1. Field of the Invention
The present invention relates to a method of evaluating the optical performance of an optical system, and techniques associated with the same.
2. Description of the Related Art
Along with the recent increase in the packing density of semiconductor devices, the wavelength of light for use in exposure is shortening, and the NA of the projection optical system is increasing.
To meet the demands for an increase in the NA of the projection optical system, an immersion exposure apparatus in which the space between the substrate and the lowermost surface of the projection optical system is filled with a liquid has arrived on the market. In order to attain NA>1, the immersion exposure apparatus is configured such that the space between the substrate and the final lens of the projection optical system is filled with a substance (pure water in an ArF exposure apparatus) having a refractive index higher than 1. It is a common practice to use a catadioptric system as the projection optical system of the current leading-edge immersion exposure apparatus which attains NA>1.2 (“A Hyper-NA Projection Lens for ArF Immersion Exposure Tool”, Nikon Corporation, Proc. of SPIE Vol. 6154). This catadioptric system is often configured by forming holes in its constituent optical elements such as mirrors and lenses or by using meniscus optical elements (Japanese Patent Laid-Open No. 06-242379).
To increase the packing density of semiconductor devices, that is, to micropattern them, it is also important to ensure the precisions of optical elements which constitute the projection optical system. To do this, techniques of evaluating the surface shape of an optical element are used. The surface shape evaluation can include a step of measuring a surface shape, and a step of fitting a Zernike polynomial to the surface shape (Japanese Patent Laid-Open No. 2005-116852).
An error of the surface shape of the optical element accounts for deterioration in the optical performance of the projection optical system included in the exposure apparatus mentioned above. To keep up with the recent demands for a reduction in the aberration of the projection optical system, a surface shape error evaluation method which can precisely predict the optical performance of the projection optical system and precisely process the optical element to correct its surface error is necessary in a process of polishing the optical element.
Conventionally, circular optical elements are often included in the projection optical system. However, to configure a compact catadioptric system, holes are often formed in its constituent optical elements such as mirrors and lenses or meniscus optical elements are often used.
When the surface shape of a circular measured object is measured, its entire surface is measured at once, and a Zernike polynomial is commonly used to analyze and evaluate the measurement result.
In contrast, when the surface shape of a noncircular measured object is evaluated using a Zernike polynomial, even if data including errors between individual measurement apparatuses in only a small region relative to the evaluated region are used, Zernike coefficients having errors amplified are output as a consequence.
This is because the Zernike polynomial is a function orthogonalized only in a circular region. More specifically, when the Zernike polynomial is fitted to a non-orthogonalized (noncircular) region, non-orthogonalized functions cancel errors between individual measurement apparatuses in a small region. Therefore, each Zernike coefficient has a value larger than necessary.
There is also a general method of predicting the optical performance in, for example, an exposure apparatus. In this method, the optical performance is obtained by linear calculation of Zernike coefficients describing the surface shape, and the sensitivities, calculated by optical computing, of the optical performance to the Zernike coefficients describing the surface shape. In this case, when the optical performance is calculated using Zernike coefficients obtained in a noncircular region as well, it is impossible to precisely predict the optical performance because the Zernike coefficients themselves include large errors.
It is an object of the present invention to provide a method of precisely evaluating, for example, the optical performance of an optical system, and techniques associated with the same.
One of the aspect of the present invention provides a method of evaluating an optical performance of an optical system comprising a locating step of locating a plurality of circular regions in an evaluated region on an optical element included in the optical system, a fitting step of fitting a polynomial to surface shape data representing a surface shape of the optical element in each of the plurality of circular regions, and a calculation step of calculating the optical performance of the optical system based on the fitting result obtained in the fitting step in each of the plurality of circular regions.
Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings.
Preferred embodiments of the present invention will be described below with reference to the accompanying drawings.
The optical system evaluation apparatus according to the preferred embodiment of the present invention includes the surface shape evaluation apparatus 100 and an information processing apparatus 200. The information processing apparatus 200 controls the surface shape evaluation apparatus 100, and evaluates the optical performance of an optical system including the optical element 1 based on the evaluation result of the optical element 1 provided by the surface shape evaluation apparatus 100. The information processing apparatus 200 can be configured by, for example, installing a computer program for executing an optical system evaluation method on a computer such as a personal computer. The information processing apparatus 200 may execute all or part of the process by the arithmetic processing unit 3.
The original 5 is held by an original stage 6 and illuminated with exposure light emitted by an illumination system 4. The exposure light from the original 5 enters the projection optical system 7. The exposure light beams coming from arbitrary points on the original 5, that is, arbitrary object points in the projection optical system 7 enter and pass through different positions on the optical element 1 as the measured object.
The light having passed through the optical element 1 passes through other optical elements (if any) of the projection optical system 7, further passes through the liquid 8, and strikes the substrate 9. The pattern surface of the original 5 and the substrate 9 are set to hold a conjugate positional relationship by the projection optical system 7. The substrate 9 is chucked by a substrate chuck 10 mounted on a substrate stage 11. The positions of the substrate stage 11 and original stage 6 are controlled by a position control system including an interferometer and driving mechanism. When the exposure apparatus in this embodiment is configured as a scanning exposure apparatus, the substrate stage 11 and original stage 6 are scanned and driven at a speed matching the magnification of the projection optical system 7.
The optical element 1 as the measured object need only cover the light beam effective diameter in the projection optical system 7, so it can have not a circular shape but a rectangular shape from the viewpoint of the configuration of the projection optical system 7.
When Zernike coefficients describing the surface shape of the optical element 1 are determined, it is possible to calculate the optical performances of an optical system such as the projection optical system 7 including the optical element 1.
Pi=Ai1×Z1+Ai2×Z2+Ai3×Z3+Ai4×Z4+Ai5×Z5+ (1)
where Pi is the optical performance of the evaluated optical system at an evaluated object point i, Z1, Z2, Z3, . . . are Zernike coefficients obtained by fitting a Zernike polynomial to the surface shape data measured by the measurement apparatus 2, and Ai1, Ai2, Ai3, . . . are the sensitivities of the optical performance of the evaluated optical system at the evaluated object point to the Zernike coefficients.
Note that evaluation items of the optical performance of the projection optical system are assumed to be the wavefront aberration RMS (the worst value among 27 points), the width of the image plane (for NA=0.86, annular illumination (outer σ=0.9 and inner σ=0.6), exposure wavelength=248 nm, a 100-nm isolated pattern, and a halftone reticle), and the distortion (a conversion value based on a deviation from the principal ray, and the 2nd and 3rd terms of the Zernike polynomial assuming that NA=0.86 and exposure wavelength=248 nm).
The results shown in
First, in step S10 (determination step), the information processing apparatus 200 determines the object points, evaluated by the surface shape evaluation apparatus 100, in an optical system such as the projection optical system 7 including the optical element 1 as the measured object. Note that the evaluated object points need to be arrayed to be able to evaluate the overall evaluated region on the optical element 1 with a required precision.
In step S20 (locating step), the information processing apparatus 200 determines by optically computing a circular region including a region in which the light beam from each evaluated object point determined in step S10 passes through the optical element 1. This means that a plurality of circular regions are located in the evaluated region on the optical element 1. At this time, if a certain region through which the light beam passes has a noncircular shape, a circular region which includes the certain region through which the light beam passes is determined. Note that one circular region is determined for each evaluated object point determined in step S10. The circular regions may or may not overlap each other.
In step S30, the surface shape evaluation apparatus 100 evaluates the surface shape of the optical element 1 in the individual circular regions based on the location information. Note that, in a first step, the measurement apparatus 2 measures the surface shape of the optical element 1 over the entire region including the evaluated region on the optical element 1. In a second step, the arithmetic processing unit 3 extracts, based on the location information provided by the information processing apparatus 200, surface shape data in the plurality of circular regions from the surface shape data output from the measurement apparatus 2. In a third step (fitting step), the arithmetic processing unit 3 fits a polynomial such as a Zernike polynomial to the surface shape data in each circular region to determine the coefficients of the polynomial. In a fourth step, the arithmetic processing unit 3 provides the determination results (coefficient values) obtained in the third step to the information processing apparatus 200 as the surface shape evaluation results of the optical element 1.
In step S40 (optical performance calculation step), the information processing apparatus 200 calculates the optical performance of the evaluated optical system such as the projection optical system 7 based on the evaluation result (polynomial coefficient) obtained in step S30 in each of the plurality of circular regions on the optical element 1. Examples of evaluation items of the optical performance are the wavefront aberration, the width of the image plane, and the distortion. The optical performance calculation can include multiplying the coefficients such as Zernike coefficients determined by fitting in step S30 by the sensitivities of an evaluation item for the evaluated optical system to the coefficients, and adding up the products, as in equation (1). Based on the evaluation results of the optical element as the measured object obtained at arbitrary object points in the evaluated optical system including the optical element in the above-mentioned way, the influence of the optical element exerted on the evaluated optical system can be calculated. The above-mentioned sensitivities can be determined by known optical computing in step S50 prior to step S40.
Probable causes for this effect are, for example, that only a circular region including a data defect region is influenced by the data defect region, and that a Zernike polynomial is fitted to an orthogonalized circular region. When a Zernike polynomial is fitted to an orthogonalized circular region, the amount of amplification of errors is small even when the circular region includes a data defect region.
The reason why there are differences between the optical performances shown in
Although 27 object points are evaluated in the above-mentioned example, increasing the number of object points makes it possible to evaluate the optical performance with a higher precision.
When the allowable values of the optical performances (the wavefront aberration RMS, the distortion, and the width of the image plane) evaluated previously are set as exemplified in
If the optical performance obtained in the sequence illustrated in
First, in step S110 (specifying step), an object point as a factor that makes the optical performance more than the allowable value is specified. At this time, a plurality of object points may be specified. The examples shown in
In this example, in a processing amount calculation step including the following steps S120, S130, and S140, the amount of processing, to make the optical performance less than or equal to the allowable value, of a processed region corresponding to the object points specified in step S110 is determined.
More specifically, in step S120, a minimum processing amount required to make the optical performance less than or equal to the allowable value is determined as a Zernike term based on the sensitivities of the optical performance. This process is executed at each object determined in step S110.
In step S130, it is determined whether the regions which require processing overlap each other. If YES in step S130, the processing amounts in the overlapping regions are averaged.
In step S140, the required processing amount in the entire region on the optical element is determined by smoothing.
Although high-frequency filtering is performed by the averaging and the smoothing in steps S130 and S140, respectively, in this example, it may be performed by other methods. In this example, the processing amount calculation step includes steps S120, S130, and S140.
An optical element manufacturing method according to a preferred embodiment of the present invention includes a processing step of processing the processed region on the optical element 1 in accordance with the processing amount calculated in the processing amount calculation step, in addition to the processing plan creation method.
In this method, only a region which receives a light beam from an object point at which the optical performance is to be improved and its periphery are an additional processed region, as exemplified in
While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.
This application claims the benefit of Japanese Patent Application No. 2008-100864, filed Apr. 8, 2008, which is hereby incorporated by reference herein in its entirety.
Number | Date | Country | Kind |
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2008-100864 | Apr 2008 | JP | national |