FILTER ASSEMBLY, IN PARTICULAR FOR A CONTROL LOOP FOR CONTROLLING THE POSITION OF AT LEAST ONE ELEMENT

Abstract

A filter assembly, for example for a control loop for controlling the position of at least one element, comprises first and second filters. The first filter suppresses an undesired component in a signal to be filtered. The first filter produces a first signal delay in a first frequency range. The second filter produces a second signal delay in the first frequency range. The second signal delay at least partly compensates the first signal delay.

Claims

1. A filter arrangement, comprising: a first filter configured to: i) suppress an unwanted component in a signal to be filtered; and ii) cause a first signal delay in a first frequency range; and a second filter configured to cause a second signal delay in the first frequency range, wherein the second signal delay at least partially compensates the first signal delay.

2. The filter arrangement of claim 1, wherein the first signal delay is a positive signal delay generated by the first filter in a settled state, and the second signal delay is a negative signal delay generated by the second filter in the settled state.

3. The filter arrangement of claim 1, wherein the first filter comprises a low-pass filter.

4. The filter arrangement of claim 1, wherein the second filter comprises an inverse low-pass filter.

5. The filter arrangement of claim 4, wherein the inverse low-pass filter is configured to compensate for the signal delay of the first filter at a frequency of 1 Hz by at least 60%.

6. The filter arrangement of claim 1, wherein the first filter comprises a notch filter configured to locally suppress an unwanted component in the signal to be filtered.

7. The filter arrangement of claim 6, wherein the second filter comprises an inverse notch filter.

8. The filter arrangement of claim 1, wherein the second filter comprises an inverse notch filter.

9. The filter arrangement of claim 8, wherein the inverse notch filter is configured to compensate for the signal delay of the first filter at a frequency of 1 Hz by at least 25%.

10. The filter arrangement of claim 1, wherein the filter arrangement is configured to be used with a control loop configured to control a position of an optical element in an optical system.

11. A control loop configured to control a position of an element, the control loop comprising: a controller configured to control a force exerted on the element by an actuator based on a reference signal; and a filter arrangement according to claim 1, wherein the filter arrangement is configured to filter the reference signal.

12. The control loop of claim 11, wherein the element is an optical element of an optical system.

13. The control loop of claim 11, wherein the element is an optical element of a microlithographic projection exposure apparatus.

14. The control loop of claim 11, wherein the element is an optical element of an EUV microlithographic projection exposure apparatus.

15. The control loop of claim 11, wherein the reference signal is a position signal which is characteristic of a position of a further element.

16. The control loop of claim 15, wherein, relative to an optical beam path, the further element is a last optical element of a projection exposure apparatus.

17. The control loop of claim 16, wherein the further element is a supporting structure of the projection exposure apparatus.

18. The control loop of claim 11, wherein the controller is configured to control a force exerted on a further element by a further actuator based on the reference signal.

19. The control loop of claim 12, wherein the element is a mirror.

20. An apparatus, comprising: an element; a controller configured to control a position of the element by controlling a force exerted on the element by an actuator based on a reference signal; and a filter arrangement according to claim 1, wherein the filter arrangement is configured to filter the reference signal, and the apparatus is a microlithographic projection exposure apparatus.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The disclosure is explained in greater detail below on the basis of exemplary embodiments illustrated in the accompanying figures, in which:

[0045] FIGS. 1A-1C show diagrams to explain the effect achieved in possible exemplary embodiments of a filter arrangement according to the disclosure compared with a conventional filter arrangement;

[0046] FIGS. 2A-2C show diagrams to explain a decomposition for the exemplary embodiment “A” from FIGS. 1A-1C;

[0047] FIGS. 3A-3C show diagrams to explain a decomposition for the exemplary embodiment “B” from FIGS. 1A-1C;

[0048] FIGS. 4A-4C show diagrams to explain a decomposition for the exemplary embodiment “C” from FIGS. 1A-1C;

[0049] FIGS. 5A-5C show diagrams to explain the discretization of an exemplary embodiment for later implementation;

[0050] FIGS. 6A-6C show diagrams to explain a further possible exemplary embodiment of the disclosure;

[0051] FIG. 7 shows a schematic illustration of a coupled control loop to explain a possible application of the disclosure;

[0052] FIGS. 8A-8C show diagrams for explaining a problem occurring in a conventional control loop; and

[0053] FIG. 9 shows a schematic illustration of a projection exposure apparatus for EUV projection lithography in a meridional section.

DETAILED DESCRIPTION

[0054] FIG. 7 shows a schematic illustration of a coupled control loop to explain a possible application of the disclosure.

[0055] According to FIG. 7, two measurement signals y1 and y2 are assigned to controllers C1 and C2, respectively. The measurement signal y1 can be, for example, the last mirror, in relation to the optical beam path, of a projection lens (e.g. with the construction described with reference to FIG. 9). The measurement signal y2 can then represent the remaining mirrors of the projection lens, which are intended to follow the reference signal y1 in a follow-up control. As a result, the combination of mirrors represented by y1 and y2 should effectively behave like a single rigid minor in order to avoid an image shift and associated image errors in the optical imaging process. The actuating signal u1 affects both the measurement signal y1 via the system G11 and the measurement signal y2 via the system G21. The same applies to the actuating signal u2 and the systems G22 and G12. There is mechanical coupling of the elements represented by y1 and y2.

[0056] The existing mechanical coupling as a result of the reaction forces via the support frame very often involves the integration of a filter (designated with “700” in FIG. 7) in the feedback chain formed according to FIG. 7. With regard to the design of this filter 700, however, there is the problem, already discussed with reference to FIGS. 8A-8C, of mutually opposing or contradictory properties with regard firstly to the suppression of the excessive amplitude increase and secondly to the reduction of any delay introduced by the filter 700. The result of the introduction of a significant delay via the filter 700 would be, for example, that the group of minors to be tracked within the follow-up control no longer effectively behaves like a single rigid minor, which ultimately leads to image errors in the optical imaging process.

[0057] The diagrams of FIGS. 8A-8C proceed initially from a filter 700 with the following filter transfer function F(s) as an example:

[00002]$\begin{array}{cc}F\left(s\right)=\frac{{\left(2\pi .Math.400\right)}^2}{s^2+2.Math.D.Math.2\pi .Math.400s+{\left(2\pi .Math.400\right)}^2}& \left(1\right)\end{array}$

[0058] In FIGS. 8A-8C, for this filter transfer function F(s), the respective frequency curves of amplitude (FIG. 8A), phase (FIG. 8B) and delay (FIG. 8C) are plotted for different values of the damping parameter D (from D=0.05 to D=0.3).

[0059] A comparison of the results obtained for the different values of the damping parameter D according to FIGS. 8A-8C shows that an increase in damping to limit the amplitude magnification in the filter transfer function F(s) according to FIG. 8A is accompanied by an increase in the delay introduced by the filter 300 of the output signal of this filter 300 relative to the input signal according to FIG. 8C. This delay is equivalent to the group delay and corresponds to the negative derivative of the function which is plotted in FIG. 8B and describes the frequency dependence of the phase at the respective frequency value.

[0060] According to the disclosure, a filter transfer function is now implemented which makes it possible to reduce the delay introduced by the filter 700 within a frequency range and at the same time limit the amplitude to values that are still acceptable.

[0061] For this purpose, a plurality of filters are used in combination according to the disclosure, each of which is designed or matched to one another in such a way that at least partial mutual compensation is achieved with regard to the total delay introduced in the relevant frequency range.

[0062] In a general approach, the filter types low-pass filter, inverse low-pass filter, notch filter and inverse notch filter can be combined with each other in such a way that overall—depending on the specific desired properties in the entire optical system—a suitable compromise between the suppression attained in the range of high frequencies or the accepted amplitude increase, on the one hand, and, on the other hand, the ultimately attained reduction in delay is achieved. Here, as described below, it is also possible to combine basic filter functions (2) to (5) to form a chain of low-pass filters, inverse low-pass filters, notch filters and inverse notch filters. Each of the filter types can appear as often as desired.

[0063] A low-pass filter is described by the basic filter function:

[00003]$\begin{array}{cc}{F}_{LP}\left(s,\omega ,D\right)=\frac{{\omega }^2}{s^2+2D\omega s+{\omega }^2}& \left(2\right)\end{array}$

[0064] A notch filter is described by the basic filter function:

[00004]$\begin{array}{cc}{F}_{\mathrm{notch}}\left(s,\omega ,D,a\right)=\frac{s^2+2\frac{D}{a}\omega s+{\omega }^2}{s^2+2Da\omega s+{\omega }^2}& \left(3\right)\end{array}$

[0065] When choosing α≥1.16>1/√{square root over (0.75)}, the minimum amplitude is less than 0.75.

[0066] An inverse low-pass filter is described by the basic filter function:

F.sub.iLP(s, ω, D)=1/F.sub.LP(s, ω, D)  (4)

[0067] An inverse notch filter is described by the basic filter function:

F.sub.inotch(s, ω, D, α)=1/F.sub.notch(s, ω, D, α)  (5)

[0068] The chain formed by combining these basic filter functions (2)-(5) can be described by:

[00005]$\begin{array}{cc}F=\underset{i=1}{\overset{N_i}{.Math.}}{F}_{\mathrm{LP}}\left(s,{\omega }_i,D_i\right).Math.\underset{j=1}{\overset{N_j}{.Math.}}{F}_{\mathrm{iLP}}\left(s,{\omega }_j,D_j\right).Math.\underset{k=1}{\overset{N_k}{.Math.}}{F}_{\mathrm{notch}}\left(s,{\omega }_k,D_k,a_k\right).Math.\underset{l=1}{\overset{N_l}{.Math.}}{F}_{\mathrm{inotch}}\left(s,{\omega }_i,D_i,a_i\right)& \left(6\right)\end{array}$

where the behavior of this chain can then be influenced by the parameters indexed with i, j, k, l in equation (6). The parameters N.sub.i, N.sub.j, N.sub.k and N.sub.l are all greater than or equal to zero.

[0069] For three specific exemplary embodiments “A”, “B” and “C” of such a chain or the corresponding filter transfer function F(s), the respective frequency curves of amplitude (FIG. 1A), phase (FIG. 1B) and delay (FIG. 1C) are plotted in FIGS. 1A-1C. For comparison, the corresponding frequency curves for the conventional configuration from FIGS. 8A-8C are entered with the value of the damping parameter D=0.3 (and represented each by solid lines in FIGS. 1A-1C), see curve “D”. The effectiveness of the compensation is demonstrated in each case by FIGS. 2A-2C (=decomposition of “A”), FIGS. 3A-3C (=decomposition of “B”) and FIGS. 4A-4C (=decomposition of “C”). For the assessment of the compensation, the frequency range (0.20Hz) is used uniformly, which is greater than that according to the individual determination of the frequency f.sub.e.

[0070] The first example “A” (illustrated by dashed lines in FIGS. 1A-1C) has a very small delay in the frequency range up to 20 Hz according to FIG. 1C. According to FIG. 1A, the amplitude magnification is comparable to that of “D”. However, the suppression above 500 Hz is comparatively lower. The filter of “A” consists of three low-pass filters and three inverse low-pass filters. As shown in FIGS. 2A-2C (=decomposition of “A”), the delays of all inverse low-pass filters compensate the delay of all low-pass filters by almost 100%.

[0071] Example “B” is basically based on “A,” but improves the suppression locally at 650 Hz and 1050 Hz by using two notch filters. Conversely, the suppression above 1300 Hz drops less than in “A”. FIGS. 3A-3C (=decomposition of “B”) clearly show that the delay of all low-pass filters (1375 μs) and the delay of all notch filters (61 μs) are almost completely (100%) compensated for by the delay of all the inverse low-pass filters (−1436 μs).

[0072] The example “C” is characterized by a very low amplitude magnification and very good suppression up to 1000 Hz. In order to achieve this, there is no effective suppression above 2000 Hz. The filter shown consists of a low-pass filter, an inverse low-pass filter and four notch filters. FIGS. 4A-4C (=decomposition of “C”) show that the delay of the low-pass filter (780 μs) and that of all the notch filters (253 μs) are almost 100% compensated for by the delay of the inverse low-pass filter (−1033 μs).

[0073] A further embodiment is shown in FIGS. 6A-6C. Here, three notch filters are combined with three inverse notch filters. The overall filter has very good suppression in the range between 700 Hz and 900 Hz. The amplitude magnification now occurs at higher frequencies, here at around 1100 Hz. The compensation of the delay of all the notch filters (858 μs) and of all the inverse notch filters (−856 μs) is more than 99%.

[0074] All parameterizations of the examples given are provided below.

[0075] Example “A”: Three low-pass filters, three inverse low-pass filters

ω.sub.i={442.5, 1013, 795.2}.Math.2π

D.sub.i={0.46, 1.85, 1.28}

ω.sub.j={2483.2, 662.8, 3478.2}.Math.2π

D.sub.j={2.42, 1.9, 2.22}

[0076] Example “B”: Three low-pass filters, three inverse low-pass filters, two notch filters

ω.sub.i={418.2, 1223, 943.8}.Math.2π

D.sub.i={0.53, 1.9, 1.41}

ω.sub.j={2055, 621.6, 2957.8}.Math.2π

D.sub.j={2.23, 1.71, 2.01}

ω.sub.k={675, 1052.4}.Math.2π

α.sub.k={1.23, 1.57}

D.sub.k={0.13, 0.13}

[0077] Example “C”: A low-pass filter, an inverse low-pass filter, four notch filters

ω.sub.i=510.6.Math.2π

D.sub.i=1.25

ω.sub.j=444.9.Math.2π

D.sub.j=1.44

ω.sub.k={1839.2, 851, 1091.12, 1393.3}.Math.2π

α.sub.k={1.94, 1.64, 1.37, 1.92}

D.sub.k={0.14, 0.28, 0.12, 0.27}

[0078] Example from FIGS. 6A-6C: Three notch filters, three inverse notch filters

ω.sub.k={877.9, 638.9, 712.8}.Math.2π

α.sub.k={3.5, 2.87, 3.5}

D.sub.k={0.12, 0.4, 0.15}

ω.sub.l={578.94, 636, 1097.9}.Math.2π

α.sub.l={3.33, 2.33, 2.75}

D.sub.i={0.4, 0.08, 0.17}

[0079] For later implementation, the above time-continuous filters are discretized. This is possible, for example, by Tustin transformation without losing certain desired properties of the filter, see FIGS. 5A-5C for discretization of example “C”.

[0080] FIG. 9 schematically shows a projection exposure apparatus 1 for EUV projection lithography in a meridional section.

[0081] According to FIG. 9, the projection exposure apparatus 1 comprises an illumination device 2 and a projection lens 10. The illumination device 2 serves to illuminate an object field 5 in an object plane 6 with radiation from a radiation source 3 by way of an illumination optical unit 4. What is exposed here is a reticle 7 disposed in the object field 5. The reticle 7 is held by a reticle holder 8. The reticle holder 8 is displaceable, for example in a scanning direction, by way of a reticle displacement drive 9.

[0082] For purposes of explanation, a Cartesian xyz-coordinate system is shown in FIG. 9. The x-direction runs perpendicularly to the plane of the drawing. The y-direction runs horizontally, and the z-direction runs vertically. The scanning direction runs in the y-direction in FIG. 1. The z-direction runs perpendicular to the object plane 6.

[0083] The projection lens 10 serves for imaging the object field 5 into an image field 11 in an image plane 12. A structure on the reticle 7 is imaged onto a light-sensitive layer of a wafer 13 arranged in the region of the image field 11 in the image plane 12. The wafer 13 is held by a wafer holder 14. The wafer holder 14 is displaceable, for example in the y-direction, by way of a wafer displacement drive 15. The displacement on the one hand of the reticle 7 by way of the reticle displacement drive 9 and on the other hand of the wafer 13 by way of the wafer displacement drive 15 may take place in such a way as to be synchronized with one another.

[0084] The radiation source 3 is an EUV radiation source. The radiation source 3 can emit EUV radiation, which is also referred to below as used radiation or illumination radiation. For example, the used radiation has a wavelength in the range between 5 nm and 30 nm. The radiation source 3 may be a plasma source, for example an LPP (“laser produced plasma”) source or a GDPP (“gas discharged produced plasma”) source. It may also be a synchrotron-based radiation source. The radiation source 3 can also be a free-electron laser (“free-electron laser”, FEL). The illumination radiation 16 emerging from the radiation source 3 is focused by a collector 17. The illumination radiation 16 propagates through an intermediate focus in an intermediate focal plane 18 downstream of the collector 17. The intermediate focal plane 18 can represent a separation between a radiation source module, having the radiation source 3 and the collector 17, and the illumination optical unit 4.

[0085] The illumination optical unit 4 comprises a deflection minor 19 and, arranged downstream thereof in the beam path, a first facet mirror 20. If the first facet mirror 20 is arranged in a plane of the illumination optical unit 4 which is optically conjugate to the object plane 6 as a field plane, this facet mirror is also referred to as a field facet minor. The first facet mirror 20 comprises a multiplicity of individual first facets 21, some of which are shown in FIG. 1 only by way of example. In the beam path of the illumination optical unit 4, a second facet minor 22 is arranged downstream of the first facet mirror 20. If the second facet minor 22 is arranged in a pupil plane of the illumination optical unit 4, it is also referred to as a pupil facet minor. The second facet minor 22 comprises a plurality of second facets 23, some of which are also shown in FIG. 1 only by way of example.

[0086] The projection lens 10 comprises a plurality of mirrors Mi, which are consecutively numbered in accordance with their arrangement in the beam path of the projection exposure apparatus 1. In the example shown in FIG. 9, the projection lens 10 includes six minors M1 to M6. Alternatives with four, eight, ten, twelve or any other number of mirrors Mi are likewise possible. The penultimate mirror M5 and the last minor M6 each have a passage opening for the illumination radiation 16. The projection lens 10 is a doubly obscured optical unit. The projection lens 10 has an image-side numerical aperture that is greater than 0.5 and may also be greater than 0.6, and may be for example 0.7 or 0.75.

[0087] Reflection surfaces of the mirrors Mi can be embodied as freeform surfaces without an axis of rotational symmetry. Alternatively, the reflection surfaces of the mirrors Mi can be designed as aspherical surfaces with exactly one axis of rotational symmetry of the reflection surface shape. Just like the minors of the illumination optical unit 4, the mirrors Mi can have highly reflective coatings for the illumination radiation 16. These coatings can be designed as multilayer coatings, such as with alternating layers of molybdenum and silicon.

[0088] The projection lens 10 may for example have an anamorphic form. It can have different imaging scales β.sub.x, β.sub.y in the x- and y-directions. The two magnifications β.sub.x, β.sub.y of the projection lens 10 can be (β.sub.x, β.sub.y)=(±0.25, ±/0.125). A positive imaging scale β means imaging without image inversion. A negative sign for the imaging scale β means imaging with image inversion. The projection lens 10 thus leads to a reduction in the ratio 4:1 in the x-direction, i.e. in the direction perpendicular to the scanning direction. The projection lens 10 leads to a reduction of 8:1 in the y-direction, i.e. in the scanning direction. Other imaging scales are likewise possible. Imaging scales with the same sign and the same absolute value in the x-direction and y-direction are also possible, for example with absolute values of 0.125 or of 0.25.

[0089] Even though the disclosure has also been described on the basis of specific embodiments, numerous variations and alternative embodiments will be apparent to a person skilled in the art, for example by the combination and/or exchange of features of individual embodiments. Accordingly, it goes without saying for a person skilled in the art that such variations and alternative embodiments are concomitantly encompassed by the present disclosure, and the scope of the disclosure is restricted only within the meaning of the appended patent claims and the equivalents thereof.