Method and device for characterizing the surface shape of an optical element

Abstract

A method and apparatus for characterizing the surface form of an optical element, in particular a mirror or a lens element of a microlithographic projection exposure apparatus, includes: carrying out a plurality of interferometric measurements, in each of which an interferogram is recorded between a test wave emanating from a portion of the optical element in each case and a reference wave, the position of the optical element relative to the test wave being altered between these measurements, and calculating the figure of the optical element on the basis of these measurements. This calculation is carried out iteratively such that, in a plurality of iteration steps, the figure of the optical element is ascertained in each case by carrying out a forward calculation, each of these iteration steps being based in each case on a reference wave that was adapted based on the preceding iteration step.

Claims

1. A method for determining a figure of an optical element, for characterizing a surface form of the optical element, comprising: carrying out a plurality of interferometric measurements, in each of which an interferogram is recorded between a test wave emanating from a portion of the surface of the optical element in each case and a reference wave, wherein a position of the surface of the optical element relative to the test wave is altered between each of the measurements; and calculating the figure of the optical element based on the plurality of interferometric measurements; wherein calculating the figure comprises iterative calculations, in a plurality of iteration steps, for ascertaining the figure of the optical element by carrying out respective forward calculations, each of the iteration steps being based on a respective reference wave that was adapted based on a preceding one of the iteration steps; wherein the respectively adapted reference wave is ascertained by carrying out a backward calculation, and wherein carrying out the backward calculation comprises removing the figure from the respective interferometric measurement by calculation.

2. The method as claimed in claim 1, wherein carrying out the interferometric measurements comprises a recording of subapertures, none of which cover an entirety of the surface of the optical element.

3. The method as claimed in claim 1, wherein carrying out the respective forward calculations comprises performing a grid transformation or a transformation from a first coordinate system of a measurement setup that is used when carrying out the interferometric measurements to a second coordinate system of the optical element.

4. The method as claimed in claim 1, wherein carrying out the respective backward calculations comprises performing a grid transformation or a transformation from a second coordinate system of the optical element to a first coordinate system of a measurement setup that is used when carrying out the interferometric measurements.

5. The method as claimed in claim 1, wherein the respective iterative calculations are carried out until a predetermined convergence criterion is met.

6. The method as claimed in claim 1, wherein the respective iterative calculations are carried out for a predetermined number of iteration steps.

7. The method as claimed in claim 1, wherein altering the position of the optical element comprises preserving a position of a center of curvature of the optical element over the plurality of interferometric measurements.

8. The method as claimed in claim 1, wherein the optical element is a mirror or a lens element.

9. The method as claimed in claim 1, wherein the optical element is an optical element of a microlithographic projection exposure apparatus.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the figures:

(2) FIG. 1 shows a flowchart for explaining the method steps of a method according to an exemplary embodiment of the invention;

(3) FIG. 2A illustrates an exemplary interferometric test arrangement that is known from the prior art, but that is able to be used within the scope of the invention;

(4) FIG. 2B illustrates a plurality of overlapping individual interferometric measurements “stitched” into a single interferometric measurement;

(5) FIG. 3 shows an exemplary conventional interferometer that is able to be used with the interferometric test arrangement of FIG. 2A; and

(6) FIG. 4 shows a schematic illustration of a projection exposure apparatus designed for operation in EUV.

DETAILED DESCRIPTION

(7) FIG. 4 shows a schematic illustration of an exemplary projection exposure apparatus which is designed for operation in the EUV wavelength range and which comprises mirrors which are testable with methods according to the invention.

(8) According to FIG. 4, an illumination device in a projection exposure apparatus 410 designed for EUV comprises a field facet mirror 403 and a pupil facet mirror 404. The light from a light source unit comprising a plasma light source 401 and a collector mirror 402 is directed onto the field facet mirror 403. A first telescope mirror 405 and a second telescope mirror 406 are arranged in the light path downstream of the pupil facet mirror 404. A deflection mirror 407 is arranged downstream in the light path, said deflection mirror directing the radiation that is incident thereon onto an object field in the object plane of a projection lens comprising six mirrors 421-426. At the location of the object field, a reflective structure-bearing mask 431 is arranged on a mask stage 430, said mask being imaged with the aid of the projection lens into an image plane in which a substrate 441 coated with a light-sensitive layer (photoresist) is situated on a wafer stage 440.

(9) The optical element examined with regard to its surface shape or figure within the scope of the invention can be, e.g., any mirror of the projection exposure apparatus 410, for example the (comparatively large) last mirror 426 of the projection lens on the image plane side. In further applications, the optical element can also be a lens element of a projection exposure apparatus designed for operation in the deep ultraviolet (DUV) wavelength range (e.g., at wavelengths shorter than 250 nm, in particular shorter than 200 nm), for example.

(10) The method according to the invention is described below on the basis of an embodiment, with reference being made to the flowchart shown in FIG. 1.

(11) Here, the assumption is made that, for the purposes of characterizing the figure of a mirror, a plurality of (e.g., fifty) subapertures are recorded in individual interferometric measurements with a different positioning of the test object in each case. In particular, the term “subaperture” is intended to express that the interferometric measurements carried out to record the subapertures do not cover the entire surface of the mirror in each case.

(12) Here, a spherical mirror is assumed in the exemplary embodiment, wherein, with reference being made to FIG. 2A again, the variation of the position of the mirror 201 indicated therein is implemented in such a way that the center of curvature remains in place in each case. In further embodiments, the mirror 201 can also be a substantially flat mirror, which is displaced in translational fashion in a direction parallel to the mirror surface between the individual interferometric measurements.

(13) Moreover, a symmetry-breaking arrangement of the individual measurement positions can be chosen in embodiments of the invention. This is advantageous in that measurement results obtained in the individual subaperture measurements can be clearly divided into figure components and reference wave components.

(14) In order now to determine the total or “pieced together” figure of the mirror from said measured subapertures, the invention is based on the “stitching method,” known per se, which—as described below with reference to the flowchart in FIG. 1—is modified, however.

(15) According to FIG. 1, there is initially a first-time calculation of the figure with the specification of a specific reference wave after the start (step S110) of the method. Here, an externally determined start value or a zero function, in particular, can be specified for the reference wave. This first-time calculation of the figure also comprises, in particular, the aforementioned grid transformation or transformation from the coordinate system of the measurement setup to the coordinate system of the test object or mirror 201. The step of “stitching” the figure (at a given reference wave) is labeled “S120” in FIG. 1 and implemented by solving the following minimization problem (which yields a linear system of equations):

(16) $\begin{array}{cc}\underset{f,P_n}{\min }=\underset{i=1}{\overset{m}{.Math.}}{\int }_{x,y}[w_{x,y}^{\mathrm{PRF}}.Math.T_{i,x,y}^{\mathrm{CCD}->\mathrm{PRF}}\left(w_i^S\right).Math.{\hspace{1em}\left(T_{i,x,y}^{\mathrm{CCD}->\mathrm{PRF}}\left(S_i-I_{n-1}\right)-\underset{k}{.Math.}{f}_{\mathrm{ik}}{F}_{k,x,y}-P_{n,x,y}\right)]}^2\mathrm{dxdy}& \left(1\right)\end{array}$

(17) Here, and below, the following abbreviations and variables are used:

(18) P.sub.n: iteration n of the figure of the optical element or test object

(19) I.sub.n: iteration n of the reference wave. I.sub.0 is either an externally determined start value or a zero function

(20) S.sub.i: i-th subaperture measurement

(21) m: number of subaperture measurements

(22) F.sub.k: compensators/sensitivities, the amplitudes of which should be varied

(23) f.sub.ik: Amplitudes of sensitivity k for subaperture i

(24) w.sub.i.sup.S: subaperture masks/weight functions for subaperture i.

(25) w.sup.PRF: figure mask/weight function.

(26) T.sub.i.sup.CCD.fwdarw.PRF: function that transforms a function defined on the measurement grid for the i-th measurement to the test object grid.

(27) In contrast to the conventional (non-iterative) method, the reference wave is now “stitched” according to the invention on the basis of the information received about the figure of the optical element or mirror; this includes a back transformation of the figure into the coordinate system of the measurement setup, in particular. The backward calculation implemented here taking into account the previously ascertained figure leads to more precise or improved information about the reference wave, the corresponding step (i.e., a “stitching” of the reference wave in the case of a given figure) being denoted “S140” in FIG. 1.

(28) The “stitching” of the reference wave I.sub.n in the case of a given figure P.sub.n is implemented by solving the following minimization problem (which also yields a linear system of equations):

(29) $\begin{array}{cc}\underset{f,I_n}{\min }=\underset{i=1}{\overset{m}{.Math.}}{\int }_{x,y}[w_{x,y}^{\mathrm{PRF}}.Math.T_{i,x,y}^{\mathrm{CCD}->\mathrm{PRF}}\left(w_i^S\right).Math.{\hspace{1em}\left(T_{i,x,y}^{\mathrm{CCD}->\mathrm{PRF}}\left(S_i-I_n\right)-\underset{k}{.Math.}{f}_{\mathrm{ik}}{F}_{k,x,y}-P_{n,x,y}\right)]}^2\mathrm{dxdy}& \left(2\right)\end{array}$

(30) In embodiments (e.g., to limit the computing time and/or the memory requirement), the “stitching” of the reference wave can also be carried out using only a portion or selection of pixels.

(31) In accordance with FIG. 1, a new forward calculation is implemented in the next iteration step, corresponding to a renewed “stitching” of the figure, etc., on the basis of the improved or more precise information about the reference wave obtained thus.

(32) In embodiments of the invention, the subaperture masks/weight functions or the figure mask/weight functions can be mask functions (function values 0 or 1) which separate valid regions from invalid regions in each measurement. In further embodiments, the subaperture masks/weight functions or the figure mask/weight function can also be “real” weight functions (function value≥0), which are calculated from local measurement errors.

(33) In embodiments of the invention, a relatively smaller weight or even a weight of zero can be used for image regions with a comparatively large measurement error. Moreover, the weights can be refined dynamically over the course of the iterative method.

(34) In principle, the number of measurement positions can be suitably chosen as desired, the number being at least two.

(35) Instead of minimizing the deviation of the model from the real measurements, it is also possible, in analogous fashion, to minimize the difference between two measurements in the overlap region. Such a procedure provides similar solutions and only differs in the choice of weights w.sub.i.sup.S.

(36) The grid transformation function T can be selected on the basis of the specific circumstances, in particular with regard to the test object (i.e., adapted to the specific stitching problem). Here, there can be a grid transformation onto a Cartesian grid on the test object, in particular.

(37) The pixel grid spanned on the test object, which is used in “stitching” the figure, can be varied both in respect of the total number of pixels and in respect of the distortion of the grid.

(38) In the exemplary embodiment of FIG. 1, this iterative method ends (in step S150) as soon as a predetermined convergence criterion has been reached in accordance with the query in step S130. In further embodiments, a predetermined number of iteration steps can also be defined in advance; once this number has been reached, the iteration is terminated and the last ascertained figure is output.

(39) Even though the invention has been described on the basis of specific embodiments, numerous variations and alternative embodiments will be apparent to the person skilled in the art, for example through combination and/or exchange of features of individual embodiments. Accordingly, such variations and alternative embodiments are concomitantly encompassed by the present invention, and the scope of the invention is restricted only within the meaning of the appended patent claims and equivalents thereof.