Classifications

• • G—PHYSICS
  • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
  • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
  • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
  • G03F7/70—Microphotolithographic exposure; Apparatus therefor
  • G03F7/70058—Mask illumination systems
  • G03F7/70125—Use of illumination settings tailored to particular mask patterns
• • G—PHYSICS
  • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
  • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
  • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
  • G03F7/20—Exposure; Apparatus therefor
  • G03F7/2022—Multi-step exposure, e.g. hybrid; backside exposure; blanket exposure, e.g. for image reversal; edge exposure, e.g. for edge bead removal; corrective exposure
• • G—PHYSICS
  • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
  • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
  • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
  • G03F7/70—Microphotolithographic exposure; Apparatus therefor
  • G03F7/70216—Mask projection systems
  • G03F7/70241—Optical aspects of refractive lens systems, i.e. comprising only refractive elements
• • G—PHYSICS
  • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
  • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
  • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
  • G03F7/70—Microphotolithographic exposure; Apparatus therefor
  • G03F7/70408—Interferometric lithography; Holographic lithography; Self-imaging lithography, e.g. utilizing the Talbot effect
• • G—PHYSICS
  • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
  • G03F—PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
  • G03F7/00—Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
  • G03F7/70—Microphotolithographic exposure; Apparatus therefor
  • G03F7/70425—Imaging strategies, e.g. for increasing throughput or resolution, printing product fields larger than the image field or compensating lithography- or non-lithography errors, e.g. proximity correction, mix-and-match, stitching or double patterning
  • G03F7/7045—Hybrid exposures, i.e. multiple exposures of the same area using different types of exposure apparatus, e.g. combining projection, proximity, direct write, interferometric, UV, x-ray or particle beam

Definitions

• the present invention relates, generally, to the use of interferometric techniques to produce repetitive stmctures during semiconductor fabrication and, more particularly, to the integration of interferometric lithography with optical lithography to produce arbitrarily complex patterns on wafers.
• VLSI very large scale integration
• 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.
• optical lithography has remained the dominant lithographic technique for manufacturing applications.
• optical lithography 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 I-line (365 nm) to 248 DUV (KrF laser).
• KrF laser Currently, 193 nm ArF laser-based steppers are being developed, continuing this historical trend.
• optical systems have been improved from numerical apertures (NA) of 0.2 to -0.6-0.7.
• EUV lithography is a promising approach based on a laser-produced plasma source and 5X reduction, aspheric, all-reflective optics with multi layer reflectors.
• 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.
• Interferometric lithography i.e., the use of the standing wave pattern produced by two or more coherent optical beams to expose a photoresist layer
• 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 Lithography: U.S. Patent No. 5,216.257, issued June 1, 1993, to Steven R.J. Brueck and Saleem H. Zaidi. entitled Overlay ofSubmicron Lithographic Features; U.S. Patent No. 5,343,292, issued August 30.
• Devine entitled Methods and Apparatuses for Lithography of Sparse Arrays of Sub-Micrometer Features , filed , by S.R.J. Brueck, An-Shiang Chu, Saleem Zaidi, and Bruce L. Draper, entitled Method for 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. Brueck, entitled Arrangement for Producing Large Second-Order Optical Nonlinearities in a Waveguide Structure Including Amorphous SI02; U.S. Patent No. 5,239,407, issued August 24, 1993.
• the limiting spatial frequency in interferometric lithography is generally regarded as ⁇ /2, where ⁇ is the laser wavelength, and the critical dimension (CD) for 1 : 1 lines and spaces is ⁇ /4.
• CD critical dimension
• k t is a function of manufacturing tolerances as well as of the optical system
• NA is the numerical aperture of the imaging optical system.
• Typical values of k 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 193 wavelength optical lithography tool are an NA of 0.6 which leads to a limiting CD of ⁇ 0.19 micrometer.
• interferometric lithography has a limiting resolution of ⁇ 0.09 micrometer.
• 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 a NA 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 Interferometric Lithography and in Jour. Vac. Sci. Tech. Bl l 658 (1992).
• interferometric and optical lithography may be combined as also described in the above patent.
• 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, but still repetitive structures.
• interferometric lithography techniques lack a well-defined synthesis procedure for obtaining a desired structure.
• 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.
• an optical system is provided which facilitates the integration of interferometric lithography and optical lithography to produce complex structures on the same workpiece, for example a semiconductor wafer.
• 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.
• 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.
• a formal parsing procedure is proposed for separating an arbitrary desired pattern into a number of specified interferometric and optical lithography exposures.
• 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.
• 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.
• Figure 1 is a 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 0.18 micrometers CD written by diffraction-limited optical lithography tools at prescribed wavelengths and NAs; 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 9 A 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;
• Figure 13 sets forth schematic examples of VLSI patterns at 0.18 micrometer CD written at a wavelength of 365 nm by a combination of interferometric lithography using the arrangement of Figure 11, and imaging optical lithography (IIL).
• IIL imaging optical lithography
• 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.
• 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 k. components of the wavevector. Mathematically, this is described in the plane of the mask as:
• P 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 desired pattern into rectangles. That is:
• a t (b,) is the extent of each rectangle in x (y)
• c, (d is the offset of the rectangle center from the coordinate origin in x (y).
• the imaging optical subsystem imposes a modulation transfer function (MTF) on the propagation of the Fourier components onto the image (wafer) plane.
• MTF modulation transfer function
• NA the numerical aperture
• ⁇ the center wavelength.
• the MTF is given by see Goodman, Introduction to Fourier Optics, 2nd Ed. (McGraw Hill, NY 1996):
• this transfer function is suitably applied to the optical electric fields before evaluating the aerial image intensity.
• the transfer function, T mct)ll is applied to each Fourier component of the intensity pattern at the mask.
• T wc ⁇ lh is applied to each Fourier component of the intensity pattern at the mask.
• T ⁇ nmh is applied to the Fourier components of the electric field at the mask and the intensity is evaluated at the wafer plane.
• optical transfer function for interferometric lithography (23) that extends to 2/ ⁇ .
• the graph of Figure 2 is drawn for a NA of 0.6; the normalization to k/k , removes any explicit dependence on ⁇ .
• the image intensity at the wafer plane is transferred to the resist, which typically exhibits a nonlinear response.
• both positive and negative tone resists are commonly used in the industry.
• 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.
• the photoresist response will be approximated as a step function.
• 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.
• 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.
• an example of prior art techniques shows the results of applying this analysis to the printing of a typical VLSI gate pattern at a 0.18 micrometer CD with optical lithography tools at 365, 248 and 193 nm (bottom to top, respectively).
• the desired pattern 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.
• an I-line optical lithography tool is not capable of conveniently writing a 0.18 micrometer CD structure (e.g., minimum resolution of ⁇ kfklNA ⁇ 0.8 X J65/.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.
• 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 of the edges and deviations from the desired structure. Even the patterns available from a 193 nm tool are far from ideal.
• 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
• the spatial frequency is given by
• the modulation transfer function for an interferometric exposure is typically unity for all k ⁇ konul, in contrast to the sha ⁇ 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 k Struktur pr
• a defined procedure for exposing a desired pattern in accordance with the present invention surrounds optical and interferometric lithographies.
• the optical lithography is primarily used for the lower frequency components
• 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).
• the left hand column shows examples of setting frequency limits.
• 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.
• FIG. 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.
• the top left panel of Figure 5 shows the image resulting from printing (incoherent imaging) only the low spatial frequency components (up to k ( ⁇ l - NA/ ⁇ ) 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).
• 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.
• the optical beam is expanded and transformed into a uniform intensity across the field size.
• 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 surrounds the diffraction effects of the aperture. From diffraction theory, these extend - 10 v /Z, into the pattern where L is the distance from the field stop to the wafer. For a practical separation distance of L ⁇ 1 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.
• 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 distance/ before first lens 33, wherein the separation between the lenses is suitably/ +/, and the wafer 32 is placed a distance/ behind second lens 34.
• the magnification of the image is given by -/ .
• 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. (cf. 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:
• M(k ⁇ .k ) is the Fourier transform of the mask transmission function and for convenience is assumed discrete.
• the summations over k y , k. are replaced by integrals in the usual fashion. Passing through the optical system imposes a modulation transfer function:
• E mask (x,y) ⁇ M(k x ,k y )T E (k x ,k y )e' ⁇ e
• ⁇ is the Fourier transform of the intensity, real for a simple transmission mask
• the primes on k x and k v ' indicate that, as a result of the squaring operation, they are composed of appropriate sums of the k x and k y of the electric field Fourier transform and extend out to
• the low frequency pattern defined by the mask can be shifted to higher spatial frequencies by splitting the optical path and introducing interferometric optics.
• 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.
• 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.
• 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 .
• interferometric optics are introduced in order to provide the high frequency bias.
• the interferometric optical system shown in Figure 7 suitably comprises a plurality
• 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.
• 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.
• 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.
• Equation (13) corresponds to the mask image modulated by the high frequency interferometric pattern.
• the resulting printed pattern will be a high spatial frequency line:space pattern, delimited at the edges by the field stop.
• the edge of the field stop is typically defined to within a distance of - ⁇ lNA 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.
• FIG. 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 ( ⁇ l/NA-4 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 13 can be rewritten to emphasize the distribution of spatial frequency contributions associated with this image, viz.:
• 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.
• Figure 10A 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.
• the full extent of available frequency space is modeled as the large circle 104 with radius k consult - 21 ⁇ , with the three filled-in circles 106. 108, and 1 10 representing the aforementioned three regions of frequency space with significant frequency content.
• 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.
• the lens optical system alone ( Figure 6) is incapable of creating the 0.9 mm period grating
• 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.
• 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 ⁇ CD in x, 5 *CD in y) are needed to reproduce the pattern (see, for example, the above discussion of Figures 1, 3, 4 and 5).
• 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 k x - and &,,-axes may vary from pattern to pattern, it is likely that two exposures will be required. The NA of ⁇ /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 k - and A: -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.
• Equation 12 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:
• I ⁇ ⁇ *-y 1 + ⁇ i , (k y -'e M'y + 2 J ⁇ i , (*;,*; " ⁇ V" ' * c «( ⁇ « ⁇ )
• Equation 17 was derived under the assumption that the field stop is sufficiently large that the Fourier components associated with M u 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 pattern to the area defined by the field stop. That is: ⁇ 2 l *.x ⁇ 2n*, v
• 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, w to makeup, 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
• the prism could be placed in front of the mask; it could be replaced by an appropriate diffraction 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.
• the top panel on the left 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.
• IIL imaging interferometric lithography
• the imaging interferometric exposure may be advantageously biased, for example at a y-spatial frequency of 0.5 by prism 71 of Figure 11.
• 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.
• the Int function returns the integer portion of the argument.
• the bottom left panel shows a similar calculation for a lens N ⁇ of 0.7.
• 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.
• 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 ⁇ / J in place of the traditional optical exposure.
• the result is very similar to the previous panel, but the exposure required is much simpler.
• 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.
• 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 pattern 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.
• 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.
• the intensity was adjusted to provide a very qualitative best fit to the desired pattern.
• 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.
• w h ⁇ wl in the spatial frequencies imaged by the optical system (lenses 33 and 34).
• the intensity pattern at the wafer plane is given by:
• this intensity pattern can be used to expose a mask blank (83) which is subsequently developed and patterned to form a submask.

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• Physics & Mathematics (AREA)
• General Physics & Mathematics (AREA)
• Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)
• Exposure Of Semiconductors, Excluding Electron Or Ion Beam Exposure (AREA)
• Preparing Plates And Mask In Photomechanical Process (AREA)

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