STC.UNM v. Intel Corporation

Filing 112

DECLARATION re 110 Brief of Brian Ferrall by Intel Corporation (Attachments: # 1 Exhibit 1, # 2 Exhibit 2, # 3 Exhibit 3, # 4 Exhibit 4, # 5 Exhibit 5, # 6 Exhibit 6, # 7 Exhibit 7, # 8 Exhibit 8, # 9 Exhibit 9)(Atkinson, Clifford)

Exhibit 1

111111

United States Patent

[19]

Brueck et ai.

1111111111111111111111111111111111111111111111111111111111111
US006042998A

[11]

[45]

[54]

METHOD AND APPARATUS FOR
EXTENDING SPATIAL FREQUENCIES IN
PHOTOLITHOGRAPHY IMAGES

[75]

Inventors: Steven R. J. Brueck; Saleem H. Zaidi,
both of Albuquerque, N.Mex.

[73]

Assignee: The University of New Mexico,
Albuquerque, N.Mex.

[ *]

Notice:

[21]

Appl. No.: 08/932,428

[22]

Filed:

[51]
[52]

Int. CI? ....................................................... G03C 5/00
U.S. CI. .......................... 430/316; 430/312; 430/323;
430/394
Field of Search ..................................... 430/396, 397,
430/313,312,314,316,322,323,394

This patent is subject to a terminal disclaimer.

[58]

[56]

References Cited
U.S. PATENT DOCUMENTS
4,859,548
5,116,718
5,216,257
5,343,292
5,415,835
5,486,449
5,705,321
5,759,744
5,790,254
5,801,075

8/1989
5/1992
6/1993
8/1994
5/1995
1/1996
1/1998
6/1998
8/1998
9/1998

Reise et al. ................................. 430/1
Dalton et al. ........................... 430/327
Brueck et al. .......................... 250/548
Brueck et al. .......................... 356/363
Brueck et al. .......................... 430/311
Rosono et al. ......................... 430/328
Brueck et al. .......................... 430/316
Brueck et al. .......................... 430/312
Ausschnitt .............................. 356/372
Gardner et al. ......................... 438/197

OlliER PUBLICATIONS
D. H. Ziger and C. A. Mack "Generalized Approach toward
Modeling Resist Performance," AIChE Jour. 37, 1863-1874
(1991).

6,042,998
*Mar. 28, 2000

W. D. Hinsberg, S.A. MacDonald, L. A. Pederson, and C. G.
Willson "A Lithographic Analog of Color Photography:
Self-Aligning Photolithography Using a Resist with Wavelength-Dependent Tone," Jour. Imaging Sci. 33, 129-135
(1989).

Primary Examiner-Janet Baxter
Assistant Examiner-Jill N. Holloman
Attorney, Agent, or Firm-Snell & Wilmer, L.L.P.
[57]

Sep. 17, 1997

Patent Number:
Date of Patent:

ABSTRACT

The present invention extends the available spatial frequency content of an image through the use of a method and
apparatus for combining nonlinear functions of intensity to
form three dimensional patterns with spatial frequencies that
are not present in either of the individual exposures and that
are beyond 2M in all three spatial directions. The resulting
pattern has spatial frequency content beyond the limits set
by optical propagation of spatial frequencies limited to 2/A
(e.g. pitch reduction from -A/2 to at least -A/4). The
extension of spatial frequencies preferably extends the use
of currently existing photolithography capabilities, thereby
resulting in a significant economic impact. Multiplying the
spatial frequency of lithographically defined structures suitably allows for substantial improvements in, inter alia,
crystal growth, quantum structure growth and fabrication,
flux pinning sites for high-Tc superconductors, form birefringent materials, reflective optical coatings, photonic
bandgap, electronics, optical/magnetic storage media, arrays
of field emitters, DRAM (Dynamic Random Access
Memory) capacitors and in other applications requiring large
areas of nm-scale features.
32 Claims, 19 Drawing Sheets

u.s.

Patent

",.

Mar. 28,2000

:.

,,""

Sheet 1 of 19

'

.

.:

6,042,998

....

'

15

Dimensions in
units of CD

10

.",' D. ,0 '

5

r'·~tD:'~···:'~?'.~!' ',.•,',~' .•'

j'.•'·1···••':::••.•..:: ',P:'•

U
LC,~',~,,:

. , . J. . ..... '."

I·: '. -.: ". .

o

o

\

. . ....

......... .. '

'L: '\~'

'L ,> '.';; ':::<

5

10

Rectangle is 6x6 unit cell

FIG. I

15

u.s.

Patent

":

.:

"

.

,",

.

".:

:', ...... . ':
'

"

····0··
.. .... ':" .
:"

.,'

. ' l

'"

'

.......
.....

".

. .'

..

6,042,998

Sheet 2 of 19

Mar. 28,2000

'

.....

:..: . .:. ....

. ".
.

",',

...... .....
'.'
.....:. .. :
.....
.,. ' .. :.'
"
"
.. ,,' .' .

,'",

"

',.'

...... .
"

:.

,"

"

"

.

.

:'.

....

,,'

. ...
.

'.

..
'.

.

.....:

.....

",

. .

.:"

"
,:

.,,'.
'.

~.' "

~

'"

~

"

..

..

,'

"

, ' ,. ,"

"

.."

"

...:

. :. ,',.:.. ....:.

..... ....
.:.:. " '....

"

......... ': .: ..
..
....
. ....
': ..:.. :. :".".
....
...: ..
,. :,'
,':..
.... :. .. ", .
..
. ..,,':: 0:,' Eo ;',
:.
.: .....
'.
...... . ..... :
. .... ,'"
.: .. ... ... : .. .....
.... .
".
.' ..
".
.... ," .
...

,'

,

~

","

',

"':

.. :'
"

,.

.;

','

.

~

. .,'. . ...

~

'.

Q:.;.': :><.::'. :~:.: '.; . . ·i5..::'::· .: '.':;..,. ' .";': .:
':."

..

.... :

FIG. 2A

'

"

....

"t ••

','

I,

'

'

./

.'

,',"

FIG. 28

'

:.:

"

u.s.

Patent

"

:

,

"

..

"

'.

..:

:

..

.

'.

",

"
"

I

'"

"

'.

•

"

".

,

" "

:

'.

"

.: :

.

6,042,998

Sheet 3 of 19

Mar. 28,2000

,',

,

.'

,.

,',

'

'.

"

"

'

"

J

,

,"

"

:

"

"
I,

.:

'.

'.

'"

.

,.

"

'.

010

"

..

r

'

"

-

.."

."

"

'
"

.'

"

"

"
,"

'.'

...

~

.:
"

~

.'

.'

'.

"

"

,

,',

: "

'.

.

:

.. .

"

, '

"

"

"

.

:

.

.:

I:.

:

"

:

"
:

(

..

"/

"

•

"

"

.

'.

",

,

'. .

.-,

"

:

..

,',

.

; "

'.

•

'.

..
'.

.... "'.
"

"

:'
~,

"

FIG. 3

'.

.'

.,

~,

....

u.s. Patent

Mar. 28,2000

Sheet 4 of 19

6,042,998

(I)
(I)

Q)

c:
~
c:

1

.r:

l+'

.!Q
(I)

~

0
0

+'

.r:

a.

"'0
Q)

a.
0

Q)

>
Q)

c

00

1

E(fluence)

FIG. 4

1. n=5
2. n=10
3. limit n-infinity

u.s. Patent

Mar. 28,2000

6,042,998

Sheet 5 of 19

-3p -2p -p

0

P

2p 3p

0

P

2p 3p

FIG. 5A

-

-3p - 2p -p

FIG. 58

.
-

u.s.

Patent

Mar. 28,2000

Sheet 6 of 19

FIG. 5C

6,042,998

u.s. Patent

Mar. 28,2000

6,042,998

Sheet 7 of 19

'::. '. .:>. . . . : :....... ":. :"
.

'"
•

'.:.,':'•• :• • • • • • :••••• :

"

FIG. 6A

: • .",

'

..

:'

:..

.'" .. :1 ...: .. :. :.: ..... " .

. ::.,'
....... .......
..

'

!. f

.:,.,

,
•

'.'

'

FIG. 68

•

':"

...

',:',:

''\0.'

,-

u.s. Patent

Mar. 28,2000

Sheet 8 of 19

FIG. 7A

6,042,998

u.s.

Patent

Mar. 28,2000

Sheet 9 of 19

6,042,998

u.s. Patent

Mar. 28,2000

..... ..,.
"
.....
,;,',

.

.. :,

'"

.,'

,':

'

..

:' ',::

.

::
:.-,

..

D':"'>""~:':":':"'::O':':

:
"

"

:,,:,',

..

'.

,

,,',.

"

'.:'

.

.',

~.:'

',

,,','

,.: .:;

. '. ....

-'.

"

.
',:

,'".

.

"

.....

',',

. .~'.,...>;;,·':'<5~;';:.i:<=>."
..
. :.: .:.-:...

','

"

';'

. ......
:0.

..

,'

:

'.

.', ".:'

6,042,998

Sheet 10 of 19

,'\

'

..

..

. ......
,

....

'

.... : :',:
. :.

....

.' ....:.

,--,:.

.'. .

.
;',

FIG. 8A

FIG. 88

~ . ~:,':,O::;;~c;::::~'::O;'~i:~~

,';.,

:'.'

:'

','

:" .' .:'

.. ' .. ' t.:. ~ .. :'."

FIG. 8e

'.

'

..

:>:.:....(':.:

u.s. Patent

Negative Tone

Subtractive

~::
48

48

40

~rt::;:r:;::r:;:::r::;:::+

~6

44

FIG. 98

42

~

FIG. 9C

40

,,-J

Processing

FIG. 9A

6,042,998

Sheet 11 of 19

Mar. 28,2000

P

44

~

~42
50

50

FIG. 90

44

FIG. 9E

42

u.s. Patent

6,042,998

Sheet 12 of 19

Mar. 28,2000

Positive Tone
Additive/Subtractive
Processing

60

,J

~::

FIG. lOA
6

66

FIG. lOB
68

FIG. 10C

68

~:;
72

FIG. 100

64
62

72

FIG. 10E
FIG. 10F

64
62

u.s.

Patent

Mar. 28,2000

Sheet 13 of 19

F(G~

IIA

FIG~

liB

6,042,998

u.s.

Patent

Mar. 28,2000

FIG.

Sheet 14 of 19

~

·1.

i . . '.

,···.C.

6,042,998

u.s.

Patent

Mar. 28,2000

Sheet 15 of 19

FIG. 12

6,042,998

u.s.

Patent

Mar. 28,2000

Sheet 16 of 19

FIGa 13A

FIGt 138

6,042,998

u.s.

Patent

Mar. 28,2000

Sheet 17 of 19

6,042,998

u.s.

Patent

Mar. 28,2000

Sheet 18 of 19

'F .G"~ ,
. ·····I ......

...

'

'

'I'.

5··.... .

6,042,998

u.s.

Patent

Mar. 28,2000

Sheet 19 of 19

6,042,998

6,042,998
1

2

METHOD AND APPARATUS FOR
EXTENDING SPATIAL FREQUENCIES IN
PHOTOLITHOGRAPHY IMAGES

content of an image, and more particularly, to a method and
apparatus for combining nonlinear functions of intensity of
multiple images to form three dimensional patterns with
spatial frequencies that are not present in any of the individual exposures and whose magnitudes are larger than 2A,
the limit of linear optical system response, in all three spatial
directions.

RELATED APPLICATIONS
5
The following patents and patent applications are herein
incorporated by reference: U.S. Pat. No. 5,216,257-S. R. J.
Brueck and Saleem H. Zaidi, Method and Apparatus for
Alignment and Overlay of Submicron Lithographic Features
(issued Jun. 1, 1993); U.S. Pat. No. 5,343,292-S. R. J.
Brueck and Saleem H. Zaidi, Method and Apparatus for 10
Alignment of Submicron Lithographic Structures (issued
Aug. 30, 1994); U.S. Pat. No. 5,415,835-S. R. J. Brueck
and Saleem Zaidi, Method and Apparatus for Fine-Line
Interferometric Lithography (issued May 16, 1995); U.S.
Pat. No. 5,759,744-S. R. J. Brueck, Xiaolan Chen, DaniellS
J. Devine and Saleem H. Zaidi, Methods and Apparatuses
for Lithography of sparse Arrays of sub-micrometer Features (issued Jun. 2, 1998); U.S. patent application Ser. No.
08/614,991-S. R. J. Brueck, Xiaolan Chen, Daniel J.
Devine and Saleem H. Zaidi, Methods and Apparatuses for 20
Lithography of sparse Arrays of Sub-micrometer Features (a
continuing, applicator was filed on Jul. 15, 1998 now U.S.
Pat. No. 5,674,652); U.S. patent application Ser. No. 07/662,
676-K. P. Bishop, S. R. J. Brueck, S. M. Gaspar, K. C.
Hickman, J. R. McNeil, S. S. Naqvi, B. L. Stallard and G. 25
D. Tipton, Use of Diffracted Light From Latent Images in
Photoresist for Exposure Control (filed Feb. 26, 1991); U.S.
Pat. No. 5,705,321-S. R. J. Brueck, An-Shiang Chu, Saleem Zaidi, and Bruce L. Draper, Method for Manufacture of
Quantum Sized Periodic Structures in Si Materials (issued 30
Jan. 6, 1998); U.S. patent application Ser. No. 081786,066,
now abandoned,-S. R. J. Brueck, Xiaolan Chen, Andrew
Frauenglass and Saleem Hussain Zaidi, Method and Apparatus for Integrating Optical and Interferometric Lithography to Produce Complex Patterns (filed Jan. 21, 1997); 35
Semiconductor Industry Association, National Technology
Roadmap for Semiconductors (1994); J. W. Goodman,Introduction to Fourier Optics, 2nd Ed., (McGraw Hill, New
York, 1996); J. W. Goodman, Statistical Optics, (John Wiley,
New York, 1985); Xiaolan Chen, S. H. Zaidi, S. R. J. Brueck 40
and D. J. Devine, "Interferometric Lithography of Submicrometer Sparse Hole Arrays for Field-emission Display
Applications," Jour. Vac. Sci. Tech. B14, 3339-3349 (1996);
S. H. Zaidi and S. R. J. Brueck, "Multiple-exposure interferometric lithography," Jour. Vac. Sci. Tech. Bll, 658 45
(1992); R. Ziger and C. A. Mack "Generalized Approach
toward Modeling Resist Performance," AIChE Jour. 37,
1863-1874 (1991); Introduction to Microlithography, Second Edition, L. F. Thompson, C. Grant Willson and M. J.
Bowden, eds. (American Chemical Society, Washington 50
D.C., 1994) and, W. D. Hinsberg, S. A. McDonald, L. A.
Pederson and C. G. Willson, "A Lithographic Analog of
Color Photography: Self-Aligning Photolithography using a
Resist with Wavelength-Dependent Tone," Jour. Imaging
Sci. 33, 129-133 (1989).
55
FEDERALLY-SPONSORED RESEARCH OR
DEVELOPMENT
The United States Government has a paid-up license in
this invention and the right in limited circumstances to
require the patent owner to license others on reasonable
terms as provided by the terms of Grant No. N66001-96C-8617 awarded by the United States Department of the
Navy.
FIELD OF THE INVENTION
The present invention is related, generally, to a method
and apparatus for extending the available spatial frequency

60

65

BACKGROUND OF THE INVENTION
The quality of an image is limited by the spatial frequencies within the image. In general, the maximum spatial
frequency contained in an optically defined image is
-2NNA where NAis the lens numerical aperture (the radius
of the lens aperture divided by the distance from the exit face
of the lens to the focal plane) and A is the optical wavelength. Thus, decreasing A and increasing NA typically
results in increased spatial frequency content and in an
improved, higher resolution image. The convention adopted
throughout this disclosure is that spatial frequencies are
given as the inverse of the corresponding length scale in the
image. Therefore, a factor of 2Jt is necessary to convert these
spatial frequencies to the magnitude of wavevectors for
detailed modeling. Hereinafter, "pitch," with dimensions of
nm, is used to refer to the distance between features of a
periodic pattern while "period," with dimensions of nm- 1, is
used interchangeably with spatial frequency.
Historically, the semiconductor industry has worked to
both decrease A and increase NA in its steady progress
towards smaller feature sizes. There are several factors that
together suggest that continued improvements to A and NA
are most likely not feasible and the industry will have to
undergo a significant change in lithographic technique.
Problems typically include the reduction of the feature size
to below the available optical wavelengths, often decreasing
the manufacturing process window, while at the same time
demanding increased linewidth control for high-speed circuit operation. Moreover, for wavelengths below the 193nm ArF wavelength, transmitting optical materials are typically no longer available, forcing the need for an allreflective system. However, an all-reflective system is often
problematical since current multi-layer reflector and
aspheric optical technologies are typically not sufficiently
developed to meet the feature size needs. The transition to
reflective optics will most likely result in a significant
reduction in the possible NAs, thereby reducing the benefit
of shorter wavelengths. Optical sources with wavelengths
shorter than 193 nm may also not provide sufficient average
power for high throughput manufacturing.
Furthermore, the complexity of the masks typically
increases by a factor of about four for each ultra-large scale
integration (ULSI) generation (i.e. about four times as many
transistors on a die). Additionally, many of the potential
advances in optical lithography, often collectively know as
resolution-enhancement techniques, typically lead to
increased mask complexity (serifs, helper bars, and other
sub-resolution features) or require a three dimensional mask
in place of the traditional chrome-on-glass two-dimensional
masks (phase shift techniques). The increased complexities
often increase the manufacturing difficulties and costs,
thereby commonly reducing the yield of the complex masks.
Moreover, the transition to wavelengths shorter than 193 nm
will most likely require a drastic changeover to reflective
masks since transmissive optical materials with adequate
optical quality are typically not available.
The limiting CD (critical dimension) of imaging optical
systems is usually stated as K1A/NA, where Kl is a function

6,042,998

3

4

of manufacturing tolerances as well as of the optical system,
perature superconductors are often limited by the motion of
Ie is the center wavelength of the exposure system and NA
flux lines that induces loss and heating resulting in a phase
is the numerical aperture of the imaging optical system.
transition to a non-superconducting state. The critical curTypical values of Kl range from about 1.0 down to -0.5.
rent density is the current density at which this transition
Projections for the 193 nm optical lithography tool are an 5 occurs. An improvement potentially could be achieved by a
NAofO.6 which leads to a limiting CD of -0.16 micrometer.
fabrication technique that provides a predetermined density
Alternative lithographic technologies are being investigated
and spatial pattern of flux pinning sites by inducing localized
including, inter alia, X-ray, e-beam, ion-beam and probe-tip
defects in the film to trap the flux lines. In order to achieve
technologies. However, none of these technologies has as
the desired critical currents, the density of trap sites typically
yet emerged as a satisfactory alternative to opticallithogra10 needs to be on the nm-scale (-5-50 nm spacings).
phy for volume manufacturing applications.
In the area of periodic structures, such as gratings, which
Existing nanofabrication techniques, such as e-beam
play a very important role in optics, periodicities shorter
lithography, have been used to demonstrate nm-scale feathan the optical wavelength could give rise to significant
tures for a variety of applications including, inter alia,
modifications in both the linear and nonlinear optical
textured substrates for crystal growth, quantum structure
growth and fabrication, flux pinning sites for high-Tc 15 response of materials. For example, one-dimensional gratings with pitches much less than the wavelength can result
superconductors, form birefringent materials, reflective optiin a birefringent response such that the reflectivity and
cal coatings, artificially created photonic bandgap materials,
electronics, optical/magnetic storage media, arrays of field
transmission differs between light polarized along the gratemitters, DRAM (Dynamic Random Access Memory)
ing and light polarized perpendicular to the grating.
capacitors and in other applications requiring large areas of 20
Reflective optical coatings, known as Bragg reflectors,
nm-scale features. However, these existing nanofabrication
often consist of layered stacks of different materials with
techniques typically remain uneconomic in that the techeach layer having a Y4-wave optical thickness. Very high
niques do not allow low cost manufacturing of large areas of
reflectivities can be achieved, even with relatively small
nm-scale patterns.
refractive index differences between the materials by using
In the field of textured substrates for crystal growth, 25
a sufficient number of layers. The extension of this concept
researchers have investigated vicinal growth (epitaxial
to a periodic three dimensional optical structure is usually
growth on a crystal substrate polished several degrees offknown as a photonic crystal. In the same way as semiconaxis to expose steps in the crystal faces) to provide seeding
ductor crystals have forbidden energy gaps within which
sites for growth initiation. This approach is often problematic in that the crystal steps are not well-defined and the 30 there are no allowed electronic states, photonic crystals can
exhibit photonic bandgaps where specific wavelength bands
variations lead to inhomongeneous nucleation. Moreover, in
of light cannot penetrate. The ability to incorporate defects
prior art epitaxial growth, the strain often limits the thickin this structure can give rise to important classes of optical
ness of the film before dislocations and other defects are
emitters with unique properties such as thresholdless lasers.
formed to relieve the stress.
This new class of materials could most likely be applied to
The field of quantum structure growth and fabrication is
35 a wide range of applications.
often similar to the above crystal growth application usually
In the electronic field, semiconductor electronics have
with the exception that the growth would involve at least two
typically been following an exponential growth in the nummaterials: a lower bandgap material typically surrounded by
ber of transistors on a chip, increasing by a factor of four
a higher bandgap material to provide a quantum wire or a
quantum dot. Most of the current work on extremely thin 40 each generation (with a typical 3-year duration for each
generation). As discussed above, conventional optical
heterostructure materials is typically concentrated on quanlithography is reaching practical limits set by available Ie and
tum wells, 2-D planar films with thickness on the order of
NA, therefore, an advancement in lithographic techniques
electronic wavefunctions (-0.1-50 nm) sandwiched
will be needed to manufacture these circuits.
in-between larger bandgap materials that form a potential
In the field of storage media, both magnetic and optical
barrier to confine charge carriers. These quantum well 45
storage densities (bits/cm 2 ) typically have been increasing
materials have progressed from scientific study to important
dramatically. The increased storage densities are typically a
applications in high speed transistors and in optoelectronic
result of improvements to magnetic/optical read/write heads
devices such as lasers and detectors. Attempts at further
and to the storage media. However, traditional continuous
reducing dimensionality from 2-D sheets to 1-D wires and
O-D boxes are often classified into three major directions: (1) 50 media often allows domains to compete and grow at the
expense of other domains to find the most energetically
lithographic definition limited to -100 nm by current techfavorable configuration. Moreover, as densities continue to
niques (primarily electron-beam lithography) and not presincrease, it becomes increasingly difficult for the tracking
ently scalable to large areas; (2) orientationally selective
electronics to resolve smaller distances. A cost-effective
growth on wafers with large-area (urn-scale) patterns which
typically has significant problems with defects associated 55 lithographic patterning technology that allows nano-scale
segmentation of the storage medium potentially could
with the imprecise fabrication and the three orders-ofaddress both of these issues.
magnitude scale reduction required, from -1000 nm to -1
nm; and (3) self-assembled quantum dots usually based on
Field-emitters are potentially a promising technology for
modifying the growth conditions to achieve nucleation of
cold cathode electronic devices, such as, for example,
isolated dots of material. The size and placement uniformity 60 mm-wave tubes and displays. These devices rely on high
of the dots produced by this technique is often limited by the
electric field extraction of electrons from extremely small
unavoidable randomness of the nucleation and growth proemission areas. In the prior art, field emitter tips are typically
cesses. The development of a method for uniformly defining
formed by conventional lithographic definition and processnucleation sites by a lithographic process would have a
ing "tricks" such as shadow evaporation or threemajor impact on this field.
65 dimensional oxidation of Si to form the nanostructures.
In the field of flux pinning sites for high- Tc
However, the feature and current densities resulting from the
superconductors, allowable current densities in high temprior art lower resolution lithographic techniques is not

6,042,998

5

6

typically sufficient for many applications. A higher
NA-0.3 ,urn, interferometric lithography has a limiting resolution of -0.09 ,urn at the same wavelength. Using the 193
resolution, nano-scale lithographic technique would have a
significant impact on the development of these technologies.
wavelength, the limiting resolution of interferometric lithography is -0.05 ,urn which is already better than the current
In the area of DRAMs, noise considerations in readout
circuitry typically require a substantially fixed capacitance 5 projections for EUV lithography (a wavelength of 13 nm and
a NA of 0.1 leading to a CD of 0.08 ,urn at a Kl of 0.6).
for DRAM circuits independent of the total number of
One of the major challenges for interferometric lithogramemory cells. Since the two-dimensional footprint available
for the capacitor decreases by a factor of approximately two
phy is developing sufficient pattern flexibility to produce
each DRAM generation (e.g., the 256-Mbit generation usuuseful circuit patterns. A two-beam interferometric exposure
ally is scaled for a smallest printed feature (or critical 10 produces a periodic pattern of lines and spaces over the
dimension (CD)) of 0.25 ,urn and this scaling is reduced to
entire field. Multiple beam (4 or 5) exposures typically
produce relatively simple repeating two-dimensional pata CD of 0.18 ,urn for the 1-Gbit generation; [(0.18/0.25)
2_0.5]), simple scaling would result in an approximate factor
terns such as holes or posts. More complex structures can
of two reduction in the capacitance each generation. One
often be formed by using multiple interferometric exposures
possible approach to maintaining the needed minimum 15 as described in U.S. Pat. No. 5,415,835-S. R. J. Brueck and
Saleem H. Zaidi, Method and Apparatus for Fine-Line
capacitance is to use the third dimension by convoluting a
thick capacitor structure to increase the surface area within
Interferometric Lithography (filed Sep. 16, 1992; issued
May 16, 1995) and in Jour. Vac. Sci. Tech. Bll, 658 (1992),
the same two-dimensional footprint. This requires a lithowhich are herein incorporated by reference. Additional flexgraphic capability beyond that required to define the circuit.
However, since the industry is typically at the limits of its 20 ibility can often be attained by combining interferometric
current lithographic capability in fabricating the circuit
and optical lithography as also described in the above patent.
patterns, an improved nano-scale lithographic process is
However, thus far, demonstrations have typically been limrequired to meet these needs. Random process such as the
ited to fairly simple examples, e.g. defining an array of lines
deposition of nano-grain particles as etch masks have been
by interferometric lithography and delimiting the field by a
demonstrated. However, the control of particle size and 25 second optical exposure. Even with multiple exposures,
placement is typically inadequate for a high-yield manufacmore complex structures are often produced, but the overall
turing process. Here again, development of controlled nanopatterns are restricted to repetitive structures.
scale lithography process would potentially have a signifiImaging interferometric lithography (IlL) has recently
cant impact.
been developed [See U.S. patent application Ser. No.
Interferometric lithography, the use of the standing wave 30 08/786,066-S. R. J. Brueck, Xiaolan Chen, Andrew
Frauenglass and Saleem Hussain Zaidi, Method and Appapattern produced by two or more coherent optical beams to
expose a photoresist layer, often provides a very simple
ratus for Integrating Optical and Interferometric Lithogratechnique to produce the requisite scale for the next several
phy to Produce Complex Patterns (filed Jan. 21, 1997)] as an
ULSI generations. Compared to the aforementioned probapproach to extending the spatial frequency space available
lems with lithographic and non-lithographic techniques, 35 for imaging, and hence allowing higher resolution images of
interferometric lithography typically provides a simple,
arbitrary patterns than are usually possible with conveninexpensive technique for defining extreme submicron array
tional optical imaging approaches. IlL is based on a linear
patterns over a large area without the need for a photomask.
systems approach wherein the spatial frequency space limiInterference effects between two coherent laser beams often
tation of a traditional optical system is circumvented by
have been used to create simple grating patterns in a 40 combining optical and interferometric lithographies to print
photoresist. Furthermore, interference lithography typically
regions of frequency space. Multiple exposures in the same
has a very large depth of field, so patterns can be exposed
photoresist level are then typically used to add together the
different spatial frequency components to produce a final
over large variations in topography. Moreover, interferometimage that is significantly improved over that available with
ric lithography often allows very high resolution patterns to
be defined on a wafer, substantially finer than those available 45 traditional, single-exposure imaging optical lithography.
Using this approach, it was shown that images containing
from conventional lithographic techniques, with a throughspatial frequency components out to the limits of optics, 2A,
put often comparable to that of a conventional optical
stepper. Therefore, a large number of structures applicable to
could be achieved.
microelectronic devices and circuits can be fabricated using
As an example of the increased spatial frequency space
interferometric lithography, either alone or in combination 50 available using IlL, FIG. 1 shows a prototypical array
with other lithographic techniques such as optical steppers.
structure that might be part of a ultra-large-scale integrated
See U.S. Pat. No. 5,415,835-S. R. J. Brueck and Saleem
circuit, particularly a circuit with a large degree of repetiZaidi, Method and Apparatus for Fine-Line Interferometric
tiveness such as a memory chip or a programmable logic
Lithography (issued May 16, 1995); U.S. patent application
array. The dimensional units are in terms of the critical
Ser. No. 08/407,067-S. R. J. Brueck, Xiaolan Chen, Daniel 55 dimension (CD-smallest resolved image dimension) which
J. Devine and Saleem H. Zaidi, Methods and Apparatuses
is defined in the semiconductor industry roadmap. The
for Lithography of sparse Arrays of Sub-micrometer Feaindustry goals for the CDs are 130 nm in 2003 and 100 nm
tures (CIP filed Mar. 13, 1995); U.S. patent application Ser.
in 2006. For easy comparison, the modeling examples given
No. 08/614,991-S. R. J. Brueck, Xiaolan Chen, Daniel J.
herein are all for the 130-nm CD generation. The pattern
Devine and Saleem H. Zaidi, Methods and Apparatuses for 60 consists of staggered bars each 1x2 CD2. The repetitive cell
Lithography of sparse Arrays of sub-micrometer Features
is demarked by the dotted lines and is 6x6 CD2. For a
(divisional filed Mar. 13, 1996) and, which are herein
periodic pattern, all of the spatial frequency components are
incorporated by reference.
harmonics of the fundamental frequencies of this pattern,
The limiting spatial frequency of interferometric lithoge.g. fx=n/Lx; fy=m/Ly, where fx(fy) are the spatial frequencies
raphy is -Al2, where A is the laser wavelength, and the CD 65 in the x (y) direction, n (m) is an integer and Lx=Ly=6 CD
is the repeat distance in each direction. This pattern is only
for 1: 1 lines and spaces is -A/4. In contrast to optical
introduced to illustrate the general concepts of the invention
lithography which at I-line has a projected limit of KxA/

6,042,998
7

8

and is not intended to restrict its applicability to only this or
for I-line wavelengths, n-5-1O. FIG. 4 shows a plot of teE)
substantially similar patterns.
vs. E showing the strong nonlinearity often associated with
The goal of the lithography process is typically to reprothe photoresist process. In order to make the mathematics
duce this pattern in the developed resist profile with as high
simpler, the modeling presented herein uses a simple thresha fidelity as possible. FIGS. 2A and 2B show the exemplary 5 olding step function approximation to 'teE) shown, for
pattern achieved when a mask with the required pattern is
example, by the dotted line in FIG. 4. This approximation
used in a conventional imaging optical lithography system in
substantially retains the essential features of the photoresist
the limits of both incoherent (FIG. 2A) and coherent (FIG.
response without introducing unnecessary computational
2B) illumination. For incoherent illumination the resultant
complexity into the modeling. A more complete modeling
pattern is shortened and significantly rounded appearing
almost circular rather than rectangular; for coherent illumi- 10 effort can be created by one of ordinary skill in the art.
For a simple two-beam interference, the fluence profile is
nation only the zero-frequency Fourier component (constant
given by the expression:
intensity across the die) is transmitted by the lens for this
particular pattern, wavelength and NA combination and
there is substantially no image at all. State-of-the-art lithog- 15
E(x) = 1 + cos(4nsin(8)x / A).
(2)
raphy tools often use partially coherent illumination which
is in some ways better than either of these two limits; but still
shows many of the same limitations. Optics can, in principle,
The Fourier transform consists of three components, a unity
support spatial frequencies up to a maximum spatial freamplitude, zero frequency term and two components with
quency of 2/A. Various techniques, including multiple inter- 20 amplitude Y2 at ±2 sin (B)/A[F(E)=o(Q+Y2(o(f +2 sin (B)/
x
ferometric exposures, can almost eliminate the lens limitaA)+o(fx-2 sin (B)/A))], where F represents the Fouriertions on spatial frequencies and approach the fundamental
transform operator and fx is the spatial frequency. After
limit of a linear optical system.
passing this function through the nonlinear filter of the
FIG. 3 shows the modeling results for imaging the pattern
photoresist, represented by 'teE), the resulting thickness of
of FIG. 1 including all of the spatial frequencies available at 25
the photoresist is typically a substantially rectangular funcan imaging wavelength of 365 nm (I-line). While the image
tion and the Fourier transform is typically a substantially
is significantly closer to the desired pattern than the incosinc (sin (x)/x) function sampled at harmonics of the pitch,
herent imaging results, there is still significant rounding of
fn=2n sin (B)/A:
the corners of the printed features due to the unavailability
of the spatial frequencies needed to provide sharp corners. 30
(3)
. (2nna sin( 8) )
That is, the magnitudes of the spatial frequencies necessary
Slll--_'--------'-A'--------'-ei4Jfnx~i~e)
to define these corners are greater than 2/A, the limit of a
r[E(x)] = ~L
2nnasin(8)
linear optical system. One approach to improving upon this
A
problem is typically to decrease the wavelength, thereby
increasing the maximum available spatial frequency. 35
Decreasing the wavelength has often been a traditional
Examples of these one-dimensional real space and spatial
industry solution to the need for defining smaller and smaller
frequency space results are shown in FIGS. 5A and 5B
features. However, for the reasons cited above, it is likely
respectively.
that this solution cannot be exploited much beyond the
FIG. 5C shows an experimental realization of this sharp193-nm ArF excimer laser source wavelength.
40
ening in the z-direction. This result was obtained using two
The use of the nonlinear response of photoresist to
coherent beams from an Ar-ion laser (A=364 nm) incident on
substantially sharpen developed photoresist patterns in the
a photoresist-coated wafer at angles ±B of approximately 30°
z-direction, through the thickness of the resist, has long been
corresponding to a pitch of about 360 nm. A standard I-line
understood [see, for example, Introduction to
Microlithography, Second Edition, L. F. Thompson, C. G. 45 photoresist was used with a thickness of about 0.5 ,um. An
antireflective coating (ARC) layer was included under the
Willson and M. J. Bowden, eds. (Arner. Chem. Soc. Washphotoresist to eliminate the standing wave effects that often
ington D.C., 1994, pp. 174-180)]. To aid in understanding
occur as a result of the substantial reflectivity at the
this process, many approaches exist for modeling the phophotoresist/Si interface. The developed photoresist features
toresist response. Industry-standard modeling codes, such as
PROLITHTM and SAMPLE, typically take into account the 50 exhibit substantially vertical sidewalls. The Fourier transform of this pattern contains high spatial frequency compomany subtle effects that are often necessary to accurately
nents that go well beyond the 2/A linear systems limit of
model the lithography process. However, for the present
optics as is illustrated in FIG. 5B.
purposes, a simpler model, first presented by R. Ziger and C.
While the nonlinearity often substantially sharpens the
A. Mack [Generalized Approach toward Modeling Resist
Performance, AIChE Jour. 37, 1863-1874 (1991)], typically 55 profile in the z-direction, it does not, however, usually add
provides a good approximation. This model describes the
additional frequency components in the x-y plane. In fact,
the profiles of FIGS. 2 and 3 were calculated using this same
photoresist thickness, teE), after the photoresist develop step
photoresist filter, thus demonstrating the lack of frequency
substantially resulting from a given optical exposure fluence
components in the x-y plane. Moreover, multiple exposures
(typically normalized to a clearing fluence) E by the rela60 in the same level of photoresist without any additional
tionship:
processing result in summing the amplitudes and phases of
the spatial frequency components contained within each
(1)
-E)n
1
t(E)=1- ~
exposure. Consequently, applying and developing the pho( 1-e- 1
toresist after this summation again usually sharpens the
65 photoresist vertical profiles but does not often substantially
change the 2-D cross section at the threshold level.
where n is a parameter that characterizes the contrast of the
Mathematically, this is represented as:
resist. For typical novo lac-based photoresist commonly used

6,042,998

9

10
(4)

5

where T(x,y) is the photoresist thickness as a function of the
wafer plane Cartesian coordinates x and y and En(x,y) is the
fluence of the nth exposure at the position (x,y).
A simple two exposure situation involving only two beam
exposures can serve as a typical example of the prior art. The
first exposure writes a periodic pattern in the x-direction as
in Eq. 4, and the second exposure writes a periodic pattern
at 'h the x-pitch in the y-direction. FIG. 6Ashows the results
of a simple double exposure, as taught in U.S. Pat. No.
5,415,835-S. R. 1. Brueck and Saleem Zaidi, Method and
Apparatus for Fine-Line Interferometric Lithography
(issued May 16, 1995) which is herein incorporated by
reference. The parameters of the calculation are set for a CD
of about 130 nm and a small pitch of about 260 nm. Because
the intensities are added before the thresholding operation is
applied, the resulting shapes exhibit significant rounding of
the comers and are substantially elliptical rather than rectangular.

10

15

20

SUMMARY OF THE INVENTION
The present invention extends the available spatial frequency content of an image through the use of a method and
apparatus for combining nonlinear functions of intensity of
at least two individual exposures to form three dimensional
patterns with spatial frequencies that are not present in any
of the individual exposures and that extend beyond the limits
set by optical propagation of spatial frequencies whose
magnitudes are ~ 2(A in all three spatial directions. This
extension of spatial frequencies preferably extends the use
of currently existing photolithography capabilities, thereby
resulting in a significant economic impact. Extending the
spatial frequency range of lithographically defined structures suitably allows for substantial improvements in, inter
alia, crystal growth, quantum structure growth and
fabrication, flux pinning sites for high-Tc superconductors,
form birefringent materials, reflective optical coatings, photonic crystals, electronics, optical/magnetic storage media,
arrays of field emitters, DRAM (Dynamic Random Access
Memory) capacitors and in any other applications requiring
large areas of nm-scale features.
A first exemplary embodiment uses two photoresist layers
sensitive at different wavelengths. Additional layers are
often required in a multi-level photoresist process to protect
against interdiffusion of the various photosensitive materials. Alternatively, a hard mask (e.g. Si0 2 or Si3N4 or any
other suitable film material) is used with additional processing between exposures. In either case, a first lithographic
pattern at a first wavelength regime is suitably exposed into
the first photosensitive layer and a second lithographic
pattern in a second wavelength regime is suitably exposed
into the second photosensitive layer. Upon suitable development and/or processing the result is a layering of the two
lithographic patterns in the two layers and/or in the hard
mask layer. These layers in combination are used as masks
for further processing of the underlying wafer to transfer a
pattern that is the product of the two masks into the
underlying materials. Image reversal offers the possibility of
combining the two exposures in the same level of photoresist with intermediate processing steps to assure independent
thresholding nonlinearities.
A second exemplary embodiment of combining nonlinear
processes preferably includes the following steps: 1) deposit

25

a suitable hard mask material and a photoresist layer onto the
film stack to be patterned; 2) suitably expose and develop a
periodic pattern (at pitch Pmin~A/2 and with CD ~A!8) in
the photoresist using interferometric lithography; 3) transfer
this pattern into the hardmask by etching; 4) suitably remove
the remaining photoresist; and 5) repeat the above steps at
the same pitch, but with the pattern offset by Pmin/2 to
interpolate new features midway between the previously
defined features in the hardmask. This procedure typically
results in a pattern with 'h the pitch of the original structure.
Alternatively, this procedure may be repeated a number of
times, with appropriate offsets and CDs to produce a pitch
Pmin/N, where N=1 (original pattern), N=2 (one additional
exposure and processing sequence), N=3 (two additional
exposures and processing sequences), and so on. Structures
with linewidths as much as a factor of 40 less than the pitch
for larger pitches (0.05-,um wide line on a 2,um pitch) have
been suitably produced [see, X. Chen et aI., SPIE 1997].
In an alternative embodiment, this technique can be
extended to two-dimensional patterning by using either
multiple exposures and/or multiple-beam single exposures.
For a grid of holes or posts with equal pitches, Pl' in both the
x- and y-directions, a second exposure at the same pitch but
shifted by Pl/2 in x and Pl/2 in y decreases the pitch (now
P2) to approximately P2=P1N2. With two further exposures
a new pitch (now P3) of approximately P3=Pl/2 is achieved.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGURES

30

35

40

45

50

55

60

65

The subject invention will be hereinafter described in
conjunction with the appended drawing figures, wherein like
numerals denote like elements, and:
FIG. 1 shows a prototypical array structure (that could be
part of a memory chip or programmable logic array) having
a grid in units of critical dimensions (CD) which vary for
each generation and a repeating cell;
FIGS. 2A and 2B show exemplary modeling results for
the two limits of incoherent (FIG. 2A) and coherent (FIG.
2B) illumination using an optical system consisting of an
industry-standard I-line (365 nm) lithography tool with a 0.5
numerical aperture (NA) lens to print the pattern of FIG. 1
for a 130-nm CD;
FIG.3 shows modeling results (I-line wavelength and 130
nm CD) using all of the spatial frequencies available to a
linear optical system (to a magnitude of 2/A);
FIG. 4 shows an exemplary graph of nonlinear response
of the photoresist thickness on exposure fluence with two
approximations 1) the model of Ziger and Mack, teE) with
n=5 and with n=lO, typical of the range of commercially
available novolac resists at I-line; and 2) a simplified step
function model 'teE);
FIGS. 5A and 5B show real space (FIG. 5A) and spatial
frequency space (FIG. 5B) patterns for a simple two-beam
interference for the aerial image and the resulting photoresist
profile after the nonlinear thresholding response of the
photoresist;
FIG. 5C shows an exemplary cross section scanning
electron micrograph of a line:space pattern resulting from
developing a two beam interference exposure that illustrates
the nonlinear response of the photoresist.
FIG. 6A shows model results for the photoresist pattern
created by two two-beam interferometric lithography exposures oriented at right angles to each other with the
x-direction pitch 'h of that of the y-direction created by the
prior art process where the two exposures are summed in a

6,042,998
11

12

single layer of photoresist which is subsequently developed,
providing a thresholding nonlinearity that sharpens the resist
sidewalls but does not modify any additional spatial frequencies in the x-y plane;
FIG. 6B shows model results for the photoresist pattern
created by two interferometric lithography exposures with
the x-direction pitch 'h of that of the y-direction created by
applying thresholding nonlinearities to each exposure individually and multiplying the thresholded images to get the
final image;
FIG. 7A-7B shows an experimental demonstration of the
multiplication of two masks corresponding to two thresholded images. FIG. 7A shows an exemplary result of a
two-beam interferometric exposure (line:space pattern) that
has been transferred to a sacrificial Si3N4 layer by etching
after exposure and development of the first exposure. FIG.
7B shows an exemplary result after depositing a second
photoresist layer, exposing this second layer with a second
interferometric exposure substantially at right angles to the
first exposure, and developing the second photoresist layer.
FIGS. SA-SC show the application of the present invention to the prototypical pattern of FIG. 1 wherein FIG. SA
shows the result of a simple two-beam interferometric
exposure, FIG. SB shows the result of an incoherently
illuminated imaging optical exposure (NA=0.6@365 nm)
and FIG. SC shows the result of multiplying the two images
using a combined mask.
FIGS. 9A-9E show a preferred embodiment of a process,
using a negative photoresist, that results in a factor of two
reduction in the pitch in accordance with the present invention;
FIGS. 10A-10F show a preferred embodiment of a
process, using a positive photoresist, that results in a factor
of two reduction in the pitch in accordance with the present
invention;
FIG. HAshows an exemplary SEM after the first etch, as
demonstrated in FIG. 9C, with a pitch of approximately 260
nm in accordance with the present invention.
FIG. HB shows exemplary results after the second etch,
as demonstrated in FIG. 9F, with the pitch suitably reduced
to -130 nm and the CD to -60 nm in accordance with the
present invention;
FIG. HC shows exemplary results of an anisotropic KOH
etch of O.13-mm pitch pattern into the Si using the nitride
layer as a hard mask in accordance with the present invention;
FIG. HD shows an exemplary narrow line having superior vertical sidewalls which was produced by very high
spatial frequencies achieved from the nonlinearities in
accordance with a preferred embodiment of the present
invention.
FIG. HE shows a concept drawing of an exemplary two
color separation for a typical SRAM circuit pattern demonstrating the possibilities for using spatial frequency doubling
to enhance the pattern density.
FIG. 12 shows an exemplary result of a multiple exposure
technique including a 0.05-,um wide photoresist line on a
2-,um pitch, a line:space ratio of 1: 10 in accordance with a
preferred embodiment of the present invention;
FIG. 13 shows an example of two-dimensional patterning
with a dense array of 90-nm diameter holes defined in a
photoresist layer on a 1 SO-nm pitch in accordance with a
preferred embodiment of the present invention;
FIG. 14 shows another example of two-dimensional patterning with a dense, hexagonal close packed pattern written

with three two-beam exposures and the wafer rotated 120 0
between exposures in accordance with a preferred embodiment of the present invention;
FIG. 15 shows an exemplary 2-D hole pattern written with
a five-beam geometry in a single exposure in accordance
with a preferred embodiment of the present invention;
FIG. 16 shows an exemplary calculation of the structures
obtained with the five-beam geometry of FIG. 16 when the
exposure flux is increased to form an array of posts rather
than the array of holes.

5

10

DETAILED DESCRIPTION OF PREFERRED
EXEMPLARY EBODIMENTS
15

20

25

The present invention preferably employs nonlinear processes either in the photoresist intensity response and/or in
additional processing steps in order to create high spatial
frequencies, beyond the optical propagation limit of 2(A, in
a pattern produced on a suitable thin-film layer on a wafer
that is used, in subsequent process steps, to transfer the
structures containing the high spatial frequencies in the
plane of the wafer into the underlying film structure. In a
preferred embodiment, two (or more) exposures are individually subjected to thresholding nonlinearities, then the
images are preferably combined (added or multiplied)
resulting in a pattern containing additional spatial frequencies that are not substantially present in any of the individual
images. Mathematically, the specific embodiment of multiplication is equivalent to:

30
T(x, y) = r[E j (x, y)] xr[E2 (x, y)]

35

x ... r[En(x, y)]

(4)

where the ®
represents a convolution operation. In like manner, the
embodiment of addition is represented mathematically by:
(5)

40

45

50

55

60

65

The thresholding operation suitably results in high spatial
frequencies in the final images; the convolution operator
suitably results in a final image with spatial frequencies
corresponding to substantially all possible combinations
(sum and difference) of the frequencies in the individual
images. In a preferred embodiment, the thresholding nonlinearity results in frequency components extending beyond
the capabilities of an optical system (e. g. frequencies >2(A.
Moreover, the multiplication operation preferably extends
results in components extending into parts of frequency
space that are not substantially addressed by the individual
exposures.
In contrast to the prior art methods which typically yield
rounded comers on the structures as shown in FIG. 6A, the
present invention suitably yields the patterns shown in FIG.
6B, namely rectangles with sharp, well-defined comers. The
patterns of FIG. 6B are preferably formed in accordance
with the present invention by suitably applying the thresholding nonlinearity individually to each exposure and multiplying. Mathematically, the resulting spatial frequency
transform is preferably the product of appropriate [sin
(fxax)/fxax] and [sin (fyay)/fyay ] functions which yields the
spatial Fourier transform of the desired rectangular pattern,
VIZ:

6,042,998

13

14

resulting pattern is transferred into the sacrificial layer by a
(6)
suitable etching step. Any remaining photoresist from the
T(x, y) =
first photoresist layer is then removed and the wafer is then
preferably coated with a second photoresist layer and a
5 second exposure and develop sequence is suitably carried
out to transfer a second pattern into this second photoresist
layer. In an alternative embodiment, this second exposure is
an imaging optical exposure. A second etch step is preferably carried out to transfer the combined pattern into the
10 underlying wafer layers. The second etch step preferably
n'=-oo
uses a combined etch mask, parts of which are preferably
comprised of the nitride layer and parts of which are
comprised of the undeveloped photoresist layer. Thus, in a
FIGS. 7A-7B show an experimental realization of this
preferred embodiment, the combined etch mask provides the
pattern. A Si wafer was coated with a thin Si3N4 film and 15 multiplication operation. Finally, the remaining mask layers,
with a first photoresist layer. A two-beam interferometric
both photoresist and sacrificial material, are preferably
exposure was used to define a line:space array in this first
removed. While the aforementioned exemplary process is
photoresist layer. The pattern was developed, transferred
set forth, it will be appreciated by one of ordinary skill in the
into the nitride film, and the remaining photoresist removed.
art of semiconductor processing that many variants on this
An exemplary resulting pattern in the nitride layer is shown 20 basic process exist. For example, in an alternative
in FIG. 7A. A second photoresist layer was then applied to
embodiment, an additive step, such as deposition and lift-off,
the wafer and a second two-beam interferometric exposure,
is suitably used in place of one or another of the etch steps
substantially at right angles to the first exposure pattern, was
recited above. In another alternative embodiment, damasuitably applied and developed. FIG. 7B shows an exemscene (etching, deposition and polishing to produce an inlaid
plary resulting pattern: the vertical lines are in the nitride,
the horizontal lines are in the second photoresist layer. 25 structure) processes are incorporated into the process. In
another alternative embodiment, in certain process flows,
Together the two mask patterns provide a multiplication of
different sacrificial layers, such as, for example metals,
the individual images that have been operated on indepenpoly-Si, polymers and the like, are incorporated into the
dently with the nonlinear thresholding responses of the two
process.
photoresist layers. The composite mask pattern shows subIn practice, to reduce costs, it is typically desirable to
stantially right angles at the comers as predicted by Eq. 6 and 30
reduce the number and complexity of processes necessary to
in FIG. 6B.
FIGS. SA-SC show exemplary results from a similar
achieve the desired structure. In particular, it is desirable to
create the same combination of nonlinearities in a single
calculation for the prototypical array structure of FIG. 1.
photolithography sequence without requiring additional etch
FIG. SA shows an exemplary result of suitably applying a
thresholding nonlinearity to a simple two-beam interfero- 35 or deposition steps. To achieve the same combination withmetric lithography exposure with a CD of 130 nm and a
out additional steps, a preferred embodiment of the present
pitch of 260 nm. FIG. SB shows an exemplary pattern
invention incorporates image reversal and/or multilayer
resist systems incorporating two exposures [see, for
obtained from a conventional (incoherent illumination) optical lithography exposure of the mask corresponding to FIG.
example, Introduction to Microlithography, Second Edition,
1 [I-line (365 nm) exposure wavelength and 0.5 NA lens]. 40 L. F. Thompson, C. G. Willson, M. 1. Bowden, eds. Amer.
While the optical exposure typically cannot substantially
Chem. Soc. Washington, D.C., 25 1994, pp. 184-190,
resolve the 130-nm CD structures, it does provide informa232-251 and 347-371]. Conventionally, image reversal is
tion that can be used to suitably restrict the extent of the
often used to create a negative-tone image with a positive
interferometric exposure which exists over the entire field.
resist by exposing the resist (which is specially formulated
Finally, FIG. SC shows an exemplary result of multiplying 45 for image reversal) with a first exposure. The first exposure
the two patterns to get the final result, thereby showing the
suitably frees the bound photo active compound (PAC) in the
dramatic improvement in the profiles. This example preferresist. Depending on the resist formulation, the freed PAC is
ably involves a combination of an interferometric lithograsuitably removed from the resist film with a bake step or an
exposure to an appropriate chemical ambient. Next, a second
phy exposure and an imaging optical exposure, while the
prior example consisted of two interferometric lithography 50 exposure, usually a flood exposure without any spatial
exposures.
information, is suitably used to free the remaining bound
As mentioned, the present invention relates to the use of
PAC in the areas not exposed in the first exposure. Finally,
nonlinear processing suitably combined with multiple expoa conventional develop step results in a negative tone image.
Multilayer resist systems utilize a similar sequence (expose,
sures to extend the range of spatial frequencies beyond those
available with conventional single or additive exposure 55 process, expose, develop) with the exposure wavelengths
techniques. In implementing the nonlinear processing and
chosen to affect specific films within the multilayer resist
multiple exposures, the present invention preferably incorfilm stack.
porates any suitable combination of interferometric
In both processes, the first exposure and intermediate
process steps suitably provide a nonlinear response, while
lithography, imaging optical and/or other exposure techniques. Thus, a number of processing sequences exist that 60 the second develop step suitably provides a second nonlinear
are preferably used to achieve this sequential thresholding of
response. In a preferred embodiment of the present
each exposure and multiplication of the resulting patterns.
invention, the aforementioned flood exposure step is suitIn a preferred embodiment, a sacrificial layer, such as, for
ably replaced by a second exposure containing spatial information. In a preferred embodiment, the second exposure is
example a Si0 2 or Si3N4 layer, is used with additional
processing between the two exposures. More particularly, 65 preferably an interferometric exposure. In an alternative
embodiment, the second exposure is an imaging optical
following a suitable interferometric lithography exposure
and develop of a first pattern in a first photoresist layer, the
exposure. The replacement of the flood exposure by a

L

6,042,998
15

16

second exposure with spatial information results in the
With reference to FIG. 9D, a new photoresist layer 46 is
suitably applied and structure 40 is suitably re-exposed and
desired sequence of nonlinear steps.
developed at substantially the same pitch, but with pattern
In an alternative embodiment, the combination of nonlin50 offset by Pmin/2, thereby interpolating new lines 50
earities is suitably achieved by a multi-layer resist process
5 between (e.g. midway) previously defined lines 48 in hard
such as discussed by Willson in the above reference. A
mask 44. With reference to FIG. 9E, any suitable etching
photoresist sensitive at longer wavelengths is preferably
process preferably transfers lines 50 into hard mask material
deposited onto the wafer first, followed by a photoresist
44, thereby resulting in a pattern 48, 50 with about one half
sensitive at shorter wavelengths. The layers include any
the pitch of original structure 40. Mathematically, this
suitable photoresist, but in this embodiment, an I -line resist 10 sequence of operations is represented as:
is used for the bottom layer and a 248-nm resist is used for
(7)
T(x) = r[E j (x)] x r[E2(x)]
the top layer. The top resist is preferably selected to be
transparent to the I -line wavelength used to expose the
bottom resist, and is preferably chosen to be sufficiently
absorbing at the 248-nm wavelength to substantially block 15
any light from the exposure at this wavelength from reaching the bottom layer. In an alternative embodiment, a
non-photosensitive buffer layer is suitably deposited
2JrnaSin(8))
~
sin( - - , , - - F-lfn i~~sin(e.t2
between the two layers to assist in preserving the integrity of
"
e e
A
the individual photoresist layers. Consequently, two inde- 20
nf:'oo (2Jrna;in(8))
pendent nonlinearities (thresholding) and a layering
(multiplication) of the two exposure masks exists.
(2JrnaSin(8))
~
Sln--Alternatively, the two sensitivities are suitably combined
V
A
ei~~nxfin(e)
into a single resist with both positive and negative tonalities,
2 ~ (2Jrna;in(8))
as demonstrated by Hinsberg et al. [W. D. Hinsberg, S. A. 25
MacDonald, L. A. Pederson and C. G. Willson, "A Lithographic Analog of Color Photography: Self-Aligning Phowhere the factor of e iotn =(_lf in the second term arises
tolithography Using a Resist with Wavelength-Dependent
because of the half-pitch shift of the second pattern. As a
Tone," Jour. Imaging Sci. 33, 129-135 (1989).]
result, the even terms in the summations add, the odd terms
In a second preferred embodiment, two nonlinear func30 cancel, and the final result is just the expression for a
tions of intensity are added to create spatial frequencies in
periodic square wave structure at twice the period [4 sin
the final pattern that are not present in either of the indi(8)/1] of each exposure.
vidual exposures, resulting in frequency multiplying. More
With reference to FIGS. 10A-IOF, in an alternative
particularly, the use of spatial-frequency multiplied interembodiment, a similar process to FIGS. 9A-9E (subtractive
ferometric lithography for the reduction in pitch for the array 35 process with etching) is shown which similarly results in a
structure of FIG. I will now be described in more detail in
factor of two multiplication of the pitch, except a positive
FIGS. 9A-9E. FIGS. 9A-9E show a preferred embodiment
tone photoresist is used in an additive process (deposition).
for a sequence using subtractive fabrication processes that
Namely, photoresist layer 66 is preferably a positive tone
results in an approximate factor of two increase in the spatial
photoresist (e.g. resist is substantially removed on developperiod; i.e. a reduction of a factor of two in the pitch. With 40 ment only in the substantially exposed regions). With refrespect to FIG. 9A, a preferred exemplary structure includes
erence to FIG. lOA, a preferred exemplary structure includes
the material 42 in which a pattern is suitably formed, a thin
the material in which a pattern is suitably formed 62 and any
layer 44 of a material which suitably forms a hard mask (for
suitable positive tone photoresist layer 66. With respect to
example, an Si0 2 layer), and any suitable photoresist layer
FIG. lOB, and 10C positive photoresist 66 is suitably
46 which responds to exposure and development. In a 45 exposed using interferometric lithography and developed,
preferred embodiment, photoresist layer 46 is a negative
thereby leaving positive photoresist 66 in a substantially
tone photoresist (e.g. resist is substantially removed on
periodic pattern 68 of a pitch of about Pmin' In a preferred
development only in the substantially unexposed regions).
embodiment, periodic pattern 68 comprises an array of lines
In an alternative embodiment, a positive photoresist is used
at a substantially minimum pitch having a width substanwith an image reversal step to effectively utilize it as a 50 tially less than about Pmin/4.
negative tone material. In either case, a second optical
With reference to FIG. 10C, any suitable mask material 64
exposure in the same photoresist level may be used to
is preferably deposited substantially everywhere except in
delimit the areas of the circuit over which the interferometric
the region of positive photoresist 66, then positive photorelithography pattern is defined, for example, to the core areas
sist 66 is suitably stripped. With reference to FIG. 10D, a
of a DRAM circuit.
55 new positive photoresist layer 66 is suitably applied and
With respect to FIG. 9B, photoresist 46 is suitably
structure 60 is suitably re-exposed interferometrically and
exposed using interferometric lithography and suitably
suitably developed at substantially the same pitch, but with
developed, thereby forming a periodic pattern 48 (at pitch
pattern 70 offset by about Pmin/2, thereby leaving photoresist
Pmin) in photoresist 46. In a preferred embodiment, periodic
66 about midway between previously defined lines 68 in
pattern 48 comprises an array of lines at a substantially 60 hard mask 64. A second mask layer 72 is then suitably
minimum pitch having a width substantially less than about
deposited substantially everywhere but in the region of
Pmin/4. With reference to FIG. 9C, any suitable etching
remaining photoresist 66, thereby serving as an etch mask to
process preferably transfers periodic pattern 48 (the lines)
allow etching of etch mask 64. With respect to FIG. 10E,
into hard mask 44. In a preferred embodiment, a very thin
positive photoresist 66 is suitably stripped and, using mask
hard mask layer 44 is used such that the etching process does 65 layer 72 as an etch mask, lines 70 are suitably etched into
not have to be highly anisotropic. After etching, remaining
mask 64. With respect to FIG. 10F, any suitable stripping
photoresist 46 is suitably stripped.
process preferably removes second mask layer 72, thereby
00

=::

00

1

.

6,042,998
17

18

resulting in a pattern 68, 70 with about one half the pitch of
systems constraints apply to pattern frequencies, not to
original structure 60. In a further alternative embodiment,
linewidths. This is dramatically illustrated by the microthe process of FIGS. 10A-lOF is suitably reversed by known
graph in FIG. lID that shows a 50-nm CD line on a 2-,um
pitch, a line:space ratio of 1:20. The very high spatial
image reversal techniques using positive tone resists.
The alignment between the two exposures described 5 frequencies corresponding to this narrow line are the result
above (with respect to either FIGS. 9A-9E or FIGS.
of photoresist process nonlinearities, the exposure aerial
image was a 2-,um period sine wave. Importantly, the process
10A-lOF) can be accomplished by any suitable method. In
latitude for printing this fine line was much greater than that
a preferred embodiment, the alignment between the two
for printing the 150-nm dense line:space pattern. This is a
exposures are suitably accomplished by the techniques
described in U.S. Pat. No. 5,216,257-S. R. J. Brueck and 10 superior result in that it is always more difficult to print 1: 1
patterns since these occur very near the threshold dose for
Saleem H. Zaidi, Method and Apparatus for Alignment and
developing all the way through the resist. Larger line:space
Overlay of Submicron Lithographic Features (issued Jun. 1,
1993) and U.S. Pat. No. 5,343,292-S. R. J. Brueck and
ratios are closer to saturation where the process is very
Saleem H. Zaidi, Method and Apparatus for Alignment of
forgiving of small dose variations and the nonlinearities
Submicron Lithographic Structures (issued Aug. 30, 1994), 15 (vertical sidewalls) are larger. Thus, it is easier (greater
which are all herein incorporated by reference. In brief, the
process latitude) to print smaller CD structures at a fixed
incident writing beams (or other longer wavelength, nonpitch.
actinic beams) preferably impinge on the pattern resulting
FIG. lIE shows a concept drawing of how the aforementioned frequency doubling technique might be applied to a
from the first exposure. The beams diffracted from the
grating on the wafer surface are suitably caused to interfere 20 circuit pattern, in this case a typical SRAM pattern. The two
colors indicate the patterns written in each exposure. No two
with a standard interferometric optical system (mirrors and
features of the same color approach each other by less than
beamsplitters) and are preferably incident on an appropriate
detector. The resulting projection moire fringe pattern is
1.5 CD. The spacing is less than 2 CD because of the
suitably used to set both the spatial frequency and the phase
staggered features in the SRAM pattern, so changing the
(offset) of the second exposure. In an alternative 25 design to a CD grid would allow a straightforward doubling
embodiment, a substantially similar process to the process
of the pattern density.
described above for alignment of multiple interferometric
As shown below in FIGS. 12-17, the present multiple
lithography exposures is used to suitably align an interferoexposure technique substantially uniformly produces strucmetric lithography exposure to an optical lithography expotures with a linewidth less than the pitch and substantially
sure.
30 accurately aligns the two exposures, so the present invention
An exemplary demonstration of subtractive spatial freincreases N.
In accordance with a preferred embodiment, for larger
quency doubling is shown in FIGS. lIA-lIC. In this
pitches, structures with linewidths a factor of 40 less than the
exemplary embodiment, the starting material includes
<110> Si (to allow anisotropic KOH etching as a final
pitch have been produced. With respect to FIG. 12, a
pattern transfer step) with a thin (-50-nm) Si3N4 sacrificial 35 0.05-,um wide photoresist line on a 2-,um pitch with a
cap layer. This photoresist process uses image reversal with
line:space ratio of 1:40 is shown. This experiment used a
a 257-nm (doubled Ar-ion laser) source. FIG. lIAshows an
positive tone photoresist in accordance with FIGS. 9A-9F;
however, the process could be reversed with a negative tone
exemplary SEM after the first etch, as demonstrated in FIG.
10C, with a pitch of approximately 260 nm. FIG. lIB shows
resist or by known image reversal techniques using positive
the exemplary results after the second etch, as demonstrated 40 tone resists.
in FIG. 10F, with the pitch suitably reduced to -130 nm and
With respect to FIG. 14, an example of a dense array of
the CD to -60 nm. Finally, FIG. lIC shows the exemplary
90-nm diameter holes defined in a photoresist layer on a
1S0-nm pitch is shown. This pattern is suitably written in a
results of an anisotropic KOH etch of 130-mm pitch pattern
into the Si using the nitride layer as a hard mask. In FIG.
double exposure process with two two-beam grating expo10C, some etching of the sidewalls has occurred in the KOH 45 sures and the wafer rotated by 90° between exposures. With
etch step resulting in thinner lines and a smaller line:space
respect to FIG. 15, another example of a dense, hexagonal
ratio, namely the final Si linewidth is as small as about
close packed pattern written with three two-beam exposures
and the wafer rotated 120° between exposures is shown.
20-40 nm.
In a preferred embodiment, this multiple exposure techMultiple (greater than two) beam exposures suitably
nique (as disclosed above with respect to FIGS. 9A-9E and 50 include another degree of freedom. With respect to FIG. 16,
FIGS. 10A-lOF) is suitably repeated a number of times with
an exemplary 2-D hole pattern suitably written with a
appropriate offsets to produce pitches of about piN where
five-beam geometry in a single exposure is shown. In a
N=l (original pattern), 2 (one additional exposure and
preferred embodiment, the multiple beam exposures suitably
processing sequence), 3 (two additional exposures and procreate more complex features, with correspondingly
cessing sequences), etc.
55 enhanced surface area. With respect to FIG. 17, an exemIn an alternative embodiment, this technique can be
plary calculation is shown with the structures obtained with
extended to two-dimensional patterning by using either
the five-beam geometry of FIG. 16 when the exposure flux
multiple exposures and/or multiple-beam single exposures.
is increased to form an array of posts rather than the array
For a grid of holes or posts with equal pitches, Pl, in both the
of holes. As seen in FIG. 17, the posts are substantially
x- and y-directions, a second exposure at the same pitch but 60 hollow cylindrical forms (donuts) having both inner and
outer surfaces, thereby approximately doubling the perimshifted by P'1/2 in x and Pl/2 in y decreases the pitch (now
eter when compared with the simple hole arrays of FIG. 16.
P2) to approximately P2=P1N2. With two further exposures
The approximate doubling of the perimeter in FIG. 17 leads
a new pitch (now P3) of approximately P3=Pl/2 is achieved.
As discussed above, nonlinearities allow the extension of
to further enhanced surface area when suitably etching these
optics beyond the linear systems limit. As such, higher 65 structures into the polysilicon contact material. Compared to
the one dimensional structures, two-dimensional features
spatial frequencies can be accessed by taking advantage of
nonlinearities in processing. In other words, the linear
typically experience comparable or even greater surface area

6,042,998

19

20

enhancements. Furthermore, with two-dimensional
bandgaps where specific wavelength bands of light cannot
structures, the impact of a defect (e.g. too thin of a wall that
penetrate. The present invention provides a technique for
large-scale manufacturing of the nano-scale twocollapses) is suitably lowered.
In addition to DRAM capacitors, multiplying the spatial
dimensional patterns required for manufacturing photonic
frequency of lithographically defined structures suitably 5 crystals for the infrared, visible and ultraviolet spectral
allows for substantial improvements in, inter alia, crystal
regions. Further, using the present invention, defects may be
growth, quantum structure growth and fabrication, flux
suitably formed in this structure which give rise to important
pinning sites for high-Tc superconductors, form birefringent
classes of optical emitters with unique properties such as
thresholdless lasers.
materials, reflective optical coatings, photonic bandgap,
The present invention is also preferably used to increase
electronics, optical/magnetic storage media, arrays of field 10
the number of transistors on semiconductor electronics,
emitters and in other applications requiring large areas of
nm-scale features.
thereby allowing more and more smaller and smaller
devices.
More particularly, in another preferred embodiment, the
With respect to optical/magnetic storage media, the
present invention is suitably applied to textured substrates
for crystal growth. An array of small scale structures is 15 present invention defines individual nm-scale single-domain
suitably fabricated as the epitaxial growth surface ("bed of
sites which preferably improve the storage density by reducnanoneedles"). At the initiation of growth, small islands of
ing interactions between the information stored on indigrowth rather than the monolithic substrates are preferably
vidual sites. Moreover, by lithographically defining features
used. This approach typically has advantages for growth of
on the media in accordance with the present invention, the
strained materials where the epitaxial film has a significantly 20 tracking electronics preferably resolves smaller distances.
different lattice constant than does the substrate material. For
With respect to arrays of field emitters, as discussed above
this "bed of nanoneedles" approach, edge effects and strain
for quantum structures, for all of these techniques there can
relaxation suitably provide advantages over monolithic
be a significant advantage in terms of feature and current
growth.
density to starting with a higher resolution lithographic
Application of the present invention to quantum structure 25 technique. The present invention also suitably simplifies the
growth and fabrication is similar to the above crystal growth
fabrication process by defining the initial structures in the
application with the exception that the growth typically
nm range rather than the ,um range.
While the present invention has been described in coninvolves at least two materials: a lower bandgap material
junction with the preferred and alternate embodiments set
surrounded by a higher bandgap material to provide a
quantum wire or a quantum dot. The present invention 30 forth in the drawing figures and the specification, it will be
appreciated that the invention is not so limited. For example,
suitably further reduces the dimensionality of quantum wells
from 2-D sheets to I-D wires and O-D boxes by uniformly
the method and apparatus for multiplying spatial frequency
defining nucleation sites.
can also be used for other semiconductor-manufacturing
With respect to flux pinning sites for high- Tc
related applications including test-structures for the develsuperconductors, the present fabrication technique suitably 35 opment of next generation processing tools, flat-panel displays and any other application which requires low-cost,
provides flux pinning sites by inducing localized defects in
the film to trap the flux lines. In order to achieve the desired
large-area, nm-scale patterning capability. Various modificritical currents, the density of trap sites is preferably on the
cations in the selection and arrangement of components and
nm-scale (-5-50 nm spacings). To induce these defects, the
materials may be made without departing from the spirit and
film is preferably denatured using a lithographic step after 40 scope of invention as set forth in the appended claims.
growth. Alternatively, defects are preferably induced in the
We claim:
crystal substrate before film growth because there is less risk
1. A method for obtaining a pattern wherein the Fourier
of destroying the superconducting properties of the film.
transform of said pattern contains high spatial frequencies
The present invention suitably provides periodic
by combining nonlinear functions of intensity of at least two
structures, such as gratings, which preferably playa very 45 exposures combined with at least one nonlinear processing
important role in optics. The periodicities produced by the
step intermediate between the two exposures to form three
present invention are preferably shorter than the optical
dimensional patterns comprising the steps of:
wavelength such that the improved periodicities give rise to
coating a substrate with a first photoresist layer;
significant modifications in both the linear and nonlinear
exposing said first photoresist layer with a first exposure;
optical response of materials. For example, the resulting 50
developing said first photoresist layer to form a first
one-dimensional gratings with pitches much less than the
pattern in said first photoresist layer, said first pattern
wavelength preferably result in a birefringent response such
containing spatial frequencies greater than those in a
that the reflectivity and transmission differs between light
two dimensional optical intensity image imposed onto
polarized along the grating and light polarized perpendicular
said photoresist layer in said first exposure as a result
to the grating. Since the pitch is less than the wavelength, 55
of a nonlinear response of said first photoresist layer;
there are no diffracted orders from such a grating, implying
coating said substrate with a second photoresist layer;
high efficiency. This is known as form birefringence and
exposing said second photoresist layer with a second
offers the potential for a wide range of optical components.
exposure;
Reflective optical coatings, known as Bragg reflectors,
developing said second photoresist layer to form a second
often consist of layered stacks of different materials with 60
pattern in said second photoresist layer, said second
each layer having a Y4 wave optical thickness. Very high
pattern containing spatial frequencies greater than
reflectivities are preferably achieved, even with relatively
those in a two dimensional optical intensity image
small refractive index differences between the materials. The
imposed onto said photoresist layer in said second
extension to a periodic three dimensional optical structure is
exposure as a result of a nonlinear response of said
known as a photonic crystal. In the same way as semicon- 65
second photoresist layer;
ductor crystals have forbidden energy gaps within which
electrons cannot exist, photonic crystals exhibit photonic
combining said patterns to provide a final pattern.

6,042,998

21

22

2. The method of claim 1 wherein said first exposure
10. The method of claim 8, wherein said material includes
includes a plurality of exposures forming a plurality of
an Si0 2 overlayer configured to act as a hardmask during
images.
said etching step.
3. The method of claim 1 wherein said second exposure
11. The method of claim 8, wherein said step of depositing
includes a plurality of exposures forming a plurality of 5 a photoresist includes depositing at least one of a negative
images.
photoresist, a positive photoresist and a positive photoresist
4. The method of claim 1, wherein a minimum of said
with an image reversal step.
spatial frequencies along at least one direction in said first or
12. The method of claim 8, wherein said step of exposing
second pattern is smaller than 2/A.
a photoresist includes exposing using interference lithogra5. The method of claim 1, wherein said intermediate 10 phy.
nonlinear processing step enables a frequency distribution of
13. The method of claim 8, wherein said step of exposing
a photoresist includes exposing using interference lithograsaid pattern which is altered from frequency distributions of
phy in combination with another lithographic technique.
only said first and said second exposure.
14. The method of claim 8, wherein said step of exposing
6. A method for obtaining a pattern wherein the Fourier
transform of said pattern contains high spatial frequencies 15 a photoresist includes exposing using interference lithograby combining nonlinear functions of intensity of at least two
phy in combination with an optical stepper.
exposures combined with at least one nonlinear processing
15. The method of claim 8, wherein said step of exposing
a photoresist includes image reversal.
step intermediate between the two exposures to form three
16. The method of claim 8, wherein said step of develdimensional patterns comprising the steps of:
coating a substrate with a first mask material and a first 20 oping said periodic pattern includes etching said pattern into
a hardmask.
photoresist layer;
17. The method of claim 8, wherein said exposing step
exposing said first photoresist layer with a first exposure
includes exposing with at least one of multiple exposures
developing said photoresist to form a first pattern in said
and multiple-beam single exposures.
first photoresist layer, said first pattern containing spa18. The method of claim 8, wherein said step of depostial frequencies greater than those in a two dimensional 25
iting a material includes depositing a material on at least one
optical intensity image imposed onto said photoresist
of a textured substrate, a quantum structure, a flux pinning
layer in said first exposure as a result of a nonlinear
site for high-Tc superconductors, a birefringent material, a
response of said first photoresist layer;
reflective optical coating, a photonic bandgap, an electronic
transferring said first pattern into said first mask material, 30 device, an optical storage media, a magnetic storage media,
said first mask material comprising at least one of Si0 2 ,
an array of field emitters and a Dynamic Random Access
Si3 N 4 , a metal, a polysilicon and a polymer;
Memory capacitor.
coating said substrate with a second photoresist;
19. A method for multiplying the spatial frequency conexposing said second photoresist with a second exposure
tent of a one-dimensionalline/space pattern consisting of the
developing said second photoresist layer to form a second 35 steps of:
pattern in said second photoresist layer, said second
providing a substrate;
pattern containing spatial frequencies greater than
depositing a material on said substrate;
those in a two dimensional optical intensity image
depositing a photoresist on said material;
imposed onto said photoresist layer in said second
exposing and developing a periodic pattern in said
exposure as a result of a nonlinear response of said 40
photoresist, said periodic pattern having a pitch Pmin
second photoresist layer;
and a linewidth less than Pminl2;
transferring said first pattern and said second pattern into
transferring said periodic pattern into said material by a
said substrate using a combined mask including parts of
process step;
said first mask layer and said second photoresist;
removing said first mask material and said second pho- 45
removing said first photoresist layer;
toresist.
depositing a second photoresist layer;
7. The method of claim 6 wherein said transferring step
exposing said second photoresist layer with said periodic
includes at least one of etching, deposition and-lift off, and
pattern offset by Pminl2;
damascene.
repeating the exposing, developing and transferring steps
8. A method for increasing spatial frequency content of 50
N times with offsets of pmin/N, thereby interpolating N
lithographic patterns comprising the steps of:
new said patterns equally spaced midway between said
depositing a material;
pattern,
depositing a photoresist on said material;
etching exposed said material down to a predetermined
exposing a periodic image in said photoresist, said peridepth, thereby transferring said pattern through said
55
odic image having a pitch Pmin and a linewidth less than
material;
Pminl2 ;
transferring said pattern into said substrate.
developing said periodic image to form a periodic pattern
20. The method of claim 19, wherein said step of deposin said photoresist;
iting a material includes depositing in-situ doped polysilitransferring said periodic pattern to said material;
60 con.
depositing a second photoresist layer on said material;
21. The method of claim 19, wherein said material
offsetting said periodic pattern by Pminl2;
includes an Si0 2 overlayer configured to act as a hardmask
repeating said exposing, developing and transferring
during said etching step.
steps, thereby interpolating new said pattern midway
22. The method of claim 19, wherein said step of deposbetween said pattern.
65 iting a photoresist includes depositing at least one of a
9. The method of claim 8, wherein said step of depositing
negative photoresist, a positive photoresist and a positive
a material includes depositing doped polysilicon.
photoresist with an image reversal step.

6,042,998

23

24

23. The method of claim 19, wherein said step of exposing
28. The method of claim 19, further comprising at least
a photoresist includes exposing using interference lithograone of multiple exposures and multiple-beam single expophy.
sures.
24. The method of claim 19, wherein said step of exposing
29. The method of claim 19, wherein said pattern size
a photoresist includes exposing using interference lithogra - 5 avoids overlapping of pattern features upon doubling of said
phy in combination with a lithographic technique.
frequency.
25. The method of claim 19, wherein said step of exposing
30. The method of claim 19, further comprising registera photoresist includes exposing using interference lithograing said periodic pattern to a contact patterning.
phy in combination with an optical stepper.
31. The method of claim 19 further comprising the step of
26. The method of claim 19, wherein said step of exposing 10 allowing about 100 nm between adjacent said patterns.
32. The method of claim 19, wherein said step of deposa photoresist includes image reversal.
27. The method of claim 19, wherein said step of develiting a material includes depositing an NO layer.
oping said periodic pattern includes etching said pattern into
a hardmask.
* * * * *