, Chebyshev, or other more advanced filters, can be used to improve the rate of convergence to an acceptable quality. In practicing the invention, the cutoff frequency of the filter is varied during the progressive iterations, typically proceeding from higher bandwidths to lower bandwidths, with the final iterations being performed using the transform of the ion beam removal or deposition function as the filter. The ion beam removal or deposition function is the optimal filter because it eliminates any frequencies not present in the ion beam itself, alleviating restoration difficulties in equation 4.

To further speed the convergence, the filters are set during early iterations to amplify, in some cases nonlinearly, some of the frequencies in the pass band. This builds up the nonphysical data areas more quickly than when conventional normalized filters are used.

Additional gains in edge smoothness are obtained in some cases by offsetting the object surface with respect to its reference plane. This costs additional figuring time during which the centroid of the ion beam is mostly off of the surface of the object being figured. However, this produces higher quality edge figure.

The invention is applicable to the production of large optical or other surfaces due to its inherent scalability. As the size of a work piece is increased, ion beam current can be increased by using larger ion sources or by using a plurality of smaller ion sources which can be run simultaneously. The use of a plurality of sources reduces the time needed to figure a particular surface and distributes the thermal load across the surface of the element during fighting to thereby reduce thermally induced distortion. The plurality of sources may all be of the same size or more likely, of different selected sizes to minimize object figuring time. The use of several size ion sources also provides figuring over large spatial frequency bands which results in a better final surface figure as previously discussed with reference to FIGS. 4A-4D. Spatial ion beam current density can be dynamically tuned using single or plural sources in practicing the invention to provide an optimal final surface figure.

Because weight loading due to gravity and forces applied in conventional figuring techniques and mechanical distortion caused by polishing tool weight are eliminated, very light weight and flexible optical and other elements can be figured using the invention.

As an example of the tuning of a coating, the following situation can be considered. The FIG. 5 structure 100 comprises a base object 102, a coating 104 of 0.5.lambda. SiO.sub.2, a coating 106 of 0.25.lambda. Al.sub.2 O.sub.3, and a top coating 108 of 0.25.lambda. SiO.sub.2, where .lambda. is the wavelength of light. The coatings 104, 106 and 108 comprise an anti-reflecting coating for the visible wavelengths. This design is for 632 nm (HeNe laser red). If the individual film layers are too thick by 1/20th of a wavelength (.lambda.), the transmission spectrum is distorted significantly from that desired.

In accordance with the invention, etching can be accomplished using the algorithm to correct the layer thicknesses. For example, if the layers are corrected to .+-.1/100th of a wavelength, the transmission spectrum is very much improved. Other techniques, including interferometry, can be used to monitor the layer thickness. For example, "Sensitive Techniques for Measuring Apparent Optical Figure Error Caused by Coating Nonuniformity" (H. E. Bennett and D. K. Burge, Proc. Boulder Damage Symposium 1981, Laser Induced Damage in Optical Materials: 1981, NBS Special Pub. 638, pp. 421) shows that monitoring the optical phase by ellipsometry is a very sensitive technique.

The transmission spectra for the ideal, incorrect, and algorithm corrected film stacks were computed using a thin films design and analysis program. The transmission spectrum for the ideal case (perfect layer thickness) is shown in FIG. 6A, the spectrum corresponding to the case where the layers are too thick is shown in FIG. 6B and the corrected stack (layers individually monitored and corrected) has the transmission spectrum shown in FIG. 6C.

Tables A, B, and C show the layer thicknesses for the FIGS. 6A, 6B, and 6C examples.

The thickness of the layers are preferably monitored after deposition by spectrophotometric techniques, although in some cases, interferometry may be adequate. If spectrophotometry is used, the measurement is spatially resolved to obtain the thickness at all points on the surface, as prescribed by the IBF control algorithm.

Various grid structures, such as those described in U.S. patent application Ser. No. 028,246, of which this is a continuation-in-part, can be used to practice the method of the invention, which is particularly suitable for figuring the surfaces of large optics and other elements.

In practicing the invention, after a surface is figured, it may be coated with an additional material. Thus, the invention can be used to manufacture a mirror by etching or depositing material to figure a surface and then coating the surface by ion assisted or other deposition with a reflective coating. Similarly, a nonreflective or other coatings may be added to an object figured in accordance with the invention. The method of the invention is particularly useful to coat objects which are damaged when heated, since many conventional coating techniques require the substrate be heated to between 150.degree. and 300.degree. C. Ion assisted deposition of coatings may be carried out using a magnetron or other such device.

Although the invention has been described with reference to these preferred embodiments, other embodiments can achieve the same results. Variations and modifications of the present invention will be obvious to those skilled in the art and it is intended to cover in the appended claims all such modifications and equivalents.