BACKGROUND OF THE INVENTION Optical lithography has become a key technology for the fabrication of electrical and optical integrated circuits of various kinds. Since the smallness of such circuits is mainly determined by the imaging systems of the litho- graphic devices used in the fabrication process, consider- able efforts have been spent on improving the resolution of these imaging systems.

One way to achieve higher imaging resolutions in such sys- tems is to use shorter wavelengths. At present, commer- cially available projection exposure systems with the high- est resolutions use W light of wavelengths 193 nm or 157 nm. Research and development activities already consider to enter the domain of extreme ultraviolet radiation in which "soft"X-rays are used having wavelengths of about 10 nm to 30 nm. One of the main problems encountered when using such

small wavelengths is the fact that conventional optical re- fractive components such as lenses are almost completely opaque in this wavelength range. Future X-ray projection systems are therefore likely to contain only reflective op- tical components, i. e. mirrors of various kinds.

However, due to the high energy of electromagnetic radia- tion in this extreme W domain, heating of the mirrors is of major concern. The mirrors envisaged for the application in projection optical systems are made of a mirror support on which a layered stack of dielectrics is deposited form- ing a reflective layer. Although reflectivity of this layer may be well beyond 50%, the absorbed radiation dissipated on the surface of the mirror amounts to a considerable amount of heat during projection. This heat results in a temperature increase of the reflective layer and also of the mirror support that, hence, changes its shape due to thermal deformation.

In order to avoid imaging aberrations caused by deforma- tions of the mirrors, it has been proposed to employ a metal as material for the mirror supports, thereby increas- ing the heat abduct from the mirror, and to use active cooling for these metal mirror supports, see for example EP 0 955 565 Al. Active cooling, however, increases system complexity and costs. Systems without active cooling cannot sufficiently eliminate the image deteriorations. Apart from that, metal surfaces have to be further processed before the reflective stack of layers can be deposited thereon.

Another approach for solving the mirror heating problem has been described in DE 100 40 998 Al, corresponding to US Ser. No. 09/934 252. According to this known approach, a change of the imaging properties of a lens due to illumina- tion-induced heating is at least partly compensated by an opposite illumination-induced change of the imaging proper- ties of a mirror. This approach is based on the observation that changes in the radius of curvature of optical compo- nents, for example a reduction in the radius of curvature of a concave optical surface, have opposite effects on the optical imaging properties of said surface depending on whether the surface is a reflecting or a refractive one. In the projection exposure systems considered herein using wavelengths in the extreme ultraviolet, however, there are usually no refractive optical components that could be used for compensating thermally induced aberrations.

According to another approach known from WO 01/08163 Al, the operating temperatures of the mirror supports are de- termined beforehand. Then the coefficients of thermal ex- pansion of the mirrors are adjusted such that each mirror support has, at its respective operating temperature, a co- efficient of thermal expansion centered about 0. Adjusting the coefficients of thermal expansion is achieved by con- trolled tuning of a Ti dopant concentration in high purity SiO2 glass. However, such materials are expensive and con- siderably increase the overall system cost.

Therefore there is a need for a projection exposure appara- tus comprising mirrors in which the amount of thermally in- duced aberrations is reduced, but without increasing the system complexity by active cooling devices.

SUMMARY OF THE INVENTION To meet the above objective, the present invention provides for a projection exposure apparatus for transferring an im- age of a patterned reticle onto a substrate. The projection exposure apparatus comprises an illumination optical system for generating and directing an exposure beam onto the re- ticle, and a projection optical system provided between the reticle and the substrate. The projection optical system has a plurality of imaging mirrors each having a mirror support made of a support material. The support materials are subject to thermal expansion during projection that in- duces imaging aberrations at substrate level. The support materials are selected such that an aberration merit func- tion, which is indicative of the overall amount of at least one type of the thermally induced aberrations, is minimized by mutual compensation of contributions of the mirrors to the one type of thermally induced aberrations.

The invention is based on the finding that different mir- rors may display opposite responses to thermal expansion as far as image aberrations are concerned. This means for ex- ample that a particular type of aberration, e. g. coma or spherical aberration, that is caused by a thermally induced

deformation of a first mirror can be partly or even com- pletely offset by a thermally induced deformation of a sec- ond mirror on the condition that the coefficients of ther- mal expansion of both mirrors are appropriately selected.

The compensating effect exploited by the invention may re- sult from the geometry of the mirrors, the materials of the mirror supports or both. To be more precise, a concave mir- ror having a particular coefficient of expansion may offset the aberration caused by another mirror made of the same material but shaped in convex form. On the other hand, two identically shaped mirrors may compensate each other in view of a particular thermally induced aberration if the mirror supports are made of materials having coefficients of thermal expansion that have a different sign. This means that one of these mirror supports expands when heated while the other shrinks. Such materials are known in the art as such. For example, Zerodur may be fabricated with coeffi- cients of thermal expansion between about-10-7 to +10-7 K-1.

Thus, instead of attempting to prevent mirror supports from deforming under the influence of heat, the invention allows for such deformations but seeks to achieve a mutual compen- sation of the effects of these deformations. As a result, the support materials will generally be different and have, when heated during exposure to their operating temperature, may also have different coefficients of thermal expansion.

This approach considerably reduces system cost since expen-

sive materials having a low coefficient of thermal expan- sion may completely dispensed with.

The merit function is to be determined according to the needs in a particular application. For example, if only a specific type of thermally induced aberration, e. g. coma, is of particular interest in a given projection apparatus, the merit function may be proportional to the amount of this aberration. As a measure for the amount of an aberra- tion Zernike coefficients may be used that characterize wavefront deformations of the projection beam.

If, however, the projection optical system is to be opti- mized with respect to a plurality of thermally induced ab- errations, the aberration merit function may be propor- tional to a weighed sum of amounts of these aberrations.

Instead of weighing these amounts it is also possible to use a mean value for the aberrations, for example a RMS of Zernike coefficients.

The computation of the minimal merit function becomes par- ticularly simple if the latter is defined as being propor- tional to a linear combination of aberration vectors. The aberration vectors shall represent the amounts of different types of aberrations for a single mirror and may, for exam- ple, be constituted by a set of Zernike coefficients that are determined for a preset coefficient of thermal expan- sion. Minimizing such a linear combination results in a set of coefficients whose physical meaning is that of modifica-

tion factors for the preset coefficient of thermal expan- sion.

An even better compensation of thermally induced aberra- tions can be achieved if at least one of said mirrors is mounted such that it can be displaced in at least one di- rection. Preferably this includes displacements in a direc- tion that at least substantially coincides with a direction along which light impinges on said at least one mirror.

This allows for compensation of thermally induced first or- der aberrations such as radius variations or translational movements of the mirrors.

BRIEF DESCRIPTION OF THE DRAWINGS Various features and advantages of the present invention may be more readily understood with reference to the fol- lowing detailed description taken in conjunction with the accompanying drawing which shows a projection exposure ap- paratus according to the invention in a schematic represen- tation that is not to scale.

DETAILED DESCRIPTION The only Figure shows a projection exposure apparatus indi- cated in its entirety by 10. Projection exposure apparatus 10 comprises an illumination optical system 12 that con- tains a light source 14 emitting an exposure light beam 16 having a wavelength in the extreme ultraviolet, e. g. 13 nm.

Illumination optical system 12 further comprises an imaging system indicated by 18 for directing light beam 16 onto a reticle 20. Illumination optical system 12 is known in the art as such, for example from EP 1 123 195 A1, and will therefore not be described in further detail.

Light reflected from reticle 20 enters a projection optical system 22 that comprises six imaging mirrors M1, M2,..., M6.

Each mirror M1 to M6 has a mirror support 241, 242,..., 245 and 246, respectively, on which a reflective stack of lay- ers (not shown) is deposited. These layers are made of al- ternating materials, for example Mo and Si. Projection op- tical system 22 produces a reduced image of reticle 20 on a light sensitive layer 26 disposed on a wafer 28. The gen- eral arrangement of projection optical system 22 is known, for example, from US 6,353, 470 B1, the contents of which being incorporated herein by reference.

Each mirror support 241 to 246 is made of a material that is selected according to criteria that will in the follow- ing be described in more detail.

Table 1 shows an array of functions that shall indicate the amount of different aberrations present in projection opti- cal system 22. These functions depend on the coefficient of thermal expansion tj of the respective mirror Mj. For exam- ple, d1 = d1 (α1), a1 = ai (ai),..., and d2 = d2 (a2), a2 = a2 (a2),..., and correspondingly for the other mirrors M3 to M6. It will be readily appreciated that the selection of aberrations shown in Table 1 is arbitrarily and does not restrict the scope of the invention. MIRROR DISTORTION ASTIGMATISM COMA SPHERICAL RMS ABERRATION M1 d1 a1 c1 s1 r1 M2 d2 a2 c2 s2 r2 M3 d3 a3 c3 s3 r3 M4 d4 a4 c4 s4 r4 M5 d5 a5 c5 s5 r5 M6 d6 a6 c6 s6 r6 SUM d a c s r

Table 1: Aberrations resulting from thermally induced deformations The functions given in Table 1 may depend on the thermal coefficient of expansion and may correspond to Zernike co- efficients, or to combinations thereof, that are character- istic for a particular aberration. For example, the func- tions ci for coma aberration may correspond to Zernike co- efficient Z7/8, whereas function di for spherical aberra- tion may correspond to Zernike coefficient Z9. These func- tions, however, could also represent other values that are selected to characterize the amount of the particular aber- ration.

These functions can be derived from theoretical considera- tions or, if the figures in Table 1 are determined by meas- urements, from appropriate series of measurements carried out for different coefficients of expansion.

In the last line in Table 1 the sum of the figures of each column is given. This sum represents the overall amount of the respective aberration for the whole arrangement of mir- rors Ml to M6 and is therefore characteristic for the per- formance of the projection optical system 22. In an ideal system, all these sums equal zero.

It should be noted that, depending of the kind of mirror, the values of the functions given in Table 1 may have dif- ferent signs for a given set of coefficients of thermal ex- pansion. As a result, the sum d of functions di, for exam- ple, is in general smaller than the sum of the absolute values of di, i. e.

The same applies for the other aberrations as well.

In a next step a merit function MF is determined that char- acterizes a desired thermally induced aberration or combi- nation of several such aberrations. In the simplest case in which only one type of the aberrations exemplarily enumer- ated in Table 1 is of particular concern, the merit func- tion MF is the sum for this aberration functions as shown in the last line of Table 1. If, for example, projection optical system 22 is used in an application in which even the smallest distortion is to be avoided whereas other types of aberrations can be tolerated at least to a certain degree, the merit function MF could be defined as

Since the aberration figures di depend on the coefficient of thermal expansion ai, MF is itself a function of these coefficients.

If no distortion shall be present in projection optical system 22, MF has to be zero. From this condition a set of values for the coefficient of thermal expansion ai can be determined such that MF (a1, t2, 3, C4, W5, t6) = 0. A solu- tion for this equation may be found by numerical methods as are contained in standard mathematical software libraries.

The materials for the mirror supports 241 to 246 of mirrors M1 to M6 are then selected according to this solution. This means that the material of support 241 of mirror MI is se- lected to have al as coefficient of thermal expansion, the material of support 242 of mirror M2 is selected so to have 2 as coefficient of thermal expansion and so on.

If more than one type of aberration shall be minimized, the merit function MF can be defined as a weighed sum of dif- ferent aberration functions, i. e. with Wj, j=1, 2,3, 4 being weighing coefficients that may be selected according to the weight the respective aberra- tion has for the overall performance of projection optical system 22. Since in general not all aberrations can be com-

pletely eliminated (this would correspond to MF = 0), a set of values for the coefficients of thermal expansion has to be numerically determined such that IMFI = min (4) Another way of defining the merit function MF is to deter- mine for each mirror M1 to M6 a mean aberration function ri, for example the RMS so that the merit function becomes It is to be understood that not all mirrors M1 to M6 con- tained in optical projection system 22 have to be included into the method of selecting materials for mirror supports 241 to 246. It is also possible to optimize only a re- stricted number of mirrors, e. g. three mirrors out of six.

This simplifies the numerical solution of equation (4) and often yields a sufficiently high reduction of aberrations.

Furthermore, the computation as explained above can be con- siderably simplified if the values given in Table 1 are not to represent functions but merely values for the aberra- tions, e. g. Zernike coefficients. It is then assumed that

each mirror is heated up to an elevated temperature that can be determined by computing the heat dissipation in each mirror M1 to M6, and that, in a first place, all coeffi- cients of thermal expansion are equal, i. e. aj = ao with j = 1, 2,..., 6 indicating the mirrors M1 to M6. If further- more a linear dependence of the aberration values upon the coefficients of thermal expansion is assumed, the merit function can be defined as a linear combination of aberra- tion vectors Vi that are given by Vi = (di, ai, ci, si) for mirror Mi and do not depend on the coefficient of thermal expansion: with ki being the coefficients of the linear combination.

These coefficients can be interpreted as factors for the preset coefficient of thermal expansion ao. For example, if the solution of equation (4) gives a set of 6 values for the coefficients ki, the material for mirror support 241 of mirror M1 has to be selected such that its coefficient of thermal expansion equals al = kl O The same applies, mutatis mutandis, for the remaining mir- rors M2 to M6. Such a selection ensures that the absolute value of the linear combination of equation (7) is minimal.

An even better compensation of thermally induced aberra- tions can be achieved if an additional degree of freedom is introduced by mounting some or all mirrors displaceably in at least one direction. This makes it possible to compen- sate thermally induced first order aberrations such as ra- dius variations or translational movements of the mirrors.

In the figure mirror M5 is exemplarily attached to a ma- nipulator 30 that allows to precisely move mirror M5 along a Z direction indicated by arrow 32. This direction sub- stantially coincides with the propagation direction of light beam 14. It is readily understood that not only mir- ror M5 but also some or all of the other mirrors M1 to M6 can be displacably mounted correspondingly. It should be further understood that the mirrors M1 to M6 can also be mounted so as to be displaceably in other directions, par- ticularly the X and Y direction being perpendicular to the Z direction.