Bnckgroul1ld Art and Technical Problems Progress in the production of integrated circuits employing very large scale integration (VLSI) has been characterized by an ever decreasing feature size. Transverse dimensions of transistor features have decreased from 5 micrometers in 1970 (4K DRAM) to 0.35 micrometers today (64M DRAM). This continuous improvement in feature size is an integral part of"Moore's Law", which projects an exponential feature size decrease characterized by a reduction of 30% in linear dimensions every three years.

This "law" underlies the semiconductor industry planning as exemplified in the "National Technology Roadmap for Semiconductors" (Semiconductor Industry Association, 1994), incorporated herein by this reference.

Throughout this progress, optical lithography has remained the dominant lithographic technique for manufacturing applications. Many advances have been made in optical lithography to allow this dramatic scale reduction. The optical wavelength used in state-of-the-art lithographic tools has decreased from mercury G-line (436 nm) to mercury 1-line (365 nm) to 248 DUV (KrF laser). Currently, 193 mn ArF laser-based steppers are being developed, continuing this historical trend. At the same time optical systems have been improved from numerical apertures (NA) of 0.2 to -0.6-0.7.

There are several factors which together suggest that additional major improvements along these directions are not likely, and that the industry will have to undergo a significant change in lithographic technique. Chief among these factors is the reduction of the feature size to below the available optical wavelengths. Additionally, there is an increasing premium on line width control for high-speed circuit operation,

even as the scale reduction below the wavelength is making line width control more difficult. For wavelengths below the 193 nm ArF wavelength, transmitting optical materials are believed to be unavailable, and a transition to an all-reflective system will likely be required. This is problematical since current multi-layer reflector and aspheric optical technologies are not sufficiently developed to meet these needs. Most likely, the transition to reflective optics will result in a significant reduction in the possible NAs, reducing the benefit of shorter wavelengths.

Optical sources with sufficient average power for high throughput manufacturing are another major problem for wavelengths shorter than 193 nm. EUV lithography is a promising approach based on a laser-produced plasma source and 5X reduction, aspheric, all-reflective optics with multi layer reflectors. However it is not yet clear whether this program will lead to a cost effective lithography tool that can timely meet the needs of the industry for the next generation lithographic capability.

A further factor suggesting a substantial change in lithographic techniques surrounds the complexity of the masks required for future ULSI generations. This complexity is. by definition. increasing by a factor of four each generation (i.e. four times as many transistors on a chip). In addition. many of the potential solutions to the optical lithography problem. collectively known as resolution-enhancement techniques, lead to increased mask complexity (e.g., with the introduction of 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). These trends are increasing the difficulty and cost of producing ULSI structures at high yields.

A number of alternative lithographic technologies are being investigated. These include: X-ray. e-beam. ion-beam and probe-tip technologies. Each of these has its advantages and disadvantages. but it is safe to state that none of them has as yet emerged as a satisfactory altemative to optical lithography.

Interferometric lithography, i.e., the use of the standing wave pattern produced by two or more coherent optical beams to expose a photoresist layer, has recently been demonstrated to provide a very simple technique to produce the requisite scale for the next several ULSI generations. See for exan1p1e, U.S. Patent No. 5,415,835, issued May 16, 1995. to Steven R.J. Brueck. Saleem Zaidi and An-Shyang Chu, entitled Fine-Line Interferometric Lilho,£raphy; U.S. Patent No. 5,216.257, issued June 1, 1993, to Steven R.J. Brueck and Saleem H. Zaidi. entitled Overlay of Submicron Lithographic Features;

U.S. Patent No. 5,343,292, issued August 30, 1994, to Steven R.J.Brueck and Saleem H. Zaidi, entitled Method and Apparatus for Alignment of Submicron Lithographic Features; U.S. Patent Application SN 07/662,676, filed February 2, 1991, by Kenneth P. Bishop, Steven R.J. Brueck, Susan M. Gaspar, Kirt C. Hickman, John R. McNeil, S.

Sohail H. Naqvi, Brian R. Stallard and Gary D. Tipton, entitled Use of Diffracted Light from Latent Images in Photoresist for Exposure Control; U.S. Patent Application SN 08/399,381, filed February 24, 1995, by Steven R.J. Brueck, Xiaolan Chen, Saleem Zaidi and Daniel J. Devine, entitled Methods and Apparatuses for Lithography of Sparse <BR> <BR> <BR> <BR> Arrays of Sub-Micrometer Features #, filed #, by S.R.J. Brueck.

An-Shiang Chu, Saleem Zaidi, and Bruce L. Draper, entitled Methodfor Fabrication of Quantum Wires and Quantum Dots and Arrays of Same; U.S. Patent No. 5,247,601, issued September 21, 1993, to Richard A. Myers, Nandini Mukherjee and Steven R.J. <BR> <BR> <BR> <BR> <P>Brueck, entitled A rrangement for Producing Large Second-Order Optical Nonlinearities in a Wave guide Structure Including Amorphous SIO2; U.S. Patent No. 5,239,407, issued August 24, 1993, to Steven R.J. Brueck, Richard A. Myers. Anadi Muskerjee and Adam Wu, entitled Atethods and Apparatus for Large Second-Order Nonlinearities in Fused Silica; U.S. Patent No. 4,987,461. issued January 22, 1991, to Steven R.J. Brueck, S.

Schubert, Kristin McArdle and Bill W. Mullins, entitled High Position Resolution Sensor with Rectifying Contacts; U.S. Patent No. 4,881.236 issued November 14, 1989. to Steven R @ Brueck, Christian F. Schauss. Marek A. Osinski, John G. McInerney M.

Yasin A. Raja. Thomas M. Brennan and Burrell E. Gammons, entitled Wavelength- Resonant Surface-Emitting Semiconductor Laser; U.S. Patent Application SN 08/635,565. filed September 16. 1992. by Steven R.J. Brueck, Saleem Zaidi and An- Shyang Chu. entitled Method for Fine-Line Interferometric Lithographiy; U.S. CIP Patent Application SN 08/407.067. filed March 16. 1995. by Steven R.J. Brueck, Xiaolan Chen, Saleem Zaidi and Daniel. Devine. entitled Methods and Apparatus for Lithography of Sparse Arrays of Sub-Micrometer Features; U.S. Patent Application SN 08/123.543. filed September 20. 1993. by Steven R.J. Brueck. An-Shyang Chu, Bruce L. Draper and Saleem H. Zaidi, entitled Method for Manufacture of Quantum Sized Periodic Structures in Si Materials: U.S. FWC Patent Application SN 08/490,101, filed June 6, 1995, by Steven R.J. Brueck. An-Shyang Chu. Bruce L. Draper and Saleem Zaidi, entitled Method for Manufacture 9f Quantum Sized Periodic Structures in Si Materials, U.S. DIV Patent Application SN 08/719.896, filed September 25, 1996, by Steven R.J. Brueck, An-

Shyang Chu, Bruce L. Draper and Saleem H. Zaidi, entitled Manufacture of Quantum Sized Periodic Structures in Si Materials; U.S. Patent Application SN 07/847,618, filed March 5, 1992, by Kennets P. Bishop, Lisa M. Milner, S. Sohail H. Naqvi, John R.

McNeil and Bruce L. Draper, entitled Use of Diffracted Light from Latenl Images in Photoresistfor Optimizing Image Contrast; U.S. Patent Application SN 08/525,960, filed September 8, 1995, by Steven R.J. Brueck and Xiang-Cun Long, entitled Technique for Fabrication ofa Poled Electrooptic Fiber Segment; U.S. Patent No. 5,426,498, filed June 20, 1995, by Steven R.J. Brueck, David B. Burckel, Andrew Frauenglass and Saleem Zaidi, entitled Method and Apparatus for Real-time Speckle Interferometry for Strain or Displacement of an Object Surface; SIA, National Technology Roadmap for Semiconductors (1994); J.W. Goodman, Introduction to Fourier Optics, 2nd Ed.

(McGraw Hill. NY 1996); J.W. Goodman, Statistical Optics (John Wiley, NY 1985); Xiaolan Chen, S.H. Zaidi, S.R.J. Brueck and D.J. Devine, Interferometric Lithography of Sub-Micrometer Sparse Hole Arrays for Field-Emission Display Application (Jour.

Vac. Sci. Tech B14, 3339-3349, 1996); S.H. Zaidi and S.R.J. Brueck, Multiple-Exposure Interferometric Lithography (Jour. Vac. Sci. Tech. Bl 1, 658, 1992); A. Yariv, Introduction to Optical Electronics (Holt. Reinhard and Winston, NY 1971). The entire contents of the foregoing are hereby incorporate herein by this reference.

The limiting spatial frequency in interferometric lithography is generally regarded as A/2, where A is the laser wavelength. and the critical dimension (CD) for 1:1 lines and spaces is A/4. This should be contrasted with the limiting CD of imaging optical systems which is usually stated as ka A. where k, is a function of manufacturing tolerances as well as of the optical system. A Is the center wavelength of the exposure systems and NA is the numerical aperture of the imaging optical system. Typical values ofk range from 1.0 down to - 0.6. This is an oversimplified description of the limiting scales, but serves to illustrate the major points. Projections for the 1 93 wavelength optical lithography tool are an NA of 0.6 which leads to a limiting CD of - 0.19 micrometer. In contrast. at I-line (365 nm) interferometric lithography has a limiting resolution of - 0.09 micrometer. Using the 193 wavelength, the limiting resolution of interferometric lithography is - 0.05 micrometer. This is already better than the current projections for EUV lithography (a wavelength of 13 nm and aNA of 0.1 leading to a CD of 0.08 micrometer at a k, of 0.6).

A major obstacle associated with interferometric lithography surrounds the development of sufficient pattern flexibility to produce useful circuit patterns in the VLSI and ULSI context. A two-beam interferometric exposure simply produces a periodic pattern of lines and spaces over the entire field. Multiple beam (4 or 5) exposures produce two-dimensional structures, but also of relatively simple repeating patterns such as holes or posts. More complex structures can be made by using multiple interferometric exposures, for example as described in U.S. Patent No. 5,415,835, issued May 16, 1995, to S.R.J. Brueck and Saleem H. Zaidi, entitled Method and Apparatus for Fine-Line lnterferon1elrc Lithography and in Jour. Vac. Sci. Tech. Bi 1 658 (1992).

Additional flexibility may be attained by combining interferometric and optical lithography as also described in the above patent. Thus far, demonstrations include relatively simple examples, e.g., defining an array of lines by interferometric lithography and delimiting the field by a second optical exposure. Multiple exposures have been demonstrated to produce more complex, bdt still repetitive structures.

In addition to limited pattern flexibility. presently known interferometric lithography techniques lack a ell-defined synthesis procedure for obtaining a desired structure.

A technique is thus needed which overcomes, inter alia. the foregoing drawbacks associated with prior art techniques.

Summarv of the Invelltioll The present invention provides methods and apparatus for integrating optical lithography and Interferometric lithography in a manner which overcomes many of the shortcomings of the prior art.

A preferred embodiment of the present invention provides methods and apparatus for parsing the lithographic tasks between optical and interferometric lithographic techniques. ln accordance with a particularly preferred embodiment an optical system is provided which facilitates the integration of interferometiic lithography and optical lithography to produce complex structures on the same workpiece. for example a semi- conductor wafer. In a pre el-l-ed exemplary embodiment two masks are configured to intercept two portions of a uniform. collimated optical beam which is imaged by the optical system onto the wafer. An interferometric optical system is incorporated into the apparatus to bring the two mask images onto the wafer at substantially equal and opposite

angles with respect to a wafer normal plane. In accordance with this preferred embodiment, the masks are suitably tilted relative to the optical axis in order to produce image planes which are coincident with the wafer plane after passing through the interferometric optics.

In accordance with a further aspect of the present invention, a formal parsing procedure is proposed for separating an arbitrary desired pattern into a number of specified interferometric and optical lithography exposures.

In accordance with a further aspect of the present invention, multiple beam interferometric lithography is extended to include a number of discrete spatial frequencies or, alternatively, a continuous range of spatial frequencies, to thereby facilitate writing more complex repetitive as well as non-repetitive patterns in a single exposure.

In accordance with a further aspect of the present invention. methods and apparatus are provided for combining extended multiple beam interferometric lithography with optical lithography to produce arbitrary structures at a resolution which is higher than that currently available using known optical lithography alone.

In accordance with a further aspect of the present invention, methods and apparatus are provided for optically defining the masks employed in interferometric exposures.

In accordance with yet a further aspect of the present invention. methods and apparatus are provided for reducing the complexity of masks used in the optical lithography portion of a combined optical and interferometric lithography exposure.

BriefDescriptioz70ffl1eDronvil7" Figures The present invention will hereinafier be described in conjunction with the appended drawing figures, wherein like designations denote like elements, and: Figure lisa schematic representation of the decomposition of a specific structure into rectangles for facilitating a Fourier transform. with the rectangles shown slightly offset for clarity; Figure 2 is an exemplary graph of optical transfer functions for coherent and incoherent illumination; Figure 3 are graphical examples of prior art VLSI patterns at a 0.1 8 micrometers CD written by diffraction-limited optical lithography tools at prescribed wavelengths and AJAX; the left-hand column represents the results of incoherent illumination. and the right- hand column sets forth the results of coherent illumination;

Figure 4 illustrates examples of VLSI patterns at a 0.18 micrometer CD written using a combination of optical and interferometric exposures; Figure 5 sets forth a simplification of the mask structure in the context of integrated optical and interferometric lithographic techniques; Figure 6 is a schematic representation of an exemplary optical system useful in imaging a field stop onto a wafer in accordance with a preferred embodiment of the present invention; Figure 7 is a schematic representation of the optical system of Figure 6, extended to include interferometric lithographic techniques; Figures 8A and 8B are schematic representations of alternate interferometric optical systems useful in producing mask images biased to high spatial frequencies; Figures 9A and 9B depict. respectively, in-focus and out-of-focus SEM micrographs of the edge regions of a rectangular aperture imaged using the optical system of Figure 8A; Figure 10 is a schematic diagram representing the spatial frequency space representation of the combination of imaging optical and interferometric exposures; Figure 11 is a schematic representation of an optical system for biasing the spatial frequency content of an image away from the zero center frequency in accordance with a preferred embodiment of the present invention: Figure 12 is a schematic representation of an optical system for imaging a sub- mask using a mask of the full pattern along with a prism to bias the frequency components away from low frequency; and Figure 13 sets forth schematic examples ot VLSI patterns at 0.1 8 micrometer CD written at a wavelength of 365 nm by a combination of interferometric lithograplly using the arrangement of Figure 11, and imaging optical lithography (IIL).

Detailed Description Of Preferred Exemplnrv Embodiments Before describing the subject invention in detail, a review of Fourier optics is presented. See also. J.W. Goodman, InlsAoductiol1 to Fourier Optics 2nd Ed. (John Wiley Press, NY 1996). the entire contents of which are hereby incorporated herein by this reference.

For simplicity, the ensuing discussion assumes the use of incoherent illumination, so that each Fourier component of the image can be treated and evaluated independently.

The discussion will then be extended to the limit of coherent illumination where each component refers to the electric field and the result squared to determine the intensity at the exposure plane. In practice, actual optical lithography tools typically employ partially coherent illumination. For a more detailed discussion of partial coherence, see, for example, J.W. Goodman, Statistical Optics (John Wiley, NY 1985). Although the use of partially coherent illumination adds to the computational complexity of the mathematical analysis, it does otherwise significantly impact the present invention as set forth herein.

An optical lithography system can be separated into an illumination subsystem, a mask, the imaging optical subsystem, and the photoresist optical response. The purpose of the illumination subsystem is to provide uniform illumination of the mask. On passing through the mask, the optical beam is diffracted into a number of plane waves corresponding to the Fourier components of the mask pattern. Each of these plane wave components propagates in a different spatial direction, characterized by the k, and components of the wavevector. Mathematically, this is described in the plane of the mask as: where the summations run over the allowed spatialfrequencies, k@ = nlPx, n = 0, ,#1,#2, ky ky = m/P,4 m = 0, l, 2 ..., and Px and Py are the repeat periods of the pattern in the x andy directions, respectively. Px and P, can be as large as the exposure die size for a non-repeating pattern. Since a chrome-on-glass mask has a binary transmission function (each pixel is either unity or zero), the Fourier transform in (1) is just given by a sum over sin(x)/x functions with appropriate phase shifts corresponding to a decomposition of the <BR> <BR> <BR> <BR> desired pattern into rectangles. That is:<BR> sin(2#kxai/2)sin(2#kybi/2<BR> <BR> <BR> <BR> <BR> <BR> (2) F(kx,ky) = #aibi ei2#(k,c,+k@d@)<BR> <BR> <BR> <BR> <BR> <BR> <BR> 2#kxai/2 2#kybi/2 where a1 (bi) is the extent of each rectangle in x (y), and ci (di) is the offset of the rectangle center from the coordinate origin in x (y).

With momentary reference to Figure 1, the foregoing decomposition of the desired pattern into rectangles is illustrated schematically for a typical VLSI gate structure. In

particular, an exemplary pattern, shown in the illustrated embodiment as a typical gate 11, is decomposed into a plurality of rectangles 12-16, shown offset in the Figure for clarity.

The imaging optical subsystem imposes a modulation transfer function (MTF) on the propagation of the Fourier components onto the image (wafer) plane. For diffraction limited optics with circular symmetry, the transfer function is characterized by a spatial frequency, k", = NA/A where NA is the numerical aperture and A the center wavelength.

In the limit of incoherent illumination, the MTF is given by see Goodman, Introduction to Fourier Optics, 2nd Ed. (McGraw Hill, NY 1996): where k = v'kx2 + k; and Tincoh(kx,ky) = 0 for k s2k"p,. For a coherent optical system, the transfer function is simply (4) Tcoh(hx,ky) = 1 for k # kopt, and Tcoh(kx,ky) = 0 for k > kopt, where, as noted above, this transfer function is suitably applied to the optical electric fields before evaluating the aerial image intensity.

Referring now to Figure 2, these two transfer functions are shown along with the transfer function for interferometric lithography that will be discussed in more detail below. The scale is set by k ,*, = NA/A where NA is the optical subsystem numerical aperture and A is the center wavelength of the illumination system. For incoherent illumination, the transfer function, Twc.()h, is applied to each Fourier component of the intensity pattern at the mask. For coherent illumination, the transfer function, Tincoh, is applied to each Fourier component of the intensity pattern at the mask. For coherent illumination, the transfer function, Tincoh is applied to the Fourier components of the electric field at the mask and the intensity is evaluated at the wafer plane. Also shown is the optical transfer function for interferometric lithography (23) that extends to 2/X.

The parameters used to plot the Figure are A = 365 nm and NA = 0.65. The graph of

Figure 2 is drawn for a NA of 0.6; the normalization to k/k;q,t removes any explicit dependence on A.

Finally, the image intensity at the wafer plane is transferred to the resist, which typically exhibits a nonlinear response. In this regard, both positive and negative tone resists are commonly used in the industry. For the sake of definiteness, the calculations presented herein are for negative tone resist (i.e., illuminated regions of the resist are retained on developing, non-illuminated regions are removed). It will be understood that the calculations could equally be made to apply to a positive tone resist with a simple inversion of the mask to reverse the illuminated and non-illuminated regions. For simplicity of calculation, the photoresist response will be approximated as a step function. That is, for local intensities below a threshold value the photoresist is assumed to be fully cleared upon development, while for local intensities above the threshold value, the resist thickness is unaffected by the development process. In practice, the resist has a finite contrast and non-local intensities impact the development. The impact of these realistic considerations is to remove some of the high spatial frequency variations in the results presented below, and to yield finite sidewall slopes rather than the abrupt sidewalls predicted by this simple model. However, these effects do not impact the scope or content of the subject invention.

Referring now to Figure 3, an example of prior art techniques shows the results of applying this analysis to the printing of a typical VLSI gate pattern at a 0.1 8 micrometer CD with optical lithography tools at 365, 248 and 193 nm (bottom to top, respectively).

The desired pattem is shown as the dotted lines in each cell. Only the perimeters of the patterns printed by the optical tools are shown. Inside of these perimeters the resist is exposed and remains intact on developing; outside of the perimeters the resist is unexposed and is removed during development (negative resist). As noted above. it is a simple modification to the analysis to reverse this response for positive resist. The patterns are periodic; hence, in an actual exposure, each cell would be repeated many times and, of course, the frames delineating each cell would not be printed. To provide more information in the Figure, adjacent cells are shown with the results of different exposure tools and illumination conditions. The NAs were set at 0.65 for the 365 nm (I- line) tool and at 0.6 for the 248 nm (KrF laser source) and 193 nm (ArF laser source).

The left column shows the results for incoherent illumination, the right column for coherent illumination. As expected from the simple analysis presented in the background

section, an I-line optical lithography tool is not capable of conveniently writing a 0.18 micrometer CD structure (e.g., minimurn resolution of - k,XlNA - 0.8 X .365/.65 - 0.45 micrometer). The printed shapes show severe distortions resulting from the limited frequency components available; indeed, the coherent illumination image is not even two separated features but merges into a single structure. Although not shown in Figure 3, the patterns are also very sensitive to process variations, showing large changes for small variations in optical exposure levels. The patterns available from a 248 nm optical tool are significantly improved; however, they still show significant rounding ofthe edges and deviations from the desired structure. Even the patterns available from a 193 nm tool are far from ideal.

The foregoing procedure can be used to parse the lithographic task between optical and interferometric lithographies. This parsing technique is at the heart of the subject invention.

Before illustrating the subject parsing techniques in detail, an evaluation of the MTF for interferometric lithography is first presented.

More particularly, in its simplest form IL uses two coherent optical beams incident on the substrate with equal and opposite azimuthal angles (q) in a plane normal to the wafer. The intensity at the wafer is given by (5) IlL (x) = 2 jti.+ + cos(4r:k sin(#)x + (P );I where the intensity of each beam individually is l0. k = 1/R with A the wavelength of the coherent beam and the phase factor.j describes the position of the pattern with respect to the wafer coordinate system. It may be necessary to adjust this phase factor appropriately in multiple exposures (i.e., inter-exposure alignment) in order to form the desired final pattern. This is a MTF of unity, i.e., the intensity goes to zero at the minima. The spatial frequency is given by (6) kx =2ksin(()) and the maximum spatial frequency is kx|max #kII. = 2/X. This should be compared with the maximum spatial frequency for an imaging optical system, viz. k tr = kopt = 2NA/A.

Further, the modulation transfer function for an interferometric exposure is typically unity

for all k < kIL, in contrast to the sharp drop-off for a traditional optical system. This is illustrated in Figure 2 along with the corresponding MTFs for both coherent and incoherent illumination optical imaging systems. It is important to remember that the MTF for coherent illumination is applied to the Fourier components of the electric field rather than of the intensity. The nonlinear squaring operation involved in taking the intensity produces frequency components extending out to 2 x Thus a defined procedure for exposing a desired pattern in accordance with the present invention surrounds optical and interferometric lithographies. In accordance with a particularly preferred embodiment, the optical lithography is primarily used for the lower frequency components, and the interferometric lithography is primarily used to provide the higher spatial frequency components. Thresholds can be set on the interferometric exposures both in frequency (i.e., a maximum and a minimum spatial frequency) and in amplitude (eliminating any frequency components whose Fourier amplitude is below a preset level). This is illustrated in Figure 4 for the same VLSI pattern used in the prior art example (Figure 3).

With continued reference to Figure 4, the left hand column shows examples of setting frequency limits. For the top left panel, the entire frequency space available by interferometric lithography is used and, hence, there is no need for an optical lithography step in this case. The resulting pattern is a closer representation of the desired pattern that any of the prior art examples, even those at substantially shorter wavelengths; however, 51 exposures were required in this example. The lower two panels in the left column show examples of restricting first the low frequencies, and then both low and high frequencies. In each case the low frequency components are driven from an optical exposure. The right hand column shows the results of setting a threshold on the intensity of interferometric lithography exposures. Progressively higher thresholds (top to bottom) yield progressively fewer interferometric lithography exposures and progressively less ideal approximations to the desired structure. This phenomenon underscores the tradeoff between the number of exposures, which relates to manufacturing cost in terms of exposure time. and the pattern fidelity. This tradeoff may be advantageously optimized within each level's specific context in accordance with the teachings of the present invention.

As noted above, one of the major difficulties facing optical lithography is the increasing complexity of the required masks. Since the parsing procedure outlined herein

advantageously exploits optical lithography for the low spatial frequency components of the image and supplies the high spatial frequency components by interferometric lithography, the mask complexity can be dramatically reduced.

Referring now to Figure 5, an exemplary VLSI pattern similar that shown in Figure 4 is again shown using the foregoing paradigm, namely, wherein optical lithography is leveraged for the low spatial frequency components and interferometric lithography is employed for the high spatial frequency components of the mask. More particularly, the top left panel of Figure 5 shows the image resulting from printing (incoherent imaging) only the low spatial frequency components (up to k", = NA/A) using the full mask structure (shown as the dotted lines). The top right panel shows the results of adding 51 interferometric exposures (solid lines) (see Figure 4 top left panel) and on restricting the interferometric lithography to only seven exposures with a simple amplitude threshold (dashed lines). These results are substantially equivalent to those shown in Figure 4. The middle left panel of Figure 5 shows a much simpler mask (labeled simplified mask A and shown as a dotted line) and the resulting intensity profile when the image from this mask is passed through the imaging system with no restriction on spatial frequency beyond that inherent in the imaging system. This is a much simpler mask than the full pattern, but it produces very similar results within the restricted frequency space of the optical tool. Mask pattern A was derived by simple trial and error from the low frequency results in the panel above by passing the A pattern through the imaging simulation described in the preceding paragraphs. Note that because of the repetitive patterning, pattern A is simply a single rectangular aperture per reperirion unit.

With continued reference to Figure 5, the middle right panel shows the results of using simplified pattern A for the optical exposure and adding interferometric lithography exposures (no threshold, full range of available spatial frequencies) is very close to that for the full mask. The dashed curve is for seven interferometric lithography exposures.

The low frequency mask can be simplified even further to the simple straight line segment shown in the bottom left panel. Because of the repetitive pattern, this is just a wide line extending the full height of the die.

The bottom right panel of Figure 5 shows the results of adding high frequency components using 51 (solid) and 7 (dashed) interferometric lithography exposures. The results are very close to those obtained with the full mask and are again much better than

those available even from a 193 nm optical exposure tool. There is very little difference between the resulting exposures showing that a simplified mask can be used for the optical lithography step, easing the mask making difficulty, while still retaining good pattern fidelity. As above, a careful tradeoff between number of exposures (manufacturing throughput) and pattern fidelity needs to be made for individual levels.

It is also possible to reduce the number of interferometric exposures by combining multiple (more than two) beams in a single exposure. A simple example of this is discussed at some length in related U.S. Patent Application SN 08/399,381, filed February 24, 1995, by Steven R.J. Brueck, Xiaolan Chen, Saleem Zaidi and Daniel J.

Devine, entitled Methods and Apparatuses for Lithography of Sparse Arrays of Sub- Micrometer Feature. This earlier application provides a series of techniques for writing a particular two-dimensional exposure, specifically a sparse array (> 1:3 hole diameter:interhole distance) of holes in a positive photoresist layer. Specific examples of three, four and five beam exposures are provided therein.

It is often desirable, and often necessary, to delimit the field of an interferometric lithography exposure. Typical die sizes (today on the order of 20x30 mm2) for single exposures are much smaller than wafer sizes (200 mm to 300 mm diameter). In order to obtain a uniform exposure over the die, the optical beam is expanded and transformed into a uniform intensity across the field size. However, the edges of the beam are necessarily nonuniform and if allowed to expose the wafer would result in a substantial pattern nonuniformity. One technique to address this is simply to add a field stop aperture just above the wafer to delimit the exposed area. A significant problem with this approach, however, surrounds the diffraction effects of the aperture. From diffraction theory. these extend - 10 8/IL into the pattern where L is the distance from the field stop <BR> <BR> <BR> <BR> to the wafer. For a practical separation distance of L ~ I mm, this diffraction ringing extends - 0.3 mm into the pattern. In many applications, this is an unacceptable result.

One technique for eliminating this ringing is to make the aperture rough on the scale of the wavelength, so that fields scattered from the edge to not add coherently away from the edge.

Another alternative, more in keeping with traditionally lithography and providing significantly enhanced flexibility, is to move the field stop away from the wafer and add an optical system that provides two functions simultaneously: 1) image the field stop onto

the wafer, and 2) transform the collimated beam incident onto the field stop into a collimated beam at the wafer.

Referring now to Figure 6, a preferred exemplary embodiment of an optical system used to image a field stop 31 onto a wafer 32 comprises respective lenses 33 and 34 having focal lengths, and where the mask 31 is placed a distances before first lens 33, wherein the separation between the lenses is suitably 7; +j), and the wafer 32 is placed a distancef2 behind second lens 34. The magnification of the image is given by off2. The field stop is suitably disposed before the first lens 33 and illuminated by a laser source that is collimated (i.e., the wavefront has a very large radius of curvature) and approximately uniform across the area of the field stop. In this configuration, the curvature of the wavefront is substantially unaffected by this optical system. The diffraction-limited edge definition of the field stop image at the wafer is suitably proportional to the wavelength and inversely proportional to the numerical aperture of the optical system. This is only one of a class of optical systems that serve to transfer both the mask image and at the same time retain the overall wavefront flatness. The general condition specifying suitable optical systems is that the B and C terms of the overall ABCD ray transfer matrix describing the optical system be zero. (ef A. Yariv, Introduction to Optical Electronics (Holt, Reinhart and Winston, NY 1971), for a discussion of ABCD ray-tracing transfer matrices).

The mathematical description of this imaging system is straightforward in terms of the Fourier optics concepts introduced above. Since the mask illumination is with a coherent uniform beam. a coherent imaging analysis is appropriate. The electric field just after the mask can be written as: where A4(k,,k) is the Fourier transform of the mask transmission function and for convenience is assumed discrete. For an aperiodic mask pattem, the summations over k, are replaced by integrals in the usual fashion. Passing through the optical system imposes a modulation transfer function:

where the E subscript is a reminder that this transfer function is applied to the electric field rather than the intensity. Then the electric field at the wafer is given by: and the intensity is given by where A is the Fourier transform of the intensity, real for a simple transmission mask, and the primes on kx ', and k,,'indicate that, as a result of the squaring operation, they are composed of appropriate sums of the k and ky of the electric field Fourier transform and extend out to 2xk,.

The low frequency pattern defined by the mask can be shifted to higher spatial frequencies by splitting the optical path and introducing interferometric optics.

Referring now to Figure 7, a preferred exemplary embodiment of the present invention illustrates the optical system of Figure 6 extended to include apparatus for integrating interferometric techniques into the lithography system. More particularly, respective masks 41 and 42, which are not necessarily identical, are suitably introduced into two portions (e.g.. halves) of the optical beam, shown on the figure as upper and lower. In order to compensate for any tilt introduced into the phase front by the final optical elements, these masks may be advantageously placed at a tilt so that the final image plane is in the wafer normal. The optical system consists of lenses 33 and 34 positioned as described in reference to Figure 6. Finally, interferometric optics are introduced in order to provide the high frequency bias.

The interferometric optical system shown in Figure 7 suitably comprises a plurality (e.g. four) of mirrors (45, 46, 47 and 48) that split the optical beam into respective segments (e.g., two) and cause these segments to interfere at the plane of wafer 15. In the illustrated embodiment, the interferometric optical system is suitably configured to bring the mask images onto the wafer at substantially equal and opposite angles to the wafer normal. The advantages of this system include equal center path lengths for the two beams and an absence of induced astigmatism.

Referring now to Figure 8, various alternate embodiments may be employed to produce mask images biased to high spatial frequencies. In particular, Figure 8A employs a simple Fresnel configuration comprising a Fresnel lens 23 and a mirror 51 configured to apply the mask image to the workpiece (e.g., wafer) 32. Although the configuration of Figure 8A is attractive in that it is a much simpler configuration involving only one mirror (51), the two center path lengths are unequal, requiring different mask planes for the two masks. Figure 8B shows a prism (52) configuration, where the center path lengths are equal, but the prism introduces an astigmatism requiring different mask planes for x-lines and y-lines.

The mathematical description of these systems will now be derived in terms of Figure 7. Small changes that do not affect the essential results are required to adapt this description to the alternate optical schemes of Figure 8. Adapting Equation 9 to the optical system of Figure 7 gives: where subscripts u, A have been added to the mask Fourier transforms to indicate that they are not necessarily identical; ll=2psinq/R is the spatial frequency bias added to each beam by the interferometric optics. Taking the intensity gives the image printed on the photoresist laver. viz.:

and in the special case that the two masks are identical this reduces to: Equation (13) corresponds to the mask image modulated by the high frequency interferometric pattern. For example, if the mask pattern is simply a field stop, then the resulting printed pattern will be a high spatial frequency line:space pattern, delimited at the edges by the field stop. As noted above, the edge of the field strop is typically defined to within a distance of - AINA by the limitations of the optical system. More complex mask patterns are clearly possible; indeed any mask pattern within the spatial frequency limits of the optical system can be reproduced with the additional, high-spatial-frequency modulation introduced by the interferometric optical system in accordance with the present invention.

Referring now to Figure 9, a plurality of SEM micrographs are presented illustrating an initial experimental demonstration using the optical arrangement of Figure 8A to print a uniform line:space pattern within a finite field. The optical source was a Ar- ion laser at 364 nm. This was a very low NA optical system ( 0.06), using only single- element, uncorrected, spherical lenses, so that the diffraction limited edge definition was only - 6 mm and there is probably a significant contribution from lens aberrations. The top two SEMs (Figure 9A) show the in-focus case. Both the vertical edge of the field stop (parallel to the interferometric grating lines) and the horizontal edge (perpendicular to the interferometric grating lines) are defined to within - 10 mm. This edge definition is within a factor of 2 to 3 of the theoretical diffraction limit (Al/NA4 mm). Notice that the grating period of 0.9 mm essentially provides a built-in measuring apparatus. In contrast, the bottom SEMs (Figure 9B) show similar results for an out-of-focus condition. The intensity fringing at the edges is due to diffraction; the distance to the first fringe of - 30 mm can be used to calibrate the distance from the focal plane (i.e., the defocus) at about 3.5 mm.

Equation 1 3 can be rewritten to emphasize the distribution of spatial frequency contributions associated with this image. viz.:

Close scrutiny of Equation (14) suggests that there are three regions of frequency space with significant frequency content: the low frequency region modified by the lens system and represented by the intensity term, and two replicas of this intensity pattern, one shifted by +2wx and one by -2wx as a result of the interferometric optics. This situation is illustrated in Figure lOA which suitably models the full extent of frequency space covered by the exposure described in Equation 14 using an exemplary optical system such as that shown in Figure 8A. In particular, the full extent of available frequency space is modeled as the large circle 104 with radius k" = 2/A, with the three filled-in circles 106. 108, and 110 representing the aforementioned three regions of frequency space with significant frequency content. For the optical system used in the demonstration of Figure 9, the low frequency region is contained within a circle of radius 2kepi = 2NA/A, with NA = 0.06. and the two interferometrically created regions are offset by 2w 2sin(qYA and sin(q) = 0.2 for a 0.9 mm pitch grating. The radius of each offset region is equal to that of the low frequency region. From Equation 3, the MTF of the optical system decreases monotonically along a radial direction in each of these frequency regions and is zero at the edges of the circles depicted in Figure 10A. Note that the lens optical system alone (Figure 6) is incapable of creating the 0.9 mm period grating, whereas the interferometric system combined with the lens system (Figure 8A) has shifted the frequency content of the image to the higher frequencies necessary to produce the grating while retaining the low frequency content that defines the area of the image.

Importantly. the combined optical system results in an image whose frequency content covers continuous regions of frequency space; this should be contrasted to the discussion of periodic structures above in which only points in frequency space, relatively widely separated for the small period pattern (12 >cCD in x, 5 XCD in y) are needed to reproduce the pattern (see, jor example. the above discussion of Figures 1, 3, 4 and 5).

For this first demonstration, a very modest optical system was used. As is clear from Figure iOA, the resulting pattern covers only a very small region of the available frequency space. Figure 10B shows the possibility of covering much of spatial frequency space with a small number of exposures and a modest optical system, e.g., for a lens NA of 0.33. Offset regions in frequency space are shown in both the k,- and k!.-directions.

These could be provided in two exposures using optical systems analogous to those shown in Figures 7 and 8. or in a single exposure with a four-beam interferometric system as is discussed for the plane wave case (e.g., single points in frequency space) in U.S. Patent Application SN 08/399,381, filed February 24, 1995, by Steven R.J. Brueck, Xiaolan Chen, Saleem Zaidi and Daniel J. Devine, entitled Methods and Apparatuses for Lithography of Sparse Arrays of Sub-Micrometer Features. Because the relative phases of the frequency components along the kx- and k!-axes may vary from pattern to pattern, it is likely that two exposures will be required. The NA of A/3 was chosen since this is the smallest NA for which, along a diameter between three circles, continuous coverage of frequency space is achieved. Since the frequency response of the optical system is inadequate at the edges of the circles, either additional exposures or a larger NA optical system are required to achieve full coverage. Rectilinear patterns have the majority of their frequency content concentrated close to the ky and k!,-axes; so that this frequency space coverage may be satisfactory. If not, additional exposures, or additional beam paths. or both may be employed, as desired.

Even with sufficient exposures at a large enough NA to assure complete coverage of frequency space, this arrangement does not conveniently permit the imaging of arbitrary patterns. This is because each intensity pattern represents a real mask image; this places some constraints on the Fourier components. Specifically, for a simple transmission mask described by Equation 10 the requirement that the intensity after the mask is real and positive requires (15) I(kx,ky)=I#(-kx,-ky) This same relationship must hold for the final image. However, the interferomenic optical system imposes a more constraining relationship, e. g.

@(kx,ky) = @ @(-kx,-ky) (16) =1(kx + 2w ky) = l (-kx - 2w-ky) =@(kx - 2w,ky) = @ @(-kx + 2w,-ky)

Again, for the final image, the pairwise relationships shown on each line must hold, but the requirement that the relationships hold between these pairs overly constrains the final image.

In accordance with the present invention, there are at least three approaches solutions to reconciling the foregoing constraints: (I) overlap multiple exposures to break this symmetry; (2) use phase masks or other three-dimensional masks to break the overall symmetry described by Equation 15; and (3) modify the optical system by using different masks in the upper and lower arms and by introducing additional optics to shift the center of the frequency response away from k, = k = O so that the positive and negative frequency terms are weighted differently by the lens MTF.

A special case of (3) (above) of significant practical importance may be obtained by placing only a field stop aperture in one arm, for example the upper arm, and a more complex mask in the lower arm of the interferometric system. Then, Equation 12 can be written:

Equation 17 was derived under the assumption that the field stop is sufficiently large that the Fourier components associated with Mu are at much smaller frequencies than those included in M,. More particularly, each frequency in the summations in Equation 17 may be replaced by an appropriate function to restrict the panern to the area defined by the field stop. That is: where a and b are the linear dimensions of the field stop and use has been made of the equivalence between multiplication and convolution in Fourier transform pairs.

This result still may not fully resolve the constraint issue noted in connection with Equation 16.

In particular, there are constraints on the Fourier coefficients, e. g., A4t(k, kJ Affil *(-kR -kJ that are not consistent with an arbitrary final image. As noted above, this can be avoided by shifting the optical system center frequency response away from lkl = 0.

One possible optical scheme that accomplishes this is shown in Figure 11.

Referring now to Figure 11, effective masks 41 and 42 are employed, with mask 41 suitably comprising a simple open field stop aperture. A prism 71 is suitably disposed behind mask 42 to provide an angular offset of the frequency components. Center optical rays 72 and 73 are shown to provide additional information. Prism 71 may be advantageously chosen such that zero frequency rate emerging from mask 42 is directed to the edge of the aperture of lens 33. In this configuration, prism 71 effectively imparts an overall tilt, or bias, w1111, to the frequency components accepted by the lens system. In the illustrated embodiment, the prism angles are selected to tilt the zero spatial frequency ray emerging from mask 42 so that it just misses the aperture of the first lens (33).

Specializing this result to a simple field stop aperture as the upper mask, and again in the approximation that the nonzero Fourier coefficients of this aperture are at much lower frequencies than those of the mask and can initially be neglected, the total field at the mask becomes and the intensity is By adjusting My,,, SO that for example, only positive kx are accepted by the lens system, the final constraints on forming an arbitrary image are removed. It should be noted that there are many possible variants to using the prism as illustrated in Figure 11. For example, the prism could be placed in front of the mask; it could be replaced by an

appropriate diffiaction grating used either in transmission or in reflection; Fourier plane filters could be used (e. g., apertures at the focus of the first lens (33) in the optical system) to select only appropriate subsets of the mask transmission.

Calculations of patterns that can be generated using this idea are shown in Figure 13. The top panel on the left (labeled All freq.) shows the result of using all reasonably available interferometric exposures. This panel is included for comparison to show the best pattern yet obtained with a large number of exposures and is essentially the same as the top left panel of Figure 4. The middle left panel shows the results of a double exposure: an imaging interferometric exposure and an incoherently illuminated optical exposure. This middle left panel shows the result of combining a single imaging interferometric lithography (IIL) exposure, offset (biased) in they or vertical direction, using the arrangement of Figure 11, and a traditional incoherently illuminated optical exposure, both with modest lens NA of 0.4. In the example shown in the middle left panel, the imaging interferometric exposure may be advantageously biased, for example at a y-spatial frequency of 0.5 by prism 71 of Figure 11. In accordance with a preferred embodiment, this bias is then effectively canceled out by the interferometric optics (e.g., mirrors 45-48 of Figure 7) to ultimately yield the proper frequency distribution for the pattern. A mask with the desired pattern is suitably placed in one arm of the optical system, and an open aperture delineating the field is suitably placed in the other arm. For <BR> <BR> <BR> <BR> the example shown in Figure 13, the pattern is repetitive with a period P = 12@CD in the horizontal (x) direction and P, = 5'CD in the vertical (i') direction. The Fourier series representation of the pattern has frequency components k"", = 2p(nxlPr+l11ylP!). The corresponding spatial frequencies, normalized to the CD. are CD/Pv = 0.083 and CD/Pv = 0.2 and the current practically realizable maximum values of (n, m) supported by interferometric lithography are (11, 5), i.e., nmax = Int(2Px,CD/#l) = Int(Px,kII), where the Int function returns the integer portion of the argument. The prism 71 was chosen to tilt all of the frequencies by 04,j, = 0.5. Therefore. the high spatial frequency Fourier components. e.g.. m=3. 4 are shifted into the collection cone of the lens 33. The bias, wH, introduced by the interferometric optics. e.g., mirrors 45-48 in Figure 7, were chosen so that 2wH, = W"/, and the offset tilt just cancels the bias added by the interferometric optics.

With continued reference to Figure 13, the bottom left panel shows a similar calculation for a lens NAof 0.7. Interestingly, while the extreme left and right edges of the pattern are more filled out for the higher NA, the tab at the center of the bottom feature

is less well defined at the higher NA. This is largely because this feature requires higher spatial frequency components in the x-direction that are not optimally supplied by either the interferometric or the imaging optical exposure. This may be remedied in the top right panel which shows the results of two imaging interferometric exposures, one biased by the same w,j" = 0.5 in y and one biased by the same amount in x to provide the spatial frequencies. necessary to more satisfactorily define this feature, along with an incoherently illuminated standard optical exposure, all at a lens NA of 0.4. Clearly, the tab is better defined for this exposure. The undulation of the horizontal bars results because the lower frequency components are not present in exactly the correct amplitude and phase. These components arise from each of the imaging interferometric exposures (second term in Equation 19) as well as from the optical exposure. Since most realistic microelectronic patterns will inevitably have small features in both directions, two interferometric exposures are likely to be necessary. The middle right panel shows the result of substituting a single, low frequency interferometric exposure (at a frequency of RIP) in place of the traditional optical exposure. The result is very similar to the previous panel, but the exposure required is much simpler. Finally, the bottom right panel shows a calculation of the image for two imaging interferometric exposures using a NA = 0.7 lens along with a single interferometric exposure at hlq,. This result is almost comparable to the best possible pattern shown on the top left, but requires only three exposures and is compatible with the full complexity of microelectronic processing. These examples serve to illustrate the flexibility permitted by the combination of imaging interferometric and traditional imaging exposures. There are many ways to get to the desired result.

Very importantly, imaging interferometric exposures are not restricted to periodic arrays of structures. This is clearly demonstrated by the earlier example of imaging the non-repetitive field stop. Any arbitrary pattem can be described as a Fourier series, where the repetitive period is the exposure field. For typical ULSI scales this means that there are a very large number of Fourier components that must be included (e.g., potentially on the order of 100 million). Clearly, this is unrealistic if individual Fourier components are separately exposed; but is not a problem for imaging interferometric exposures which combine the capabilities of imaging optics to deal with large numbers of frequency components and those of interferometry to allow high spatial frequencies.

There are several possibilities for optimization which may be further explored in the context of the present invention. For example. where the total exposure is divided

into several sub-exposures, it becomes a straightforward procedure to adjust the relative intensities ofthese exposures. Further, the imaging interferometric exposures involve two (or perhaps more) optical paths and again it is possible to adjust the intensities of the optical beams in these paths. Additionally, as the last two panels discussed illustrate (Figure 13), it is sometimes advantageous to adjust the lens NA between the various sub- exposures. That is, the lens NA for the incoherent optical exposure could have been reduced to the point that it only passed the single frequency component used in the simple interferometric exposure. The two beam intensities in the interferometric exposures were taken as equal, and the intensities of each exposure were also equal for all of the imaging exposures. For the simple interferometric exposure (i.e., just two beams only, field-stop apertures in each arm), the intensity was adjusted to provide a very qualitative best fit to the desired pattern.

It remains to specify a procedure for specifying and manufacturing the masks that are needed tp define an arbitrary image. Note that this is now a series of sub-masks since different regions of frequency space require different sub-masks to form the complete image. The total number of sub-masks is determined by, inter alia, the spatial frequency content of the image, by the NAs of the optical systems used in the exposure and by the required image fidelity. The mathematics outlined above yields a functional design apparatus. However, the complexity of real ULSI patterns makes this a difficult task. In principle, the number of spatial frequencies to be reproduced may be as large as the number of pixels in the image, which for a 2x3 cm2 image and a CD of 0.18 mm may be as large as 2x1010! Referring now to Figure 12, another approach is to use optics to produce the masks from an original mask that completely defines the pattern. A complete pattern mask (81) written by current mask making procedures, for example. electron-beam direct-write patterning without any resolution enhancements such as serifs, helper bars, or phase shifts, is illuminated by incoherent light. Behind the mask is a prism (82) that tilts the exiting wavefronts, similar in function to the prism in Figure 11. This introduces a bias. lvllj,a, in the spatial frequencies imaged by the optical system (lenses 33 and 34). The intensity pattern at the wafer plane is given by: Instead of imaging the wafer, this intensity pattern can be used to expose a mask blank (83) which is subsequently developed and patterned to form a submask. This is precisely the submask that may be advantageously used in the arrangement of Figure 11 to produce the required Fourier components at the wafer. It is straightforward to show that satisfying the relationship, 22 2w = wbias facilitates production of the proper spatial frequencies at the wafer plane.