Method and apparatus for ion deposition and etching

The disclosure relates to maskless deposition and etching and more particularly to maskless deposition and etching of the surface of objects using single and multiple ion sources.

DETAILED DESCRIPTION OF THE INVENTION 
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 
EQU F(u,v)-D(u,v)=T(u,v)H(u,v). (3) 
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 
EQU E(u,v)=F(u,v)-D(u,v)-T(u,v)H(u,v) (5) 
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 
EQU r=Ht (6) 
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 
EQU t=H.sup.-1 r (7) 
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 
EQU e=r-H.sup.-1 t (8) 
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. 
TABLE A 
______________________________________ 
Layer Material Index Waves Microns thk 
______________________________________ 
104 SiO.sub.2 1.4500 0.50000 0.21793 
106 Al.sub.2 O.sub.3 
1.6500 0.25000 0.09576 
108 SiO.sub.2 1.4500 0.25000 0.10897 
______________________________________ 
Light Polarization 
Reflectance % 
Transmission % 
______________________________________ 
s-pol 0.7476 99.2523 
p-pol 0.7476 99.2523 
both 0.7476 99.2523 
______________________________________ 
TABLE B 
______________________________________ 
Layer Material Index Waves Microns thk 
______________________________________ 
104 SiO.sub.2 1.4500 0.55000 0.23972 
106 Al.sub.2 O.sub.3 
1.6500 0.30000 0.11491 
108 SiO.sub.2 1.4500 0.30000 0.13076 
______________________________________ 
Light Polarization 
Reflectance % 
Transmission % 
______________________________________ 
s-pol 1.5927 98.4072 
p-pol 1.5927 98.4072 
both 1.5927 98.4072 
______________________________________ 
TABLE C 
______________________________________ 
Layer Material Index Waves Microns thk 
______________________________________ 
104 SiO.sub.2 1.4500 0.51000 0.22229 
106 Al.sub.2 O.sub.3 
1.6500 0.24000 0.09193 
108 SiO.sub.2 1.4500 0.26000 0.11332 
______________________________________ 
Light Polarization 
Reflectance % 
Transmission % 
______________________________________ 
s-pol 0.7542 99.2458 
p-pol 0.7542 99.2458 
both 0.7542 99.2458 
______________________________________ 
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.