U.S. patent application number 11/315136 was filed with the patent office on 2006-05-11 for advanced exposure techniques for programmable lithography.
This patent application is currently assigned to Pixelligent Technologies LLC. Invention is credited to Andrew Case, Gregory D. Cooper, Erin Fleet.
Application Number | 20060098181 11/315136 |
Document ID | / |
Family ID | 27541098 |
Filed Date | 2006-05-11 |
United States Patent
Application |
20060098181 |
Kind Code |
A1 |
Case; Andrew ; et
al. |
May 11, 2006 |
Advanced exposure techniques for programmable lithography
Abstract
Advanced techniques for programmable photolithography provide
enhanced resolution and other aspects of a photolithography system.
A combination of multiple exposures and movement of a substrate
relative to a programmable mask in a photolithographic system
accomplishes single shutter exposure overlaps to create features
smaller than the single shutter intensity profile, i.e., sub-pixel
resolution. Advanced timing adjustment capabilities are used to
modulate the light so that no unwanted features are created.
Additionally, a library of shapes may be used, one shape on each
pixel, with the small features of the shapes created by phase
shifting. Patterns are built up by multiple exposures with relative
movement of the mask and resist so as to place each shape from the
library where it is needed on the resist. Electro-Optic phase
shifting material may be applied to the shutter so as to adjust the
single shutter intensity profile, or to adjust the interaction of
adjacent shutters. An apodizing mask may be used to engineer the
wavefronts of the light striking the resist in such a manner to
achieve better resolution.
Inventors: |
Case; Andrew; (Silver
Springs, MD) ; Cooper; Gregory D.; (Alexandria,
VA) ; Fleet; Erin; (Alexandria, VA) |
Correspondence
Address: |
NIXON & VANDERHYE, PC
901 NORTH GLEBE ROAD, 11TH FLOOR
ARLINGTON
VA
22203
US
|
Assignee: |
Pixelligent Technologies
LLC
College Park
MD
|
Family ID: |
27541098 |
Appl. No.: |
11/315136 |
Filed: |
December 23, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10283322 |
Oct 30, 2002 |
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11315136 |
Dec 23, 2005 |
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60330765 |
Oct 30, 2001 |
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60330745 |
Oct 30, 2001 |
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60331038 |
Nov 7, 2001 |
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60331039 |
Nov 7, 2001 |
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60331515 |
Nov 19, 2001 |
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Current U.S.
Class: |
355/67 ; 355/53;
355/77 |
Current CPC
Class: |
G03F 7/70291 20130101;
G03F 7/70466 20130101; G03F 7/70283 20130101 |
Class at
Publication: |
355/067 ;
355/053; 355/077 |
International
Class: |
G03B 27/54 20060101
G03B027/54 |
Claims
1. A method for exposing a substrate using a programmable mask
having plural pixels, the method comprising: controlling the plural
pixels of said programmable mask to provide an exposure pattern;
applying a first phase shift amount to at least a first of said
plural pixels; applying a second phase shift amount different from
said first phase shift to at least a second of said plural pixels;
and exposing the substrate by passing illuminating energy through
said programmable mask, said applied first and second phase shift
amounts adjusting the intensity exposure profile of energy striking
the substrate.
2. The method of claim 1 wherein said first phase shift amount
differs from said second phase shift by about 180 degrees.
3. The method of claim 1 wherein said applying steps are performed
by passing said illuminating energy through an optical material
having a refractive index.
4. The method of claim 3 wherein said exposing step includes
directing electromagnetic energy through said programmable mask and
said optical material toward the substrate.
5. The method of claim 3 further including selectively applying an
electric field to said material to selectively change the phase
shift applied thereby.
6. The method of claim 1 further including providing an
electro-optical material having an array of discrete programmable
phase shift elements corresponding to at least some of said
programmable mask plural pixels, and said applying steps comprise
programmably determining the amount of phase shift to be applied at
each of said discrete programmable phase shift elements.
7. The method of claim 1 wherein said applying steps each comprise
selectively applying an electric field to discrete electro-optical
programmable phase shift elements to provide programmable
pixel-by-pixel phase shifts for the plural pixels.
8. The method of claim 1 wherein said applying steps includes
controlling said first and second phase shifts in accordance with a
pattern.
9. The method of claim 1 wherein said applying steps include
providing a constructive or destructive interference pattern
corresponding to at least part of a desired exposure pattern.
10. A system for exposing a substrate comprising: a programmable
mask having plural pixels; a controller coupled to said
programmable mask, said controller controlling the plural pixels of
said programmable mask to provide an exposure pattern; a phase
shifting arrangement optically coupled to said programmable mask,
said phase shifting arrangement applying a first phase shift amount
to at least a first of said plural pixels and applying a second
phase shift amount different from said first phase shift to at
least a second of said plural pixels; and a source that directs
illuminating energy through said programmable mask toward said
substrate, said applied first and second phase shift amounts
adjusting the intensity exposure profile of energy striking the
substrate to provide a desired exposure pattern.
11. The system of claim 10 wherein said phase shift arrangement
applies said first phase shift amount that differs from said second
phase shift by about 180 degrees.
12. The system of claim 10 wherein said phase shift arrangement
applies said first phase shift amount of about zero and applies
said second phase shift amount different from zero.
13. The system of claim 10 wherein said phase shift arrangement
comprises an optical material having a refractive index.
14. The system of claim 13 wherein said source directs
electromagnetic energy through said programmable mask and said
optical material toward the substrate.
15. The system of claim 13 wherein said phase shifting arrangement
selectively applies an electric field to said material to
selectively change the phase shift applied thereby.
16. The system of claim 10 wherein said phase shifting arrangement
comprises an electro-optical material having an array of
programmable phase shift elements corresponding to said
programmable mask plural pixels, and said controller is coupled to
said phase shifting arrangement and programmably controls the
amount of phase shift to be applied at each of said programmable
phase shift elements.
17. The system of claim 16 wherein said controller selectively
applies an electric field to said programmable phase shift elements
to provide programmable pixel-by-pixel phase shifts for the plural
pixels.
18. The system of claim 10 wherein said phase shifting arrangement
controls said phase shifts in accordance with a pattern.
19. The system of claim 10 wherein said phase shifting arrangement
provides a constructive or destructive interference pattern
corresponding to at least part of a desired exposure pattern.
Description
CROSS-REFERENCES TO RELATED APPLICATIONS
[0001] This is a divisional application of application Ser. No.
10/283,322, filed Oct. 30, 2002 now allowed, which application
claims priority from the following U.S. provisional patent
applications each of which is incorporated by reference herein as
if expressly set forth: [0002] application No. 60/330,765 filed
Oct. 30, 2001 entitled "Pattern Decomposition" (2476-12); [0003]
application No. 60/330,745 filed Oct. 30, 2001 entitled
"Programmable Phase-Shifting" (2476-11); [0004] application No.
60/331,038 filed Nov. 7, 2001 entitled "Pattern Decomposition"
(2476-19); [0005] application No. 60/331,039 filed Nov. 7, 2001
entitled "Programmable Phase-Shifting" (2476-18); and [0006]
application No. 60/331,515 filed Nov. 19, 2001 entitled "Method and
Apparatus For Exposing Photoresists Using Programmable Masks"
(2476-15).
[0007] This application is also related to commonly-assigned
application Ser. No. 09/871,971, now U.S. Pat. No. 6,480,261 B2, to
Cooper et al. entitled "Photolithographic System For Exposing A
Wafer Using A Programmable Mask" and filed Jun. 4, 2001 (attorney
docket 2476-9) incorporated by reference herein.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0008] Not applicable.
FIELD OF THE INVENTION
[0009] This invention relates to programmable mask lithography, and
more particularly to the use of a programmable mask for exposing a
photoresist. In more detail, the invention relates in at least one
of its aspects to techniques for building up the desired pattern of
resist exposure in a manner which permits the pattern to be created
by a sequence of exposures using a programmable mask, including
pattern decomposition for exposure using pixel overlap, the use of
a shape library of phase shifted pixels, programmable phase
shifting of pixels, and/or apodization of pixels.
BACKGROUND AND SUMMARY OF THE INVENTION
[0010] By way of general background, lithography is used to
transfer a specific pattern onto a surface. Lithography can be used
to transfer a variety of patterns including, for example, painting,
printing, and the like. More recently, lithographic techniques have
become widespread for use in "microfabrication"--a major (but
non-limiting) example of which is the manufacture of integrated
circuits such as computer chips or semiconductor wafers.
[0011] In a typical non-limiting microfabrication operation,
lithography is used to define patterns for miniature electrical
circuits. Lithography defines a pattern specifying the location of
metal, insulators, doped regions, and other features of a circuit
printed on a silicon wafer or other substrate. The resulting
semiconductor circuit can perform any of a number of different
functions. For example, an entire computer can be placed on a
chip.
[0012] Improvements in lithography have been mainly responsible for
the explosive growth of computers in particular and the
semiconductor industry in general. The major improvements in
lithography are mainly a result of a decrease in the minimum
feature size (improvement in resolution). This improvement allows
for an increase in the number of transistors on a single chip (and
in the speed at which these transistors can operate). For example,
the computer circuitry that would have filled an entire room in
1960's technology can now be placed on a silicon "die" the size of
a thumbnail. A device the size of a wristwatch can contain more
computing power than the largest computers of several decades
ago.
[0013] One idea to improve lithography performance is to use a
programmable mask to expose the substrate. Generally, a
programmable mask is a large array of "pixels" that can be
individually controlled to either be open (transmit light to the
substrate) or be closed (not transmit light to the substrate).
There have been several suggested mechanisms for making
programmable masks. One is to use liquid crystals to rotate the
polarization of light incident on a pixel. In this case only the
rotated (or not rotated) polarization would be transmitted to the
substrate, and the other polarization would be blocked. Another
mechanism for making the pixels is to use mechanical mirrors that
can move to either reflect light into or out of the optics of the
lithography system. Yet another mechanism is to use electric fields
to make semiconductor pixels either transparent or not transparent
(pixels made using the semiconductors or liquid crystals can also
be referred to as shutters). By individually controlling the
shutters, any desired pattern can be easily produced and then
easily changed to produce any other pattern. See for example
commonly-assigned U.S. Pat. No. 6,291,110 to Cooper et al. entitled
"Methods For Transferring A Two-Dimensional Programmable Exposure
Pattern For Photolithography" incorporated herein by reference.
[0014] Using a programmable mask allows the lithography process to
have a high throughput as in conventional parallel lithography
since a large number of features are printed in each step. A
non-exhaustive list of some of example and illustrative features
and advantages provided by performing lithography using a
programmable mask may be found in the above Cooper et al. U.S. Pat.
No. 6,291,110.
[0015] While programmable masks have the potential to fundamentally
improve modern photolithography, further improvements are possible
and desirable to take better advantage of programmable lithographic
techniques and to solve problems related to the use of programmable
lithography. We have developed such improvements and enhancements
in the following areas: [0016] pattern decomposition methods and
systems that control the shutter opening and closing, and movement
of, a programmable mask to create a desired pattern; [0017] methods
and systems that use predetermined phase shifting material on
exposure pixels to optimize the basic patterns to be exposed on a
semiconductor wafer or other substrate; [0018] programmable
phase-shifting methods and systems that use and control
programmable mask shutters to programmably control the phase of
photons passing through the mask; [0019] methods and systems that
use apodization to tailor photon distribution at the resist.
[0020] These various techniques can be used independently, together
in any combination, and/or in combination with other techniques
(e.g., photoresist exposure techniques such as disclosed in our
copending commonly-assigned application Ser. No. 10/298,224 filed
Nov. 18, 2002, now U.S. Pat. No. 6,879,376, based on provisional
application No. 60/331,515 filed Nov. 19, 2001), to improve
performance such as resolution of programmable
photolithography.
[0021] For example, one issue that arises is the variability of
feature placement and size. In conventional parallel lithography,
the feature size and pitch are limited by the smallest achievable
intensity profile. However, the features can be placed with an
accuracy significantly greater than resolution, and can have an
arbitrary size so long as it is larger than the minimum resolution.
With a programmable mask, the shutters are spaced at regular
intervals so it can be more difficult to place a feature with very
high accuracy, or of arbitrary size. Using each shutter in a
programmable mask to expose a portion of resist equal in size to
the single shutter intensity profile may limit the minimum feature
size to the size of the single shutter intensity profile.
[0022] One way of dealing with this is to have the exposure system
do multiple exposures. In between each exposure, it is possible to
move the mask a small amount relative to the wafer. A combination
of multiple exposures and movement of the mask relative to the
wafer may correct for defective pixels and allow one to choose the
location of the feature.
[0023] Another way of dealing with feature size limitations due to
pixel size and to diffraction limits is to use one (or more)
darkfield exposure(s) in combination with programmable lithography,
in such a way that the inherent limitations of the darkfield method
(excessive space between features) is overcome. This is achieved by
overlapping pixel images at the resist in such a way as to create
dark regions which are closely spaced, as detailed below.
[0024] Yet another approach to improved resolution is to directly
modify the single pixel intensity profile (the spatial distribution
of energy at the resist due to a single shutter, or pixel) so as to
improve the overall flexibility of the programmable lithography
system. In certain circumstances it is advantageous to have a steep
sided intensity profile, such as in the case where features are
created using pixel overlap. In other circumstances it is
advantageous to have a peaked intensity profile, such as in the
case where feature widths are adjusted by adjusting the amount of
time during which light is permitted to fall on the resist (timing
control).
[0025] Another area in which programmable lithography can be
improved is in the case where there is some amount of overlap (due
to diffraction) between the light distribution of adjacent
shutters. Depending on the pattern being exposed, this may be
either desirable or undesirable. In the case where it is desirable,
obviously we need do nothing. But in the case where overlap is
undesirable, we can compensate for its effects by placing a phase
shifting material on one or both shutters, so that the light
passing through one shutter is phase-shifted, e.g. by 180 degrees,
relative to the light passing through the other shutter. The light
in the region of overlap then interferes destructively, reducing
the total energy deposited in the overlap region. However, we
cannot necessarily predict a priori whether or not we will need to
phase-shift a particular set of shutters, since the same mask will
be used to expose multiple patterns.
[0026] We can solve this problem of arbitrary feature size and
placement by, for example, using multiple exposures with local
control of the exposure timing, by the use of a phase shifted shape
library, by use of pixel-by-pixel programmable phase shift, and by
the use of apodization of the limiting aperture of the optical
system.
[0027] For example, an illustrative method for decomposing a
desired resist exposure pattern and using the decomposed pattern to
perform programmable lithography involves expressing the desired
resist exposure pattern in vector form, and expressing the
relationship between the shutter energies and the resulting total
energy delivered to the various regions of the resist as a matrix.
The pseudo-inverse of the matrix is then calculated, and applied to
the desired resist exposure pattern in vector form in order to
generate a vector representing the shutter exposure energies. A
mask is programmed using the generated shutter exposure energy
vector. Electromagnetic energy is then passed through the
programmed mask to expose a substrate having resist disposed
thereon.
[0028] Another example non-limiting method for exposing a resist by
use of programmable lithography involves the use of a library of
shapes. These shapes can for example be created by the use of phase
shifting or other means. The desired pattern of resist exposure is
built up by successive exposures of the resist, with possible
relative movement of the programmable mask and the wafer between
exposures.
[0029] A material with changeable refractive index can be applied
to the shutters of a programmable mask, or on a separate submask
interposed between the programmable mask and the resist, such that
the phase of the light from an individual shutter may be
programmably changed so as to modify the intensity distribution of
light impinging upon the resist.
[0030] A material can be applied to the limiting aperture of a
lithography system, with specified refractive index and
transparency such that the phase and amplitude of the light passing
through the limiting aperture are modified so as to create features
on the resist smaller than the features created by the system in
the absence of said material.
BRIEF DESCRIPTION OF THE DRAWINGS
[0031] These and other features and advantages provided in
accordance with presently preferred exemplary embodiments of the
invention will be better and more completely understood by
referring to the following detailed description in connection with
the drawings, of which:
[0032] FIG. 1 shows exemplary, illustrative sub-pixel resolution by
exposure overlap;
[0033] FIG. 2 shows example unwanted overlap of single shutter
exposure patterns;
[0034] FIG. 3 shows exemplary, illustrative application of timing
control to prevent unwanted features;
[0035] FIG. 4 shows an example illustrative stepper system that
implements the FIG. 3 approach;
[0036] FIG. 5 shows a flowchart of an example process used to
expose a resist using multiple exposures and movement of a
substrate relative to a mask;
[0037] FIGS. 6A-6D shows example overlap of shutter exposures on a
single grid unit;
[0038] FIG. 7 shows an example desired exposure pattern;
[0039] FIG. 8 shows example overlap of shutters with grid
units;
[0040] FIG. 9 shows example idealized single shutter intensity
profile;
[0041] FIG. 9A is a flowchart showing an example pattern
decomposition process;
[0042] FIG. 10 shows an example of diamond shaped grid units built
from hexagonal shutters;
[0043] FIG. 11 shows an example illustrative Programmable Phase
Shift Mask shape library;
[0044] FIG. 12 shows an example use of phase shift in combination
with darkfield exposure to create narrow features;
[0045] FIG. 13 shows an exemplary Darkfield shutter pattern overlap
for resolution enhancement;
[0046] FIG. 14 shows an example Homogeneous programmable phase
shifting to adjust interaction between shutters;
[0047] FIG. 15 shows exemplary illustrative Inhomogeneous phase
shifting to adjust individual shutter intensity profiles;
[0048] FIG. 16 shows an example illustrative apodized point spread
function;
[0049] FIG. 17 shows an example illustrative apodized point spread
function multiplied by an exemplary Gaussian;
[0050] FIG. 18 shows an example phase shift of an illustrative
apodization pupil used to produce the apodized point spread
function of FIG. 16; and
[0051] FIG. 19 shows exemplary transparency of the exemplary
apodization pupil of FIG. 18.
DETAILED DESCRIPTION OF PRESENTLY PREFERRED EXAMPLE ILLUSTRATIVE
EMBODIMENTS
Illustrative Pattern Decomposition Techniques, Methods and
Systems
[0052] In an illustrative and exemplary embodiment, we use a
combination of multiple exposures and movement of the mask relative
to the wafer to overlap single shutter exposures to create features
smaller than the single shutter intensity profile (sub-pixel
resolution). An example process for doing this is illustrated in
FIG. 1. We can also avoid the problem of unwanted overlap when we
wish to put two sub-pixel features with less than two full single
shutter intensity patterns between them, as illustrated in FIG. 2.
Our example and illustrative solution is to use the advanced timing
adjustment capabilities provided by programmable lithography to
modulate the light so that no unwanted features are created, as
shown in FIG. 3.
[0053] The examples given so far have all been one dimensional.
However, the resist pattern we want is inherently two dimensional,
so the problem is appreciably more complex, since there is risk of
overlap between many more shutter exposures in even the simplest
case.
Example Preferred Embodiment Photolithographic System Including
Shutter Timing Control to Prevent Unwanted Features
[0054] FIG. 4 shows an example mass production photolithographic
system for exposing substrates such as but not limited to
semiconductor wafers having photo-resist thereon. In the example
embodiment shown in FIG. 4, a substrate such as a photo-resist
coated wafer ("W") is placed on a stage ("S") which is used to move
and position the substrate. A source of electromagnetic energy
("I") such as, for example, visible light, x-rays, ultraviolet
wavelengths, or other electromagnetic radiation wavelengths
appropriate for the particular substrate and exposure processes
being performed emits electromagnetic energy. In the example and
illustrative embodiment, this electromagnetic energy is passed
through a programmable mask ("M") and then. through an optical
system of lenses and the like ("L") that projects and demagnifies
the image of the mask. The optical system may optionally include a
programmable phase shifting mask ("P"), which may be separate from
the programmable mask or physically part of the programmable mask,
and may also optionally include an apodizing mask ("A") may be
placed at the limiting aperture of the optical system. The
resulting electromagnetic radiation pattern is used to expose a
photo-resist coated wafer. A computer ("C") accurately controls the
position of the substrate S relative to the exposure pattern by
moving and positioning the stage. The computer C also controls the
exposure subsystem including the operation of the programmable mask
M and the programmable phase shifting mask P.
[0055] In the example embodiment, programmable mask M may be of the
type described in U.S. Pat. No. 6,291,110 referenced above.
Generally, this programmable mask is an array of shutters used to
expose a resist or other substrate. Each shutter in the
programmable mask M preferred implementation comprises a single
light modulating element on the programmable mask. In one example
implementation, this single light modulating element may comprise a
wide band gap semiconductor with an opacity that may be changed by
an applied electric field. However, in other implementations, a
shutter may comprise a micromirror, a wide band gap semiconductor
in transmission mode or in reflection mode, or any other means of
modulating light.
[0056] In the example embodiment, the exposure system permits the
pattern of electromagnetic radiation to pass through the
programmable mask M at a given position. In general, the mask M
and/or the substrate S is moved and multiple exposures made in
order to create a desired pattern. In the exemplary embodiment, a
resist pattern (i.e., the pattern on the photoresist of areas
exposed to electromagnetic energy) is formed.
[0057] The example and illustrative embodiment controls the
intensity profile of the pattern of light that is passed through
the mask M to the substrate S. The resulting resist pattern results
from selective exposure of areas of the substrate to light
intensities above and below a predetermined threshold. Generally, a
photo-resist will change its physical and/or chemical properties
when it receives electromagnetic energy exposure above a certain
intensity threshold. The preferred embodiment takes advantage of
this threshold by in some cases providing exposure of the resist
while ensuring that in the regions of overlap between pixels, where
a feature is wanted, the combined effect of the exposures from the
pixels contributing to the overlap region is enough to result in
exposure of the resist above the threshold, while in those regions
of overlap where no feature is wanted, the combined exposures from
the pixels contributing to said region is below the threshold for
change in the physical or chemical properties of the resist.
[0058] FIG. 5 is a flowchart of an example process used to form a
resist pattern using a combination of multiple exposures and
movement of the substrate relative to the mask to overlap single
shutter exposure to create features smaller than the single shutter
intensity profile (i.e., to achieve sub-pixel resolution).
Example Intensity Control Technique
[0059] For concreteness, let's look at a specific illustrative but
non-limiting example of how computer C determines the programmable
configuration of shutters of programmable mask M to achieve
sub-pixel resolution. Let the desired resist pattern lie on a 3 by
3 grid, with an L shaped feature to be exposed. We'll assume that
the size of the single shutter exposure pattern is twice the size
of an individual grid square (side length--four times the area--see
FIGS. 6A-6D). An example desired illumination pattern is shown in
FIG. 7. The procedure we will follow is this: First we write down a
set of equations relating the exposure energies of each shutter at
each mask location to the resulting total light intensity at each
grid location. Then we try to solve the resulting set of
simultaneous equations for the exposure energies in terms of the
desired resist pattern.
[0060] Since we have 9 grid units in this example, we will have 9
equations, each with 4 unknowns (for each of the 4 exposures per
grid unit). Example overlap of shutters with grid units is shown in
FIG. 8 where the shutters are indicated by E.sub.x in the upper
left corner, and the grid squares are indicated by G.sub.x near the
center. Note that since there are 4 grid units per shutter, the
edges of the shutters extend one grid unit past the edge of the
desired resist pattern on all sides.
[0061] The resulting set of coupled equations for the grid unit
exposures is E.sub.1+E.sub.2+E.sub.5+E.sub.6=G.sub.1
E.sub.2+E.sub.3+E.sub.6+E.sub.7=G.sub.2
E.sub.3+E.sub.4+E.sub.7+E.sub.8=G.sub.3
E.sub.5+E.sub.6+E.sub.9+E.sub.10=G.sub.4
E.sub.6+E.sub.7+E.sub.10+E.sub.11=G.sub.5
E.sub.7+E.sub.8+E.sub.11+E.sub.12=G.sub.6
E.sub.9+E.sub.10+E.sub.13+E.sub.14=G.sub.7
E.sub.10+E.sub.11+E.sub.14+E.sub.15=G.sub.8
E.sub.11+E.sub.12+E.sub.15+E.sub.16=G.sub.9
[0062] From the grid unit exposure equations we can construct the
matrix equation: ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 ) .times. ( E 1 E 2 E 3 E 4 E 5
E 6 E 7 E 8 E 9 E 10 E 11 E 12 E 13 E 14 E 15 E 16 ) = ( G 1 G 2 G
3 G 4 G 5 G 6 G 7 G 8 G 9 ) ##EQU1## which can be written in more
compact form as .cndot.{right arrow over (E)}={right arrow over
(G)}
[0063] By means discussed in the next section, we construct a
matrix, {tilde over (X)}: X ~ = ( 9 16 - 3 8 3 16 - 3 8 1 4 - 1 8 3
16 - 1 8 1 16 3 16 3 8 - 3 16 - 1 8 - 1 4 1 8 1 16 1 8 - 1 16 - 3
16 3 8 3 16 1 8 - 1 4 - 1 8 - 1 16 1 8 1 16 3 16 - 3 8 9 16 - 1 8 1
4 - 3 8 1 16 - 1 8 3 16 3 16 - 1 8 1 16 3 8 - 1 4 1 8 - 3 16 1 8 -
1 16 1 16 1 8 - 1 16 1 8 1 4 - 1 8 - 1 16 - 1 8 1 16 - 1 16 1 8 1
16 - 1 8 1 4 1 8 1 16 - 1 8 - 1 16 1 16 - 1 8 3 16 1 8 - 1 4 3 8 -
1 16 1 8 - 3 16 - 3 16 1 8 - 1 16 3 8 - 1 4 1 8 3 16 - 1 8 1 16 - 1
16 - 1 8 1 16 1 8 1 4 - 1 8 1 16 1 8 - 1 16 1 16 - 1 8 - 1 16 - 1 8
1 4 1 8 - 1 16 1 8 1 16 - 1 16 1 8 - 3 16 1 8 - 1 4 3 8 1 16 - 1 8
3 16 3 16 - 1 8 1 16 - 3 8 1 4 - 1 8 9 16 - 3 8 3 16 1 16 1 8 - 1
16 - 1 8 - 1 4 1 8 3 16 3 8 - 3 16 - 1 16 1 8 1 16 1 8 - 1 4 - 1 8
- 3 16 3 8 3 16 1 16 - 1 8 3 16 - 1 8 1 4 - 3 8 3 16 - 3 8 9 16 )
##EQU2## so .times. .times. that ##EQU2.2## A ~ X ~ = ( 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 ) = I ~ 9 .times. 9 ##EQU2.3##
[0064] Now we need to come up with some numbers: let the exposed
grid elements (G.sub.2, G.sub.5, G.sub.6) have a target exposure
value of 1.2 (taking 1 a the threshold) and assign all the others a
value of 0.6. Multiplying {right arrow over (G)} by {tilde over
(X)} we obtain an estimate for {right arrow over (E)} (why this
works will be clarified below). ( E 1 E 2 E 3 E 4 E 5 E 6 E 7 E 8 E
9 E 10 E 11 E 12 E 13 E 14 E 15 E 16 ) = ( 0 0.3 0.15 - 0.15 0 0.3
0.45 0.15 0.15 0.15 0.3 0.3 0.15 0.15 0 0 ) ##EQU3## where values
smaller than 10.sup.-15 have been rounded to 0.
[0065] Obviously E.sub.4=-0.15 is unacceptable, since it means we
have a negative exposure energy, which is impossible. Since we
don't care about details of grid element exposure (the numbers
chosen earlier were only for concreteness, so we could calculate
exposure values), only whether it is above or below threshold we
can simply set the offending element to zero, calculate the grid
exposure, and see if the result is satisfactory. Setting E.sub.4=0
and carrying out the matrix multiplication, we find ( G 1 G 2 G 3 G
4 G 5 G 6 G 7 G 8 G 9 ) = ( 0.6 1.2 0.75 0.6 1.2 1.2 0.6 0.6 0.6 )
##EQU4## which is perfectly acceptable as an exposure pattern. The
only change is that the exposure of the G.sub.3 grid square is now
0.75 instead of 0.6, which is still comfortably below threshold. In
the event that we need finer control (imperfect resists and
diffracted exposure patterns), this may not be acceptable, in which
case we would have to turn to tweaking by a more refined technique
such as a genetic algorithm based optimization, or some similarly
sophisticated technique. Example Technique for Setting Up the
Solution
[0066] We start with a desired pattern to be projected onto a
resist using a programmable mask. For now we make the following
assumptions: [0067] 1. The shutters are square, of side length w
[0068] 2. The desired pattern lies on a square grid consisting of
square grid units (like the squares on a sheet of graph paper) of
side length d. Grid units may be either exposed or not exposed,
thus creating the pattern. [0069] 3. There are an integer number
grid units per shutter, so that n.times.n grid units make up one
shutter (in the example above n=2). [0070] 4. The shutters have an
ideal intensity profile, that is, vertical sides, no light outside
the illuminated area, and uniform illumination inside (see FIG. 9).
[0071] 5. The resist has an ideal response curve, that is, for
total exposure doses below some threshold energy T, the resist is
completely unaffected, and above T the resist undergoes a
discontinuous change in properties from unexposed to exposed.
[0072] 6. The mask may be aligned to the wafer in successive steps
with arbitrary precision.
[0073] These requirements are imposed purely to simplify the
presentation of the technique in an illustrative, non-limiting
example. They may be relaxed or changed in different contexts
depending on requirements. Further discussion of the effect of
relaxing these assumptions is set forth below in this document.
[0074] The process of exposing the desired pattern involves moving
the mask to an initial position, opening the shutters for the
appropriate time (or number of pulses of the light source if
pulsed), and then moving to the next position and repeating the
process. In each step each shutter may be open for a different
amount of time, independent of what neighboring shutters are doing,
so that the exposure dose is controlled shutter by shutter. It is
this individual shutter exposure dose that we wish to calculate,
based on the desired resist pattern.
Example Technique for Finding Exposure Values
[0075] In order to find the desired value of the individual shutter
energies at each mask position, we start by assigning a variable to
each such energy: E.sub.1, E.sub.2, . . . , E.sub.q. Next we apply
the constraints--for each grid square, let the desired total energy
be G, so that we have a set G.sub.1, G.sub.2, . . . , G.sub.m,
where m is the total number of grid squares. FIG. 8 shows an
example relation between a set of shutters and the underlying grid,
showing that a given grid square is exposed by multiple shutters,
and a given shutter exposes multiple grid units, leading to a set
of coupled equations: A 11 .times. E 1 + A 12 .times. E 2 + + A 1
.times. q .times. E q = G 1 .times. .times. .times. .times. A m1
.times. E 1 + A m2 .times. E 2 + + A mq .times. E q = G m ( 1 )
##EQU5## where the coefficients A.sub.xy have the value 1 if the
corresponding exposure value E.sub.y contributes to the resist
exposure G.sub.x and have the value 0 otherwise.
[0076] This set of coupled equations may be solved using the
technique of matrix inversion (though note that at this point we
have not assigned any values to the grid exposure variables G). We
may write the equations in matrix form as .cndot.{right arrow over
(E)}={right arrow over (G)} with solution {right arrow over (E)}=
.sup.-1.cndot.{right arrow over (G)} where is a matrix of ones and
zeros placed according to equations (1). However: unless is square
(i.e. m=q ) the matrix .sup.-1 does not exist. Since in general is
not square, we need to come up with an alternative technique. The
technique we need involves the generalized inverse, a matrix,
{tilde over (X)}, which satisfies .cndot.{tilde over (X)}.cndot. =
The generalized inverse is also known as the pseudo-inverse,
semi-inverse, reciprocal inverse, reflexive generalized inverse,
normalized generalized inverse, weak generalized inverse, general
reciprocal, generalized inverse, and Moore-Penrose inverse--some of
these names refer to more restrictive subsets of the matrix we
want, but all include it. Given such an matrix, if we have
.cndot.{tilde over (X)}.cndot.{right arrow over (G)}={right arrow
over (G)} then the general solution for the shutter exposure
energies is {right arrow over (E)}={tilde over (X)}.cndot.{right
arrow over (G)}+( -{tilde over (X)}.cndot. ).cndot.{right arrow
over (T)} where is the identity matrix and {right arrow over (T)}
is an arbitrary vector. The freedom we have due to the fact that
our system of equations is underdetermined is embodied in {right
arrow over (T)}, which allows us to tweak the solution to ensure
that all shutter energies are positive, and to meet additional
constrains we may impose on the system.
[0077] The matrix {tilde over (X)} may be found using well known
techniques (for example, the Mathematica function PseudoInverse[]
calculates {tilde over (X)} given ). This leaves the condition that
.cndot.{tilde over (X)}.cndot.{right arrow over (G)}={right arrow
over (G)}
[0078] This condition is satisfied if {right arrow over (G)} is an
eigenvector of {tilde over (M)}= .cndot.{tilde over (X)} with
eigenvalue 1. Fortunately, {tilde over (M)} is idempotent, so it
has only two eigenvalues, 1 and 0, and the eigenspace of the unit
eigenvalue is the column space of {tilde over (M)}. This allows us
to easily assess whether or not we can create the whole desired
pattern in a single set of exposures, or whether we need to do one
set of exposures, etch, reapply resist, and expose the remainder of
the pattern. Assuming we find {tilde over (X)} by known methods, we
calculate {tilde over (M)}, and project {right arrow over (G)} onto
the rowspace of {tilde over (M)}. If we find that {right arrow over
(G)} is in the rowspace of {tilde over (M)}, then we know we can
create the desired pattern in a single set of exposures. We then
use the freedom offered by {right arrow over (T)} to tweak the
shutter energies to optimize the resist exposure pattern (and to
ensure that all shutter energies are positive). If {right arrow
over (G)} is not in the rowspace of {tilde over (M)}, then we will
need multiple expose/etch cycles. The only caveat is that if we
cannot ensure that all exposure energies are positive by using the
freedom given by {right arrow over (T)}, or by adjusting the values
in {right arrow over (G)}, then we will need to break the pattern
down further.
[0079] The matrix may be very large (on the order of 10.sup.10
elements), so inversion by non-optimized techniques is likely to
take too long to be of any practical use. Fortunately, is sparse,
and there is regularity in the ordering of the nonzero elements, so
fast inversion routines may be used which yield a result quickly.
In addition, due to the fact that the exposure pattern will
probably require some tweaking after initial determination of the
pattern, we can use approximate methods for inversion, leading to
still greater reductions in time required to compute the
generalized inverse. Fast routines for finding the pseudo inverse
based on regularities in the matrix being inverted are known, as
are fast routines for finding approximations to the pseudo
inverse.
[0080] Finally, some comments on the nature of {tilde over
(T)}--this is the vector that permits tweaking of the solution: In
practice, the thing we add to the solution in our exemplary
embodiment is not {tilde over (T)}, but ( - .cndot.{tilde over
(X)}).cndot.{tilde over (T)}. This vector has no effect on the
derived values for {right arrow over (E)} because it lies in the
null space of the operator . The operator ( - .cndot.{tilde over
(X)}) projects any vector into the null space of . With this
observation, we can simplify the equation for a solution to {right
arrow over (E)}={tilde over (X)}.cndot.{right arrow over
(G)}+{right arrow over (T)}.sub.N(A), where {tilde over
(T)}.sub.N(A) is any vector lying in the null space of . Using
standard techniques we can calculate a set of vectors spanning the
null space of , and therefore construct a basis for {tilde over
(T)}.sub.N(A). It is entirely possible that our pseudo inverse is
such that there is no null space (i.e. .cndot.{tilde over (X)}= ),
in which case we have to turn to other methods of tweaking the
exposure values, such as adjusting the grid pattern vector {right
arrow over (G)} for example.
Example Pattern Decomposition Process
[0081] FIG. 9A shows an example pattern decomposition process
provided by a presently preferred illustrative but non-limiting
embodiment of the present invention. In the FIG. 9A example, a
shutter-grid map matrix A is constructed (block 202) and inverted
to obtain X as discussed above (block 204). A desired grid exposure
vector G is then built based upon the X matrix (block 206). The
shutter energy required to obtain vector E is found (block 208) and
is checked for physical realizability (block 210). If the energy
vector E is physically realizable (no negative in values), then the
process is then complete (block 212). Otherwise, negative values in
the vector E are set to 0 (block 214) and new grid exposure values
are found (block 216) and tested against required limits (block
218). A modified target and exposure vector G' is constructed
(block 220) and used to determine a new required shutter energy
vector E (block 208). This process may iterate as many times as is
necessary to obtain a physically realizable energy vector E (blocks
210-220).
Example Relaxation of Illustrative Constraints
[0082] We now return to the assumptions made at the beginning and
examine how relaxing them affects the technique presented above.
Examining each assumption in order: [0083] 1) The shutters need not
be square. Round shutters might be used, but the overlap pattern
would be harder to calculate. Shutters could potentially be
hexagonal, on an underlying triangular grid, or triangular on a
triangular grid, an example is given in FIG. 10. Each possible
exposure location has, in one example arrangement, a unique
identifier (E.sub.1, E.sub.2, . . . above), and each grid square
has a unique identifier (G.sub.1, G.sub.2, . . . above). The
identifiers need not be in any particular order, though
considerable simplification may be achieved by ordering the
identifiers in a manner that reflects the structure of the grid and
the pattern of the exposures. [0084] 2) The grid need not be
square, as suggested above. The grid need not even tile the plane,
as long as the regions not covered are generally not important. For
example, the grid could consist of circles with some space between
them, as long as we do not care whether the resist between the
circles is exposed or not. [0085] 3) We must have an integer number
of grid units per shutter in order to be able to construct the
equations describing the relation between shutters and grid units.
The large flexibility in choosing the grid, however, allows us to
compensate for this. [0086] 4) A non-ideal intensity profile (for
example, due to diffraction) may introduce some uncertainty into
the exact location of the edges of exposed regions. However, the
location of the edge can be calculated from knowledge of the
intensity profile. The freedom embodied in {right arrow over (T)}
may then be used to adjust the location of the edge so that the
ideal edge location is achieved. In addition, the diffraction
pattern may be used to precisely locate the edges of exposed
regions with a precision greater than the grid spacing, allowing
for features which are not an integral number of grid units in
width. One possible approach is to use the technique outlined here
to create an initial guess, and then use the freedom embodied in
{right arrow over (T)} to optimize the pattern based on the known
non-ideal intensity profile by use of genetic algorithms or some
other method. In addition, the resist exposure pattern may be
tweaked by directly adjusting individual shutter energies, as done
in the example. [0087] 5) The resist need not have an ideal
response curve. The non-ideality may be taken into account in the
analysis of the uncertainties of feature sizes, and therefore
compensated for using the flexibility in {right arrow over (T)}.
[0088] 6) The mask alignment need not be arbitrarily precise.
Imprecision in mask alignment will be reflected in imprecision in
feature size. Example Wavefront Engineering
[0089] The technique of wavefront engineering provides for closer
control of the light intensity pattern at the resist surface. This
precise control is attained by selectively shifting the phase of
the light and correcting for proximity effects so as to improve
depth of focus and reduce feature size.
[0090] The light passing through a clear area of the mask will
spread out due to diffraction as it passes through the optical
system to the resist. The limit on the separation of adjacent
features due to diffraction is given by the lithographer's equation
d=k.sub.1.lamda./NA where d is the feature size (d can also be the
feature separation), .lamda. is the wavelength, NA is the numerical
aperture, and k1 is a process constant. Values of k1 as low as 0.1
have been reported when treated as a process constant. In
conventional lithography the pitch (feature size+feature
separation) may be greater than 0.5.lamda./NA.
[0091] The image formed at the resist consists of the convolution
of the (demagnified) image of the mask (or pixel) with the imaging
system point spread function. In classical lithography (and
microscopy/telescopy) the imaging system point spread function is
the Airy disc. The Airy disc produces a small central spot
containing most of the power, with very small wings, and it is
derived from an imaging system with a clear circular aperture.
[0092] One way that features substantially smaller than the
wavelength of light can be created is by using not the light to
create the features, but rather the dark spaces between light
patches. This technique is called darkfield exposure. The obvious
drawback of using darkfield to create features is that the minimum
separation of features (the pitch) is the width of the bright spots
on either side, which are still constrained by the lithographer's
equation. In order to use darkfield exposure to create narrow
features it is desirable in one exemplary illustrative arrangement
to have very sharp edged bright regions (so that they can be placed
close together while defining a clear edged dark region). One
technique which has been shown to meet this criterion is to use a
phase shift mask (PSM) in which the dark features are defined by
phase edges. The mask in this case has regions selectively etched
(or with phase shift material selectively applied) so that the net
phase shift between adjacent regions is 180 degrees. The wavefronts
passing through the mask then interfere destructively at the resist
in regions corresponding to the lines on the mask marking the
boundaries of phase shifted regions. The destructive interference
produces a very narrow and sharp edged dark region which is ideal
for darkfield exposure. In the literature it has been reported that
features as small as .about.25 nm have been fabricated using 248 nm
light. See M. Fritze, et al., "Sub-100 nm silicon on insulator
complimentary metal-oxide semiconductor transistors by deep
ultraviolet optical lithography," J. Vac. Sci. Technol. B 18(6)
2886-2890. The features exposed by this technique are necessarily
separated by large distances, as explained above.
Programmable Phase Shift Mask with Shape Library
[0093] The combination of phase shifting and programmable
lithography enables the rapid and convenient exposure of large,
complex patterns with a minimum of difficulty, and with a
substantial improvement in resolution. As an example (non-limiting)
implementation, consider a programmable mask consisting of an array
of square shutters with phase shift material applied to them so
that the pattern of light and dark at the resist is as shown in
FIG. 11.
[0094] In order to explain how to place darkfield features closer
together than the width of the adjacent bright patches, we need to
look closer at how the phase shift mask produces narrow lines.
[0095] An exemplary process is illustrated in FIG. 12 (where the
plots are approximate, intended only to show major features). This
figure shows a cross section through a programmable shutter with
phase shift material applied, along with the corresponding
amplitude and intensity measured at the resist.
[0096] The phase shifting produces an amplitude pattern as in the
upper plot of the figure, with a resulting intensity pattern as in
the lower plot. Because the resist responds to intensity rather
than amplitude, a narrow gap is formed between the peaks. This gap
defines the width of the dark field exposed feature. The region
outside the intensity pattern also remains unexposed in this
example--this will be addressed below.
[0097] In one exemplary arrangement, it is desirable that the
resist `remembers` the intensity of the light to which it has been
exposed, even though the intensity may not have exceeded the
threshold for exposure. Variations on this technique may use
advanced resists (i.e., non-integrating photoresists) that do not
integrate the total light dose, but for the purposes of this
illustrative discussion we restrict ourselves to a simple resist
which integrates the total intensity to which it is exposed without
regard for the details of exposure timing, etc.
[0098] Given an integrating resist and a programmable pixel with a
pattern of phase shift material applied to it as in FIG. 12 we can
create narrow features with a small pitch by overlapping successive
exposures with a small amount of movement between the exposures, as
shown in FIG. 13.
[0099] From the figure we can see that the overlap of two
successive exposures, each one individually below the threshold for
the resist, can create darkfield exposed features that are closer
together than would be allowed by the lithographers' equation. As
in FIG. 12 we have regions outside the exposed area in which the
resist is unexposed. Because the features are defined by the dark
regions the resist outside will have to be exposed separately in
order to ensure that we only have the two features we want.
[0100] We now have all of the elements needed to create a pattern
of densely packed small features on the resist. The exemplary
shapes shown in FIG. 11 allow us to create a network of
interconnects and pads needed to pattern an entire wafer. We can
space lines closely by using the overlap technique, and we can
connect lines by butting shutter exposures up against one another.
Where the unexposed resist does not contain any features we can use
the small solid shape to fill in the gaps between features. In
order to implement this we need a programmable mask with phase
shift material on the pixels, with some pixels having material
applied in such a way as to generate each of the patterns in FIG.
11, along with any other patterns that might by useful, such as
smooth curves or pads with leads.
[0101] In order to create the desired pattern on the resist the
pattern must first be analyzed and broken down into a set of
discrete exposures suitable for application by either overlapping
or by abutting shutter patterns. Because the edges of the shutter
intensity patterns are not sharp, but rather smoothly go to zero,
butting shutter exposures together potentially presents some
problems. The total intensity when two shutter exposures are
adjacent is ideally flat at the transition region. This will not
necessarily be realized in practice. For this reason one of the
shutter shapes should be a simple small shape with no darkfield
features. This shutter shape can then be used to smooth out the
boundary region between shutter exposures. In addition this shape
can be used to locally enhance the energy deposited in a given
region, either to delineate a shape not already on a shutter, or to
make fine adjustments in the shape projected by another
shutter.
Example Variations
[0102] There are many variations on the technique presented above.
The shape library need not be placed directly on the shutter. The
phase shift material that creates the shapes could be placed on a
diffraction limiting mask near the wafer, or on a separate mask
close to the shutters, or at some other location within the optical
train. Separating the phase shift material from the shutter itself
makes it simpler to use a micromirror array. In addition separating
the phase shift material from the shutters permits greater
flexibility in that it permits custom shape library phase shift
submasks to be used depending on the particular type of pattern
being exposed. Different phase shift submasks may be needed because
the shapes being exposed are different, or simply for process
optimization, in which case the number of any given shape may vary
from mask to mask, even though all shapes are present on both
submasks. This allows for phase shift submasks to be selected based
on which will give the greatest throughput.
[0103] The shapes in the phase shift submask library need not be
those intended to be present in the final resist pattern. They may
be selected so that they give the greatest flexibility when
overlapped, or so that the overlap of certain shutter exposures
produces desirable resist patterns. This is one possible technique
for reducing the number of elements needed in the phase shift shape
library, while maintaining the ability to expose the desired
pattern.
Programmable Phase Shift Shutters
[0104] It is well known that there are certain materials whose
refractive index depends on the applied electric field, either
linearly (Pockels effect) or quadraticaly (Kerr effect). In such
materials, an applied electric field modifies the manner in which
light interacts with the material, so that the light passes through
the material either slower or faster than it would without the
applied electric field. In the case of a linear material the
refractive index varies as n(E)=n.sub.0+aE
[0105] where E is the applied electric field. The coefficient a is
typically very small, but this can be compensated by making E
large. In the case of a quadratic material we have
n(E)=n.sub.0+bE.sup.2
[0106] where again the coefficient b is very small.
[0107] One illustrative arrangement places an electro-optic
material (EOM) on each shutter of a programmable mask, along with
electrical contacts to apply an electric field individually to the
material on each shutter. The phase shift material may be used in
two ways, either in a homogeneous mode (a uniform field applied
across the whole of the EOM) or in an inhomogeneous mode (in which
the field is non-uniform across the EOM).
[0108] Where the phase-shifting is done homogeneously, it can be
used to compensate for interference between the light distributions
of adjacent shutters in a manner analogous to the way PSMs are used
in conventional lithography. In this case the phase-shifting is
electronically controlled, so it may be used only where it is
helpful. Since the programmable mask will have different shutters
open at different times, the most desirable phase-shift pattern
will vary depending on the pattern of shutters open and closed.
Homogenous programmable phase shifting allows the phase shift
pattern to be intelligently programmed to give the best results
based on the particular pattern being exposed at the time.
[0109] In the case where the programmable phase shift is done
inhomogeneously, the effect is to either focus or defocus the light
from the shutter. In this case the advantage conveyed by the
programmable phase shift is in control over the detailed shape and
width of the single shutter intensity profile. In conjunction with
the advanced exposure techniques described elsewhere, this provides
additional flexibility, and therefore a greater degree of control
over the exposure dose at the resist. Control of the single shutter
intensity profile provides an additional degree of freedom which
may be exploited to improve resolution, throughput, or both.
Homogeneous Phase-Shifting
[0110] Homogeneous phase-shifting corrects for the effects of
overlapping nearby shutter intensity profiles, or enables the
overlap to be used to create pattern elements.
[0111] From exemplary non-limiting FIG. 14 it is clear that the
light intensity in the overlap region is substantially modified by
phase shifting one pixel relative to another. The overlap region
can be either exposed or not exposed, depending on whether the
phase shift material is active or not. This application of
homogeneous phase shifting allows for adjustment of exposure in the
overlap region, effectively creating a `virtual shutter` covering
only the overlap region. Additionally, in the case where the
overlap is between pixels which are more widely separated (not just
adjacent pixels), the programmable phase shift permits us to
correct for proximity effects based on the exact pattern of pixels
which are on or off for any given exposure. In this second case the
programmable phase shifting is used to correct for potentially
undesirable effects of pixel overlap.
Inhomogeneous Phase-Shift
[0112] Inhomogeneous phase-shift allows the intensity profile of a
single shutter to be individually adjusted, either to steepen the
sides or to make the sides of the pattern less steep. This permits
greater flexibility in the application of advanced exposure
techniques.
[0113] In FIG. 15, the exemplary intensity pattern is less
steep-sided with the phase-shifter active, but this need not be the
case--the two intensity patterns could be reversed if that turned
out to be more convenient. In addition, since the electro-optic
effect depends on the applied field, we can vary the degree of
modification of the intensity pattern by adjusting the magnitude of
the applied field, further increasing the flexibility of the
system.
[0114] The exemplary inhomogeneous effect shown in FIG. 15 can be
achieved either with a nonuniform electric field, or with
nonuniform application of EOM to the pixel, or by allowing the
physical properties of the EOM to vary over the area of the
pixel.
[0115] Other exemplary arrangements can provide the phase shift
elements in a structure that is physically separate from or
integrated with the programmable mask. For example, the phase shift
elements might comprise a separate plate or other structure
defining an array of programmable or non-programmable (i.e., fixed
refraction index) phase shift elements, or the phase shift elements
and the pixels of the programmable mask can be integrated into a
common structure. In one illustrative arrangement, the phase
shifting structure comprises an array of phase shift elements in
registry with and having correspondence (e.g., one-to-one or other
correspondence) with pixel elements of a programmable mask. The
phase shift elements can have fixed or programmable phase shifts.
Fixed or programmable phase shifts might for example provide a
"checkerboard" pattern of alternating phase shift amounts (e.g., a
certain angle A, and A.+-.180 degrees). In the case of a
programmable array, the particular phase shifts being applied by
particular phase shift elements in the array can be changed by
applying a stimulus such as an electric field, a voltage, a
current, magnetic stimulus, etc.
Sub Wavelength Pixel Images by Apodization
[0116] The image formed at the resist consists of the convolution
of the (demagnified) image of the mask (or pixel) with the imaging
system point spread function. In classical lithography (and
microscopy/telescopy) the imaging system point spread function is
the Airy disc. The Airy disc produces a small central spot
containing most of the power, with very small wings, and it is
derived from an imaging system with a clear circular aperture.
[0117] If we apply material to the limiting aperture which modifies
the phase and amplitude of the incoming light we can reduce the
size of the central spot, which can come at the cost of reducing
the energy in the central spot and creating larger wings (e.g.,
there is a redistribution of energy from the central spot to the
sidelobes). The apodization function is the phase and amplitude
modulation at the limiting aperture, and it is this apodization
which allows superresolution for a finite field at the image plane.
In this finite field the point spread function can be substantially
smaller than the Airy function and in certain cases can be
approximated by a delta function. This technique has been discussed
in detail by Frieden (Frieden, B. Roy, "On arbitrarily perfect
imagery with a finite aperture," Optica Acta, Vol. 16, pp. 795-807,
1969) for the specific cases of microscopy and telescopy.
[0118] In the Fraunhofer approximation (low Numerical Aperture, NA)
the point spread function a(x) is related to the optical pupil
function U(.beta.) through a Fourier transform: a .function. ( x )
= .intg. - .beta. 0 .beta. 0 .times. .times. d .beta. .times.
.times. U .function. ( .beta. ) .times. exp .function. ( j.beta.
.times. .times. x ) ##EQU6## where x is the radial coordinate at
the image plane and .beta.=2.pi./.lamda.R.times.pupil radial
coordinate. The R is the image distance (focal length in the case
of parallel incoming rays). Note that the Fourier transform in
question is not the conventional one in which the integral extends
from .+-..infin., but rather a finite Fourier transform. The
desired ideal point spread function (a delta function) with a
limited field is expanded in a series of prolate spheroidal wave
functions. These functions have the useful property of being their
own finite Fourier transform, and of forming a complete orthogonal
set over a finite field. Exemplary Apodization Method
[0119] To derive the desired pupil function, we first select the
desired finite field at the image plane over which we wish to
approximate a delta function. For the purposes of programmable
lithography this field need not be particularly large, since we can
eliminate light outside the field with a diffraction limiter or we
can use a non-integrating resist such as a two-photon resist with
light of the second wavelength concentrated inside the field.
[0120] The technique described here expands the desired point
spread function in terms of normalized "angular functions" given by
.psi..sub.n(x)=(.lamda..sub.n/N.sub.n).sup.1/2S.sub.0n(c,
x/x.sub.0) where .lamda..sub.n is the eigenvalue corresponding to
the function S.sub.0n, and x.sub.0 is the radius of the field,
c=.beta..sub.0x.sub.0 and N n = .intg. - 1 1 .times. .times. d t
.function. [ S 0 .times. n .function. ( c , t ) ] 2 ##EQU7## The
point spread function is given by a .function. ( x ) = n = 0
.infin. .times. .lamda. n - 1 .times. .psi. n .function. ( 0 )
.times. .psi. n .function. ( x ) ##EQU8## And the corresponding
pupil function is U .function. ( .beta. ) = ( x 0 / 2 .times.
.pi..beta. 0 ) 1 / 2 .times. n = 0 .infin. .times. j n .times.
.lamda. n - 1 .times. .psi. n .function. ( 0 ) .times. .psi. n
.function. ( .beta. .times. .times. x / .beta. 0 ) ##EQU9## In
practice we can't sum to infinity, so the sum should be truncated
at some point. Where we choose to truncate will dictate how wide
the central peak is, and how much power is lost.
[0121] An example illustrative apodized point spread function is
shown in FIG. 16. This function is probably unsuitable for use in
most lithography due to the large sidelobes (larger than the
central peak). This apodization was produced for a 3 cm aperture
radius, 10 cm focal length, i-line illumination, and
x.sub.0=.lamda./2.
[0122] In order to control the sidelobes we can either apply an
additional apodization, modify the apodization we already have, or
use a diffraction limiting mask close to the resist (but not
necessarily in contact). If we choose to use a diffraction limiting
secondary mask, we can have a standoff distance on the order of a
wavelength or so, unlike the case of a diffraction limiter used
with an unapodized imaging system.
[0123] The point spread function of example FIG. 16 can be improved
if we multiply it by a gaussian transmission function, the result
of which is shown in FIG. 17. The gaussian is wide enough that it
should be possible to implement it in the apodization. One
possibility is to take advantage of the fact that Fourier space
multiplication is real space convolution and vice versa, in which
case the net apodization should be the convolution of the apodizing
pupil function that generates FIG. 16 with the fourier transform of
the desired gaussian.
Exemplary Implementation (Lithography)
[0124] The apodization techniques known in the literature (see
Frieden) are generally used in purely imaging systems, i.e.,
systems that capture as opposed to projecting an image. In the case
of programmable lithography, however, we have substantially
complete control over the object being imaged onto the resist
(namely the pixel). It is very likely that proper shaping of the
pixel will allow for improvements in or reduce the side effects
from the apodizing aperture. It may be possible to apply phase
shift material and opaque material directly to the pixel itself in
place of the apodizing aperture. In this concept, the pixel itself
effectively becomes the apodizing aperture.
[0125] An exemplary apodization function that produces the
exemplary FIG. 16 behavior is shown in FIG. 18 and FIG. 19. It is
clear from the figures that approximating the function using a
stepped approximation will probably introduce errors.
[0126] The phase shift can be introduced with varying thicknesses
of material with a high index of refraction, such as quartz. The
opacity can be implemented by applying layers of semi-opaque
material in various thicknesses.
Example Implementation (Metrology)
[0127] In order to implement an apodized imaging system for
metrology, we can take one of several approaches. For example, we
can apodize the imaging system or we can create an apodized
projection system which projects a substantially sub-wavelength
spot onto the wafer or mask being imaged, and the spot is scanned
to image the whole object.
[0128] In the case of an apodized imaging system, we choose the
apodizing function to create a narrow central distribution with a
flat region on either side. The size of this flat region dictates
the maximum size of the region on the object that can be imaged at
any one time. The sensor used to detect the image (for example a
CCD) need be no larger than the size of this flat region. In order
to image the whole of the object the imaging system must be scanned
relative to the object, unless the object is so small that it fits
entirely within the flat region. One possible improvement is to
implement the metrology system as a series of parallel imaging
systems. The individual optical columns can each have their own
apodized pupil and CCD so that large wafers can be imaged
efficiently.
[0129] In the case of an apodized illumination source, the source
optics are apodized to produce a small (substantially
sub-wavelength) spot. This spot can be scanned so as to build up a
rasterized image of the object. The scattered light from the
scanning spot can be detected by a CCD or other imaging device.
This technique would be similar to confocal microscopy.
Example Implementation to Expose Semiconductor Wafers
[0130] Any or all of the above techniques can be used in
programmable lithography using steppers or other known apparatus to
expose semiconductor wafers. For example, one type of lithography
that is commonly used in the mass production of computer chips is
known as "parallel lithography". Parallel lithography generally
prints an entire pattern (or a significant portion of a pattern) at
one time. This is usually accomplished by projecting photons
through a mask onto a photoresist-coated semiconductor wafer. The
mask provides a template of the desired circuit. A photoresist
coat, which may be a thin layer of material coated on the wafer
which changes its chemical properties when impinged upon by light,
is used to translate or transfer the mask template onto the
semiconductor wafer. The mask allows photons (e.g., incident light)
to pass through the areas defining the features but not through
other areas. An example of a typical mask construction would be
deposits of metal on a glass substrate. In a way analogous to the
way light coming through a photographic negative exposes
photographic paper, light coming through the mask exposes the
photoresist. The exposed photoresist bearing the pattern
selectively "resists" a further process (e.g., etching with acid,
bombardment with various particles, deposition of a metallic or
other layer, etc.) Thus, this lithography technique using
photoresist can be used to effectively translate the pattern
defined by the mask into a structural pattern on the semiconductor
wafer. By repeating this technique several times on the same wafer
using different masks, it is possible to build multi-layered
semiconductor structures (e.g., transistors) and associated
interconnecting electrical circuits.
[0131] For mass production, parallel lithography is usually done
using a machine known as a "stepper." Generally, a stepper consists
of a light source, a place to hold a mask, an optical system for
projecting and demagnifying the image of the mask onto a
photoresist-coated wafer, and a stage to move the wafer. In each
exposure, a stepper only exposes a small part of the wafer,
generally the size of one chip. Since there are often many separate
chips on each wafer, the wafer must be exposed many times. The
stepper exposes the first chip, then moves ("steps") over to expose
the next chip and repeats this process until the entire wafer is
exposed. This process is known as "step and repeat" and is the
origin of the name "stepper."
[0132] A stepper is generally capable of precisely positioning the
wafer relative to the mask. This precise positioning (overlay
accuracy) is needed because each lithography step must line up with
the previous layer of lithography. A stepper spends a significant
portion of its time positioning the stage and the rest exposing the
photoresist. Despite the great precision necessary, steppers are
also capable of high throughput to be useful for mass production.
For example, there are steppers that can process one-hundred 8-inch
wafers per hour.
[0133] One way to increase the usefulness of a chip is to increase
its size. In the "step and repeat" example described above, the
size of the chip is limited to the exposure size of the stepper.
The exposure size is small (roughly 20 mm.times.40 mm) because of
the cost of an optical system that is capable of projecting a high
quality image of the mask onto the wafer. It is very expensive to
increase the size of a chip by increasing the exposure size of the
stepper (for example, this would require larger lenses--which by
themselves can cost millions of dollars). Another approach is to
modify a stepper so that light only shines on a subsection of the
mask at a given time. Then, the mask and wafer can be scanned
(moved relative to the fixed light source) simultaneously until the
entire mask is imaged onto the wafer. This modified stepper is
known as a "scanner" or "scanner/stepper". The scanner serves to
disconnect the exposure size from the chip size.
[0134] Scanners offer increased chip size at the expense of
increased complexity and mask costs. Because scanner masks are
larger, the masks are more fragile and are more likely to contain a
defect. The increased size and fragility of the mask mean that the
masks for a scanner will be more expensive than the masks for a
stepper. Also, because the image is being demagnified, the mask and
wafer must be scanned at different speeds. Because of the great
precision required, differential scanning increases the cost and
complexity of a scanner when compared with a stepper.
[0135] Many chip manufacturers are looking toward future
improvements in resolution and/or exposure size to help continue
the growth that has driven the semiconductor industry for the past
thirty years. Improvements in these areas have been partly the
result of improvements in the optical systems used to demagnify the
mask and of the use of shorter wavelength light. In particular,
modern lithography systems used for mass production are
"diffraction limited", meaning that the smallest feature size that
it is possible to print is determined by the diffraction of light
and not by the size of features on the mask. In order to improve
the resolution, one must use either a shorter wavelength of light
or other techniques such as optical proximity correction or phase
shifting. The wavelength used in leading edge lithography has
shifted from 436 nm to 365 nm to 248 nm to 193 nm and is expected
to move to 157 nm in the future. There is also considerable efforts
to move to much shorter wavelengths such as EUV (13 nm) and x-rays
(1 nm). Additionally there are research efforts to use other forms
of radiation such as electron (SCALPEL and EPL) and ions (IPL)
which have still shorter wavelengths.
[0136] While the invention has been described in connection with
what is presently considered to be the most practical and preferred
embodiment, it is to be understood that the invention is not to be
limited to the disclosed embodiment, but on the contrary, is
intended to cover various modifications and equivalent arrangements
included within the scope of the appended claims.
* * * * *