The invention relates to an optical system with birefringent optical elements.
The birefringent property of the optical elements can be caused, e.g., by stress-induced birefringence, intrinsic birefringence, or by a dependence of the reflectivity on the direction of polarization, as is known to occur in mirrors or in anti-reflex coatings of lenses. Stress-induced birefringence occurs when the optical elements are mechanically stressed or as a side effect of the manufacturing process of the substrate materials for the optical elements.
Systems in which the birefringent property of optical elements has a detrimental influence are, for example, the projection systems used in the field of microlithography.
Projection objectives and projection apparatus are known, e.g., from WO 0150171 A1 (U.S. Ser. No. 10/177,580) and the references cited therein. The embodiments described in that patent application represent purely refractive as well as catadioptric projection objectives with numerical apertures of 0.8 and 0.9 at operating wavelengths of 193 nm as well as 157 nm. The birefringent optical components in these projection objectives lead to a reduced image quality of the projection objectives.
A projection objective with birefringent optical elements is known from DE 19807120 A1 (U.S. Pat. No. 6,252,712). The birefringent optical elements cause optical path differences for two mutually orthogonal states of polarization in a bundle of light rays, where the path differences vary locally within the bundle of light rays. To correct the detrimental influence of the birefringent phenomenon, DE 19907120 A1 proposes the use of a birefringent element with an irregularly varying thickness.
In the not prepublished patent application DE 10127320.7 by the applicant, possibilities for compensating and thereby reducing the detrimental influence of birefringence are presented which include rotating the lenses relative to each other in the case of projection objectives with fluoride crystal lenses. The patent application just mentioned shall hereby be incorporated by reference in the present application.
In the not prepublished patent application DE 10123725.1 by the applicant, possibilities for compensating and thereby reducing the detrimental influence of birefringence are presented, wherein an optical element with a location-dependent property of rotating the polarization state or shifting the optical phase is arranged close to a diaphragm plane. The patent application just mentioned shall hereby be incorporated by reference in the present application.
The birefringent phenomenon also has an undesirable effect in illumination systems of projection systems. The illumination systems may have a light homogenizer in the form of an integrator rod, as described for example in DE 195 48 805 (U.S. Pat. No. 5,982,558).
Illumination systems with an integrator unit that has two integrator rods are known from U.S. Pat. No. 6,028,660.
The present invention has the objective to propose optical systems with birefringent optical elements employing a simple means for significantly reducing the influence of the birefringent phenomenon.
To meet the foregoing objective, the present invention proposes an optical system, an illumination system, a method of producing an optical system, and an optical system that is produced according to one of the methods described herein.
In order to reduce the unwanted influence of the birefringent properties of optical systems, it is proposed to build an optical system from two subsystems with an optical retarding system arranged between the subsystems.
The optical system may, e.g., be an objective, or also a partial objective belonging to the objective. Thus, the objective can be composed of several optical systems that are configured according to the present invention. The objective may, e.g., be a microscope objective or a projection objective for use in projection lithography. The unwanted effects of birefringence are particularly noticeable in objectives where fluoride crystal lenses are used at wavelengths in the deep ultraviolet range (<250 nm). The optical system may also be part of an illumination system, e.g., an integrator unit for generating an illumination with a homogeneous intensity distribution. The integrator unit can likewise have several of the inventive optical systems.
According to the invention, each of the two optical subsystems has at least one birefringent optical element. The birefringent property of an optical element can be due, e.g., to the material properties of the element (intrinsic birefringence), or to extraneous factors (stress-induced birefringence), or to coatings such as anti-reflex coatings or mirror coatings. Examples of optical elements are refractive or diffractive lenses, mirrors, retarding plates, and also include integrator rods.
The optical retarding system includes at least one optical retarding element, which introduces a lag of half of a wavelength between two mutually orthogonal states of polarization. The optical retarding element may be, e.g., a half-wave plate, a birefringent optical element or a coating on an optical element, where the optical element or the coating would be designed to produce an effect corresponding to a half-wave plate. The optical retarding element may be, for example, a fluoride crystal lens or a crystal plate of calcium fluoride in (110)-orientation, where one would make use of the intrinsic birefringence of calcium fluoride or apply a controlled state of stress. Birefringent crystals of magnesium fluoride are suitable for producing the optical retarding element, based on their favorable transmission properties in the deep ultraviolet range, e.g., at 193 nm or 157 nm. It is also possible to use retarding elements made of quartz with a controlled state of stress-induced birefringence, e.g., according to DE 196 37 563 (U.S. Pat. No. 6,084,708). The optical retarding element can also be connected to an adjacent optical element of one of the two subsystems, e.g., by a seamless joint or wringing fit.
Without the optical retarding system, a light ray traversing the birefringent elements in the two subsystems would be subject to an optical path difference for two mutually orthogonal states of polarization. The effects of the two optical subsystems would in this case be cumulative. The retarding system now has the advantageous effect that the two states of polarization are exchanged with respect to each other. As a consequence, the optical path difference caused in the light ray by the first subsystem can be at least partially canceled in the second subsystem.
It is advantageous to arrange in the optical retarding system an additional optical retarding element that introduces a retardation of half of a wavelength between two mutually orthogonal states of polarization. The optical retarding element may be, e.g., a half-wave plate, a birefringent optical element or a coating on an optical element, where the optical element or the coating would be designed to produce an effect corresponding to a half-wave plate. The fast axis of the first optical retarding element should enclose an angle of 45°±10° with the fast axis of the second optical retarding element, 45° being the ideal amount. The term “fast axis” is known from the field of polarization optics. The concept of using two retarding elements that are rotated relative to each other has the advantage that two mutually orthogonal states of polarization of a light ray are exchanged with respect to each other by the optical retarding system and furthermore, that the exchange occurs independently of the state of polarization of the incident light ray. It is therefore possible in a bundle of light rays with different states of polarization to exchange the mutually orthogonal states in all of the rays in the bundle. If all of the light rays of the bundle had the same state of polarization, it would be sufficient to use a single retarding element of appropriate orientation. If two optical retarding elements are used, they can be joined, e.g., by a seamless connection or by a wringing fit.
It is advantageous to divide the optical system into the two optical subsystems in such a manner that a light ray traversing the optical system takes on a first optical path difference ΔOPL1 for two mutually orthogonal states of polarization while traveling through the first subsystem and then takes on a second optical path difference ΔOPL2 for two mutually orthogonal states of polarization while traveling through the second subsystem, with the two optical path differences being of similar magnitude. The absolute values of the two optical path differences should deviate from each other by less than 40%, wherein this number refers to the maximum value of the two optical path differences. In this case, the compensating effect on the unwanted influence of birefringence will be particularly favorable, because the two mutually orthogonal states of polarization of a light ray take on a first optical path difference in the first subsystem, are then exchanged by the retarding system, and subsequently take on a second optical path difference in the second subsystem, where the first and second optical path differences have equal absolute amounts but opposite signs. Consequently, the resulting optical path difference is significantly smaller than in an optical system without a retarding system.
The polarizing effects of the two optical subsystems can also be described through Jones matrices. The definition of the concept of Jones matrices is known from the field of polarization optics. Using this approach, a Jones matrix can be calculated for each of the two optical subsystems to describe the polarizing effects of the two optical subsystems on the mutually orthogonal states of polarization of a light ray traversing the optical system. Commercially available software programs are available for the calculation of the Jones matrices, such as for example CodeV® by Optical Research Associates, Pasadena, Calif., USA. It is advantageous to normalize the Jones matrix of a subsystem with its determinant. However, other normalizations are also possible. The compensation of the unwanted influence of birefringence by means of the retarding system is particularly successful if the coefficients of the normalized Jones matrices of the two subsystems agree with each other as much as possible. The absolute values of the corresponding matrix coefficients should deviate from each other by less than 30%, wherein this number refers to the maximum value of the two corresponding matrix coefficients. In this case, a light ray traversing the optical system will not be subjected to an optical path difference between two mutually orthogonal states of polarization. However, it is possible that the two states of polarization will be exchanged, depending on the nature of the birefringent optical elements.
If one considers an entire bundle of light rays, the optical system can be divided into two optical subsystems in such a manner that the distribution profile of the optical path differences for two mutually orthogonal states of polarization will show significantly reduced values in comparison to an optical system without a retarding system. The values are considered to be significantly reduced if the maximum value in the distribution profile of the optical path differences with the retarding system amount to no more than 50% of the maximum value observed without the retarding system.
The invention can be advantageously used in an integrator unit for generating an illumination with a homogenous intensity distribution. In this embodiment of the invention, the integrator unit consists of at least two integrator rods that are arranged in series. The integrator rods can have birefringent properties, for example stress-induced birefringence caused by the holder arrangement for the integrator rods, or intrinsic birefringence inherent in the rod material itself, or birefringence caused by total reflection at the lateral surfaces of the rods. A birefringent effect also occurs in an integrator rod that is configured as a light pipe, if the rays are split into differently polarized components at the mirror-coated lateral surfaces. As a consequence of the birefringent effect of the integrator rods, the state of polarization of a bundle of rays is altered inside the integrator unit. As an example, if the integrator unit is used in an illumination system for a catadioptric projection objective with a polarization beam splitter, it is desirable if the integrator unit changes the state of polarization of a bundle of light rays only within narrow limits. By inserting the retarding system between the two integrator rods, it is possible to significantly reduce the unwanted influence of birefringence.
As a condition that the optical path differences for two mutually orthogonal states of polarization caused by the two rod integrators will to a large extent compensate each other, it is advantageous if the two integrator rods have nearly identical dimensions. More specifically, the lengths and cross-sectional areas of the two integrator rods should differ from each other by less than 30%, wherein this number refers to the maximum values of the corresponding lengths and cross-sectional areas.
At wavelengths in the deep ultraviolet range, particularly at 193 nm and 157 nm, fluoride crystals such as, e.g., calcium fluoride, are used as raw material for the rods because of their higher transmissivity. In this case, the angle-dependent intrinsic birefringence of the fluoride crystals is felt as a noticeable inconvenience. In a favorable arrangement, both integrator rods consist of the same kinds of fluoride crystals, and the fluoride crystals in the two integrator rods have equivalent crystallographic orientations. As an example, the longitudinal axes of the two integrator rods can be aligned with a principal crystallographic direction, e.g., in the <100>- or <111>-direction. The principal crystallographic directions of cubic crystals, i.e., the class that includes fluoride crystals, are <110>, <{overscore (1)}10>, <{overscore (1)}{overscore (1)}0>, <101>, <10{overscore (1)}>, <{overscore (1)}01>, <{overscore (1)}0{overscore (1)}>, <011>, <0{overscore (1)}1>, <01{overscore (1)}>, <0{overscore (1)}{overscore (1)}>, <111>, <{overscore (1)}{overscore (1)}{overscore (1)}>, <{overscore (1)}{overscore (1)}1>, <{overscore (1)}1{overscore (1)}>, <1{overscore (1)}{overscore (1)}>, <{overscore (1)}11>, <1{overscore (1)}1>, <11{overscore (1)}>, <100>, <010>, <001>, <{overscore (1)}00>, <0{overscore (1)}0> und <00{overscore (1)}> auf. For example, the principal crystallographic directions <100>, <010>, <001>, <{overscore (1)}00>, <0{overscore (1)}0> und <00{overscore (1)}> are equivalent to each other, because of the symmetries of cubic crystals, so that any statements made in reference to one of the aforementioned crystallographic directions will also be valid for the other, equivalent crystallographic directions.
It is advantageous to provide an arrangement whereby the clamping force of a mounting device of an integrator rod can be varied. This offers the possibility to vary the stress-induced birefringence inside the integrator rod and to thereby improve the compensation.
If the optical retarding system in the integrator unit consists of only a single optical retarding element, it is advantageous if the fast axis of the optical retarding element encloses an angle of 45°±5° with one of the edges of a rod-integrator surface facing the optical retarding system. When used in connection with integrator rods consisting of fluoride crystal material whose <100> axis is aligned in the direction of the longitudinal axes of the integrator rods, this arrangement provides a high degree of compensation of the unwanted effects of intrinsic birefringence.
If one uses two retarding elements rotated at 45° in relation to each other in the integrator unit, it is possible to also use other crystallographic orientations. In this case, it is advantageous if the optical path difference for two mutually orthogonal states of polarization in a light ray traversing the first integrator rod is of nearly equal magnitude as for the same light ray traversing the second integrator rod.
An optical retarding system in an integrator unit can also be arranged within an image-projecting system, which projects the exit surface of the first integrator rod onto the entry surface of the second integrator rod. The image-projecting system in this arrangement consists of a first and second optical device portion with the optical retarding system arranged between the first and second optical device portion. The first optical subsystem is now composed of the first integrator rod and the first optical device portion, and the second optical subsystem is composed of the second integrator rod and the second optical device portion. If the first and second optical device portions themselves include birefringent optical elements, it is advantageous if the optical path difference for two mutually orthogonal states of polarization in a light ray traversing the first optical device portion is of nearly equal magnitude as for the same light ray traversing the second optical device portion.
The integrator unit of the foregoing description is used to particular advantage in an illumination system within a projection apparatus.
The invention can further be used to advantage, if the optical system is an objective that projects an object plane onto an image plane. The optical system can also be represented by a partial objective of an image-projecting objective, or it can be one of several partial objectives within an image-projecting objective.
The compensation leads to a noticeable reduction of the unwanted effects caused by birefringence, if the optical path differences for two mutually orthogonal states of polarization are calculated for an entire bundle of light rays in the first and second optical subsystem. The light rays of the bundle will pass through the diaphragm plane of the objective for example in an even distribution. The calculated path differences for each optical subsystem will follow a respective distribution profile whose respective maximum absolute value can be determined. The optical retarding system is advantageously arranged at a position within the objective where the maximum absolute value of the first distribution profile deviates by no more than 40% from the maximum absolute value of the second distribution profile.
Likewise, the respective Jones matrices of the first and second optical subsystem can be calculated for each light ray in a bundle of rays. Each ray will thus have eight Jones coefficients in the two optical subsystems, four of which will correspond to each other in each case. Based on the values of the mutually corresponding Jones coefficients, the values of the differences are established for each ray. The birefringence effects can be advantageously corrected, if the maximum among the values of the differences is smaller than 30% of the maximum of the amounts of the Jones coefficients of the first Jones matrices.
The invention can be used advantageously in an objective that has at least one fluoride crystal lens in each of the two optical subsystems, where the lens axis is oriented in a principal crystallographic direction of the fluoride crystal. The lens axes are considered to be oriented in a principal crystallographic direction if the maximum deviation between lens axis and principal crystallographic direction is less than 5°. The lens axis in this case is represented, e.g., by the axis of symmetry of a rotationally symmetric lens.
If the lens has no axis of symmetry, the lens axis can be defined by the central ray of an incident bundle or by a straight line in relation to which the angles of all rays within the lens are minimal. The range of lenses that can be considered includes, e.g., refractive or diffractive lenses as well as corrective plates with free-form corrective surfaces. Planar-parallel plates, too, are considered as lenses, if they are arranged in the light path of the objective. The lens axis of a planar-parallel plate runs perpendicular to the plane surfaces of the plate. Since each of the two optical subsystems contains a fluoride crystal lens in a given orientation, the unwanted influence of one lens can be compensated by the other lens, because the optical retarding system exchanges the two states of polarization against each other. It is particularly favorable if the two lenses consist of the same fluoride crystal material and the lens axes are oriented in the same crystallographic direction or in equivalent crystallographic directions.
The optical retarding system with at least one optical retarding element can be advantageously combined with other birefringence-compensating methods that are described in the not pre-published patent applications DE 10127320.7 and DE 10123725.1, whose entire content is included by reference in the present application. In particular, the unwanted influence of birefringence can already be noticeably reduced with fluoride crystal lenses whose lens axes are oriented in the same principal crystallographic direction by rotating the fluoride crystal lenses relative to each other. A further reduction of the unwanted influence of birefringence can be achieved through the additional use of a birefringence compensator consisting of a birefringent lens with a location-dependent thickness profile in the area of the diaphragm plane of an image-projecting objective.
In objectives, a retarding element of the retarding system can be realized by applying a retardant coating to an optical element that belongs to the first or second subsystem where the retardant coating is designed to effect a retardation by one-half of a wavelength. This is possible, e.g., with a magnesium fluoride coating in which the birefringent effect is achieved through the vapor-deposition angle in the production process of the coating. The retarding element belongs therefore to the first or second subsystem and to the retarding system.
If the numerical aperture of the objective on the image side is larger than on the object side, it is advantageous to place the optical retarding system between the diaphragm plane of the objective and the image plane of the objective. The reason why this arrangement is preferred is that large angles of incidence at air/glass interfaces and large angles of the light rays inside the lenses, which occur in the optical elements near the image plane, lead to large optical path differences between two mutually orthogonal states of polarization. For the compensation of the path differences, it is therefore necessary to also include in the first subsystem some of the lenses that are positioned in the light path after the diaphragm plane, i.e., lenses that are between the diaphragm plane and the image plane.
The invention also proposes a method of producing an optical system in which the birefringent effects are compensated. The configuration and in particular the number n of optical elements of the optical system are given factors known at the outset. However, the compensation will only be successful if the optical system includes at least two birefringent optical elements. The objective of the inventive method is to find the number m of consecutively adjacent optical elements that are to be assigned to the first subsystem, where the remaining number n−m of consecutively adjacent optical elements will make up the second subsystem. Having determined the respective elements for the first and second subsystems, one will achieve a noticeable reduction of the unwanted influence of birefringence by inserting the optical retarding system between the first and second optical subsystems. A plurality of steps are proposed under the method, as follows:
It is advantageous to perform the calculation in steps C and D of the method for several light rays. In an image-projecting objective, the light rays can, for example, come from one object point and pass through the diaphragm plane at evenly distributed locations.
It is also possible
The following variant of the method can likewise be advantageously used for producing an optical system. It has the following steps:
The foregoing method does not require the calculation of the Jones matrices for every value m between 1 and n−1. The optimization process is finished after a solution has been found for the system where the differences of the Jones coefficients are below a prescribed threshold value or target value. The optical system determined in this manner meets the prescribed criterion in regard to unwanted birefringence effects. If no value can be found for m so that the differences are less than the threshold value, one will have to raise the threshold value. In this case, it needs to be evaluated whether the optical system can meet the requirements that were specified for the optical system. If the requirements cannot be met, one will have to change the optical design of the optical system, the choice of materials, or the technique of mounting the optical elements.
It is also possible in a variant of the last mentioned method
The optical systems produced according to either of the aforedescribed methods show noticeably less of the undesirable effect of birefringence. The improvement has been achieved by taking a simple measure, namely by inserting one or two retarding elements, each of which causes a retardation of one-half of a wave length in a light ray with two mutually orthogonal states of polarization. By inserting simple half-wave plates, one can in many cases dispense with the use of complicated birefringence compensators or improve the effectiveness of a compensators by additionally using half-wave plates.
The invention will be explained in more detail below, making reference to the drawings, wherein:
The Jones matrix of a known polarization-optics system or subsystem can be determined with the optics software program Code V®. The Jones matrix can be determined in two steps. For this example, we consider a basis of linear polarization states which are mutually orthogonal. However, any set of two mutually orthogonal states can in principle be used. In the first step of the computation process, the calculations are performed for a light ray having a first state of linear polarization. The Jones vector at the exit of the system is in this case equal to the first column of the Jones matrix. The second column is obtained in a second step by considering a light ray having a second state of linear polarization which is orthogonal to the first state of polarization. Furthermore, since only the optical effect on the polarization is relevant, it is advantageous to normalize the Jones matrix with a suitable normalization basis. A suitable basis is represented, e.g., by the determinant. Only Jones matrices normalized in this manner will be used hereinafter. If the individual Jones matrices of the optical subsystems 3 and 5 of the optical system 1 are known, the Jones matrix of the optical system 1 can be calculated as the multiplication product of the individual Jones matrices.
If the optical system 1 is subdivided into two optical subsystems 3 and 5 with nearly identical Jones matrices, a compensation of the unwanted influence of birefringence can be achieved by inserting a retarding system 13, hereinafter referred to as a 90°-rotator. The 90°-rotator 13 is arranged between the two optical subsystems 3 and 5. To give an intuitive explanation, the path difference that has been accumulated between the two mutually orthogonal states of polarization of a light ray during its passage through the first optical subsystem 3 is subsequently reversed and thereby canceled as the same light ray passes through the second optical subsystem 5. After the light ray has passed through the 90°-rotator 13, the two components of the Jones vector are exchanged with respect to each other and in addition, the sign of one of the two vector components is inverted. The Jones matrix R of a 90°-rotator is therefore:
With T designating the Jones matrix of each of the two nearly identical optical subsystems 3 and 5, and R designating the Jones matrix of the 90°-rotator 13, the Jones matrix J for the overall system after inserting the 90°-rotator 13 is obtained by the following calculation:
A compensation of the system is achieved if the Jones matrix of the optical system 1 does not mix the components of the Jones vector of the incident light ray 11 and does not weaken one component in relation to the other. An attenuation that is equally shared by both components can be corrected by scalar means such as gray filters and thus will likewise lead to a compensation of the undesirable polarization-related properties. In this case, the Jones matrix takes on one of the forms
In general, p will be a scalar complex amplitude factor, including the special case of a pure phase. The compensation can be achieved, e.g., in a first case where T is a symmetric matrix, i.e., Txy=Tyx. This applies, e.g., for
Compensation can further be achieved if T is a unitary matrix, i.h. T−1=TT. In this case, the factor P is a pure phase. This applies, e.g., for
The following description relates to an embodiment of the 90°-rotator 13. The 90°-rotator 13 is obtained by combining two half-wave plates 15 and 17 that are rotated by 45° relative to each other. A schematic view of the two half-wave plates 15 and 17 is shown in
The Jones matrix R of the 90°-rotator 13 can be obtained by the following mathematical derivation. Two half-wave plates whose fast axes enclose an angle α are equivalent to a rotator with a rotation angle of 2α.
As the result of the equation shows, an angle α=45° produces a 90°-rotator.
The two half-wave plates 15 and 17 can be realized in different ways. To name one possibility, the two border surfaces of the two optical subsystems 3 and 5, e.g., lens surfaces, which are facing towards the 90°-rotator can be coated with a retardant coating of MgF2 that is applied to the surfaces under specific vapor-deposition angles and effects a retardation by one-half of a wavelength. It is alternatively possible to install conventional half-wave plates between the two subsystems As a material for the half-wave plates, one can use a birefringent magnesium fluoride or calcium fluorids in <110>-orientation at a wavelength of 157 nm.
In a first embodiment, the invention is used in a rod integrator of the kind used in an illumination system for a projection apparatus. Illumination systems of this type are known from DE 195 48 805 A1 (U.S. Pat. No. 5,982,558).
As an example of an optical system in which the unwanted influence of birefringence is compensated,
A first unwanted effect of birefringence is due to the reflection on the side surfaces. A light ray 311 passing through the first integrator rod 303 will be reflected n times, where n could be any positive integer. At each reflection, the optical path difference in the light ray 311 between a first state of polarization E1 and a second state of polarization E2 that is orthogonal to E1 will have grown by a certain amount. For example in the state E1, the light ray may have a linear polarization in the direction perpendicular to the plane of incidence of the light ray. Accordingly, for the state E2, the direction of polarization lies in the plane of incidence. Due to the increase of the optical path difference at each reflection, the optical integrator rod 303 will introduce an optical path difference ΔOPL1 between the states of polarization E1 and E2. The half-wave plate 309 rotates the directions of the two states of polarization E1 and E2 by 90°, so that the states of polarization E1 and E2 of the light ray 311 are in effect exchanged with respect to each other. Thus, if the state E1 has an optical path difference in comparison to the state E2 after the first integrator rod 303, the optical path difference between the states E1 and E2 will decrease again at each reflection in the second integrator rod 305. As a result of the reflections in the second integrator rod 305, the light ray 311 will be subjected to an optical path difference ΔOPL2 between the states of polarization E1 and E2. The optical path difference ΔOPL2, however, has the opposite sign of ΔOPL1. Therefore, if the number of reflections in the first integrator rod 303 is the same as in the second integrator rod 305, the cumulative optical path difference ΔOPL over the two integrators will be compensated because ΔOPL2=−ΔOPL1. Since the number of reflections in the second integrator rod 305 can only be n−1, nor n+1, there can be no perfect compensation.
In addition to the birefringent effect of the reflections on the side surfaces, the intrinsic birefringence of the rod material also causes optical path differences in a light ray 311 between a first state of polarization E1 and a second state of polarization E2 that is orthogonal to E1. The intrinsic birefringence of fluoride crystals such as, e.g., calcium fluoride, which is the material of the integrator rods 303 and 305, is associated with a characteristic spatial arrangement of the slow crystallographic axes and amounts at most to about 11 nm/cm at a wavelength of 157 nm. It is possible to calculate the change in the state of polarization that the intrinsic birefringence of calcium fluoride causes in a light ray and to develop a compensation arrangement. It is advantageous if the symmetry of the distribution of the slow axes matches the fourfold symmetry of the integrator rods. Accordingly, it is of advantage if the longitudinal axes of the integrator rods 303 and 305 are aligned with the crystallographic direction <100>. In the arrangement shown in
In a specific practical embodiment for an integrator unit 301 according to
In a further embodiment, the single half-wave plate 309 of
The following analysis is for a light ray traversing the integrator unit at an oblique angle. The path of the light ray starts at the center of the entry surface of the first integrator rod and has the direction (0.110, 0.0, 0.994). The Jones matrix for this light ray and for the integrator unit is
The Jones matrix indicates that light with a (1, 0)-polarization at the starting point (Jones-vector
remains more or less unaffected. The same applies to light with a linear (0, 1) polarization at the start (Jones-vector
This can be concluded from the phase differences between the components of the Jones vectors after applying the Jones matrix, which in this case are close to 0° or 180°.
If one takes the 90°-rotator out of the integrator unit, light which had a (1, 0)- or (0, 1)-polarization at its entry into the rod is turned into elliptically polarized light. This can be concluded from the columns of the Jones matrix for the light ray in the now modified system:
The phase difference between the matrix components after applying the Jones matrix J amounts in this case to about 80°. However the amplitude of one of the two components predominates, so that the ellipse that describes the state of polarization is quite flat.
In the arrangement of the two integrator rods that are separated by a 90°-rotator as described above, the Jones matrix J for a light ray traversing the system is composed of the matrix T1 of the first integrator rod, the matrix R for the 90°-rotator, and the matrix T2 for the second integrator rod. Based on the equal geometries and polarization properties of the integrator rods, the Jones matrices for the glass rods are nearly equal, due to reasons of symmetry based on the assumption that the light ray before and after the 90°-rotator traverses equal paths in equal directions through the material. For all possible light rays, this is largely the case. The compensation is achieved as a result of the 90°-rotator, which has the effect of exchanging the two mutually orthogonal states of polarization against each other.
In the case of stress-induced birefringence, the detrimental influence in an integrator unit may be compensated as follows:
To control the stress-induced birefringence and to thereby compensate the undesirable birefringent effects, it is advantageous to provide a possibility for adjusting the clamping force of a clamping device. In the arrangement shown in
If the invention is to be applied to optical systems that consist of a multitude of optical elements with birefringent properties, one will first have to delimit the optical subsystems between which a retardation system, the so-called 90°-rotator, is to be arranged in order to achieve a substantial reduction of the undesirable influence of birefringence. The limits between the two optical subsystems can be determined in different ways. It is possible to use the aforementioned technique of computing the Jones matrix of the optical system through an optics software program such as CodeV® for all of the possible optical subsystems. Based on the results, one can select the partitioning of the system into the two subsystems in such a manner that the normalized Jones matrices of the selected optical subsystems are approximately equal. In the case of a projection objective, where the birefringent effect is caused primarily by the intrinsic birefringence of fluoride crystal lenses, a possible place for inserting the 90°-rotator can be determined by taking the thickness dimensions of the lenses and the maximum angles of incidence into account. It is typical for projection objectives that the lenses which cause large path differences for two mutually orthogonal states of polarization are located in the part of the objective that is closest to the image plane.
For the embodiment of
As an example, the Jones matrix T1 for ray 2 of Table 2 is evaluated below. The first optical subsystem 703 has a normalized Jones matrix T1 and a determinant D1 of the Jones matrix before the latter has been normalized.
The second optical subsystem 705 has for the same light ray a normalized Jones matrix T2 and a determinant D2 of the Jones matrix before the latter has been normalized.
Table 4 illustrates that the optical path difference in all light rays is reduced to 40%, and in some cases to less than 10% of the value observed in an objective 711 that is not equipped with the retardation system 715. Thus, the invention leads to a decisive improvement of the optical qualities of the projection objective.
Table 3 demonstrates that for all light rays, the optical path difference is reduced to 40%, and in most cases to less than 10% of the value observed in a system that is not equipped with a 90°-rotator. Thus, the invention leads to a decisive improvement of the optical qualities of the projection objective.
Table 4 lists the respective optical path differences ΔOPL1 and ΔOPL2 for each of the four light rays in the first optical subsystem 703 and the second optical subsystem 705.
The projection apparatus 801 can be used, for example, in the manufacture of microstructured devices such as integrated circuits. In such a case the reticle 807 may generate a circuit pattern corresponding to an individual layer of the integrated circuit. This circuit pattern can be imaged onto the light-sensitive substrate 813.
The minimum size of the structural details that can be resolved in the projection depends on the wavelength λ of the light used for illumination, and also on the numerical aperture on the image side of the projection objective 811. With the embodiment shown in
Number | Date | Country | Kind |
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102 11 762.4 | Mar 2002 | DE | national |
This application is a continuation of International Application Serial No. PCT/EP02/12446, filed Nov. 7, 2002 and published in English on Sep. 18, 2003 under the international publication number WO 03/077011, which is still pending, and which claims priority from German Patent Application No. 102 11 762.4, filed Mar. 14, 2002, all of which are hereby incorporated by reference in their entirety.
Number | Date | Country | |
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Parent | PCT/EP02/12446 | Nov 2002 | US |
Child | 10922380 | Aug 2004 | US |