Method and system for optimizing illumination in an optical photolithography projection imaging system

A method and system for finding and setting the illumination in a projection imaging system to achieve optimum imaging. The global optimum illumination is found based on the desired characteristics of the image irradiance distribution as embodied in a target aerial image. The system employs an optimization algorithm that finds the best combination of projected mask images, each such image formed by directing source illumination to selected regions (e.g., pixels) in the entrance pupil (each such region location and size corresponding to a nominal illumination direction and a particular range of angles about the nominal). The optimum illumination is defined as that illumination which produces an aerial image closest to the predefined target aerial image. The system then sets the illuminator to produce the source distribution necessary to achieve this optimal illumination. The set of aerial images created by addressing the available entrance pupil regions with illumination is determined either by numerical calculation or by scanning and recording the individual aerial images produced by the projection system.

FIELD OF THE INVENTION 
The present invention relates to projection imaging systems and, more 
particularly, to methods of optimizing the illumination generated by such 
systems. 
BACKGROUND OF THE INVENTION 
Optical photolithography has been widely used in the semiconductor industry 
in connection with the formation of a wide range of structures in 
integrated circuit (IC) chips. The fabrication of IC chips requires 
imaging systems that can suitably print, over a reasonable focal depth, 
the smallest structures required for the operation of the circuit. 
As the device density in IC chips has increased, the size of the structures 
making up the devices has approached the wavelength of the exposure 
(actinic) light used in photolithographic optical projectors. The 
diminution in feature size relative to the actinic wavelength, combined 
with the limitations on the projector's ability to capture light 
diffracted by such structures, adversely affects the resolution of optical 
lithography. To deal with this problem, techniques and equipment have been 
developed to optimize the resolution of conventional optical lithography 
systems. For example, Ausschnitt et al. disclose in U.S. Pat. No. 
4,890,239 a lithographic process analysis and control system for 
determining feature width, exposure and focus based on a predetermined 
mathematical model. Unfortunately, such techniques and equipment typically 
do not achieve sufficient resolution where features smaller than 0.5 
microns are to be imaged. This suggests that to achieve future density 
increases in IC devices, alternative imaging techniques will be required. 
Phase-shift mask technology is an example of one such alternative 
technology. Phase-shift mask technology relies on a variety of methods for 
introducing relative phase shifts in the electromagnetic field at the 
object (mask) plane. The introduction of phase shifts between two 
different transmitting regions of a fine-line lithographic mask feature 
causes destructive interference, darkening regions in the image where 
diffraction would otherwise cause residual constructive interference. 
While the effectiveness of phase-shift masks has been widely demonstrated, 
the technology is still nascent, due in part to the difficulty of 
constructing the phase-shifting regions for the variety of lithographic 
structures required for IC manufacturing. The phase-shifters represent an 
additional level of mask structure that must be aligned with the 
non-phase-shifted patterns, and in addition the shifters require a tighter 
and more complex set of fabrication tolerances than conventional mask 
patterns. Thus, even when phase-shift masks are made to work in practice, 
they typically provide only a one-shot improvement, because the above 
fabrication difficulties make impractical an iterative improvement of the 
masks to correct imaging problems found empirically. Moreover, phase-shift 
masks work by manipulating the image-forming process, instead of simply 
relying on image formation alone to faithfully reproduce an input pattern, 
as with standard masks. Phase-shift masks allow printed patterns with 
finer pitch than standard masks, but targeting a particular set of ground 
rules thus becomes more complicated. Thus, phase-shift mask technology, at 
least in its current state of development, does not appear to constitute 
an optimal solution to the problem of insufficient resolution of optical 
lithography in sub-0.5 micron regimes. 
Alternative Illumination schemes, sometimes referred to as "off-axis" 
illumination, have been proposed to extend the range of conventional 
optical photolithography, e.g., the SHRINC system sold by Canon. Like 
phase-shift mask techniques, off-axis illumination methods manipulate the 
effective object phase, but they do so by adjusting the phase of the 
illuminating wavefront. Each direction of illumination produces a distinct 
continuous phase variation across the mask surface. Such variations have 
advantages and disadvantages compared with the discrete phase levels 
provided by phase-shifters on the mask. Another difference between 
conventional phase-shift masks and multiple illumination direction systems 
is that the images arising under the multiple phase distributions produced 
by the latter are incoherently superimposed with one another. For the 
oft-cited example of a grating, proper off-axis illumination directions 
serve to vary the illuminating phase between alternate grating bars in 
such a way that one of the first order diffracted beams (i.e. +1 or -1) is 
deviated outside the entrance pupil of the projector imaging lens. The 
effect is to produce a two-beam interference pattern on the wafer which is 
similar to the two-beam interference pattern produced by a 
Levenson-Shibuya phase mask, in which phase-shifters are used to alternate 
the phase at the mask. In other cases, the phase variation over the bright 
regions of the mask is sufficient to diminish the otherwise dominant 
zeroeth diffraction order, without eliminating it altogether. The effect 
is to weight the higher diffracted order terms more in the formation of 
the image, resulting in increased contrast, resolution and/or depth of 
focus. 
Other off-axis illumination schemes are sometimes regarded as replacements 
for mask phase-shifting techniques. These schemes generally resemble the 
technique reported by M. Noguchi et al. in the article "Sub-half micron 
lithography system with phase-shifting effect," SPIE Proceedings, Vol. 
1671-Optical/Laser Microlithography L J. Cuthbert, Ed. (Society of 
photo-Optical Instrumentation Engineers, Bellingham, Wash., 1992), pages 
92-104. The Noguchi et al. scheme involves the use of four off-axis disk 
sources to image a sub-resolution grating (i.e., if the grating linewidth 
is expressed as k.sub.1 .lambda./NA, then the method is particularly 
suitable for k.sub.1 &lt;0.7). While this arrangement works reasonably well 
for grating-like features within a particular range of k.sub.1 values, 
changing the orientation, pitch, line size, or pattern shape would 
necessitate altering the illumination arrangement, thereby adding to the 
cost and complexity of the system. An illumination system which is capable 
of providing different intensity distributions of the light source in a 
projection exposure system is described in U.S. Pat. No. 5,363,170 (the 
"'170 patent"). The invention described in the '170 patent includes a 
primary light source, an afocal optical system with variable magnification 
and an optical integrator. By varying the magnification of the afocal 
optical system disposed between the primary radiation source and the 
optical integrator, the intensity distribution defining a secondary source 
can be varied. While this system allows for some flexibility in changing 
the illumination, it is only capable of producing a limited number of 
different secondary sources. Moreover, the '170 patent does not teach a 
method of finding the optimum effective source size and shape for a given 
object or objects to be imaged and then providing such illumination. 
Successful IC fabrication and manufacturing with alternative illumination 
schemes will require the ability to image a wide variety of shapes, sizes, 
orientations, and periodicities. Known systems and techniques are either 
not believed to provide such imaging capabilities or are not able to 
provide such imaging on a cost effective, easily repeatable, basis. 
Therefore, a need exists for techniques and equipment for enhancing the 
resolution of conventional optical projection systems, particularly 
conventional optical lithography systems. 
SUMMARY OF THE INVENTION 
One aspect of the present invention is a method for optimizing illumination 
for forming an image of a reticle object in a radiation-sensitive medium 
with an imaging system having a depth of focus and entrance pupil, an 
imaging plane located within the depth of focus, and a source of 
illumination. The method comprises a first step of optimizing the 
illumination provided by the source of illumination for imaging the 
reticle object through the entrance pupil and onto the imaging plane. 
Then, as a second step, the reticle is exposed to the optimized 
illumination to form an aerial image of the reticle feature and to 
transfer the aerial image into the radiation- sensitive medium placed at 
the imaging plane located within the depth of focus of the imaging system. 
Another aspect of the present invention is an illumination optimization 
system designed for use with an imaging apparatus including a source of 
illumination, an imaging lens with an entrance pupil and a depth of focus, 
a reticle with one or more features to be imaged, and an imaging plane. 
The optimization system includes means for determining reticle feature 
aerial images at the imaging plane, such as an image scanning system, 
which converts irradiance into an electronic signal. Typically, many 
individual aerial images are formed by illuminating the reticle with light 
from different directions, one direction at a time. Each aerial image then 
corresponds to an individual illumination component directed into a given 
region in the entrance pupil. The aerial images are then stored 
electronically in an image analyzing means, such as a computer, where they 
are combined in a way that creates a single reticle feature image that 
most closely resembles the target image. The optimum illumination is 
defined as the illumination that forms a reticle image that differs the 
least from a target image. The system then sets the source of illumination 
to provide the optimal illumination via an illumination control means 
coupled to the image analyzer.

For clarity of presentation, the diagrams are not necessarily drawn to 
scale. 
DETAILED DESCRIPTION OF THE INVENTION 
The present invention is a method of evaluating and optimizing illumination 
for optical projection systems, e.g., imaging systems of the type used in 
optical lithography, and a projection imaging system that operates in 
accordance with such method. Projection imaging system 20 of the present 
invention, which is schematically illustrated in FIG. 1, comprises an 
illumination controller 22 and an illumination source 24 coupled with and 
controlled by the controller so that the illumination the source generates 
is optimized. As described in more detail hereinafter, illumination 
controller 22 provides such control either by using illumination 
information obtained by scanning the image created at the image plane or 
by using numerical techniques based on a mathematical description of the 
projection system. System 20 also includes a reticle 26 positioned 
adjacent the output of source 24 and an entrance pupil 28 for projection 
imaging lens 30. The image plane for system 20 is identified at 32. 
Referring to FIGS. 1 and 2, the construction and mode of operation of 
illumination source 24 may vary significantly, while still falling within 
the scope of the present invention. However, it is important that source 
24 be capable of addressable imaging illumination within given coordinates 
of finite extent, hereinafter referred to as pupil pixels 40 (FIG. 2), in 
entrance pupil 28 of projection imaging lens 30. Pupil pixels 40 may, for 
example, represent the minimum area in the entrance pupil that is 
addressable with illumination, though the illumination sequences used in 
deriving the ultimate optimum illumination may be directed over an area in 
entrance pupil 28 greater than a single pixel. Source 24 should also be 
capable of illuminating reticle 26 with very good uniformity 
(approximately.ltoreq..+-.5%). Furthermore, it is preferred that source 24 
be capable of illuminating reticle 26 with light from a range of angles. 
Each illumination direction produces a particular phase runout in 
illuminating reticle 26 and, in the absence of scattering by the reticle, 
will focus the light to a single pupil pixel 40. When source 24 is capable 
of providing illumination from a wide range of directions, the coherence 
in the overall phase distribution on reticle 26 is decreased, thereby 
reducing coherent ringing artifacts in the image formed at image plane 32. 
Thus, source 24 may, for instance, comprise a unitary point source as shown 
in FIG. 3, such as an excimer laser that is designed to be scanned rapidly 
enough to create an effective extended source (not shown) in a plane 42, 
conjugate to the plane of entrance pupil 28. It will be appreciated by 
those skilled in the art that the concept of rapidly scanning a narrow 
beam say, with an electronically controlled mirror, to create an effective 
extended light source, is one obvious means for providing suitable 
illumination for the present invention. The concept of such an 
illumination system was presented by Douglas Goodman in "Optics of 
Photolithography" short course notes, Optical Society of America, OptCon 
Meeting, Santa Clara, Calif., 1988, pp. 112-117. By controlling the 
direction and intensity of the light generated by the point source on a 
pixel-by-pixel basis for the pixels 40 in entrance pupil 28, the best 
possible image can be constructed. 
Alternatively, source 24 may consist of a cluster of closely spaced beams 
that are scanned simultaneously. The range of illumination directions 
subtended by this cluster (with the scanner turned off) should be 
sufficiently narrow (for example, NA'/10, where NA' is the numerical 
aperture of projection imaging lens 30 on the image plane side) that all 
beams produce essentially identical images. For this reason, the cluster 
can still be regarded as effectively a point source. Such a simultaneously 
scanned multiplicity of beams produces a smoother illumination of more 
uniform intensity in the reticle region where the beams overlap than could 
be readily accomplished with a single beam. Thus, use of a cluster source 
may be desirable where a relatively tight uniformity of illumination is 
preferred. Servaes and Reynolds have proposed in U.S. Pat. No. 4,560,235 a 
duster source composed of optical fibers of different length to eliminate 
coherence effects which could be employed as source 24. An alternate means 
for providing suitable uniform illumination is described in U.S. Pat. No. 
4,819,033, which discloses an illumination apparatus for projector imaging 
based on an excimer laser light source whose pulse-to-pulse intensity can 
be controlled, and whose optics direct the illumination into the entrance 
pupil of the projection lens from more than one direction at a time. 
When the projection system 20 of the present invention is to be used in 
optical lithography, it is omen preferred that source 24 have x and/or y 
mirror symmetry, to accommodate the common microcircuit design practice of 
mirroring circuit patterns into the four quadrants of a chip, and also as 
a means of providing inversion symmetry through focus. To achieve this 
symmetry, illumination produced by source 24 and focused at position (x,y) 
in the pupil is focused as well at positions (x,-y), (-x,y), (-x,-y). It 
will be appreciated by those skilled in the art that reference to the 
coherent illumination produced by addressing a single pupil pixel 
describes, in a shorthand way, the highly structured coherence produced 
by, e.g., a four-fold pupil pixel with (x,y) mirror symmetry, possibly 
including a multiplicity of beams tightly clustered about each of these 
four minored directions. 
Reticle 26 contains features to be imaged onto image plane 32. If system 20 
is used in the microscopy art, reticle 26 may consist of a slide 
containing a test sample to be examined. Alternatively, when system 20 is 
to be used in optical lithography reticle 26 may consist of a mask 
containing features to be imaged in a selected thickness of photoresist 
(not shown) at image plane 32. Although not shown in FIG. 1, one or more 
lenses making up the imaging optics of system 20 are typically positioned 
between source 24 and reticle 26. Similarly, although projection imaging 
lens 30 is illustrated as a single lens, in practice a plurality of lenses 
may be used. System 20 may also include a conventional support (not shown) 
used for holding and positioning a radiation-sensitive medium, such as a 
semiconductor wafer coated with photoresist, in image plane 32. 
Describing projection imaging system 20 in more detail, in the first 
embodiment of the invention; the illumination to be generated by system 20 
is optimized based on information obtained by scanning the aerial image 
created at image plane 32. Referring to FIG. 3, such scanning is 
accomplished with a scanning system 50 and an image analyzer 52. Scanning 
system 50 is designed to provide an electronic output signal that varies 
as a function of the irradiance to which it is exposed. More particularly, 
system 50 is designed to provide such electronic output signal on a mapped 
basis, whereby for each x-y coordinate or pixel in the image being scanned 
an associated illumination intensity value is generated. To achieve this 
function, scanning system 50 includes a scanner (not shown) such as an 
optical slit detector and an x-y translation assembly (not shown) for 
moving the scanner back and forth along parallel paths lying in image 
plane 32. 
A suitable image scanning system that could be used as scanning system 50 
is described in the article by Patio, Fields and Oldham entitled "Direct 
Aerial Image Measurement as a Method of Testing High Numerical Aperture 
Microlithographic Lenses" presented at the 37th International Symposium on 
Electron, Ion, and Photon Beams, San Diego, Calif., in June of 1993. This 
system consists of a transmission grating placed over a photodetector and 
an electronic means for storing the measured signals. Constructing the 
grating with narrow openings separated by a suitable distance (in the 
Parlo et al. article, 0.2 .mu.m openings separated by 0.4 .mu.m), makes 
for a nearly ideal intensity sampling mechanism. The amount of light 
passing through the grating and hitting the photodetector is directly 
proportional to the intensity in the aerial image for the given position. 
Image analyzer 52 correlates the output signal from the scanner of system 
50 with x-y address information from the x-y translation assembly of 
system 50 to form an electronic representation of the aerial image created 
in image plane 32. As described here mailer, this electronic 
representation of the aerial image is analyzed by illumination controller 
22 to optimize the illumination provided by light source 24. 
It should be appreciated that the image scanning system 50 used in the 
present apparatus need not have a resolution as high as that required in 
other applications. A blurring of up to about 20% of the aerial image 
caused by the scanning system 50 would, in most cases, be acceptable here. 
In the present invention, the scanning system 50 provides image data only 
for the purpose of maximizing image slope. System 50 need not actually 
determine the numerical value of the slope, or more generally the "true" 
aerial image, with great precision. 
In a second embodiment of projection imaging system 20, instead of scanning 
the aerial image at image plane 32, the aerial image is derived 
numerically by describing the optical projection system mathematically and 
computing the image using the known projector parameters and appropriate 
imaging equations. In the case of a projection imaging lens 30 having a NA 
(on the image plane side) of less than about 0.5 or 0.6, a scalar 
diffraction-based model is adequate. One such model was developed by H. H. 
Hopkins and is described in a number of papers, such as "Image Formation 
with Coherent and Partially Coherent Light," Photographic Science and 
Engineering, v. 21, #3, May/June 1977, p. 114, presented at the SPSE 
International Conference of Image Analysis and Evaluation, Toronto, 
Ontario, Canada, Jul. 19-23, 1977 and published by the Society of 
Photographic Scientists and Engineers (now called the Society of Imaging 
Science & Technology, or IS&T), Washington, D.C., 20037. The Hopkins model 
treats the electric field forming the image as a scalar and assumes the 
object being imaged is sufficiently thin so that its effect on the 
incident field is represented by a multiplicative function. It is 
advantageous to perform the image formation analysis in the Fourier domain 
(frequency space) in order to deal with the pupil function of the imaging 
system rather than the amplitude response function and with the angular 
distribution or "effective source" rather than with the mutual intensity. 
The pupil function H(f,g) describes the imaging lens pupil shape and 
wavefront aberrations and can be measured interferometrically. The 
effective source J(f,g) describes the angular illumination distribution 
and is mathematically simpler and more directly measurable than its 
Fourier counterpart, the mutual coherence. The object amplitude 
transmittance, given by O(x,y), has a Fourier transform O(f,g), which 
describes the spatial frequency content of the object. 
For the spatial image irradiance or aerial image I(x,y), the projector 
equation in the frequency domain, which describes the spatial frequency 
content of the image, is given by 
EQU I(f,g)=.intg.df.sub.1 df.sub.2 dg.sub.1 dg.sub.2 .delta.(f-f.sub.1 
+f.sub.2).delta.(g-g.sub.1 
+g.sub.2).times.C(f.sub.1,g.sub.1,f.sub.2,g.sub.2)O(f.sub.1 g,.sub.1) 
O*(f.sub.2 g,g.sub.2) 
where 
EQU C=.intg.dfdgJ(f,g)H(f+f.sub.1,g+g.sub.1).times.H*(f+f.sub.2,g+g.sub.2) 
with the superscript "*" representing the complex conjugate. I(f,g) is then 
inverse Fourier transformed to obtain the spatial aerial image, I(x,y). 
There are several computer programs commercially available that calculate 
aerial images based on the Hopkins model. Finle Technology, PO Box 162712, 
Austin, Tex., 78716, offers three different programs, Prolith/2,Proxlith/2 
and Imagepro/2. The University of California at Berkeley, Department of 
Electrical Engineering and Computer Science, Berkeley, Calif., 94720, 
offers a program called SPLAT. In addition, Vector Technologies, PO Box 
3020, Princeton N.J., 08543, offers a sophisticated aerial image 
calculation program called FAIM (Fast Aerial Image Model). 
When the NA of projection imaging lens 30 (on the image plane side 32) is 
higher than about 0.6, a vector diffraction imaging model is preferred. 
This is because at high NA, the interfering electric field components of 
the radiation forming the image become significantly non-parallel and thus 
incapable of producing complete destructive or constructive interference. 
In addition, for photolithographic applications, the interaction of the 
polarized beam incident on a film stack at non-normal incidence may make 
it necessary to conduct illumination optimization based on the image 
formed within the film volume rather than with the aerial image per se for 
certain objects. A suitable vector diffraction imaging model is described 
by D.G. Flagello and A. E. Rosenbluth in the article "Vector Diffraction 
Analysis of Phase-mask imaging into Photoresist," presented at SPIE 1993 
Microlithography Conference, San Jose, Calif., 1993. The 
Flagello-Rosenbluth vector imaging model contains several key assumptions. 
The first is that the lens provides stationary (isoplanatic) imaging over 
regions that are large compared to the imaging lens resolution. In 
addition, diffraction from the mask is modeled as a scalar process, so 
that the polarization is not appreciably changed upon diffraction from the 
object. The assumption is also made that meridional rays serve as an 
adequate model of the polarization behavior of light through the lens. As 
each ray emerges from the exit pupil, it will have a polarization 
amplitude for each Cartesian component that depends on the exiting 
direction and can be calculated trigonometrically. Further, the Debye 
approximation is used, which allows for the amplitude of plane waves 
constituting an angular spectrum of such waves converging onto the image 
plane to be approximated by rays emerging from the exit pupil with the 
same direction and amplitude. In a vector approach, each polarization of 
the ray must be considered. A family of coherent rays emerging from some 
point in the exit pupil can be considered to represent diffraction of a 
single illuminating beam by a particular spatial frequency in the object, 
and to have a common phase representing the lens aberration. If the 
optical axis coincides with the z coordinate, with x and y the transverse 
axes, the angular spectrum component of the electric field vector E 
propagating from the exit pupil with (x,y) direction cosines (a',b') gives 
rise to incident electric field plane wave components at the air/film 
interface given by 
##EQU1## 
Here, q refers to the initial polarization of the electric field vector E 
at the source (x or y), r references the Cartesian E component incident at 
the image plane, and 1 indicates the coupling between the q and r 
components in either S or P polarization at the air/film interface. Also, 
primed and unprimed coordinates refer to the image and object spaces, 
respectively. T (a', b') is the transmission function of the lens. The 
exponential term describes residual aberration in terms of wavefront phase 
error W(a',b'). P(a',b') is the polarization projection function across 
the exit pupil. O (ma',mb'; m) is the amplitude diffracted by the mask 
into object space directions a=ma' and b=mb', with m repeated as a 
separate argument to indicate that the diffractive properties of the mask 
object will in general change if the pattern reduction is changed. The 
term (l/m)c/c'!.sup.1/2 is a radiometric obliquity factor needed to 
conserve power between the object and image space. Propagation of the 
plane waves into the film stack, if required, is carried out by standard 
thin-film matrix methods, such as described in the book by P. H. Berning, 
Physics of Thin Films, G. Hass, Ed. (Academic Press 1963), pp. 69-121. 
Integration of the above equation over the range of direction cosines a' 
and b', summing both S and P polarizations for a particular z value, gives 
the component image field amplitude E'(x',y',z'). The coherent irradiance 
for each initial polarization state is proportional to the sum of the 
component square magnitudes of the field, calculated by performing the 
following summation: 
##EQU2## 
The partial coherence case is treated by doing the above summation for 
discrete source points. In accordance with the above process and 
methodology, Flagello and Rosenbluth developed a computer program called 
Vector Imaging Code (VIC) to perform the numerical calculations, as 
discussed in their article referenced above. Such programming is normally 
required for all but the most trivial of imaging scenarios and can be 
readily accomplished by those skilled in the art. In addition, the 
aforementioned commercially available program FAIM includes a vector model 
which gives accurate aerial image results for high NA polarized 
illumination. 
Referring to FIGS. 2 and 3, the optimization of illumination and subsequent 
setting of source 24 whether by actual scanning of the image or by 
numerical calculation of same, as discussed above, can be described in 
terms of three cases. In the first case, source 24 is controlled by 
illumination controller 22 so that each pupil pixel 40 may be addressed 
with any desired irradiance. On a normalized scale where the brightest 
illuminated pupil pixel 40 is 1 and an unilluminated (i.e., dark) pupil 
pixel is 0, such a system is designed to provide any irradiance between 0 
and 1. For this first case, source 24 preferably comprises either a 
unitary point source that may be controllably scanned so as to illuminate 
selected pupil pixels 40 with illumination of desired intensity, or a 
cluster of point sources that are either moveable or are of sufficient 
density to permit selected pupil pixels 40 to be illuminated at a selected 
intensity. In the second case, source 24 may be controlled by illumination 
that addresses any pupil pixel 40, but provides only a normalized 
irradiance of 0 or 1. Alternatively, a relatively simple source 24 capable 
of providing such illumination can be obtained, at the expense of light 
loss, by flood exposing a custom aperture plate (not shown) placed in a 
plane 42 (FIG. 3) conjugate to the projection imaging lens entrance pupil 
28. The custom aperture plate is constructed so that (1) an opening exists 
associated in position with each pupil pixel 40 having an irradiance value 
of 1 and (2) a solid, light blocking portion exists associated in position 
with each pupil pixel 40 having an irradiance value of 0. A library of 
aperture plates may be maintained for each image pattern to be generated. 
Unless the plate has graded transmittance, or unless many plates are 
sequentially exposed, such a system is only capable of providing an on/off 
switching at each pupil pixel 40. 
In the third case, source 24 has restricted capabilities, in that it cannot 
address selected pupil pixels 40. Instead, source 24 generates selected 
geometric shapes that are imaged in entrance pupil 28. Although the 
intensity of the images created may be controlled, such control is 
effected on the gross image level and not on a pixel-by-pixel basis. 
Images may be created using flood illumination and an aperture plate with 
physical apertures to vary the illumination as discussed above. 
Alternatively in the third case, source 24 may comprise moveable fiber 
bundles, or an illuminator which addresses a roughly circular array of 
pixels in the pupil, with the radius of such array being adjustable. In 
this latter case, apparatus such as described in the '170 patent, which 
teaches varying the effective source distribution by the use of a variable 
magnification afocal system interposed between the primary source and an 
optical integrator, could be employed. 
In all three cases, projection imaging system 20 must provide means for 
determining the optimum global configuration of the light to be imaged at 
entrance pupil 28, and hence which pupil pixels 40 are to be illuminated. 
In the first case, the optimum configuration is specified as a list of (a) 
pupil pixels 40 to be illuminated and (b) the normalized irradiance for 
each such pupil pixel. A similar list is made for the second case, except 
that the irradiances are restricted to either 0 or 1. In the third case, 
the optimum configuration is specified via different variables, usually 
fewer in number, such as aperture fill radii or (x,y) fiber bundle 
coordinates, which are related in a simple but non-linear way to the point 
source irradiance values. In all three cases, entrance pupil 28 may be 
divided into any convenient number of pupil pixels 40, e.g., 40-2000 
pixels. The extended source comprising the irradiance values which produce 
the optimum wafer image for a given mask or masks is a list or vector 
hereinafter referred to as S. 
An important aspect of the present invention is the technique for 
generating the list of pupil pixels 40 to be illuminated and the intensity 
of illumination of such pixels, i.e., the technique for optimizing the 
illumination of source 24. As described hereinafter, and as illustrated in 
FIGS. 4a-4c, the technique for optimizing illumination is identical for 
each of the three cases described above, except for the final step of the 
technique (involving the minimization of a set of matrix products), as 
described hereinafter. 
The first step in the general procedure for finding the optimal 
illumination, illustrated in FIG. 4a, step 100, is to identify the mask 
(or reticle) feature or features required to be imaged by projection 
imaging system 20, along with a target image, and input the information 
into illumination controller 22. The target image is defined as the aerial 
image irradiance distribution that is ultimately desired. In most cases, 
the target image pattern is simply identical to the mask feature (or, more 
precisely, the mask feature's irradiance transmission). However, there may 
be situations where it is preferable to optimize to a target image that is 
different from the mask feature, such as when the mask feature is of a 
particularly complicated shape, if there is a portion of the feature whose 
resolution is particularly critical, or if the invention is used in 
conjunction with phase-shift masks. When this is the case, the target 
image information needs to be included as part of step 100. The ability to 
define a desired target image allows for wide latitude in finding an 
illumination to suit a variety of objective and subjective imaging needs, 
such that the "optimal" illumination refers to that illumination which 
provides an aerial image closest to the target image. 
When the target image pattern is just the mask feature itself, the 
necessary information for step 100 may be obtained from conventional 
electronic mask design databases. Such databases typically store the 
pattern in digital form as a series of square pixels (hereinafter referred 
to as mask pixels) laid out in a rectangular grid. Most commonly, the 
database information in effect specifies which mask pixels are clear and 
which are opaque. The mask feature (and hence, target image pattern) can 
always be described with such a specification in terms of exposed and 
unexposed regions. Traditionally, in order to be written on the mask 
blank, the feature is divided up into pixels by applying a step known as 
postprocessing, and is encoded in the design database. In today's 
technology, typical widths of individual mask pixels are about 0.25 .mu.m 
to 0.5 .mu.m, but narrower pixels such as 0.125 .mu.m might be specified 
to accommodate patterns with non-x,y orientation or a curved perimeter. 
These mask pixels are often demagnified by 4X or 5X when projected on the 
wafer. 
Thus, as indicated by step 100, FIG. 4a, the object and target image 
patterns are identified and then transferred, preferably in electronic 
form, to illumination controller 22 from the source where such patterns 
are stored, e.g., a mask database. Next, at step 102, the user has the 
option of identifying key pattern features, and providing numerical 
weights to emphasize those features which are deemed particularly crucial, 
as described in more detail hereinafter. Typically, the key pattern 
features to be identified will be those features having a size and/or 
configuration approaching the resolution limit of the projection imaging 
system. This weighing option can be used in combination with a target 
image pattern that is the mask feature itself, in lieu of having to resort 
to a target image pattern that differs from the mask feature. 
Illumination controller 22 then prepares matrices that are used in 
determining the optimum illumination to be generated by source 24, as 
indicated by step 104. The operations performed at step 104 are described 
hereinafter and are illustrated in the more detailed flow diagram of FIG. 
4b. 
The matrices prepared at step 104 contain information pertaining to the 
image formed at image plane 32. As the first step in generating this 
information, step 200 in FIG. 4b, a convenient number of sample positions, 
such as about four, or such as about one per each .lambda./NA step, are 
chosen along the edge extending between each pair of adjacent comers, 
which edge separates dark pixel regions from bright pixel regions in the 
desired image. These sample positions are defined by (x,y) coordinates 
generated based on the (x,y) coordinates of the selected comers and edges 
which are known from the mask database. Next, at step 202, (x,y) 
coordinates of additional sample points located on either side of the 
edges are calculated. Once again, a convenient number of sample positions 
is chosen on each side of the edges, e.g., about four, or about one per 
each .lambda./NA step. It may be convenient to locate these sample 
positions at about 0.5 k.sub.1 .lambda./NA away from the edge, where 
k.sub.1 refers to the minimum width feature in the pattern. An additional 
set of sample points at a distance of about k.sub.1 .lambda./NA can be 
further used to identify bright and dark areas, for those patterns that 
are wider than twice the minimum k.sub.1. 
As the next step 204, a single pixel 40 (FIG. 2) or group of such pixels in 
entrance pupil 28 is addressed with illumination. Then, as indicated in 
step 206 and 208, the bright and dark areas of the feature image (step 
206) and the edges of the mask feature image (step 208), the locations of 
which were defined in step 200 and 202 respectively, are scanned using 
image scanning system 50, or alternatively, are calculated numerically 
using image analyzer 52. As indicated by query step 210, the steps 204 
through 208 are repeated until all the pixels or regions of pixels are 
addressed with illumination. 
Finally, in step 212, the information collected in the illuminating and 
scanning steps 204 through 208 is used to create several matrices used for 
performing the optimization calculation. One matrix that is generated in 
step 212 is a matrix M, whose nth column is simply a list of the wafer 
plane irradiance values that were measured when the nth source pixel was 
illuminated. Additional measurements or calculations are made of the image 
slope .eta..gradient.I at those sample points that lie on feature edges 
(step 208). Here, .eta. is the unit vector in the direction perpendicular 
to the feature edges, .gradient. is the gradient operator, and I, as 
defined earlier, is the aerial image irradiance distribution. A row is 
added to M for each such sample position, the elements of the row being 
the measured slopes. 
Also in step 212, the vector s containing the optimum source intensities is 
introduced and is used to define matrices. Given M, the list or vector u 
of optimized wafer intensities and edge slopes is defined by the relation 
u=Ms. If desired, the matrix M can be pre-multiplied by a diagonal matrix 
whose elements are user-input weights, as described above, relative to 
step 102, FIG. 4a. 
One goal in optimizing the image is to have a constant intensity along the 
desired perimeter of the circuit features. This makes it possible to 
adjust the lithographic process in such a way that the resist images are 
developed out to this target perimeter. This goal cannot be satisfied 
perfectly, due to the finite resolution of the lens, but can be 
approximately satisfied in the following manner. The image analyzer 52 
generates a matrix S.sub.0 in step 212 that selects those sample positions 
in u which lie on feature edges identified in step 200. Columns of S.sub.O 
corresponding to such edge sample positions contain a single 1, with the 
remaining elements set to 0. If the m.sup.th sample position does not lie 
on an edge, but instead falls within a light or dark area, then the 
m.sup.th column of S.sub.0 is filled entirely with 0's. Each row of So 
contains a single 1. Similarly, matrices S.sub.dark and S.sub.bright are 
constructed as arrays of 1's and 0's that select the dark and bright 
sample areas identified in step 202. Thus, for example, for a given column 
in matrix S.sub.bright, which corresponds to a given sample position, all 
the rows in the column would consist of 0's unless there is a bright 
region on one side of the edge (for the given sample position). The row in 
the given column corresponding to this bright region would consist of a 1. 
Matrices S.sub.dark and S.sub.bright are used in the inequality constraint 
identified in Step 308 of FIG. 4b, as discussed hereinafter. 
Once the edge intensities in u are selected by S.sub.0, the variation in 
intensity along the perimeter, (S.sub.0 u)-u is then selected through a 
matrix .DELTA., also calculated in step 212. Here, u represents the 
average intensity along the perimeter. As a simplified example, if we 
suppose that 4 edge elements from u have been selected by S.sub.0, then 
.DELTA. would operate on u as 
##EQU3## 
so that the i.sup.th row of .DELTA. returns the deviation of the i.sup.th 
element of u from the average of all four perimeter elements. 
Finally, to minimize the variation in intensity along the target perimeter 
of circuit features, the quantity 
EQU .SIGMA.((S.sub.0 u)-u).sup.2 =s.sup.T (M.sup.T S.sub.0 .DELTA..sup.T 
.DELTA.S.sub.0 M) S.tbd.s.sup.T Gs 
is minimized. The superscript T is used here to represent the transpose of 
a matrix. 
Resolution in photolithographic applications depends on the sharpness of 
the image, which can be defined in terms of the edge slope of the aerial 
image irradiance distribution. Thus, another goal in optimizing the primed 
patterns is to obtain maximum slope in the image u. To do this, a matrix 
S.sub.1, analogous to S.sub.0 is added in step 212, which selects the 
slope entries from u. It is convenient to define S.sub.1 to return the 
negative of the slope with the desired sign, so that the negative slope 
can be minimized. A parameter .alpha. is added to balance the impetus 
towards steeper slope with the quantity described above that specifies 
uniformity along the perimeter. Thus, the overall goal is to find the 
vector s (the illumination) that minimizes the quantity q (the difference 
between the actual aerial image formed by illumination s and the target 
aerial image), where q is prepared in step 212 and is given by 
EQU q(s)=s.sup.T Gg+.alpha.(IS.sub.1 M)s.tbd.s.sup.T Gs+.alpha.g.sup.T s.1! 
The matrix g, also generated in the matrix forming step 212, is the product 
of S.sub.1 and M, premultiplied by a vector of 1's, denoted I, which 
carries out a summation, i.e., it takes an average. 
Referring again to FIG. 4a, the next step 106 involves inputting and then 
subsequently adjusting certain parameters used in the optimization 
routines of step 108 (described below), in order to achieve the most 
satisfactory image. When finding the optimum F, an important physical 
constraint is that all the source intensities be non-negative. In 
addition, when optimizing illumination patterns for very narrow width, 
such as k.sub.1 &lt;0.5, or when optimizing patterns in defocused planes, it 
is also preferable to include constraints that force the image to have 
proper topology. First, it is required that the image be dimmer than the 
resist threshold T.sub.resist at pixels in the middle of the dark area, 
and second, that the intensity be above some complementary threshold 
T.sub.expose in the bright areas. Thus, the two key parameters that are 
inputted or adjusted as part of step 106 are T.sub.expose, T.sub.resist. 
Methods for finding the minimum of q (Eq. 1), as called for in step 108, 
FIG. 4a, are well known to those skilled in the art. Referring now to FIG. 
4c describing step 108 of FIG. 4a in more detail, step 300 calls for 
choosing one of three available models, depending on the type of 
illumination. Step 302 pertains to the first illumination case (case I), 
where the elements of s are continuous in the interval between 0 and 1. 
This type of minimization is a so-called quadratic programming problem, as 
described by R. Fletcher in Practical Methods of Optimization, vol. 2, 
Constrained Optimization, Wiley, 1981. There also exists computer 
software, such as IBM's Optimization Subroutine Library (OSL), as 
described in IBM Systems Journal, vol. 31, no. 1, 1992 (IBM publication 
#sc23-0519-03), which contains routines that will return the optimum q in 
this case, and will return the global optimum q so long as Eq. 1, above, 
is convex. Thus, in calling optimization programs as per step 108, the 
quadratic model of step 302 in FIG. 4c would be specified in this case. 
Step 304 of FIG. 4c pertains to the second case (case 2), where the 
elements of s are either 0 or 1. This is an example of a so-called binary 
mixed integer problem, also described by Fletcher. Routines are available 
to solve such mixed integer problems, but the quality of the solution can 
be significantly influenced by the choice of initial trial solution. A 
suitable initial solution is obtained by thresholding the solution 
obtained for the first case, setting all addressed pupil pixels between 
0.5 and 1 to unity, and setting to zero all addressed pupil pixels below 
0.5. An alternative when the number of pupil pixels is sufficient, such as 
about 300 or more in each quadrant, is to derive a solution for the second 
case by half-toning the resulting solution calculated from the first case. 
Thus, in calling the optimization programs as per step 108, the quadratic 
model of step 304 of FIG. 4c would be specified in this case. 
Step 306 involves finding a solution for q for the third case (case 3), 
where certain pupil pixels are not addressable, and requires more of a 
brute force approach. Specific methods are described, for example, by M. 
Avriel in Non-linear Programming, Prentice Hall, 1976. Fortunately, the 
demerit function in Eq. 1, obtainable with the apparatus described herein, 
can be evaluated quite rapidly, given its simple matrix form. This, 
together with the small number of variables typically encountered in this 
case, makes an exhaustive search of the parameter space to find a solution 
quite feasible. Thus, in calling the optimization programs as per step 
108, the non-linear model of step 306 of FIG. 4c would be specified in 
this case. 
After the appropriate illumination case and corresponding optimization 
routine is identified in step 108 (as being either step 302, 304 or 306), 
the parameters defined in step 106 are combined in step 308 (of step 108) 
to specify the inequality constraint, 
EQU As.gtoreq.b 
or, writing A and b in more detail, 
##EQU4## 
A fourth constraint can be added at this point, namely that the sum of the 
s.sub.i (the elements of s) be 1, but it is usually preferable to dispense 
with this through proper normalization of the other parameters. 
Once steps 300 through 308 are performed, the next step, 310, is carried 
out, which calls the appropriate solving routine, as described above, for 
the illumination case identified in step 300. Once an s is found by the 
solving routing called in step 310 (thus completing step 108 in FIG. 4a), 
as the next step, 110, FIG. 4a, it is useful to display and examine the 
aerial image formed by the illumination defined by s. In this step, it is 
preferable to display a numerically calculated aerial image, since it may 
take several iterations to adjust the parameters initially set in step 106 
and would likely prove more time consuming if the actual image has to be 
scanned for each iteration. If the image displayed is not entirely 
suitable, say for example, the irradiance contours do not correspond 
closely enough to the target aerial image, then the query step 112 ("Image 
OK?") would be answered in the negative, and the input parameters are 
adjusted as per step 106. Then, the steps 302 through 310 (i.e., all the 
steps comprising step 108) are repeated until the query step 112 can be 
answered in the affirmative. Once the query step 112 is answered in the 
affirmative, the illumination source 24 (FIG. 1) is then set by the 
illumination controller 22, as per step 114, to provide, what at this 
point, is the optimum illumination defined by s. Then, as the final step 
116, reticle 26, e.g., a mask, is exposed with such illumination to print 
the reticle feature in a radiation-sensitive medium, e.g., a semiconductor 
wafer coated with photoresist, conjugate the reticle. 
The improvement in resolution obtainable by customizing the illumination in 
accordance with the present invention is illustrated in FIGS. 5 through 7. 
FIG. 5 is a phase-mask object that represents in a generic way the kind of 
structures that might be found in a future generation memory chip. The 
specific dimensions and phase values of the array of rectangles 602 in 
FIG. 5 were determined through application of the mask-design groundrules 
disclosed by T. Brunner in the article "Rim Phase-Shift Mask Combined with 
Off-Axis Illumination: a Path to 0.5 .lambda./NA Geometries," SPIE 
Proceedings, Vol. 1927--Optical/Laser Microlithography, J. Cuthbert, Ed. 
(Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 
1993), pages 54-62. All regions of the mask have unit irradiance 
transmittance, but the regions labeled "-1" are phase-shifted by 180 
degrees, so that their amplitude transmittance is -1. 
FIG. 6 shows equi-spaced 0.2 normalized irradiance contours of a 
numerically calculated aerial image 600 of the phase-mask object of FIG. 
5. The dashed lines in FIG. 6 represent the rectangular object 602 of the 
phase-shift mask object of FIG. 5, and serve as the target aerial image. 
The rectangular objects 602 of FIG. 5 that are actually used on the mask 
are biased inwardly (i.e., are narrower) relative to the target image, as 
disclosed by Bruner in the above-cited reference. The target irradiance in 
the interior of rectangles 602 is 0 (dark) while the surrounding areas 
have a target irradiance of 1 (bright). 
The projection imaging lens assumed for the calculations has a wafer-side 
NA of 0.5, an operating wavelength of nominally 248 nm, and is free of 
optical aberrations. The gap 604 (FIGS. 5 and 6) across the widths of 
adjacent rectangles 602 is a k.sub.1 =0.5 feature for this lens. The image 
plane 32 (FIG. 1) has been displaced 0.5 .mu.m from the position of best 
focus in order to simulate performance under the type of focal deviation 
likely to be encountered in practice. The illumination source is a 
standard Canon "C-Quest" quadruple 800 illustrated in FIG. 8a. This source 
is known to be suited to the fabrication of equal line/space patterns, and 
the image shows reasonably good contrast in alternating light/dark slices 
across the widths of the rectangles 602. Moreover, as disclosed by Brunner 
in the reference cited above, a synergistic benefit obtains when a 
quadrupole illumination is used in conjunction with the phase-shift mask 
of the type shown in FIG. 5. Despite this benefit, the equi-irradiance 
contours 608 in FIG. 6 are rounded across the ends of the rectangles 602, 
indicating that the contrast there is not very good. 
Referring now to FIG. 7, the object, imaging plane and projection imaging 
lens is the same as for FIG. 6, but the illumination pattern in the 
imaging lens entrance pupil has been changed from pattern 800 (FIG. 8a) to 
that of pattern 802 (FIG. 8b), in accordance with the procedure of the 
present invention described above. 
More particularly, a case 3 optimization was carried out, with some steps 
done by hand. The starting solution was a set of four source points (i.e., 
disks with very small radii), arranged in x-y mirror symmetric fashion, as 
described above. A second pair of source points (of stronger irradiance 
than the first set) was positioned in mirror symmetric form along a 
horizontal axis. A non-linear optimization was then performed with the 
disk radii and positions of the source points as free parameters, and the 
rectangles 602 serving as the target image. As can be seen from the 
rectangular shape of the equi-irradiance contours 708 (FIG. 7), the source 
provides high contrast across both the width and ends of rectangles 602, 
the critical edges in the pattern. It is important to note that it is not 
immediately obvious that the shape of the illumination pattern 802 would 
provide such a drastic improvement in the aerial image 708 relative to the 
target image 602. In fact, the optimized source shape of FIG. 8b is 
somewhat unexpected, and does not fall into any of the source categories 
(disks, annuli, and quadrupoles) that are presently familiar to those 
skilled in the art. The present invention provides a ready means for 
finding such optimal illumination. In addition, aerial image 708 was 
created using illumination pattern 802 (FIG. 8b) comprised of 
super-imposed disks with normalized irradiance values of only 0 or 1 (case 
3 illumination), and that even further improvement in the aerial image 708 
can be achieved by performing a case 1 optimization, whereby the pixels 40 
(FIG. 1) comprising illumination source 802 can range anywhere from 0 to 1 
in normalized irradiance. 
There are several refinements of the present invention that may be used to 
achieve additional imaging advantages over the prior art. One such 
refinement involves extending the depth of focus. To this end, u is 
lengthened by, say, twice as many elements, in order to include data taken 
in two or more focal planes. The number of rows in M must be 
correspondingly increased in order that the image data for the new focal 
planes be included. Alternatively, if the submatrices of M representing 
the different focal planes are summed (leaving the length of u unchanged), 
a new matrix M is obtained that is suitable for the so-called FLEX 
technique as described in the patent by H. Fukuda, N. Hasagawa, T. Tanaka, 
and T. Kurosaki, Method of Forming Pattern and Projection Aligner for 
Carrying out the Same, U.S. Pat. No. 4,869,999, issued Sep. 26, 1989, in 
which images in multiple focal planes are superimposed on a wafer. The 
present invention also allows the FLEX method to be extended. Formally, 
this is accomplished by using the image data from defocused planes to 
increase the number of columns in M, instead of the number of rows. If the 
length of the source vector s is then increased accordingly, each focal 
component of the FLEX sequence can have independently optimized 
illumination. 
Another refinement of the present invention, which results in changes to M, 
(described below), involves dividing the desired wafer patterns among more 
than one mask, most conveniently two different masks, or two sequentially 
illuminated areas on a single mask. Such a technique, for conventional 
lithographic systems, has been described by H. Sewell, "A new dimension in 
phase-shift mask technology," presented at SPIE Microlithography 1993, San 
Jose, Calif. The present invention allows such techniques to be extended, 
as illustrated in FIGS. 9 and 10. If the exposures from the individual 
bright features on these different masks do not overlap on the wafer, but 
instead print as completely separated patterns, then each mask exposure 
can be dealt with independently, as per the above described system. To 
obtain the optimized illumination for such overlapped double exposures, 
the length of s can be doubled so that each half specifies the optimum 
illumination for one of the masks. The number of columns in matrix M is 
also doubled to accommodate the calculations or measurements for each 
mask. In this way independently optimized illumination for patterns in a 
chip kerf versus patterns in the primary circuit array can be realized. 
Alternatively, there are many cases in which it would be desirable to butt 
the exposures from the two mask sets. FIG. 9 illustrates schematically how 
such an exposure might be accomplished, with a first mask 900 exposed with 
optimum illumination, using the procedures described above, then a second 
mask 902 aligned to the first exposure and exposed with an optimum 
illumination different from that used in the first exposure, also using 
the optimization procedures described above. The resulting wafer image 
resulting from the superimposed images is represented by 904, FIG. 9. 
H. Jinbo and Y. Yamashita of OKI Corporation have proposed another use of 
overlapping exposures, in which negative-tone contact holes are printed by 
superimposed exposures of x and y oriented phase edges, as described in 
their article "0.2 Micron or Less Mine Lithography by Phase-Shifting Mask 
Technology," IEDM 1990 Technical Digest, p. 825, published by IEEE, 1990. 
A related idea is to overlap exposures of x and y oriented grouped lines 
in order to print rectangles, as illustrated in FIG. 10, where mask 
feature 910 is imaged with optimal illumination, and then mask feature 912 
is imaged with optimal illumination different from that used in the first 
exposure to create the superimposed image 914. Here, too, optimal 
illumination for features 910 and 912 is determined in accordance with the 
procedures described above. 
The present invention, as described above, is a method for determining and 
setting the optimum illumination directionality in a photolithographic 
projection system. However, it is to be appreciated that the particular 
methodology and application as it pertains to optimizing illumination may 
be used for purposes other than photolithographic projection printing. For 
instance, the present invention may be used for optimizing illumination 
for optical inspection, or other applications of optical projectors which 
employ the process of illuminating from a multiplicity of locations (or 
equivalently, directions) and optimizing the source distribution based on 
a superposition of illuminating positions (directions). 
The present invention has several advantages over the prior art. One such 
advantage is that the present invention allows for the best possible 
illumination to be determined and then used for a given reticle feature 
and optical projection system. In addition, the best possible illumination 
can be used as the basis for determining and setting the "next best" 
illumination in the case where the illumination source is limited in its 
ability to illuminate the reticle. The present invention also provides for 
great flexibility in ameliorating imaging difficulties peculiar to optical 
lithography, such as so called "proximity effects" that arise when 
printing small features that are placed close together on the reticle. The 
ability to correct or reduce such problems through optimizing illumination 
eliminates the need for time-consuming and costly measures, such as having 
to create additional masks because the required features for a particular 
fabrication step cannot print satisfactorily when combined onto a single 
mask. For example, it is often the case in lithography that yield problems 
associated with particular mask features do not surface until the masks 
are made and then actually used to fabricate integrated circuits. Such 
yield problems are often addressed by changing exposure times or other 
adjustment of the photoresist process. The present invention allows 
adjustment of many new degrees of freedom in the lithographic process 
(i.e., illumination of pixels 40 in FIG. 2), and also provides a system 
for and method of adjusting them systematically, in that the flow chart of 
FIG. 4 can be re-executed with adjustments at steps 100, 102 and 106 to 
compensate for yield problems as they arise. 
Since certain changes may be made in the above methodology and system 
without departing from the scope of the invention described herein, it is 
intended that ail matter contained in the above description or shown in 
the accompanying drawings shall be interpreted in an illustrative and not 
in a limiting sense.