US20050016446A1 - CaF2 lenses with reduced birefringence - Google Patents

CaF2 lenses with reduced birefringence Download PDF

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US20050016446A1
US20050016446A1 US10885863 US88586304A US2005016446A1 US 20050016446 A1 US20050016446 A1 US 20050016446A1 US 10885863 US10885863 US 10885863 US 88586304 A US88586304 A US 88586304A US 2005016446 A1 US2005016446 A1 US 2005016446A1
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crystal
disk
birefringence
optical
trimming
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John Abbott
David Wilcox
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Corning Inc
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Corning Inc
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    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B6/00Light guides
    • G02B6/10Light guides of the optical waveguide type
    • G02B6/12Light guides of the optical waveguide type of the integrated circuit kind
    • G02B6/12004Combinations of two or more optical elements
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B82NANOTECHNOLOGY
    • B82YSPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y20/00Nanooptics, e.g. quantum optics or photonic crystals
    • CCHEMISTRY; METALLURGY
    • C30CRYSTAL GROWTH
    • C30BSINGLE-CRYSTAL-GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
    • C30B29/00Single crystals or homogeneous polycrystalline material with defined structure characterised by the material or by their shape
    • C30B29/10Inorganic compounds or compositions
    • C30B29/12Halides
    • CCHEMISTRY; METALLURGY
    • C30CRYSTAL GROWTH
    • C30BSINGLE-CRYSTAL-GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
    • C30B33/00After-treatment of single crystals or homogeneous polycrystalline material with defined structure
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B6/00Light guides
    • G02B6/10Light guides of the optical waveguide type
    • G02B6/12Light guides of the optical waveguide type of the integrated circuit kind
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B6/00Light guides
    • G02B6/24Coupling light guides
    • G02B6/42Coupling light guides with opto-electronic elements
    • G02B6/4201Packages, e.g. shape, construction, internal or external details
    • G02B6/4204Packages, e.g. shape, construction, internal or external details the coupling comprising intermediate optical elements, e.g. lenses, holograms
    • G02B6/4214Packages, e.g. shape, construction, internal or external details the coupling comprising intermediate optical elements, e.g. lenses, holograms the intermediate optical element having redirecting reflective means, e.g. mirrors, prisms for deflecting the radiation from horizontal to down- or upward direction toward a device
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS, OR APPARATUS
    • G02B6/00Light guides
    • G02B6/24Coupling light guides
    • G02B6/42Coupling light guides with opto-electronic elements
    • G02B6/43Arrangements comprising a plurality of opto-electronic elements and associated optical interconnections ; Transmitting or receiving optical signals between chips, wafers or boards; Optical backplane assemblies
    • HELECTRICITY
    • H01BASIC ELECTRIC ELEMENTS
    • H01LSEMICONDUCTOR DEVICES; ELECTRIC SOLID STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H01L21/00Processes or apparatus adapted for the manufacture or treatment of semiconductor or solid state devices or of parts thereof
    • H01L21/70Manufacture or treatment of devices consisting of a plurality of solid state components formed in or on a common substrate or of parts thereof; Manufacture of integrated circuit devices or of parts thereof
    • H01L21/77Manufacture or treatment of devices consisting of a plurality of solid state components or integrated circuits formed in, or on, a common substrate
    • H01L21/78Manufacture or treatment of devices consisting of a plurality of solid state components or integrated circuits formed in, or on, a common substrate with subsequent division of the substrate into plural individual devices
    • H01L21/82Manufacture or treatment of devices consisting of a plurality of solid state components or integrated circuits formed in, or on, a common substrate with subsequent division of the substrate into plural individual devices to produce devices, e.g. integrated circuits, each consisting of a plurality of components
    • H01L21/84Manufacture or treatment of devices consisting of a plurality of solid state components or integrated circuits formed in, or on, a common substrate with subsequent division of the substrate into plural individual devices to produce devices, e.g. integrated circuits, each consisting of a plurality of components the substrate being other than a semiconductor body, e.g. being an insulating body
    • HELECTRICITY
    • H01BASIC ELECTRIC ELEMENTS
    • H01LSEMICONDUCTOR DEVICES; ELECTRIC SOLID STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H01L27/00Devices consisting of a plurality of semiconductor or other solid-state components formed in or on a common substrate
    • H01L27/02Devices consisting of a plurality of semiconductor or other solid-state components formed in or on a common substrate including semiconductor components specially adapted for rectifying, oscillating, amplifying or switching and having at least one potential-jump barrier or surface barrier; including integrated passive circuit elements with at least one potential-jump barrier or surface barrier
    • H01L27/12Devices consisting of a plurality of semiconductor or other solid-state components formed in or on a common substrate including semiconductor components specially adapted for rectifying, oscillating, amplifying or switching and having at least one potential-jump barrier or surface barrier; including integrated passive circuit elements with at least one potential-jump barrier or surface barrier the substrate being other than a semiconductor body, e.g. an insulating body
    • H01L27/1203Devices consisting of a plurality of semiconductor or other solid-state components formed in or on a common substrate including semiconductor components specially adapted for rectifying, oscillating, amplifying or switching and having at least one potential-jump barrier or surface barrier; including integrated passive circuit elements with at least one potential-jump barrier or surface barrier the substrate being other than a semiconductor body, e.g. an insulating body the substrate comprising an insulating body on a semiconductor body, e.g. SOI
    • HELECTRICITY
    • H01BASIC ELECTRIC ELEMENTS
    • H01LSEMICONDUCTOR DEVICES; ELECTRIC SOLID STATE DEVICES NOT OTHERWISE PROVIDED FOR
    • H01L31/00Semiconductor devices sensitive to infra-red radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation and adapted either for the conversion of the energy of such radiation into electrical energy or for the control of electrical energy by such radiation; Processes or apparatus peculiar to the manufacture or treatment thereof or of parts thereof; Details thereof
    • H01L31/0248Semiconductor devices sensitive to infra-red radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation and adapted either for the conversion of the energy of such radiation into electrical energy or for the control of electrical energy by such radiation; Processes or apparatus peculiar to the manufacture or treatment thereof or of parts thereof; Details thereof characterised by their semiconductor bodies
    • H01L31/0352Semiconductor devices sensitive to infra-red radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation and adapted either for the conversion of the energy of such radiation into electrical energy or for the control of electrical energy by such radiation; Processes or apparatus peculiar to the manufacture or treatment thereof or of parts thereof; Details thereof characterised by their semiconductor bodies characterised by their shape or by the shapes, relative sizes or disposition of the semiconductor regions
    • H01L31/035236Superlattices; Multiple quantum well structures
    • H01L31/035254Superlattices; Multiple quantum well structures including, apart from doping materials or other impurities, only elements of Group IV of the Periodic System, e.g. Si-SiGe superlattices

Abstract

The invention is directed to the trimming and grinding of disks to make lens blanks and/or lenses for lithographic stepper camera optical systems, and in particular to disks made of calcium fluoride (CaF2), metal fluorides of general formula MF2 where M is calcium, magnesium, barium and strontium, and other materials suitable for use in optical systems

Description

    PRIORITY
  • [0001]
    This application claims the priority of U.S. Provisional Application No. 60/489,321, filed Jul. 21, 2003 and titled “CaF2 LENSES WITH REDUCED BIREFRINGENCE”.
  • FIELD OF THE INVENTION
  • [0002]
    The invention is directed to the trimming and grinding of disks to make lens blanks and/or lenses for lithographic stepper camera optical systems, and in particular to disks made of calcium fluoride (CaF2), metal fluorides of general formula MF2 where M is calcium, magnesium, barium and strontium, and other materials suitable for use in optical systems
  • BACKGROUND OF THE INVENTION
  • [0003]
    CaF2 is used for lenses in short wavelength lithographic systems which require the lenses to have a high transmission at these wavelengths. For example, lithographic systems operating at 157 nm and 193 nm may require the use of CaF2 lenses in place of high purity fused silica lenses (“HPFS”) lenses used at wavelengths above 200 nm because of the superior transmission properties of CaF2 at wavelengths below 200 nm.
  • [0004]
    For use in optical lithographic systems, it is important that the CaF2 disk used for the lens (or disk made of other suitable material for the wavelength utilized) used for the lens have minimal levels of birefringence and homogeneity, and, because CaF2 is crystalline, that the CaF2 disk be a single crystal, oriented in a specific direction. The birefringence (“BR”) and index homogeneity (“IH”) are determined by the thermal history of the CaF2 disk and any residual thermal stresses. In some cases the disk may be given one or more secondary annealing steps. However, even with a long and careful annealing process, there will always be some residual thermal stresses. This invention explains one method to mitigate these effects and achieve even lower levels of BR and IH.
  • [0005]
    The invention is directed to the trimming and grinding of CaF2 disks to make lens blanks and/or lenses for lithographic stepper camera optical systems. Although the examples and discussion herein focus on CaF2 disks, it is to be clearly understood that the principle behind the invention can be applied to disks of other materials, for example disks of high purity fused silica (HPFS), magnesium fluoride (MgF2) and other materials. The principle applies to wavelengths shorter than or longer than those that are currently used with CaF2 optics.
  • SUMMARY OF THE INVENTION
  • [0006]
    Using an implicit or explicit knowledge of the residual thermal stresses in a CaF2 disk, either from measurement, modeling, or experiment, the trimming and grinding of the disk to produce a CaF2 lens for short wavelength lithographic applications is optimized according to the invention to reduce the birefringence and inhomogeneity. If the final CaF2 lens has different radii of curvature R1 and R2 on each side of the lens, the choice of which face of the initial disk to associate with R1 and R2 is determined in such a way as to minimize the birefringence and index homogeneity in the finished lens. If the thickness of the lens is different from the thickness of the original disk, the choice of how much material to remove from the ‘top’ face vs. the ‘bottom’ face is determined in such as way as to minimize the birefringence and inhomogeneity of the finished disk. The determination can be done using designed experiments and/or trial & error, measurement, or modeling. This optimization of trimming and grinding will be of increasing importance as the size of the lens increases. Calculations supporting the invention assume a diameter of 300 mm, and the invention would be more essential as the diameter increased. The invention also allows the use of a shorter annealing cycle to save time and reduce the cost of the CaF2 disk, because the thermal stresses thus produced can be eliminated through appropriate trimming and grinding.
  • [0007]
    The invention is directed to a method of preparing an optical lens suitable for use in optical lithographic systems utilizing a selected wavelength of electromagnetic radiation including:
  • [0008]
    providing a disk of an optical crystal material having a selected crystallographic orientation and suitable for use at a selected wavelength of electromagnetic radiation, said disk having a top face and a bottom face and a thickness,
  • [0009]
    determining the crystal orientation of the optical crystal material at both the top and the bottom face of the disk and comparing said measured values to the selected crystal orientation.
  • [0010]
    trimming optical crystal material from one or both of said faces so as to maximize the amount of the optical material with minimum tilt relative to the selected crystal orientation.
  • [0011]
    In another embodiment, the invention is directed to a method of preparing an optical element suitable for use in optical lithographic systems utilizing a selected wavelength of electromagnetic radiation, said method comprising the steps of growing a metal fluoride single crystal according to any method known in the art and recording the temperatures during growth; determining the temperature profile within a crystal as it is being grown; determining the crystallographic orientation of the grown crystal; using the temperature profile to determine the thermal stresses within the crystal; using the thermal stress data to build a birefringence model; using the birefringence model to determine the parts of the crystal that should be trimmed away to form an optical element suitable for use in an optical lithography system; and trimming the crystal to form said optical element.
  • [0012]
    In yet another embodiment, the invention is directed to a method of preparing an optical element suitable for use in optical lithographic systems utilizing a selected wavelength of electromagnetic radiation, said method comprising the steps of selecting a disk of a single crystal material made by any method known in the art; annealing the disk by any method known in the art; recording the temperatures during annealing; determining the temperature profile within a crystal as it is being annealed; determining the crystallographic orientation of the annealed crystal; using the temperature profile to determine the thermal stresses within the crystal; using the thermal stress data to build a birefringence model; using the birefringence model to determine the parts of the crystal that should be trimmed away to form an optical element suitable for use in an optical lithography system; and trimming the crystal to form said optical element.
  • [0013]
    The invention is also directed to an optical element, for example a lens that is suitable for use in an optical lithographic system. The lens is prepared from a selected optical material suitable for use in the lithographic system by trimming material along the top and bottom faces of the element in order to minimize the birefringence of the element.
  • BRIEF DESCRIPTION OF DRAWINGS
  • [0014]
    FIGS. 1 and 2 herein are representations of prior art FIGS. 1B and 7 from U.S. Pat. No. 6,562,126 showing traditional and improved setups of a Bridgman Furnace for manufacturing CaF2 crystals.
  • [0015]
    FIG. 3 is similar to FIG. 2, but in this case illustrating the stack of crucibles in the lower furnace zone where cooling and/or annealing can occur.
  • [0016]
    FIG. 4 illustrates the calculated thermal profiles from a simulation of a 4-disk process
  • [0017]
    FIGS. 5 a and 5 b illustrate an example of optimal trimming/grinding of a disk whose temperature contours slope “down”
  • [0018]
    FIGS. 6 a and 6 b illustrate an example of optimal trimming/grinding of a disk whose temperature contours slope “up”
  • [0019]
    FIG. 7 illustrates model results of the birefringence of a cube with 0.1 MP pressure on two lateral faces, where the crystal orientation (θ, φ) is rotated about φ from 0→90 degrees and θ is constant at 0 degrees.
  • [0020]
    FIG. 8 illustrates model results of the birefringence of a cube with 0.1 MP pressure on two lateral faces, where the crystal orientation (θ, φ) is rotated about θ from 0→90 degrees and φ is constant at 45 degrees.
  • [0021]
    FIG. 9 illustrates model results: the average birefringence of a disk after trimming.
  • [0022]
    FIG. 10 illustrates calculated (using the model) and measured birefringence.
  • [0023]
    FIG. 11 illustrates calculated (using the model described herein) and measured homogeneity.
  • DETAILED DESCRIPTION OF THE INVENTION
  • [0024]
    A brief discussion of homogeneity and birefringence is useful in understanding the invention. Homogeneity, a measurement of the index of refraction, is a property of a crystal, and what is important is to have the homogeneity uniform across the crystal. Therefore one wants to maximize homogeneity (i.e., minimize inhomogeneity). Birefringence is proportional to the maximum difference of the index of refraction of two different polarizations of light passing through a crystal. Homogeneity is concerned with the average of the two different index of refraction measurements and its uniformity across the crystal. Homogeneity is measured in ppm. Perfect homogeneity is zero ppm (0 ppm).
  • [0025]
    The disks utilized in practicing the invention can be made of a single crystal optical material of general formula MF2 where M is Ca, Mg, Ba or Sr; or of formula M′F where M′ is lithium (Li) or potassium (K). The single crystal of optical material can be made by any method known in the art, for example, the Bridgeman-Stockbarger method or improved/modified versions thereof. The disks can be of selected diameter and thickness, and are formed during the crystal growing process. Alternatively, an ingot of crystal material of selected thickness and selected length can be formed and the disks cut from the ingot. The disks of the single crystal optical material can be made to have a selected orientation, for example, along the [111], [110] or [100] axis of the crystal.
  • [0026]
    The invention is directed to the trimming and grinding of CaF2 disks to make lens blanks and/or lenses for lithographic stepper camera optical systems. Although the examples and discussion herein focus on CaF2, it is to be clearly understood that the principles behind the invention can be applied to disks of other materials, for example disks of high purity fused silica (HPFS), magnesium fluoride (MgF2), barium fluoride (BaF2), strontium fluoride (SrF2), lithium fluoride (LiF), potassium fluoride (KF) and other materials. The principles apply to wavelengths shorter than or longer than those that are currently used with CaF2 optics.
  • [0027]
    The birefringence (BR) of a crystal can be optimized by judicious trimming using both BR measurement data and also an understanding of the stresses causing the BR from a model. The model can predict the BR after trimming and thus verify the trimming before it is done, either experimentally as a development tool or to augment the accuracy in production. The advantage of using the model rather than experimentally cutting up crystals, measuring the results, and optimizing based on experimental data is that the crystals are extremely valuable (>$100,000) and we are seeking to maximize the utility of the crystals and to improve them to meet even higher specifications than are currently in place. Consequently, the decision of whether to cut up a $100,000 crystal to produce one worth $200,000 needs to be done with as much information as possible.
  • [0028]
    The CaF2 crystal blanks are typically cylindrical disks. The BR which is usually measured involves transmission through the face of the disk. This can be improved by also measuring the BR horizontally across the diameter of the disk. This can be done around the entire circumferential area of the disk. This additional BR data from the circumferential measurements are combined with insight from a thermal stress model to determine how to trim the disk. The advantage of this method is that the grinding of the disk to make a lens involves the top and bottom surfaces and, by measuring the BR transversely, one can identify high BR regions at the top and bottom and grind way more from one side or the other to achieve the required thickness of the finished lens.
  • [0029]
    Prior technology would take a CaF2 disk, measure the birefringence BR and index homogeneity IH over the face of the disk, and use the disk depending on whether it appeared to meet the requirements for the lithographic stepper camera design. In some cases a more expensive design might be used to accommodate lenses which would appear to have higher BR or IH.
  • [0030]
    The advantage of the present invention is that the BR and IH of the final lens are understood to depend on how it is cut out of the disk and how the two surfaces are ground. Depending on the curvature of the contours of thermal strain, optimizing the trimming/grinding results in an improved BR and IH.
  • [0031]
    By using optimal trimming and grinding it is possible to accept larger thermal stresses and hence a faster annealing cycle. This reduces the manufacturing cost of the CaF2 disk without affecting the BR and IH in the finished lens. This “win-win” scenario is described in the paragraphs that follow. To produce a CaF2 lens of given dimensions and radii of curvature R1 and R2, with birefringence BR and index homogeneity IH within certain tolerances, and with a manufacturing process of minimal cost and maximum output, the trimming and grinding of the lenses should be optimized to accommodate the larger thermal stresses (thermal gradients) possible.
  • [0032]
    In practicing the invention, the orientation of the disk from the process is recorded. Experimentally, if one has enough disks, one can run a designed experiment and determine the BR and IH in the final lens after a given amount of material δHtop and δHbottom is trimmed from the top and the bottom of the disk and radii R1 and R2 are ground onto top & bottom. However, the number of experimental runs can be significantly reduced using computational models of the process. It is also possible to measure the BR and IH on the same disk after incremental amounts are trimmed from top and bottom, δHtop(i) and δHbottom(i), to optimize the final trimming (or to follow this procedure on a subset of disks to determine the optimum trimming for the rest). (See FIGS. 5(a) and 5(b) and the trim lines illustrated therein by numeral 10 and the arrow.) In many if not all cases the experiments will need to test whether R1, R2 should be ground onto the top or bottom surfaces respectively.
  • [0033]
    Because the thermal stresses and temperature contours may change with process conditions, if raw CaF2 disks are purchased by a lens fabricator it may be useful to have a characterization of the disk from the original manufacturer, including, but not limited to, how the disk was cut from a large ingot (as illustrated in FIG. 1) or the placement of the disk in a stacked sequence (as illustrated in FIG. 2), as well as the orientation (labeling the “top” vs. “bottom” of the disk). [Note: FIG. 3 is similar to FIG. 2, but modified to illustrate a stack of crucible in the lower part of the furnace where it can be annealed. The numerals in FIGS. 1-3 represent elements as described in U.S. Pat. No. 6,562,126 and reference should be made to this patent for their meaning.] Thus, part of this invention includes the transferring of this information from the manufacturer of the original CaF2 disk to a customer who will trim and grind the disk to optimize BR and IH. In some cases both manufacture of the disk (including, but not limited to, crystal growth, annealing, and measurement of the initial disk) as well as trimming and grinding of the disk to make the final lens will be done by a single company, and again this invention notes that an improved BR and IH can be achieve by sharing of information between the disk manufacturing step and the lens-fabrication step.
  • [0034]
    FIG. 4 illustrates the thermal profiles from a simulation of a 4-disk process. There would be a similar variation in 4 disks cut from a single large ingot, or in a setup with 10 disks as shown in FIG. 6 b.
  • [0035]
    FIG. 5 and FIG. 6 show alternatives for trimming and grinding a convex curve to one face of a disk while leaving the other face plane. A different BR and IH distribution in the final lens will result, depending on whether the convex curve is ground from the upper or lower surface and how much is trimmed from the upper and lower surface. The BR and IH distribution will also depend on the shape of the temperature contours and hence will be different for the two disks shown in FIG. 5 and FIG. 6. The reference numeral 10 and the arrow indicate the trim lines. The material within the trim lines defines the trimmed disk of material, the trimmed material being outside the trim lines.
  • [0036]
    Once the crystal orientation through the disk is known, the optimum trimming may be adjusted so as to maximize the amount of crystal with minimum tilt relative to the desired orientation. It is known that the BR of a CaF2 crystal depends on orientation and that for crystals grown for a [111] orientation a small deviation can have a significant impact on BR. If the crystal orientation is measured for both top face and bottom face of the crystal, the strategy would be to grind away material for the convex surface from the side whose orientation as one moves from the center to the outside tilts the furthest from what is desired. There can be a benefit to this preferential trimming for other orientations (such as [100]) as well. For example, at 157 nm the stress birefringence is aggravated by so-called ‘intrinsic birefringence’ and the intrinsic birefringence for a [100] crystal may be optimized by selectively grinding away a curvature to reduce the amount of crystal tilted away from [100].
  • [0037]
    This trimming process could be done in two or more steps. First, the flat faces of the disk would be trimmed so that the axial centerline of the disk is more closely aligned with the measured crystal orientation. Second, the optimum trimming process described above is applied to the disk, yielding a lens blank with improved crystal orientation. In some cases the initial trimming to align the crystal orientation can be further optimized if the orientation varies slightly across the crystal face, by optimizing a figure of merit including, for example, the cylindrical geometry and the eventual radii of curvature to be ground.
  • [0038]
    Details above which use a ‘convex’ curvature as an example apply equally well to concave surfaces, making the necessary changes.
  • [0039]
    In addition to ‘trimming’ and ‘grinding’ the top and bottom surfaces, it may also be that the BR and IH can be significantly reduced on smaller pieces by cutting the disk in half or into quadrants. This kind of cutting is destructive compared to incremental trimming of the crystal and calculations of stress within the crystal can ensure that this cutting is optimized without costly experiments.
  • EXAMPLE
  • [0040]
    Any crystal growing and/or annealing process known in the art can be used in conjunction with the invention; for example, the processes described in U.S. Pat. Nos. 6,395,657 B2; 6,309,461 B1; 6,562,126 B2; 6,332,922 B1; 6,620,347; 6,238,479 B1; and other patent known to one skilled in the art that describes the growth and/or annealing of metal fluoride single crystals. During the growth and/or annealing process temperature distributions are recorded and used as described below. This data is then use to determine how a crystal will be trimmed to produce one suitable for lithographic use, particularly <200 nm lithography.
  • [0041]
    The invention uses a sequence of models. The first is the Thermal Stress Model in which one calculates stress from thermal gradients present during a crystal growing and/or annealing process, whichever is the last. Thermal stresses can be “frozen” in a crystal as the temperature is lowered during the cooling portion of a crystal growing or annealing cycle, and the stresses give rise to birefringence. In addition, the data obtained will depend on the crystal orientation.
  • [0042]
    The Thermal Stress Model for CaF2 described herein was obtained using FLUENT software (Fluent, Inc., Lebanon, N.H.) that is used to determine the temperature distribution (profile) within the crystal as it is being grown or annealed. The software enables one to form a detailed Thermal Model of a full growth cycle or of an annealing cycle. It generates a transient, axis-symmetric model of approximately 30,000 nodes and can depict the radiation heat transfer in a furnace, including metal fluoride properties, for example, CaF2 properties. The data so obtained can be saved by computer as a temperature profile of the growing and/or annealing process.
  • [0043]
    The temperature profile is used to determine the thermal variations within the crystal as it is being grown or annealed. Temperature variations give rise to thermal stresses. Thermal stresses are calculated a Cij matrix as shown below for a CaF2 crystal. In the matrix “σ” represents normal stress, “τ” represents shear stress, “ε” represents normal strain, “y” represents shear strain, “ΔT” is the temperature minus a selected reference temperature (typically the average temperature during the thermal process), and “α” is the coefficient of thermal expansion.
    Stress Stress/Strain Tensor Strain
    { σ xx σ yy σ zz τ xy τ yz τ xz } = [ C 11 C 12 C 12 0 0 0 C 12 C 11 C 12 0 0 0 C 12 C 12 C 11 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44 ] { ɛ xx - α · ΔT ɛ yy - α · ΔT ɛ zz - α · ΔT γ xy γ yz γ xz }
  • [0044]
    CaF2 has three (3) elastic constants (C11, C12, C44). For an isotropic material C44=½ (C11-C12). (CaF2 is an anisotropic material. The model can be used with either isotropic or anisotropic materials.) As the crystal orientation is shifted, the “Cij matrix” is transformed.
  • [0045]
    Once the thermal stress data has been obtained, the data is used to build the Birefringence Model, calculating the birefringence and index homogeneity from the stresses. This model building and the calculations are carried out using ANSYS software (ANSYS Inc., Canonsburg, Pa.). The ANSYS software, which does the Cij matrix calculations, calculates the stresses from the temperature results from FLUENT. The results are dependent on the wavelength of light being used and the crystal orientation. The ANSYS software enables one to model anisotropy, stress relaxation and other parameters. It can also perform thermal analysis such as during the annealing process, but not during the growth process. The ANSYS software also allows for arbitrary crystal orientation and anisotropy.
  • [0046]
    Birefringence and homogeneity are calculated using the following ΔB (change in birefringence) matrix equation where ΔBij gives the photoelastic effect and ΔBxx=Δ(1/n2 xx) for uniaxial stress, σ(bar) is the average sigma through the crystal, and “n” is the index of refraction. The stress-optic properties of CaF2 are defined by three stress-optic coefficients q11, q12 and q44. As the crystal orientation is shifted the “q-matrix” is transformed. { Δ B xx Δ B xy Δ B zz Δ B xy Δ B yz Δ B xz } = [ q 11 q 12 q 12 0 0 0 q 12 q 11 q 12 0 0 0 q 12 q 12 q 11 0 0 0 0 0 0 q 44 0 0 0 0 0 0 q 44 0 0 0 0 0 0 q 44 ] { σ _ xx σ _ yy σ _ zz σ _ xy σ _ yz σ _ xz }
  • [0047]
    If measurements are done along the z-axis of a crystal, then the ΔB matrix reduces to a 2×2 Δ B = [ Δ B xx Δ B xy Δ B xy Δ B yy ]
  • [0048]
    In this case the birefringence is proportional to the difference of the eigenvalues, that is, BR˜|δnx−δny|; and H is proportional to the sum of the eigenvalues, that is, H˜½(δnx+δny).
  • [0049]
    FIG. 7 illustrates the birefringence of a cube with uniform pressure on two lateral faces so the σx+constant=0.1 MPa. The BR is measured along a vertical path (z-axis), the pressure is along the x-axis resulting in σx=0.1 and the crystal orientation is θ=(0, φ, where φ is at 0, 45 and 90 degrees as illustrated. FIG. 8 shows that the birefringence goes through a minimum at 45 degrees.
  • [0050]
    FIG. 8 is similar to FIG. 7, illustrating the birefringence of a cube with uniform pressure on two lateral faces, except that in FIG. 8 φ is held constant at 45 degrees and θ is rotated from 0→90 degrees. FIG. 9 shows that minimum birefringence occurs at θ=54.74 degrees. As in the case with FIG. 7, FIG. 8 illustrates that the birefringence varies as the crystal orientation shifts from <100> to <111> to <110>. Minimum birefringence occurs when measured alone the <111> direction. In FIG. 8 the inserts designated <100>, <111> and <110> illustrate the birefringence in a crystal where the darkest areas have the lowest birefringence. As one can see from the illustration the <111> orientation> has the lowest birefringence.
  • [0051]
    FIG. 10 illustrates the calculated and measured birefringence for a crystal oriented in the [100], [110] and [111] directions. As one can see from the illustrations, the same thermal profile produces different birefringence patterns depending on how the crystal is oriented. It should also be noted that the magnitude of the birefringence also varied and the trend is captured by the model. In both model and measurement, the lowest birefringence is denoted by the color blue (numeral 20 in the Figures), intermediate values by green and yellow (numeral 30) and the highest values by red (numeral 40)
  • [0052]
    The birefringence measurements, such as those in FIG. 10, were made using a Hinds EXICOR® 450AT instrument (Hinds Corporation, Hillsboro, Oreg.). Actual measurement data and the model results were originals done in color using the standard Hinds Corporation Color Scale with blue representing areas of low birefringence and red representing areas of high birefringence. When the color figures are viewed as black-and-white reproductions it is best to observe the patterns which will be similar between the color and black-and-white copies. However, in black-and-white reproductions the areas represented by blue and red, low and high birefringence, respectively, will appear dark and areas of intermediate birefringence, represented by yellow in the color figures, will appear as light. FIG. 12 illustrates calculated (using the model) and measured index homogeneity.
  • [0053]
    Having generated a “picture” of the birefringence and index homogeneity using the software described above, one can then determine how best to trim a crystal or disk to obtain maximum performance with minimum birefringence. That is, the data will instruct the user where, on the top and/or bottom face, to trim and how much trimming will be required.
  • [0054]
    Using the method described above, the birefringence and index homogeneity of CaF2 crystals are modeled as a function of annealing conditions and crystal orientation using several CaF2 samples. FIG. 4 is an illustration of the temperature contours near the annealing point of the disk samples. Calculation of the effect of trimming a cylindrical CaF2 crystal was done using the model and thermal gradients of FIG. 4.
  • [0055]
    The resulting average birefringence as a function of the amount trimmed from the top and the bottom was modeled and is shown in FIG. 9. In this example the original cylindrical crystal is approximately 67.5 mm thick. The birefringence of the crystal trimmed to 47.5 mm is approximately ½ of that of the original crystal. As shown in FIG. 9, a lower birefringence results when more material is trimmed from the bottom of the crystal disk than when material is trimmed from the top of the crystal disk. This occurs because the bottom experiences larger thermal gradients and hence a larger residual stress occurs in the bottom of the crystal. FIG. 6 shown that after trimming 20 mm of material from the top of the disk the birefringence is 0.0902 and that after trimming 20 mm of material from the bottom of the disk the birefringence is 0.0723. Lower values of birefringence (units nm/cm) and index homogeneity (units ppm) are desired and hence in this example trimming from the bottom is preferred The difference between top and bottom trimming illustrated in FIG. 9 approximately 25% and is significant because is can enable meeting the stringent specifications required in the microlithography application.

Claims (11)

  1. 1. A method of preparing an optical lens suitable for use in optical lithographic systems utilizing a selected wavelength of electromagnetic radiation, said method comprising the steps of:
    providing a disk of an optical crystal material having a selected crystallographic orientation and suitable for use at a selected wavelength of electromagnetic radiation, said disk having a top face and a bottom face and a thickness,
    determining the crystal orientation of the optical crystal material at both the top and the bottom face of the disk and comparing said measured values to the selected crystal orientation,
    trimming optical crystal material from one or both of said faces so as to maximize the amount of the optical material with minimum tilt relative to the selected crystal orientation.
  2. 2. The method according to claim 1, wherein one of said faces is flat and one of said faces is convex.
  3. 3. The method according to claim 2, therein the optical material of the flat face is trimmed so that the axial centerline of the disk is closely aligned with the measured orientation of the crystal.
  4. 4. The method according to claim 2, wherein optical material is removed from the convex face along the side of the convex face whose orientation, in the direction from the center of the disk to the perimeter of the disk, tilts furthest from the selected crystal orientation.
  5. 5. The method according to claim 1, wherein said disk is a single crystal of a metal fluoride material of formula MF2, and M is selected from the group consisting of calcium, barium and strontium, and mixtures of two or more of the foregoing in any proportion.
  6. 6. A method of preparing an optical element suitable for use in optical lithographic systems utilizing a selected wavelength of electromagnetic radiation, said method comprising the steps of:
    growing a metal fluoride single crystal according to any method known in the art and recording the temperatures during growth;
    determining the temperature profile within a crystal as it is being grown;
    determining the crystallographic orientation of the grown crystal;
    using the temperature profile to determine the thermal stresses within the crystal;
    using the thermal stress data to build a birefringence model;
    using the birefringence model to determine the parts of the crystal that should be trimmed away to form an optical element suitable for use in an optical lithography system; and
    trimming the crystal to form said optical element.
  7. 7. The method according to claim 6, wherein the metal fluoride has the formula MF2, an M is selected from the group consisting of calcium, barium and strontium, and mixtures of two or more of the foregoing in any proportion.
  8. 8. The crystal according to claim 6, wherein the grown crystal undergoing trimming to form an optical element is in the form of a disk formed in the growth process or a disk cut from a single crystal ingot.
  9. 9. A method of preparing an optical element suitable for use in optical lithographic systems utilizing a selected wavelength of electromagnetic radiation, said method comprising the steps of:
    selecting a disk of a single crystal material made by any method known in the art;
    annealing the disk by any method known in the art;
    recording the temperatures during annealing;
    determining the temperature profile within a crystal as it is being annealed;
    determining the crystallographic orientation of the annealed crystal;
    using the temperature profile to determine the thermal stresses within the crystal;
    using the thermal stress data to build a birefringence model;
    using the birefringence model to determine the parts of the crystal that should be trimmed away to form an optical element suitable for use in an optical lithography system; and
    trimming the crystal to form said optical element.
  10. 10. The method according to claim 9, wherein the metal fluoride has the formula MF2, an M is selected from the group consisting of calcium, barium and strontium, and mixtures of two or more of the foregoing in any proportion.
  11. 11. The crystal according to claim 9, wherein the grown crystal undergoing trimming to form an optical element is in the form of a disk formed in the growth process or a disk cut from a single crystal ingot.
US10885863 2003-07-23 2004-07-07 CaF2 lenses with reduced birefringence Abandoned US20050016446A1 (en)

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KR20060040711A (en) 2006-05-10 application

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Owner name: CORNING INCORPORATED, NEW YORK

Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:ABBOTT, III, JOHN S.;WILCOX, DAVID I.;REEL/FRAME:015558/0310;SIGNING DATES FROM 20040701 TO 20040707