Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B5/00—Optical elements other than lenses
  • G02B5/08—Mirrors
• • C—CHEMISTRY; METALLURGY
  • C03—GLASS; MINERAL OR SLAG WOOL
  • C03B—MANUFACTURE, SHAPING, OR SUPPLEMENTARY PROCESSES
  • C03B19/00—Other methods of shaping glass
  • C03B19/06—Other methods of shaping glass by sintering, e.g. by cold isostatic pressing of powders and subsequent sintering, by hot pressing of powders, by sintering slurries or dispersions not undergoing a liquid phase reaction
• • C—CHEMISTRY; METALLURGY
  • C03—GLASS; MINERAL OR SLAG WOOL
  • C03B—MANUFACTURE, SHAPING, OR SUPPLEMENTARY PROCESSES
  • C03B19/00—Other methods of shaping glass
  • C03B19/09—Other methods of shaping glass by fusing powdered glass in a shaping mould
• • C—CHEMISTRY; METALLURGY
  • C03—GLASS; MINERAL OR SLAG WOOL
  • C03C—CHEMICAL COMPOSITION OF GLASSES, GLAZES OR VITREOUS ENAMELS; SURFACE TREATMENT OF GLASS; SURFACE TREATMENT OF FIBRES OR FILAMENTS MADE FROM GLASS, MINERALS OR SLAGS; JOINING GLASS TO GLASS OR OTHER MATERIALS
  • C03C10/00—Devitrified glass ceramics, i.e. glass ceramics having a crystalline phase dispersed in a glassy phase and constituting at least 50% by weight of the total composition
• • C—CHEMISTRY; METALLURGY
  • C03—GLASS; MINERAL OR SLAG WOOL
  • C03C—CHEMICAL COMPOSITION OF GLASSES, GLAZES OR VITREOUS ENAMELS; SURFACE TREATMENT OF GLASS; SURFACE TREATMENT OF FIBRES OR FILAMENTS MADE FROM GLASS, MINERALS OR SLAGS; JOINING GLASS TO GLASS OR OTHER MATERIALS
  • C03C14/00—Glass compositions containing a non-glass component, e.g. compositions containing fibres, filaments, whiskers, platelets, or the like, dispersed in a glass matrix
• • C—CHEMISTRY; METALLURGY
  • C03—GLASS; MINERAL OR SLAG WOOL
  • C03C—CHEMICAL COMPOSITION OF GLASSES, GLAZES OR VITREOUS ENAMELS; SURFACE TREATMENT OF GLASS; SURFACE TREATMENT OF FIBRES OR FILAMENTS MADE FROM GLASS, MINERALS OR SLAGS; JOINING GLASS TO GLASS OR OTHER MATERIALS
  • C03C3/00—Glass compositions
  • C03C3/04—Glass compositions containing silica
  • C03C3/06—Glass compositions containing silica with more than 90% silica by weight, e.g. quartz
• • 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
  • G03F7/708—Construction of apparatus, e.g. environment aspects, hygiene aspects or materials
  • G03F7/70858—Environment aspects, e.g. pressure of beam-path gas, temperature
  • G03F7/70883—Environment aspects, e.g. pressure of beam-path gas, temperature of optical system
  • G03F7/70891—Temperature
• • C—CHEMISTRY; METALLURGY
  • C03—GLASS; MINERAL OR SLAG WOOL
  • C03C—CHEMICAL COMPOSITION OF GLASSES, GLAZES OR VITREOUS ENAMELS; SURFACE TREATMENT OF GLASS; SURFACE TREATMENT OF FIBRES OR FILAMENTS MADE FROM GLASS, MINERALS OR SLAGS; JOINING GLASS TO GLASS OR OTHER MATERIALS
  • C03C2201/00—Glass compositions
  • C03C2201/06—Doped silica-based glasses
  • C03C2201/30—Doped silica-based glasses containing metals
  • C03C2201/40—Doped silica-based glasses containing metals containing transition metals other than rare earth metals, e.g. Zr, Nb, Ta or Zn
  • C03C2201/42—Doped silica-based glasses containing metals containing transition metals other than rare earth metals, e.g. Zr, Nb, Ta or Zn containing titanium

Definitions

• the present invention relates to substrates for mirrors for EUV lithography. Moreover, the present invention relates to substrates for mirrors for EUV lithography having an essentially periodic distribution of the thermal expansion coefficient. Furthermore, the present invention relates to a method for the production of a substrate for mirrors for EUV lithography, and to a mirror for EUV lithography.
• EUV extreme ultraviolet
• a substrate material in particular for reflective optical elements for EUV lithography, so-called zero-expansion materials are used, having a thermal expansion coefficient in the near zero range at temperatures present during lithography operation and at room temperature.
• Prime candidates are glass-ceramic materials and quartz glass doped with titanium.
• Cordierite a mineral from the silicate class of minerals, can also be used, where the thermal expansion coefficient can be influenced by adding various additives. All three material classes can be produced in such a manner that, at a temperature dependent on the actual material used, the thermal expansion coefficient, here defined as a differential for the temperature of the relative longitudinal expansion as a function of the temperature, becomes equal to zero. This temperature is also called the zero-crossing temperature. With titanium- doped quartz glass and cordierite, the zero-crossing temperature can be influenced by the content of additives, in glass-ceramic materials by recrystallization processes in strictly controlled reheating cycles.
• the thermal expansion is as small as possible in the temperature range between room temperature and the operating temperature during the lithography process.
• the tolerances for the three-dimensional profile of the optically used surfaces of the mirrors are substantially smaller than, for example, in lithography using ultraviolet radiation. It is an object of the present invention to improve already known substrates with respect to their usability as substrates for EUV mirrors.
• the object is achieved by a substrate for mirrors for EUV lithography having a mean relative longitudinal thermal expansion of not more than 10 ppb across a temperature interval ⁇ of 15°C and a zero-crossing temperature in the range between 20°C and 40°C.
• substrates having such a thermal longitudinal expansion are well suited as substrates for mirrors for EUV lithography, wherein, under operating conditions at e.g. temperatures in the range between 20°C and 40°C, the original dimensional fit has to be maintained with high precision to achieve the desired imaging properties.
• the operating conditions are determined, amongst other things, by the absorption of EUV radiation in the mirror, which can lead to a high heat load.
• Substrates having such a mean relative thermal longitudinal expansion can be obtained, for example, by combining substrate materials whose thermal longitudinal expansions are at least partially mutually compensated.
• the thermal longitudinal expansion is no more than 10 ppb across a temperature interval ⁇ of 30°C. In a further preferred embodiment, the thermal longitudinal expansion is no more than 5 ppb across a temperature interval ⁇ of 15° C.
• the above first embodiment is particularly suitable as a substrate for EUV mirrors having a particularly high heat load, as can be the case, in particular, for mirrors arranged to the front of the beam path, in particular in illumination systems.
• the substrate according to the above second embodiment is particularly well suited for mirrors that are part of the projection system of an EUV lithography apparatus. These mirrors are further back in the beam path and are thus exposed to a lower heat load. Since they are used directly for imaging structures on masks or reticles onto an element to be structured, the requirements as to the dimensional accuracy are particularly stringent.
• the substrate has a a zero-crossing temperature in the range between 28°C and 33°C.
• the object is achieved by a substrate for mirrors for EUV lithography having a volume of at least 3000 cm 3 , wherein the zero-crossing temperature averaged across any particular partial volume of up to 10 cm 3 varies by less than 2°C.
• Substrates having such zero-crossing temperature homogeneity can be manufactured by crushing, mixing and renewed melting or sintering of blanks having low homogeneity. They are particularly well suited for mirrors for EUV lithography because they allow for large and in view of geometric dimensions still thermally very stable mirrors.
• the substrate has a mean relative thermal longitudinal expansion of no more than 10 ppb across a temperature interval ⁇ of 15°C, more preferably of no more than 10 ppb across a temperature interval ⁇ of 30°C, and most preferably of no more than 5 ppb across a temperature interval ⁇ of 15°C.
• the substrate has an averaged zero-crossing temperature in the range between 20°C and 40°C, more preferably in the range between 28°C and 33°C.
• the object is achieved by a substrate having an inhomogeneous distribution of the mean thermal expansion coefficient in the direction normal to the surface of the substrate.
• the surface of the substrate refers to the surface of the substrate that is optically used by, for example, applying a reflective coating on this surface as it is further processed to a mirror.
• the inhomogeneity in the distribution of the mean thermal expansion coefficient in the direction normal to the surface of the substrate can be used to selectively adapt the substrate to the heat load to be expected during operation.
• the substrate can be combined of two or more partial substrates having different thermal expansion coefficients, or different zero-crossing temperatures. It is also possible to cut the substrate with spatial inhomogeneities from a material blank to adapt it to the heat load to be expected.
• the substrate having an inhomogeneous distribution of the mean thermal expansion coefficient has a mean relative thermal longitudinal expansion or a homogeneous distribution of the zero-crossing temperature as described above.
• the zero-crossing temperature it has proven particularly advantageous for the zero-crossing temperature to decrease in the direction normal to the surface of the substrate as the distance from the surface increases.
• the distribution of the zero-crossing temperature to the temperature distribution in the substrate to be expected under operating conditions, undesirable thermal expansions can be particularly well avoided, which would otherwise have a deleterious effect on the optical properties of an EUV mirror comprising a substrate and a highly reflective coating.
• the profile of the zero-crossing temperature can be selected across the depth in such a way that it gradually decreases in a corresponding manner as the heat load becomes smaller with increasing depth.
• the substrate comprises at least one material section of an extension of 1 centimeter or more having a higher zero-crossing temperature than the substrate material surrounding it.
• this material section is arranged at a position on the substrate at which a higher heat load is to be expected during EUV lithography than in surrounding areas.
• this material section with a higher zero-crossing temperature is arranged at the surface of the substrate so that the percentage of the EUV radiation impinging there, which is absorbed in overlying layers, such as reflective layers, as the case may be, causes as small a heat expansion as possible.
• a first material section extends across the entire surface of the substrate and is adjacent to a second material section having a lower zero-crossing temperature, also extending across the entire surface of the substrate, and such a substrate has a heating device.
• a substrate reacts like a kind of bimetal.
• the resulting deformations vary in a range of small relative thermal longitudinal expansions in the direction normal to the surface of the substrate as heat is introduced during EUV lithography.
• the heating device is arranged on the substrate surface opposite the surface on which the highest heat introduction is expected. This is often the optically used surface of the substrate.
• Such a heating device is useful on the one hand to compensate deformations caused by impinging EUV radiation during the EUV lithography process.
• selective deformation of the dimensional fit of the mirror can be caused to correct other detected imaging errors.
• the object is achieved by a substrate for mirrors for EUV lithography having an essentially periodic distribution of the zero-crossing temperature, wherein the period length in the plane of the surface of the substrate is longer than in the direction normal to the surface.
• the surface of the substrate again, refers to the optically used surface of the substrate.
• Essentially periodic distributions of the zero-crossing temperature can occur with substrate materials manufactured using the direct deposition method, in particular. Particularly frequently they can occur with titanium-doped quartz glasses. Particularly pronounced periodic variations result using direct deposition methods, for example, wherein the resulting material blank is rotated relative to the deposition device.
• the lateral distance between the maximum and minimum zero-crossing temperature in the substrate surface is as large as possible, which causes only long-wave dimensional fitting errors to be induced by any inhomogeneous thermal expansion, which are easier to correct with the aid of suitable manipulators than shorter-wave dimensional fitting errors.
• the effect can be used that in the depth below the mirror surface, the maximum and minimum zero-crossing temperatures are at a relatively short distance one below the other, so that the deformations caused by them at least partially mutually compensate each other.
• the object is achieved by a substrate for mirrors for EUV lithography comprising at least two sections arranged one on top of the other, wherein both have an essentially periodic distribution of the zero-crossing temperature and the distribution of the zero-crossing temperatures of the one section is shifted by half a period length relative to the distribution of the zero-crossing temperatures of the other section.
• the substrates for mirrors for EUV lithography have a polishing layer on their surfaces.
• the substrate surface has micro roughnesses that are so pronounced that they would propagate into a highly reflective EUV coating and would severely compromise the efficiency of this coating.
• the substrate surface can be finished so that the functionality of the reflective layer is influenced as little as possible by the substrate surface when further processed to a mirror by the application of a reflective layer.
• the object is achieved by a method for the production of a substrate for mirrors for EUV lithography, comprising the steps of:
• the object is achieved by a method for the production of a substrate for mirrors for EUV lithography, comprising the steps of:
• a desired mean zero- crossing temperature can be adjusted by selecting suitable materials and mixing ratios. If a material having a mean zero-crossing temperature in the desired range already exists, it can be homogenized with respect to the zero-crossing temperature by means of the second method.
• materials are selected having a zero-crossing temperature in the range between 20°C and 40°C, and a gradient of the relative thermal expansion as a function of the temperature with a value less than 10 ppb/K 2 .
• titanium-doped quartz glasses are selected, wherein the resulting zero-crossing temperature can be influenced very selectively by means of the titanium content.
• the object is achieved by a method for the production of a substrate for mirrors for EUV lithography having a mean relative thermal longitudinal expansion of no more than 10 ppb across a temperature interval ⁇ of 15°C, comprising the steps of:
• inhomogeneities across the entire substrate of a composite material are so small that they cannot result, for example, in undesirable roughnesses.
• an inhomogeneous distribution of the mean thermal expansion coefficient in the direction normal to the surface of the substrate can be obtained.
• materials are selected that have a zero-crossing temperature in the range between 20°C and 40°C, and a gradient of the relative thermal expansion as a function of temperature at an absolute value of less than 10 ppb/K 2 .
• titanium- doped quartz glasses are chosen on the one hand and glass-ceramic materials on the other. These two types of materials have opposed gradients of thermal expansion as a function of temperature.
• materials are preferably chosen whose zero-crossing temperatures differ by less than 2°C.
• materials with the same zero-crossing temperature are mixed with each other.
• a particularly flat profile of relative thermal longitudinal expansion as a function of temperature can be achieved by taking the different absolute values of the gradients of thermal longitudinal expansion as a function of temperature into consideration when determining the mixing ratio of the selected materials. If, for example, the gradient of thermal longitudinal expansion as a function of temperature of one material is greater than the gradient of the thermal longitudinal expansion of the material with a thermal expansion coefficient having the opposite sign, it is advantageous to add a greater percentage of the second material than of the first material.
• mixing and bonding the materials is by blending in a viscous state, in particular when titanium-doped quartz glasses are mixed with each other. If glass-ceramic materials are additionally or exclusively mixed, it can be particularly advantageous to grind the materials prior to mixing and to bond the mixture by means of sintering, so that influence can be taken on the zero-crossing temperature by means of controlled heat treatment.
• the object is achieved by a mirror for EUV lithography comprising a substrate as described above, and a reflective layer.
• the reflective layer is preferably a multilayer system. Multilayer systems are alternately applied layers of a material having a higher real part of the refractive index at the wavelength at which EUV lithography is carried out (also referred to as a spacer) and a material having a lower real part of the refractive index at the working wavelength (also referred to as an absorber), wherein an absorber-spacer pair forms a stack.
• the sequence of a plurality of stacks essentially simulates a crystal wherein the lattice planes correspond to the absorber layers, on which Bragg reflection occurs.
• the thicknesses of the individual layers as well as of the repetitive stacks can be constant across the entire multilayer system, or they can vary, depending on which reflection profile is to be achieved.
• Mirrors having one of the substrates described here have the advantage, in particular, that thermal expansion caused by EUV radiation during the lithography process and the associated heat load on the individual mirrors can be kept at a particularly low level so that there is no negative effect on the optical function of the mirrors.
• Figs. 1 a-c schematically show three embodiments of the substrate
• Fig. 2 schematically shows an embodiment of an EUV mirror
• FIG. 3 schematically shows a fourth embodiment of a substrate
• Fig. 4 schematically shows a fifth embodiment of a substrate
• Fig. 5 schematically shows a sixth embodiment of a substrate
• Fig. 6 shows thermal expansion as a function of temperature for an embodiment of the substrate according to Fig. 4;
• Fig. 7 shows the typical development of heat expansion as a function of temperature for various types of substrate materials
• Fig. 8 shows the thermal expansion as a function of temperature for two different substrate materials and for a substrate composite material manufactured therefrom;
• Fig. 9 is a graph of the gradient of thermal expansion as a function of temperature for two different substrate materials and for a substrate composite material manufactured therefrom;
• Fig. 10 shows the distribution of different zero-crossing temperatures in a material blank
• Fig. 1 1 shows a possibility of cutting a substrate from the material blank shown in Fig.
• Figs. 12a,b show a second possibility to cut a substrate from the material blank of Fig. 9;
• Figs. 13a,b show a third possibility to obtain a substrate from the material blank of Fig. 9;
• Fig. 14 shows a further embodiment of the substrate for EUV mirrors
• Fig. 15 shows a first embodiment of a method for the manufacture of substrates for
• Fig. 16 shows a second embodiment of a method for the manufacture of substrates for
• Fig. 17 shows a third embodiment of a method for the manufacture of substrates for
• Fig. 1 a schematically shows a substrate 1 for an optical element of a zero-expansion material on the basis of glass-ceramic material, titanium-doped quartz glass or cordierite.
• Glass-ceramic materials have crystals of an extension of usually less than 100 nm in a glass matrix. In certain temperature ranges, these crystals contract, while the glass matrix simultaneously expands. These two effects cancel each other out so that the thermal expansion coefficient of the glass-ceramic materials is essentially zero in this temperature range. When they are polished to obtain a dimensionally accurate fit for use as a component of a reflective optical element, there is, however, the problem that material is removed differently from the crystals than from the glass matrix. Titanium-doped quartz glass is better suited for polishing, however.
• polishing layer 2 is provided on substrate 1.
• polishing layer 2 is based on quartz glass, which can be polished as an extremely homogeneous, highly viscous liquid on very small roughnesses also on a longitudinal scale from 1 mm to 10 nm.
• quartz glass which can be polished as an extremely homogeneous, highly viscous liquid on very small roughnesses also on a longitudinal scale from 1 mm to 10 nm.
• silicon dioxide other materials well suited for polishing can also be used.
• polishing layer 2 Prior to the application of polishing layer 2 on surface 13 of substrate 1 , it is brought as close as possible to the desired final shape.
• Polishing layer 2 can be applied by means of the usual coating methods, such as chemical vapor deposition (CVD) methods, in particular plasma-based CVD methods, or physical vapor deposition (PVD) methods, in particular ion- based PVD methods.
• CVD chemical vapor deposition
• PVD physical vapor deposition
• Sol-gel methods are also possible, in particular, with a cover layer on the basis of quartz glass. If necessary, the polishing layer is polished onto the desired roughness. Any shape corrections to achieve the desired dimensionally accurate fit can be carried out, for example, by means of ion beam figuring (IBF) methods.
• IBF ion beam figuring
• FIG. 1 b A first variant of the substrate shown in Fig. 1 a is schematically shown in Fig. 1 b.
• This substrate 1 has an inhomogeneous distribution of the mean thermal expansion coefficient in the direction normal to surface 13, shown by the arrow.
• the zero-crossing temperature decreases in the direction normal to surface 13 of the substrate as the distance from surface 13 increases.
• the distribution of the zero- crossing temperature is adapted to the temperature distribution to be expected under operating conditions to avoid undesirable thermal expansions.
• Fig. 1 c schematically shows a further variant of a substrate 1 for mirrors for EUV lithography.
• Substrate 1 has a volume of more than 3000 cm 3 , wherein the zero-crossing temperature averaged across any particular partial volume 14 of a volume of up to 10 cm 3 varies about each average value by less than 2°C.
• the variant shown in Fig. 1 c of a substrate 1 can also exhibit a slightly decreasing mean zero-crossing temperature as the distance from surface 13 increases.
• Fig. 2 schematically shows an example of a mirror 3 comprising a reflective layer 4 on a substrate 1 with a polishing layer 2.
• reflective layer 4 consists of multilayer systems of alternating layers of materials having different real parts of the complex refractive index, essentially simulating a crystal with lattice planes, on which Bragg diffraction occurs.
• a material section 6 is inserted having an extension preferably slightly larger than the surface that would be illuminated by an EUV beam in an EUV lithography apparatus.
• This material section 6 has a higher zero-crossing temperature than the surrounding substrate material 5.
• a first material section 7 is provided extending over the entire surface of substrate 1 and arranged adjacent to a second material section 8 also extending across the entire surface of substrate 1 .
• material section 7 has a higher zero-crossing temperature than material section 8.
• material section 7 having the higher zero-crossing temperature is arranged on that side of substrate 1 on which a reflective layer is to be applied as it is further processed to manufacture an EUV mirror and which will thus be exposed to a greater heat load.
• the substrate can also be subdivided into three or more material sections having different zero- crossing temperatures.
• substrate 1 is subdivided into three material sections 10, 1 1 , 12, all three extending across the entire surface of the substrate.
• material section 10 has a higher zero-crossing temperature
• material section 1 1 has a moderate zero-crossing temperature
• section 12 has a low zero-crossing temperature so that the zero-crossing temperature successively decreases in the direction normal to the substrate 1 , in which material section 10 is arranged.
• material sections can be provided not extending across the entire surface.
• a special feature is that the substrate 1 thus structured behaves in an analogous fashion to a bimetal when heat is introduced.
• the magnitude of the deformation can be controlled by the temperature, wherein the temperature range that one wants to use for control is determined by the differences in the zero-crossing temperature of the two material sections 7, 8.
• a heating device 9 is provided on the surface opposite the optically used side.
• heating device 9 is composed of a plurality of individual heating elements.
• FIG. 6 The temperature behavior of the embodiment shown in Fig. 4 is shown in Fig. 6 in an exemplary manner.
• Lower material section 8 has a zero-crossing temperature of 22°C and top material section 7 has a zero-crossing temperature of 24°C.
• Both material sections 7, 8 are fixedly connected to each other by means of wringing. The result is an average thermal longitudinal expansion plotted as a medium grey curve. With an increase in temperature from 18°C to 20°C, the material of material section 8 is extended by 5 ppb and the material of the top material section 7 is shortened by 5 ppb. Depending on the size of the mirror and the thickness of the individual material sections 7, 8, this results in bending of the mirror in the nanometer range, which also results in a change in the focal length.
• the material can be based on titanium- doped quartz glass, glass-ceramic material or cordierite.
• the characteristic profile of the relative longitudinal expansion as a function of time is shown in Fig. 7 for a titanium-doped quartz glass, a glass-ceramic material and a cordierite.
• the titanium- doped quartz glass has a zero-crossing temperature of 24°C
• the glass-ceramic material has a zero-crossing temperature of 18°C
• the cordierite has a zero-crossing temperature of 21 °C.
• Both the titanium-doped quartz glass and the cordierite show a longitudinal expansion at other temperatures than the zero-crossing temperature, while the glass-ceramic material exhibits a shrinking behavior.
• the gradient is much steeper with cordierite than with the glass-ceramic material or the titanium-doped quartz glass.
• substrate base materials in particular on the basis of glass-ceramic materials and titanium-doped quartz glass, also cordierite, as the case may be, substrate materials can be created that are particularly well suited to the requirements for use as EUV mirrors.
• Titanium-doped quartz glass for example, can be cheaply manufactured in the well known manner with the usual tolerances with respect to the zero-crossing temperature.
• the zero-crossing temperature is
• the zero-crossing temperature primarily depends on the titanium content, which can be measured, for example, by means of x-ray
• the individual material samples are mixed, so that a homogeneous body having the desired zero-crossing temperature is created. This can be done, for example, by pounding or grinding the material samples into small particles and subsequent sintering. Preferably, the small material particles are blended in a hot state and thus a low-viscosity state (cf. step 203 in Fig.
• the substrate is finished (step 205 in Fig. 16) for example by cutting and polishing to final shape, coating with a polishing layer and the like.
• steps 205 in Fig. 16 the substrate is finished (step 205 in Fig. 16) for example by cutting and polishing to final shape, coating with a polishing layer and the like.
• two or more titanium-doped quartz glasses are mixed with each other, they have the same gradient of the relative thermal longitudinal expansion in a first approximation, which is about 1.6 ppb/K 2 in the case of titanium-doped quartz glasses.
• the first derivatives of the relative thermal longitudinal expansions in ppb/K are shown for two base materials, material 1 and material 2.
• the titanium-doped quartz glass material 1 has a zero-crossing
• the resulting composite material is a titanium-doped quartz glass having a zero- crossing temperature of 30°C, which also has high homogeneity of the zero-crossing temperature across the entire volume.
• this material can be crushed (cf. Fig. 15, step 101 ).
• the degree of crushing is determined, in particular, by the desired degree of homogeneity.
• the material for example, ground or pounded, is mixed and bonded, for example, by means of melting or sintering (step 103 in Fig. 15).
• the substrate can be finished (step 105 in Fig. 15).
• Glass-ceramic material or cordierite is suitable as well as titanium-doped quartz glass.
• substrates having a volume of at least 3000 cm 3 can be produced, in which the zero-crossing temperature averaged across any particular partial volume of up to 10 cm 3 varies by less than 2°C.
• Titanium-doped quartz glass on the one hand and glass-ceramic materials on the other are particularly suitable for this (cf. step 301 in Fig. 17). These at least two materials are crushed, for example, by means of grinding, and then mixed. Subsequently, they are sintered (step 303 in Fig. 17) wherein the sintering process is adapted to the requirements of the added glass-ceramic particles, since the heat behavior can be influenced by means of the heat treatment in the case of glass-ceramic material. Subsequently, the material blank is finished to a substrate (step 305 in Fig. 17).
• a composite material By choosing two materials, one of which exhibits an expansion in the range of the zero- crossing temperature and the other of which exhibits a shrinkage, a composite material can be created in which these two opposite effects partially cancel each other out so that substrates for mirrors for EUV lithography can be produced, which have an average relative thermal longitudinal expansion of no more than 10 ppb across a temperature difference ⁇ of 15°C.
• a substrate By further optimizing the material mixture, depending on the demands put on the EUV mirror to be made from the substrate, a substrate can be created that has a thermal longitudinal expansion of no more than 10 ppb across a temperature difference ⁇ of 30°C, or even has a thermal longitudinal expansion of no more than 5 ppb across a temperature difference ⁇ of 15°C.
• the thermal longitudinal expansion can be further reduced across a larger temperature range by having the zero-crossing temperatures of the materials chosen not differing excessively, preferably they differ by less than 2°C, particularly preferably, materials having the same zero-crossing temperature are selected.
• the different values of the gradients of the thermal expansion coefficients can be taken into consideration when choosing the mixing ratio of the selected materials.
• glass-ceramic material at temperatures surrounding its zero- crossing temperature, has a gradient of the relative thermal expansion as a function of temperature of about -1.7 ppb/K 2 , while with titanium-doped quartz glass it is about +1 .6 ppb/K 2 . If titanium-doped quartz glass and glass-ceramic material with the same zero- crossing temperature are selected and mixed at a ratio of 1 :1 , a composite is obtained that has a relative thermal expansion of nearly zero across a large temperature range. Only deviations from the linear behavior of the gradient of the relative thermal expansion as a function of temperature are effective, so that the material does not change its length across a large temperature range. The deviations from the linear behavior can be additionally reduced by taking the value of the gradients into consideration when determining the mixing ratio.
• Fig. 9 shows an example of a composite material in which a titanium-doped quartz glass having a zero-crossing temperature of 31 °C was mixed with a glass-ceramic material having a zero-crossing temperature of 31 °C in such a manner that 100 parts titanium-doped quartz glass were combined with 95 parts glass-ceramic material. While the titanium-doped quartz glass has a thermal longitudinal expansion of 576 ppb across the temperature range from 10°C to 40°C, and the glass-ceramic material of 612.4 ppb, the composite material only has a thermal longitudinal expansion of 5.4 ppb.
• the titanium-doped quartz glass has a relative thermal expansion of 168 ppb, the glass-ceramic material of 232.9 ppb, and the composite material of only 1.575 ppb. Since the properties of the glass-ceramic material can be destroyed by uncontrolled heating, the material made of glass-ceramic material and titanium-doped quartz glass is preferably sintered in such a way that the temperature curves, the cooling curve in particular, correspond to the manufacturing process of the glass-ceramic.
• the individual material pieces can also be sawed and polished and slightly heated, after contacting, or the contact surfaces can be treated with an alkaline solution in order to fixedly connect the individual material pieces with each other. Subsequently, the substrate is given its final shape, a polishing layer is applied, as the case may be, and this is polished to achieve as little roughness on the surface as possible which, in further processing to an EUV mirror, is provided with a reflective layer, for example a multilayer system.
• the acceptable expansion of individual material pieces can be estimated in view of the framework conditions, such as minimum and maximum temperature, to which the substrate is to be exposed, and the resulting thermal longitudinal expansions, and the acceptable resulting roughness.
• the working temperature range is 10K, which would correspond to a raw state at 22°C and an operating temperature of 32°C. It is also assumed that a relative thermal expansion of 100 ppb is reached across this temperature range and a surface deformation of 50 pm is still acceptable. Then, in a first approximation, the maximum allowable particle size can be estimated as a quotient of the acceptable surface deformation 50 pm and the relative thermal longitudinal expansion of 100 ppb, as 0.5 mm. In this case, the materials would be pounded or even ground, and subsequently sintered.
• substrates suitable as a substrate for mirrors for EUV lithography by mixing three, four or more materials.
• FIG. 10 A further approach to reduce the influence of inhomogeneous zero-crossing temperatures within a material blank is shown with reference to Figs. 10 to 14.
• This approach is particularly suitable for material blanks having an essentially periodic distribution of the zero- crossing temperature. This is the case, for example, with titanium-doped quartz glass, which can be manufactured in a cost-effective manner in the direct deposition method. It is applicable, in particular, if the resulting material blank is rotated relative to the deposition device during the deposition process. So-called boules are formed which, in a first approximation, have a cylinder shape and wherein, in a first approximation, it is assumed that the zero-crossing temperature distribution has radial symmetry.
• Fig. 10 A further approach to reduce the influence of inhomogeneous zero-crossing temperatures within a material blank is shown with reference to Figs. 10 to 14.
• This approach is particularly suitable for material blanks having an essentially periodic distribution of the zero- crossing temperature. This is the case, for example,
• FIG. 10 shows an example of the zero-crossing temperature distribution in the interior of a titanium-doped quartz glass blank in the form of a boule.
• a sectional view in the radial x direction and in z direction parallel to the rotation axis during deposition is shown. The dimensions are indicated in inches.
• the center point of the boule is on the left side of the diagram in Fig. 9.
• the distribution of the zero-crossing temperature was measured with the aid of ultrasonic waves starting only at a distance of 6 inches from the center of the boule.
• the thickness of the boule slightly exceeds 5.5 inches, wherein layers positioned at about 5.5 inches were first deposited, and the layers positioned at 0.25 inches were deposited last.
• the measured zero-crossing temperature distribution is shown as a contour line graph.
• the distribution of the zero-crossing temperatures, in a first approximation, has a periodic wave form, wherein the period is about 4 to 5 inches.
• the orientation of the mirror surface within the blank in such a manner that the period of the zero-crossing temperature distribution is as large as possible on the surface of the substrate.
• the desired average zero-crossing temperature is taken into consideration to decide whether the substrate surface is chosen along a valley or a hill or in between.
• the surface can be chosen such that the zero-crossing temperature decreases continuously as the depth increases below as large a proportion as possible of the used mirror surface, with respect to the zero-crossing temperature at the surface.
• Fig. 1 1 shows an example of how a substrate, here shown as a rectangle, could be cut from the material blank.
• the substrate is oriented in such a manner that the period length of the distribution of the zero-crossing temperature is larger on its surface O than in the direction normal to the surface.
• the minima and maxima of the distribution lie at short distances from each other which contributes to the deformations on the mirror surface being partially
• the substrate can also be composed of a plurality of material sections individually cut from the material blank.
• An example of such a substrate is shown in Figs. 12a, b.
• all three material sections, shown as rectangles R1 , R2, R3, have been cut from the material blank in such a manner that the period length in the plane of their respective surfaces is longer than in the direction normal to their respective surfaces.
• the substrate composed of the rectangles R1 , R2, R3 (cf. Fig. 12b) also fulfills this favorable condition with respect to a thermal longitudinal expansion which is as small as possible.
• the material blank was first sheared in the x direction, for example. This results in the zero-crossing distribution shown in Fig. 13b, from which subsequently the substrate is cut along the dashed lines. The period length in the then resulting surface of the substrate was increased by the shearing process and, at the same time, the period length in the direction normal to the surface was shortened in comparison to the initial material blank (cf. Fig. 13a).
• the substrate can be cut out in such a manner from material blanks having distributions of the zero-crossing temperature with particularly short period lengths across the material blank, that the period length in the plane of the surface of the substrate is as small as possible. In this case it is utilized that the contributions of the near-surface areas with different expansion behavior compensate each other effectively at exceedingly short distances in the plane of the mirror surface.
• FIG. 14 A further approach to avoid the negative influences of heat expansion, in particular with substrate materials having a periodic zero-crossing temperature distribution, is shown in Fig. 14.
• the substrate material has been subdivided into three sections A1 , A2, A3, and the sections A1 , A2, A3 have been offset with respect to each other in such a way that one section A1 , A2 has been offset by half a period length relative to each underlying section A2, A3.
• the period normal to the surface is substantially shortened to achieve better compensation of the individual areas having different zero-crossing temperatures relative to each other. While in the example shown here, three sections have been used, the effect can already be achieved with two sections, or it can be further optimized with four, five, six or more sections.

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