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EP1994446A1 - Lithographie par modulateur spatial de lumière: impression en dessous de k1 = 30 sans traitement par correction de proximite optique prealable - Google Patents

Lithographie par modulateur spatial de lumière: impression en dessous de k1 = 30 sans traitement par correction de proximite optique prealable

Info

Publication number
EP1994446A1
EP1994446A1 EP07703561A EP07703561A EP1994446A1 EP 1994446 A1 EP1994446 A1 EP 1994446A1 EP 07703561 A EP07703561 A EP 07703561A EP 07703561 A EP07703561 A EP 07703561A EP 1994446 A1 EP1994446 A1 EP 1994446A1
Authority
EP
European Patent Office
Prior art keywords
workpiece
kernel
image
slm
correction
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP07703561A
Other languages
German (de)
English (en)
Inventor
Torbjörn Sandström
Igor Ivonin
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Micronic Laser Systems AB
Original Assignee
Micronic Laser Systems AB
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Micronic Laser Systems AB filed Critical Micronic Laser Systems AB
Publication of EP1994446A1 publication Critical patent/EP1994446A1/fr
Withdrawn legal-status Critical Current

Links

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
    • G03F7/70425—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
    • G03F7/70433—Layout for increasing efficiency or for compensating imaging errors, e.g. layout of exposure fields for reducing focus errors; Use of mask features for increasing efficiency or for compensating imaging errors
    • G03F7/70441—Optical proximity correction [OPC]
    • 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
    • G03F7/70—Microphotolithographic exposure; Apparatus therefor
    • G03F7/70216—Mask projection systems
    • G03F7/70283—Mask effects on the imaging process
    • 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
    • G03F7/70283—Mask effects on the imaging process
    • G03F7/70291—Addressable masks, e.g. spatial light modulators [SLMs], digital micro-mirror devices [DMDs] or liquid crystal display [LCD] patterning devices
    • 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
    • G03F7/70308—Optical correction elements, filters or phase plates for manipulating imaging light, e.g. intensity, wavelength, polarisation, phase or image shift
    • 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
    • G03F7/70383—Direct write, i.e. pattern is written directly without the use of a mask by one or multiple beams
    • G03F7/704—Scanned exposure beam, e.g. raster-, rotary- and vector scanning
    • 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
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/70491—Information management, e.g. software; Active and passive control, e.g. details of controlling exposure processes or exposure tool monitoring processes
    • G03F7/70508—Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus
    • 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
    • G03F7/70483—Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring
    • G03F7/7055—Exposure light control in all parts of the microlithographic apparatus, e.g. pulse length control or light interruption
    • G03F7/70566—Polarisation control
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L21/00—Processes or apparatus adapted for the manufacture or treatment of semiconductor or solid state devices or of parts thereof
    • H01L21/02—Manufacture or treatment of semiconductor devices or of parts thereof
    • H01L21/027—Making masks on semiconductor bodies for further photolithographic processing not provided for in group H01L21/18 or H01L21/34
    • H01L21/0271—Making masks on semiconductor bodies for further photolithographic processing not provided for in group H01L21/18 or H01L21/34 comprising organic layers
    • H01L21/0273—Making masks on semiconductor bodies for further photolithographic processing not provided for in group H01L21/18 or H01L21/34 comprising organic layers characterised by the treatment of photoresist layers
    • H01L21/0274—Photolithographic processes
    • H01L21/0276—Photolithographic processes using an anti-reflective coating

Definitions

  • a method and device with a reduced field of interaction which simplifies and reduces the need for optical proximity correction (OPC).
  • OPC optical proximity correction
  • the present disclosure teaches a method to project an optical image of an original (typically a pattern on a photomask or a spatial light modulator (SLM)) onto a workpiece with extremely high resolution and fidelity given the constraints of the optics. Used with masks, it allows the mask to use less so called optical proximity correction (OPC), which pre-distorts or pre-adjusts a pattern to correct for optical deterioration that is normally found near the resolution limit. Therefore, patterns can be printed with the disclosed technology down to the resolution limit with high fidelity and only simple OPC processing or no OPC processing at all. With spatial light modulators (SLMs) as the image
  • CONFIRMATION COPY source e.g., in mask pattern generators and direct-writing lithographic printers
  • the disclosed technology allows the same simplification.
  • the SLM is driven by data from a data path and with the disclosed technology the data path need not apply OPC-like adjustments to the pattern data, or to apply less OPC adjustments, thereby simplifying the data channel.
  • the disclosed technology is a modification of a partially coherent imaging system, and many partially coherent systems could use and benefit from the disclosed technology: e.g., photosetters, visual projectors, various optical copying machines, etc.
  • the disclosed technology also works for image capture devices that use partially coherent light: optical inspection systems, some cameras, microscopes, etc.
  • a generic partially coherent projection system is shown in FIGS. la-b.
  • a projected optical image is always degraded by the projection system due to optical aberrations and to the finite wavelength of light. Aberrations can be reduced by design, but the influence of diffraction of the light due to its finite wavelength puts a limit to the resolution and fidelity that can be achieved.
  • This is well-know and many optical devices operate at the diffraction limit, e.g., microscopes, astronomical telescopes, and various devices used for microlithography.
  • the size of the features printed limit the density of features that can added to the workpiece and therefore the value that can be added to the workpiece at each step. Because of the strong economic forces towards smaller and more numerous features on the workpiece, the optics used in lithographic processes are extremely well designed and limited only be the underlying physics, i.e., diffraction.
  • Coherence in this application means spatial coherence and is a way of describing the angular subtense of the illumination of the object (the mask, SLM, etc.) in relation to the angular subtense picked up by the projection lens.
  • Incoherent in this sense means that the illumination as seen from the object has a larger angle range than what is transmitted by the projection lens. Tuning of the illumination angles has a profound influence on the image.
  • the incoherent projection gives an image that is pleasing to the eye with a gradual fall-off of the contrast as one gets closer to the resolution limit.
  • this fall- off means size errors for everything close to the resolution limit and the smallest features that can be printed with good fidelity are far larger than the resolution limit, hi photography, the optical resolution is often determined as the smallest high-contrast object features that appear with any visible contrast in the image.
  • the resolution is pragmatically determined as the smallest features that print with enough quality to be used. Since microlithographic patterns are imaged onto a high-contrast resist and the resist is further raised by the etching process, the quality in the image is almost entirely related to the placement and quality of the feature edges. Resolution is then the smallest size that, given the constraints of the process, gives acceptably small size errors ("critical dimension errors" or "CD”) and acceptably large process latitude.
  • FIGS. 1 a-b With partially coherent illumination, FIGS. 1 a-b, the angular range of the illuminator is limited to smaller than is accepted by the projection lens. This raises the useful resolution by introducing some amount of coherent "ringing" at the edges of the image. These ringing effects also affect neighboring edges and the image shows so called proximity effects: the placement of every edge depends on the features in the proximity to it.
  • the illumination angles i.e., the distribution of light in the illuminator aperture, can be tuned for higher useful resolution at the expense of more proximity effects and it becomes a trade-off between resolution and image fidelity.
  • pattern data files may be 50 Gbyte or more in size and even the transmission and storage of the files becomes a burden to the design houses and mask shops. Adding one more layer of OPC corrections for the printing of the mask in an SLM- based pattern generator would add more cost, overhead and make the lead time even longer.
  • FIG. Ia Simple partially coherent projection system with illumination and projection stops defined.
  • FIG. Ib Partially coherent projection system using reflecting objects, such as an SLM or a EUV mask.
  • FIG. Ic Partially coherent projection system using an SLM and relays in the illuminator and projection paths.
  • FIG. 2a Projection system with a pupil filter and a varying illumination function, either from a filter or from a diffractive optical element (DOE).
  • DOE diffractive optical element
  • FIG. 2b Projection system with an accessible pupil plane, and a pupil filter implemented by an absorbing, reflecting or phase-shifting binary pattern with features small enough to reflect or diffract light outside of the pupil stop.
  • FIG. 2c Projection system with immersion, an angle-dependent thin-film reflector as a polarization-selective pupil filter and a polarization filter in the illuminator.
  • FIG. 3a Showing semi-continuous functions.
  • FIG. 3b Rotationally symmetrical functions.
  • FIG. 3c Non-rotationally symmetrical function with symmetry for 0, 90
  • FIG. 4 Flow-chart of a method of optimization of the aperture functions.
  • FIG. 7 Corresponding CD linearities.
  • FIG. 9 CD linearity curves using the apertures in FIG. 8.
  • FIG. 11 CD linearity curves using the apertures in FIG. 10.
  • FIG. 12 CD linearity curves using the apertures in FIG. 10 showing the effect of defocus.
  • FIG. 13 Three features, two clear and one shifted, the aerial image through focus and the imaginary part of the E field that gives symmetry through focus.
  • FIG. 14 Three sets of features for simultaneous optimization.
  • FIG. 15 A single set of features that, if the pixels are smaller than the resolution of the optics, can be used to represent the range of possible patterns.
  • FIG. 16 A non-linear filter that corrects the residual CD linearity error.
  • FIG. 17 Flowchart of a method for fast OPC correction, working in the raster domain.
  • FIG. 18 Flowchart of a method for fast OPC correction, working in the vector domain.
  • FIG. 19a Two equivalent ways of implementing a pupil filter in the projection aperture. In FIG. 19a, the pupil filter 191 varies as a function of position in the aperture plane of the projection lens 190.
  • FIG. 19b The same effect is achieved with a filter 192 with an angle- dependent transmission in a plane where the beams are converging, here close to the image plane.
  • FIG. 20a Two ways of achieving the same intensity distribution in the illuminator aperture.
  • FIG. 20a shows a beam expander 201, 203 expanding the beam from the laser and shaping it with a transmission filter.
  • FIG. 20b shows the same laser beam dispersed with a diffractive element 205 which directs the beam energy into a spatial distribution equivalent to the one in FIG. 20a.
  • FIG. 20b Shows the same laser beam dispersed with a diffractive element 205 which directs the beam energy into a spatial distribution equivalent to the one in
  • FIG. 20a is a diagrammatic representation of FIG. 20a.
  • FIGS. 21a-c illustrate the nominal width, in nm, and the deviation from the nominal width, also in nm.
  • FIGS. 22a-f depict a simple reference pattern and one perturbed by adjacent lines.
  • FIG. 23 depicts visualizations for a ID case of object and projector functions that are integrated to give intensity in the image plane.
  • FIG. 24 depicts integration of an actual pattern, minus a reference pattern to equal a perturbation pattern.
  • FIG. 25 illustrates for a ID case selection of kernel elements having a predetermined significance.
  • FIGS. 26a-b depict an illuminator and combined illuminator/pupil functions.
  • FIGS. 27-28 illustrate the effect of pixel size on kernel values.
  • FIG. 29 depicts selection of kernel elements for an automatically or hand crafted kernel.
  • FIGS. 30a-d illustrate development of a pseudo-2D kernel from variations on a ID kernel.
  • FIG. 31 is a visualization of selecting element from four-dimensional space for a 2D kernel.
  • FIGS. 32a-c illustrate CD linearity with and without the correction.
  • FIGS. 33a-d depict non-corrected and corrected SLM pixel values for generating a line and line ends.
  • FIGS. 34a-b depict SLM pixel intensities and resulting residuals in the image plane for generating closely spaced contacts.
  • a generic projection system has been defined in FIG. Ia. It has an object 1, which can be a mask or one or several SLMs, and a workpiece 2, e.g., a mask blank, a wafer or a display device. Between them is a projection system 3 creating an image 5 of the image 4 on the object.
  • the object is illuminated by an illuminator 6.
  • the projection system consists of one or several lenses (shown) or curved mirrors.
  • the NA of the projection system is determined by the size of the pupil 8.
  • the illuminator 6 consists of an essentially non-coherent light source 7 illuminating the illumination aperture 9. Field lenses 10 and 11 are shown but the presence of field lenses is not essential for the function.
  • the imaging properties are determined by the size and intensity variation inside the illuminator aperture 9 in relation to the size of the pupil 8.
  • the term partially coherent beam indicates that the illuminator aperture is smaller than the pupil, but not infinitely small.
  • the basic projection system in FIG. Ia can be realized in many equivalent forms, e.g., with a reflecting object as shown in FIG. Ib.
  • the imaging power of the optical system can be refractive, diffractive or residing in curved mirrors.
  • the reflected image can be illuminated through a beam splitter 12 or at an off-axis angle.
  • the wavelength can be ultraviolet or extending into the soft x-ray (EUV) range.
  • the light source can be continuous or pulsed: visible, a discharge lamp, one or several laser sources or a plasma source.
  • the object can be a mask in transmission or reflection or an SLM.
  • the SLM can be binary or analog; for example micromechanical, using LCD modulators, or using olectrooptical, magnetooptical, electroabsorbtive, electrowetting, acoustooptic, photoplastic or other physical effects to modulate the beam.
  • FIG. Ic shows a more complex implementation of the basic structure of
  • FIG. Ib the principal layout of the optics for the Sigma7300 mask writer made by Micronic Laser Systems AB. It has an excimer laser 17, a homogenizer 18, and relay lenses 13 forming an intermediate image 14 between the SLM and the final lens.
  • the pupil of the final lens is normally located inside the enclosure of the final lens and difficult to access, but in FIG. Ic there is an equivalent location 15 in the relay.
  • the smallest of the relay and lens pupils will act as the system stop.
  • There is also a relay in the illuminator providing multiple equivalent planes for insertion of stops and baffles.
  • the Sigma7300 has a catadioptric lens with a central obscuration of approximately 16% of the open radius in the projection pupil.
  • ⁇ /NA is 275 nm.
  • the SLM mirror size is set by manufacturing constraints and is not important for this treatment. For mirrors above 2 micron size the 3D topography of the mirrors has no importance [3].
  • the SLM can be treated as a thin (Kirchoff) mask.
  • the pixel size in the image plane is important, as we will see, and will be determined below. The demagnification is then chosen to give the wanted pixel size for any given SLM mirror size.
  • the size of the illumination aperture and the intensity distribution inside it have a profound effect on resolution and image fidelity.
  • a ring with inner/outer diameters of 0.2/0.6 of the system pupil gives neutral imaging with a good trade-off between resolution and fidelity.
  • Other intensity distributions like a four-pole or a two-pole enhance certain features at the expense of others.
  • it is nearly always necessary to do an optical proximity correction of the printed features are below 0.5 N A/lambda.
  • the intensity distribution in the illumination aperture is optimized to support the pupil function and interact with it so as to produce good image fidelity.
  • Optimized CD linearity for 65nm node resolution is 81nm when keeping
  • FIG. 2 shows the same generic system as in FIG. Ia, with the addition of a pupil filter 21 and an illumination aperture filter 22.
  • the two filters can be described by a pupil function and an illuminator aperture function describing the transmission through the filters.
  • the pupil filter is complex, i.e., both phase and magnitude of the transmission are specified.
  • the illuminator aperture filter is an intensity filter, i.e., the phase is arbitrary.
  • the functions have a continuous or semi-continuous variation with the pupil and aperture coordinate coordinates. Continuous means the same as a continuous function, it does not have steps. However, due to manufacturing and design restrictions, the functions need to have discontinuities.
  • a continuously varying phase filter may be manufactured as a stepwise varying function. Likewise, truncation of the function at the edges of the aperture can be discontinuous. We will call such functions that approximate continuously varying functions over at least part of the area of the filter semi-continuous.
  • FIG. 3a shows the results of applying hypothetical examples of pupil and/or illuminator functions.
  • Line a is a top-hat disk function.
  • Line b a more complex function with varying transmitting and non-transmitting rings.
  • Lines c-f show a variety of semi- continuous functions.
  • Line e is a fully continuous function, while lines c and d show functions that are continuous but truncated.
  • line f shows a piecewise flat approximation of a continuous but truncated function.
  • Line f displays several interesting features: First it shows a "pile-up" close to the truncation edges at 0.10 and 0.90.
  • FIGS. 3b-c are examples of illuminator and pupil filters for 65nm node. Restriction for maximum allowed 90% side lobe intensity level (from the nominal intensity) is applied. Ten radial harmonics were used both for pupils and for the illuminator. The illuminator is represented by 60x60 grid pixels.
  • FIG. 8 is an example of optimized illuminator and non-polarized pupil for
  • FIG. 11 is an example of optimized CD linearity for 45nm node for the lens without obscuration.
  • CDmin value is similar to that in FIG. 9.
  • Fig 3c is an illuminator function that extends outside of the radius of the system aperture. This is like adding a small amount of dark-field imaging in a microscope and aids in optimizing the coherency function of the mask or SLM plane.
  • FIG. 10 is an example of optimized illuminator and non-polarized pupil for 45nm node. A final lens without obscuration is used. Compare with FIG. 8.
  • FIG. 11 is the CD uniformity in focal region.
  • the CD curves in focal plane are the CD curves in focal plane
  • the aperture stop has a transmission that varies in a more complex fashion.
  • the transmission varies in a more complex way than the simple clear ring that is used in Sigma7300.
  • One preferred embodiment has a phase that is everywhere 0 but an intensity transmission that is a continuous function of the radius.
  • Another preferred embodiment has the phase 0 and a stepwise varying transmission.
  • a third embodiment has a phase that varies in a continuous fashion
  • fifth embodiment has a phase that varies in a stepwise fashion.
  • both the transmission and the phase vary.
  • the transmission function is a combination of continuously and stepwise varying parts.
  • An eighth embodiment uses a function that combines continuously and/or stepwise varying transmission with a continuously and/or stepwise varying phase.
  • the aperture stop is at each point described by a complex number and the complex number varies continuously and/or stepwise over the area of the stop.
  • the illumination can vary over the illumination pupil.
  • This variation can be created in several ways, e.g., by an absorbing filter before the object, preferably near the illumination stop or an optically equivalent plane, or by a diffractive optical element (DOE) before, at, or after the stop.
  • DOE diffractive optical element
  • the illuminating intensity vs. angle function at the object plane has an intended variation more complicated than the simple clear ring with inner and outer sigmas of 0.20 and 0.60 used in the Sigma7300.
  • the quantity sigma, often used in lithography is the relation of a radius in the illuminator and the outer radius of the projection stop compared when they are projected to the same plane, e.g., in the plane of the projection stop.
  • the variation of the intensity in the illumination stop can be described by a continuous or stepwise function or a function with a combination of continuously and stepwise varying parts.
  • the illumination light can have a polarization direction (or more generally polarization state) that varies over the stop and optionally between different writing passes and writing modes.
  • the projection stop, or an equivalent plane can have a polarization-modifying property that varies over the surface and/or between writing passes and writing modes.
  • a Mueller matrix can change the state of polarization and the degree of polarization, thereby representing polarizers and depolarizers, as well as wave-plates and polarization rotators, as described in Azzam and Bashara "Ellipsometry and polarized light".
  • Each matrix element is a function over the area and can vary continuously or stepwise. If the projection stop is described by Mueller matrices, it is convenient to describe the illumination by Stokes vectors that represent intensity, polarization state and degree of polarization, as described in the textbook reference.
  • the variation at both projection and illumination stops can be fully rotationally symmetrical or it can be symmetrical under a rotation of 180, 90 or 45 degrees only. It can also be non-centro-symmetric with no rotation symmetry.
  • the pupil filter describes the variation in the projection lens aperture plane or an equivalent plane.
  • the illumination filter is the variation of the illumination versus angle as seen from the object, represented by an equivalent filter at the illuminator stop. It is useful to improve the printing resolution and fidelity the filters with a design for the printing case at hand.
  • the connection between the pupil functions and the printing properties is complex and can only be analyzed by means of specialized software.
  • FIGS. 17 and 18 show the structure of the optimization program. It has two parts, the image simulator and the non-linear optimization routine, wrapped in a shell program that administrates the data flow and input/output written in, for example, MATLAB.
  • the image simulation routine can be a commercial image simulator, see above, or a custom-developed routine. There are a number of known ways to compute the image, e.g., by the so-called Hopkins' method or by propagation of the mutual intensity. Commercial software packages that can calculate the printed image from the optical system include Solid-E from the company Sigma. C in Germany, Prolith from KLA and Panoramic from PanoramicTech, both in the USA.
  • the image should be computed with a simulator that is aware of high-NA effects, polarization and the electromagnetic vector nature of the light.
  • a simulator that is aware of high-NA effects, polarization and the electromagnetic vector nature of the light.
  • the optimization routine should handle constraints gracefully. The existence of multiple local optima should also be taken into account. This is no different from optimization in optical design, to give one example, and methods are known to handle these difficulties, e.g., parameter space sampling, simulated annealing, etc.
  • a textbook on the subject is Ding-Zhu Du et al. "Mathematical Theory of Optimization.”
  • the inventors have developed a self-contained code doing both image simulation and optimization in FORTRAN using the IMSL mathematical library for the optimization.
  • the imaging routine has been benchmarked against the high-NA vector model of Solid-E for accuracy.
  • the merit function is set up to fulfill some or all of the following objectives.
  • the first one is to make all lines larger than a specified limit print with no CD errors, i.e., to make the CD linearity plot flat above the limit. If all feature classes satisfy this, there is no influence between edges at a distance larger than the limit. This is a large benefit, since it limits the range of the OPC adjustments needed to make a pattern print accurately.
  • the computational load depends strongly on the range of interactions that need to be analyzed, and the objective here is to limit that range. We will call it the limit of no interaction.
  • the second objective is to make the resolution as high as possible, i.e., to make the linewidth where lines no longer print as small as possible.
  • Different criteria for the resolution can be used, e.g., when the line does not print at all or when it has a specific size error. We have been using a size error of -5 nm as the limit. Even if the pattern does not contain lines that are at the resolution limit, this objective is important because if makes all corners sharper and cleaner.
  • the third objective is to bring lines between the resolution limit and the limit of no interaction within acceptable bounds. Physics does not allow all lines to be printed perfectly and the optimal solution is a trade-off. If the limit of no interaction is allowed to be higher and the resolution limit lower, the intermediate range can be made better. Depending on the application and the tolerances it can be brought within acceptable bounds or it will need some adjustment in the data going to the SLM or to the mask writer in the case of a mask.
  • FIG. 9 shows four graphs which are the linewidth errors ("CD errors") of isolated lines (unexposed) and spaces (exposed), a dense line/space pattern with 50% duty cycle and a CD through pitch pattern with 130 nm dark features and varying pitch.
  • the lines marked with dots in FIG. 9 are "fences” that are limits outside of which the graphs are not allowed to go.
  • the merit function used in this case allows any variation inside the fences and optimizes the resolution at -5 nm error for isolated clear and dark features.
  • the pitch pattern behaves different from the other patterns, which is natural since compared to the dense pattern it has a wider line and a narrower space below 130 nm in the graph.
  • the solution space is scanned for solutions that touch the fence.
  • CD linearity curves are not monotonic ones in the presence of coherent light.
  • the optimization of CD linearity should be done at once for all CD target values and for all printing objects under consideration.
  • the knowledge of the allowed CD linearity error ⁇ ⁇ ⁇ (a) functions (the merit fences) for all CD target values a and for any objects n is the starting point. These merit fences are determined directly by the printing node requirements (i.e., by 65nm node requirements, for instance).
  • the light intensity J in the image of an object n is bilinear form of final lens pupil P and linear form of the illuminator intensity /:
  • h is illuminator intensity distribution
  • Pi is the pupil function for s o ⁇ p light polarizations
  • optical kernel forms which can be calculated by using a model of polarized light propagation in a stratified media [2,3], such as air-resist, for instance. Summation over repeating indexes k,l and m is assumed.
  • the pupils S>P P are, in general, the complex functions and asterix * means complex conjugation (c.c). The formula is simplified in the case of polarization independent pupil P:
  • CD linearity profile ⁇ (a) of an object n is determined implicitly by the equation:
  • FIG. 5 illustrates the conversion of the merit fences into the new coordinates for a given choice of illuminator and pupil functions.
  • the resolution CD m i n is determined by the positiveness of the intensity gap (W-B). See FIG. 5. Indeed, the CD linearity curves of all objects will stay within their merit fences if and only if B ⁇ J thresh ⁇ W . The sets of "white" W 1 and "black” B j points can be chosen at new merit fences to represent them. Thus, the optimization problem becomes the standard min-max problem of maximization of the intensity gap (W-B):
  • the optimization problem appears to be an iterative quadratic linear programming problem, since all intensity forms (W j , BjJ are bilinear for pupils and linear for illuminator intensity.
  • CD m i n 81nm is combined with keeping strict CD linearity at CD>240nm. The polarization pupils were used in the optimization.
  • the light intensity in the side lobes can be restricted by a fraction v ⁇ l of the minimal nominal intensity level B to guarantee the absence of spike appearance in the image. This can be done by application of additional constraints:
  • the amplitude pupils only should be used in optimization of the printing resolution at the focal plane. This is because the forms F in (2) becomes the Hermitian ones.
  • the optical transparency decreases in the optimized system. For instance, only 6% of the light (respectively to the case without any pupil) passes through the optimized system in FIGS. 6 and 7. This can be fixed by adding the additional restriction to the minimum allowed relative level of the nominal intensity. For instance, at least 20% transparency constraints were applied during the optimization shown in FIGS. 8-12.
  • FIGS. 8 and 10 The examples of self-consistency in the pupil and illuminator distributions are shown in FIGS. 8 and 10.
  • CD linearity curves can be optimized not only in the focal plane, but also in whole resist layer by adding into the optimization the additional "black” and "white” points. These additional points correspond to the image in the defocused planes, at the resist top and bottom planes, for instance.
  • FIG. 12 shows the comparison of CD linearity curves in defocused plane.
  • the nominal intensity ⁇ (W+B) tends to the value of iso-focal dose in most restrictive region of the merit fence, which is not necessarily the iso-focal dose at semi-infinite edge.
  • the bias application makes large change in nominal intensity (compare FIGS. 6 and 8) and, hence, is useful in the improvement of focal uniformity.
  • variable-transmission filter for example created by a varying thickness of an absorbing film on a substrate.
  • the phase of the filter has no importance and a filter with a varying absorber film would work.
  • the phase is important. Even variations from the intended function as small as 0.01 waves are significant and affect the optical quality of the image.
  • a varying absorber film cannot be made without phase variations.
  • a better alternative is to use a varying absorbing film and to compensate for the phase variation either in the surface of the substrate or by a second film with varying thickness.
  • the absorbing film can be made from molybdenum suicide and the variation in thickness can be created during deposition or by an etching or grinding step after deposition. If an additional varying film is used, it can be of quartz and either deposited or etched or polished to the desired thickness variation. If the phase effect is corrected in the substrate surface figure, the variation can be created by selective etching or by selective polishing. A further possibility of creating gradual phase and magnitude variations is by irradiation by energetic rays such as electrons, ions and or high-energy photons.
  • the disclosed technology may or may not be allowable to absorb the energy in an absorbing filter.
  • the heating by absorbed energy may cause the optical components to change in an unacceptable way and the absorption may in the long run change the optical properties of the absorbing film, creating a lifetime problem.
  • a different type of filter has a graded reflectivity for the light. Again, for the illuminator filter, the phase has no effect. For the projection filter, the phase must be controlled to the desired function.
  • the variable reflector can be designed by standard methods in the industry. A typical design would have two reflective dielectric stacks with a spacer with a varying spacer film.
  • the SLM the object
  • the resist the image
  • the projection filter can be placed in the accessible aperture plane or close to it.
  • Other projection systems may or may not have an accessible aperture plane.
  • lithographic steppers and scanners have aperture planes inside the incredibly delicate final lens assembly. Furthermore, putting a filter inside the lens would generate unwanted heat and/or stray light.
  • the aperture filter with a spatial variation (FIG. 19a) of the transmission can be converted to an equivalent filter with angle dependence of the transmission (FIG. 19b) and placed near one of the object or image planes.
  • FIG. 19 shows the two different types of filters and where they can be placed.
  • the filter with angle-dependent transmission (FIG. 19b) can be designed as a more complex Fabry-Perot filter. It can have more than two reflecting stacks and spacing between them.
  • the design can be made with commercial software such as Film Star from FTG Software, NJ, USA or The Essential Macleod from Thin Film Center Inc., AZ, USA.
  • the projection filter is phase sensitive and should have a well-specified phase function versus the aperture coordinate.
  • the complex function is or can be made to be stay on the real axis.
  • a further limitation is that it is positive real, i.e., the phase is everywhere constant zero degrees.
  • the filter function is then an intensity transmission in the range 0 - 100%.
  • a way to implement such a function is by a division-of-wavefront beam splitter, i.e., a pattern with areas that transmit the light and other areas that absorb or reflect it. The pattern creates diffracted orders that destroy the image unless they have high-enough diffraction angles to miss the image.
  • An image field stop is inserted before the image to block unwanted stray light outside of the image and it can also block diffracted light from the pattern on the division-by-wavefront beam splitter.
  • the design of the beam slitter has to be made with the diffraction in view and will be similar to the design of a diffractive optical element.
  • the non-diffracted light should have an intensity consistent with the desired aperture transmission function.
  • the first order diffraction should miss the image for all used illumination angles.
  • the blocking portion of the beam splitter can be a metal film (e.g., chrome), an absorbing film (e.g., MoSi), a reflective thin-film stack, or not be blocking at all: a dense pattern of phase-shifted structures can be used to modulate the transmission according to the desired aperture functions.
  • the design of the pattern can be done analytically or numerically by methods well-known in physical optics and by designers of diffractive elements.
  • the illuminator filter can also be made by a division of wavefront filter.
  • the illuminator filter is implemented as a real filter, much of the power from the light source is thrown away. We have found that it is better to distribute the light so that essentially the entire light beam from the source reaches the object, but with the desired angular distribution. This is done as shown in FIG. 20.
  • a diffractive optical element DOE
  • DOE diffractive optical element
  • a homogenizer is needed to assure that the object plane is uniformly illuminated.
  • the DOE can be placed before the homogenizer and the intensity distribution is preserved through it.
  • An example is an integrating rod
  • transmission filters above can also be implemented as reflection filters with no change in function or principle.
  • the optimization is similar to the scalar one.
  • a polarization-aware imaging routine must be used and the four polarization parameters of the Stokes vector are allowed to vary as functions of the illuminator aperture coordinate.
  • the projection aperture can be represented by a Mueller matrix at each point plus an absolute phase.
  • the Mueller matrix transforms the incoming Stokes vector in terms of intensity, degree of polarization and polarization parameters, plus it adds a phase delay to the light.
  • the imaging routine must be capable of using the light field defined as Stokes vectors, either explicitly or implicitly.
  • Polarization in the illuminator can be achieved by a division of amplitude polarizer, i.e., splitting the beam and using different polarizing filters on different parts of the beam.
  • a fly-eye integrator can have different polarizers for different fly eye elements.
  • Implementing a polarization-selective filter in the projection system is more difficult.
  • One possibility is to use different polarizing filters in different areas in the projection pupil stop.
  • a more practical way is to make use of the large spread in angles on the high-NA side of the lens and make a thin-film filter with angle dependent polarization properties. If the relative reflection of polarization states is controlled by the angle, the average reflection or transmission can be tuned with an absorbing filter.
  • nano-optical devices with oriented microstructures can be used in the aperture planes or other planes as polarizers, waveplates or polarization-dependent scatterers.
  • a plate with fine metallic needles, 50 nm or less in width, placed in the projection pupil will act as a full or partial transmission polarizer with a degree of polarization and a polarization direction that can change over the surface in a predetermined way.
  • Such operations can be implemented in high-speed programmable logic and can be pipe-lined with other data processing, i.e., they occur concurrently with the rasterization and add no overhead or pre-processing time to the job.
  • the local bitmap operations can either be pipe-lined to separate processors or done subsequently to the rasterization by the same processors.
  • the first case generates little delay
  • the second case does add significant delay, but a delay that may be acceptable given the fidelity improvement and constraints and trade-offs in the specific case.
  • the OPC pre-processing needed without the technology disclosed is much larger due to the long interaction ranges created by aggressive illumination schemes (quadrupole, dipole, etc.)
  • Several features affect every edge and the pre-processing needs to be done in the vector domain i.e., in the input data file.
  • changes in the input pattern created by the OPC pre-processing often make a new design-rule check necessary and can lead to an iterative workflow which increases the effort further.
  • the processing can still be done in the vector domain, e.g., in the data input to a maskwriter, but the OPC pre-processing workload is smaller and faster. After the optimal functions have been applied to the aperture filters, the remaining errors are small and need little adjustment, if any.
  • bitmap processing for a maskwriter or direct-writer the corrections are rather small and have a simple relation to the features inside the limit of no interaction.
  • a suitable method to do the correction is by convolution of the bitmap by a kernel that corrects for the residual errors.
  • bitmap operations have been described in relation to SLMs with negative complex amplitude in a patent application by the same applicant.
  • the bitmap operation for correcting residual CD-linearity errors need not be limited to SLMs using negative amplitude. Any bitmap representing an image can be corrected for short-range interactions in the same way.
  • bitmap operations are asymmetric between light and dark features, so that exposed and unexposed thin lines get corrected by different amounts.
  • This can be implemented by a modified convolution, where the added adjustment of a pixel is a non-linear function of the values of the neighbors, possibly also of the value of the same pixels.
  • the curves in FIG. 9 are generated from the image formed in the resist, not from the developed resist image.
  • the entire thickness of the resist is dissolved (in a positive resist, opposite negative ones) when the exposure dose is above a threshold dose at the top of the resist.
  • a real resist has a somewhat more complex behavior with non-zero optical absorption, finite contrast, geometric transport- limitation and shadowing during the development and etching, plus a range of reaction and diffusion phenomena during the post-exposure baking (chemically amplified resist).
  • thin spaces (exposed lines) are more difficult to form in the resist than lines (unexposed).
  • the optical absorption in the resist makes the space narrower towards the bottom of the resist and progressively more difficult to develop.
  • AI(x') 2*Re(E'(L)K'(L,x')JE(x)J(L,x)K(x,x')dx) (5)
  • AI(O) 2 * Re[E * (L)K' (L) - L)K(x)dx ⁇ (6)
  • ⁇ w + can be expressed as
  • ACD(W) j(MEEF(w) - ⁇ )dw (10)
  • incoherent J(xi-X 2 ) S(Xi-X 2 ) and full coherence J(Xj-X 2 ) — 1:
  • the correction magnitude may be only a fraction of a pixel and the needed relative accuracy in the computation is reduced accordingly, as illustrated in FIG. 22.
  • the pixel value can be used instead of the exact amplitude.
  • the perturbation computed is the one between the actual pattern and a reference pattern, an infinite edge.
  • the dose is set to print the infinite edge at the nominal position, i.e., the intensity is at the threshold value at the nominal edge position.
  • the pixel value is 50% the edge is intended to cut through the center of the pixel. Therefore we know the intended intensity at the center of the pixel. With a different pattern the intensity is slightly different and we can calculate the difference and correct it by changing the pixel value.
  • Vcorr V + W g Vpert
  • V co ⁇ is the corrected pixel value
  • V is the value from the rasterizer (assumed equal to the desired amplitude)
  • V pert the perturbation correction
  • I ref the intensity for the infinite edge
  • Wg is a weight factor that will be described below.
  • I pert is the change in edge intensity due to the actual pattern:
  • the perturbation I pert is calculated from the difference between the reference pattern P ref and the actual pattern P act .
  • the simple reference pattern is illustrated by FIG. 22a and the actual pattern by FIG. 22b.
  • Corresponding exposure profiles appear in FIGS. 22c and 22d.
  • the edge is where the intensity profile crosses the horizontal guide line.
  • the perturbation, in FIG. 22d moves the intensity crossing point to the left, as indicated by the vertical dashed line.
  • each computation only corrects one pixel, namely a gray pixel sitting on the edge.
  • the method has smallest errors when the pixel value is 50%, and the range of possible correction is also largest in this case. What about edges that pass through a pixel, but not through the center?
  • the SLM writer writes several passes, typically four, with offset pixels, as illustrated by FIGS. 22e and 22f.
  • the passes are offset in both x and y. For a long edge, one pass will have the edge close to the middle of the pixel. Two other passes will have pixel values around 25% and 75%.
  • the algorithm makes half of the total correction in the first case (most centered pass) and the other half is divided between the second and third case (25% and 75%).
  • a fourth pass, where the feature edge is close to the edge between two pixels, is not corrected. This weighting is uniquely determined by the grayness of the pixel and a weight factor w g (V) is used. For all fully white or black pixels w g 0 and the computation of the correction may be skipped.
  • xl, x2, yl, y2 are geometric coordinates
  • A(x,y) is the amplitude
  • H(x,y) is the coherent amplitude point spread function
  • J(xl,x2,yl,y2) is the coherence between the point (xl,yl) and (x2,y2) in the image plane.
  • the kernel K is four-dimensional and (4) contains (2*n ra n ge + I) 4 terms, a large number even for small interaction ranges n ra n g e-
  • the 4-D nature of model yields 130,000 terms for an interaction length of 600 nm.
  • the first simplification is to base an approximate kernel on the one- dimensional case (ID image analysis, the kernel is 2D).
  • ID image analysis the kernel is 2D.
  • An elegant graphical representation of one-dimensional imaging has been given by Goodman [4], We will start with the Goodman case and then generalize to two dimensions.
  • FIG. 23 reproduces
  • FIG. 24 illustrates the perturbation calculation. Removing the reference pattern, which is known in the absence of perturbation, the calculation focuses on how the presence of features in the actual pattern moves the edge of the reference pattern.
  • Numerically exercising the analysis depicted by FIGS. 23-24 leads to an optimized pupil function in FIG. 26a and a combined illuminator and pupil function in FIG. 26b. Note that at least FIG.
  • FIG. 25 shows a one-dimensional kernel that has been hand crafted. To simplify calculation, the most significant elements are selected. The kernel is surprisingly small.
  • An important step in simplifying the kernel is to select a pixel size in the image plane that maps a pixel onto the hot areas of the kernel.
  • a large pixel gives high throughput, but is prone to through-grid errors. These errors are strongly reduced by the use of multiple offset passes.
  • a large pixel size gives more errors, but a smaller kernel and the correction scheme disclosed have more power.
  • Kernel elements can be removed based on three principles: they are small enough to be approximated with zero, they are cancelled by surrounding elements of opposite signs for most realistic patterns, or several adjacent coefficients are small and can be accumulated and represented with a single element.
  • the removal of elements of insignificant magnitude is straightforward, and the pupil functions may be optimized to maximize the number of insignificant values.
  • the resulting kernel will have a small number of large elements, a sea of insignificant ones, mainly far from the origin, but there will remain a significant number of elements that are small but not insignificant.
  • To reduce the kernel further one needs to keep in mind that not all patterns are equally plausible or equally important. The most important pattern types are line-and- space patterns along the Cartesian axes.
  • Second in rank are line and space patterns aligned along 45 and 135 degrees. If these types of patterns are written well, it is very likely that lines and spaces in other angles are under tight control.
  • the reduction of the of kernel can be done by simulation of line and space figures with relevant sizes while elements are being removed, or while the value of one element is added to a neighbor for accumulation into a significant element or for cancellation. This is a numerically tedious process, but it can be fully automated and can be made to run in parallel.
  • the reduction process is highly simplified by the high degree of symmetry in the kernel and in the computation of a line- space pattern.
  • the kernel is known to be invariant under reversal of the signs of k, 1, m, and n, as well as under exchange of the x and y axes in the object plane.
  • the kernel elements can also be determined empirically by looking at how the image changes when only one pixel value is changed. In the Sigma7500, there is a camera that records the image formed by the SLM and this camera image can be analyzed in order to calculate the actual kernel elements.
  • the process of making the pseudo-kernel gives an enumeration of the elements to include, but the actual values are taken from the calculated full 2D kernel.
  • the accuracy can be somewhat further improved by a consolidation process where elements included in the pseudo-2D kernel pick up all or part of the values from their nearest-neighbors, which are non-included elements of the full kernel.
  • elements included in the pseudo-2D kernel pick up all or part of the values from their nearest-neighbors, which are non-included elements of the full kernel.
  • it is worthwhile to do a simulation or experimental optimization of the elements of the reduced kernel in order to trade between ID and 2D and between CD accuracy and CD-through-grid uniformity.
  • FIG. 32 shows CD linearity with and without the correction.
  • the optics is optimized for correction but no correction is applied
  • hi FIG. 32b the curves in FIG. 32a are corrected using the described method.
  • FIG. 33 depicts the expected favorable impact of our teachings on line-end behavior. Rasterizing an isolated line without adjustments (FIG. 33a) produces a narrower line (FIG. 33b) than intended, due to overshoot of exposure surrounding the line. Applying these teachings, the dose is adjusted (compare FIG. 33a with FIG. 33c) and the resulting line more nearly matches the designer's intent (compare FIG. 33a with FIG. 33d.) [00152]
  • FIG. 34 depicts the favorable impact of our teachings on neighboring contact points.
  • the operations are performed in the pixel domain, focusing on the gray pixels in the bitmap, which in a typical pattern is only a fraction of the pixels.
  • the processing unit could either be designed for the average processing needs in a pattern and process only the gray pixels based on a list, or it could scan through every pixel in the image an have capacity to process each one of them is necessary.
  • the latter design appears far safer since there is no risk of constipation and he logic is simpler.
  • the saving in capacity in he first case is offset by a more complex structure with queues and buffers. Is it possible to design a real-time OPC processing unit with enough processing power to calculate the correction in every pixel? Indeed, it is, using the algorithms described above and fast silicon.
  • the kernel taught above has 39 elements, which correspond to terms in (4) that can be implemented by one addition and two multiplications.
  • the resulting expression can be simplified and the average number of multiplications further reduced to approximately 1.5 per term.
  • a maskwriter with 68 nm pixel and 3 hours typical write time would need approximately 3 Gpixels per second during the writing stroke.
  • the OPC correction thus needs 112 billion additions and 176 billion multiplications per second.
  • This is well within the capacity of at least one commercially available FPGA device, the Xilinx Virtex-4, which has 512 embedded fix-point DSPs plus uncommitted gates to glue the data processing system together, altogether giving 256 billion additions and 256 billion multiplications per second.
  • a method for performing real-time pattern correction will be outlined in the following.
  • a printing system based on an SLM there is a rasterizer and certain mathematical operations on the rasterized data (described in publications and other patents and patent applications by Sandstrom at al.) that convert a vector description of the pattern to a printed pattern with high fidelity for large features.
  • These methods include creating a bitmap based on the overlap between a pixel and the feature in vector data, using a nonlinear look-up function to correct for non-linearities in the partially coherent image, converting the bitmap to account for the properties for the SLM pixel modulators, and sending the converted bitmap to the SLM. See FIG. 16.
  • the SLM can be based on phase modulation, amplitude modulation, or polarization modulation and it can be transmissive or reflective.
  • a reflective micromechanical SLM can be based on tilting mirrors or piston-action mirrors. In any case, there is a datapath and algorithms adapted to placing the edges accurately where they fall in the data, at least for large features with no proximity effects.
  • a real-time proximity correction scheme can be implemented as a perturbation correction to the already quite good data-to-image conversion provided by the data-path, SLM and optics. It need only correct the intensity (or E field) at the boundaries of the features. This means that we need to apply correction only to pixels at the edge or adjacent to it and they can be recognized by their grayness in an analog bitmap. Furthermore, we need only correct for the pattern inside the range of optical interaction, made small by the optimization of the optics.
  • FIG. 13 shows conceptually three features, two clear and one shifted by 180 degrees. It also shows the aerial image at best focus and at two focus positions on either side of best focus. If the image has good quality, the images on either side of best focus are essentially identical (lines cover each other in the figure). For this to occur, the imaginary part of the E field must be zero. The E field must be real and have a phase angle of either 0 or 180 degrees. The phase of the E-field at the edge, where the photoresist (or other light-sensitive substance) is exposed to the threshold intensity, is therefore known.
  • Equation (2) It can be only 0 or 180 degrees and we know from the data (or mask) which of the two values we have.
  • J and K we know E in the object and we know the approximate value of E at the edge in the image (either 0.5 + 0.0j or -0.5 + 0.Oj).
  • the operations are easy to compute in parallel and to pipeline, making an implementation with high capacity possible.
  • the interactions are made short by the optimization of the optical filters.
  • the interactions as functions of radius can be found from simulations using programs like Prolith or Solid-E or it can be deduced from CD linearity experiments.
  • one or several of the following operations are done: rasterization of vector data to a bitmap (possibly in a compressed format: zip, run- length encoded, etc.); adjustment of the bitmap for the physics of the SLM and optics; adjustment for process bias and long-range CD errors due to stray light, density, etch loading, etc.; sharpening of corners; removal of the effects of the finite pixel grid; sharpening of the edge acuity and adjustment of the exposure at the edges for proximity effects.
  • the method disclosed has been described for mask writing, but it could equally well be used for other applications of SLM imaging, e.g., maskless lithography, and it could be used with other types of pattern generators and maskless systems. It is also possible to use the same method to process vector mask data: rasterize, correct for the mask writer and/or the scanner, and de-rasterize back to vector data.
  • a method for printing highly accurate patterns including providing an image object, providing a workpiece, providing an illuminator illuminating the object and having an illuminator aperture function, further providing an optical projection system having in the projection pupil a pupil function and forming a partially coherent image on the workpiece, where said projection aperture function has a continuous or semi-continuous variation with the pupil coordinate.
  • an apparatus for printing highly accurate patterns comprising an image object, a workpiece, an illuminator illuminating the object and having an illuminator aperture function, an optical projection system having in the projection pupil a pupil function and forming a partially coherent image on the workpiece, where said projection aperture function has a continuous or semi-continuous variation with the pupil coordinate.
  • a method for printing highly accurate patterns including providing an image object, providing a workpiece, providing an illuminator illuminating the object and having an illuminator aperture function, further providing an optical projection system having in the projection pupil a pupil function and forming a partially coherent image on the workpiece, where the projection aperture function and the pupil function are chosen to provide good fidelity for a set of different feature types.
  • a method for design of an illuminator aperture and a matching pupil functions in a partially coherent projection system including providing a simulator for the partially coherent image, providing a description of the optical system, providing restrictions on the optical system, further performing an optimization of the image fidelity by modifying said two functions.
  • a method for printing a microlithographic pattern with reduced OPC correction above a specified interaction length including providing an illuminator aperture function, providing a pupil function, said functions being chosen to give essentially flat CD linearity for at least two and preferably a least three feature types above a linewidth essentially equal to said interaction length.
  • Yet another embodiment is a method of efficiently applying optical proximity correction using a spatial light modulator ("SLM”) for printing highly accurate patterns on a workpiece in microlithography.
  • This method may include correcting in a pixel domain a rasterized image of at least part of a feature, wherein the correction applies a four dimensional kernel with selected non-zero values to compensate for perturbations caused by optical proximity effects, whereby the number of additions and multiplications required to calculate the correction in the pixel domain, after selection of the non-zero values to include in the four dimensional kernel, are a substantially less than would be required for a full kernel.
  • the method may further include forming a partially coherent image on the workpiece of the at least part of the feature.
  • An aspect of this method is, optionally, performing the correcting in real time as pattern data is rasterized and fed to an SLM. This reduces the use of intermediate storage, as compared to a batch process, because the raster image is corrected and used without requiring persistence to non- volatile storage. Those of skill in the art will recognize that a rasterized image is likely to require much more storage than a vector image.
  • SLM spatial light modulator
  • This method may include correcting in a pixel domain a rasterized image of at least part of a feature, wherein the correction applies a kernel having selected non-zero kernel elements to compensate for perturbations caused by optical proximity effects, wherein the correction applies a four dimensional kernel with selected non-zero values to compensate for perturbations caused by optical proximity effects, whereby the number of additions and multiplications required to calculate the correction in the pixel domain, after selection of the non-zero values to include in the four dimensional kernel, are a substantially less than would be required for a full kernel.
  • the method may further include forming a partially coherent image on the workpiece of the at least part of the feature. This variation can be combined with the real time aspect described in the preceding paragraph.
  • Yet another variation on the embodiments above is a method of efficiently applying optical proximity correction for printing highly accurate patterns on a workpiece in micro lithography.
  • This method may include rasterizing at least part of a feature including assigning pixel gray values and correcting edge perturbations caused by additional features within a range of interaction from the part of the feature by applying a correction kernel to the pixel gray values. It further may include printing a microlithographic pattern on the workpiece.
  • This variation can be combined with the real time aspect applicable to the preceding embodiments.
  • Any of these embodiments extend to producing features of a semi- conductor device. In one method, a feature is patterned, developed and produced on a mask, which is, in turn, used to pattern and produce a feature on a semiconductor substrate.
  • a feature is patterned, developed and produced by direct writing to a workpiece, such as a semiconductor substrate.
  • Direct writing applications of SLM technology are described in several patent applications that name inventor Sandstrom and in several papers by Sandstrom in the field of microlithography. Direct writing has been well-described elsewhere and therefore need not be repeated here.
  • SLM-based system or, more generally, a rasterizing microlithographic printer, with appropriate logic and resources to practice the methods disclosed will be a further embodiment of this technology.
  • a subsystem of an SLM-base system or rasterizing microlithographic printer that controls the gray scaling of SLM elements is another embodiment.
  • the subsystem may include some or all of gray-scaling control logic, a datapath, an optical path and/or an SLM controlled by the control logic, all of which can be combined with any or all of the subsystems of a maskwriter or direct writer.
  • the method embodiments also can be practiced as articles of manufacture, namely computer or machine readable media impressed with logic to carry out the method embodiments.
  • the media may be rotating memory, such as magnetic or optical disks, or solid state memory, such as non-volatile updatable memory or masked memory, or volatile logic devices such as field programmable gate arrays (FPGAs) or dynamic memory of a signal processor or coupled to a processor.
  • FPGAs field programmable gate arrays

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  • Microelectronics & Electronic Packaging (AREA)
  • Power Engineering (AREA)
  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)

Abstract

L'invention concerne des procédés et des dispositifs destinés à une analyse bi-dimensionnelle d'interactions de proximité optique et de mise en forme d'un noyau efficace informatiquement à des fins de calcul rapide de réglages à effectuer. Les calculs peuvent être effectués en temps réel, l'utilisation de caractéristiques d'aide à la correction de proximité optique pouvant être réduites, ce qui permet de réaliser des économies substantielles de taille de fichiers et de nécessités informatiques.
EP07703561A 2006-02-24 2007-02-26 Lithographie par modulateur spatial de lumière: impression en dessous de k1 = 30 sans traitement par correction de proximite optique prealable Withdrawn EP1994446A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US77627506P 2006-02-24 2006-02-24
PCT/EP2007/001638 WO2007096195A1 (fr) 2006-02-24 2007-02-26 Lithographie par modulateur spatial de lumière: impression en dessous de k1 = 30 sans traitement par correction de proximite optique prealable

Publications (1)

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EP1994446A1 true EP1994446A1 (fr) 2008-11-26

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EP07703561A Withdrawn EP1994446A1 (fr) 2006-02-24 2007-02-26 Lithographie par modulateur spatial de lumière: impression en dessous de k1 = 30 sans traitement par correction de proximite optique prealable

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Country Link
EP (1) EP1994446A1 (fr)
JP (1) JP2009527911A (fr)
KR (1) KR20080106293A (fr)
WO (1) WO2007096195A1 (fr)

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Publication number Priority date Publication date Assignee Title
US20100142838A1 (en) * 2008-12-05 2010-06-10 Micronic Laser Systems Ab Gradient assisted image resampling in micro-lithographic printing
JPWO2015015749A1 (ja) * 2013-08-02 2017-03-02 株式会社ニコンエンジニアリング 露光装置
KR102847323B1 (ko) * 2019-09-06 2025-08-14 삼성전자주식회사 Opc 방법 및 그 opc 방법을 이용한 마스크 제조방법

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Publication number Priority date Publication date Assignee Title
SG139530A1 (en) * 2003-01-14 2008-02-29 Asml Masktools Bv Method of optical proximity correction design for contact hole mask
US7079223B2 (en) * 2004-02-20 2006-07-18 International Business Machines Corporation Fast model-based optical proximity correction
US6963434B1 (en) * 2004-04-30 2005-11-08 Asml Holding N.V. System and method for calculating aerial image of a spatial light modulator

Non-Patent Citations (1)

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Title
See references of WO2007096195A1 *

Also Published As

Publication number Publication date
WO2007096195A1 (fr) 2007-08-30
JP2009527911A (ja) 2009-07-30
KR20080106293A (ko) 2008-12-04

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