METHOD AND DEVICE FOR DETERMINING THE HEATING STATE OF AN OPTICAL ELEMENT IN AN OPTICAL SYSTEM

Abstract

A method and a device determine the heating state of an optical element in an optical system, for example in a microlithographic projection exposure system. Electromagnetic radiation hits an incidence surface of the optical element during operation of the optical system. Using a calibration parameter, an average temperature at the incidence surface is estimated on the basis of a temperature measurement carried out via at least one temperature sensor located a distance from the incidence surface. The calibration parameter is selected differently in accordance with the illumination setting which is set in the optical system.

Claims

1. A method, comprising: exposing an incidence surface of an optical element to electromagnetic radiation; measuring a temperature of the incidence surface using at least one temperature sensor arranged at a distance from the incidence surface; determining a calibration parameter based on an illumination setting in the optical system; and using the calibration parameter to estimate an average temperature of the incidence surface based on the temperature measurement.

2. The method of claim 1, further comprising: ascertaining a reference illumination setting; and determining the calibration parameter based on a reference calibration parameter for the reference illumination setting.

3. The method of claim 1, further comprising determining the calibration parameter based at least one measurement or simulation of a variable for the illumination setting currently set in the optical system, wherein the at least one variable depends on a thermal state of the optical element.

4. The method of claim 3, wherein the variable dependent on the thermal state of the optical element is an intensity distribution generated during the operation of the optical system in a plane located downstream of the optical element along a beam path of the electromagnetic radiation through the optical system.

5. The method of claim 3, wherein the variable dependent on the thermal state of the optical element is a wavefront generated during the operation of the optical system in a plane located downstream of the optical element along a beam path of the electromagnetic radiation through the optical system.

6. The method of claim 1, further comprising taking into the distance of the at least one temperature sensor from the incidence surface when determining the calibration parameter.

7. The method of claim 1, further comprising repeatedly making the temperature measurement using the at least one temperature sensor, thereby ascertaining a time profile.

8. The method of claim 1, wherein the at least one temperature sensor is arranged in an access channel which extends from a side of the optical element facing away from the incidence surface into the optical element.

9. The method of claim 1, further comprising using the estimated average temperature as an input signal for closed-loop control of at least one parameter characterizing the optical element and/or the optical system.

10. The method of claim 1, further comprising controlling a pre-heating of the optical element based on the estimated average temperature to at least partially compensate for changes in the heating state of the optical element over time which occur during the operation of the optical system.

11. The method of claim 1, wherein the optical element comprises a mirror.

12. The method of claim 1, wherein the electromagnetic radiation has a wavelength of less than 30 nm.

13. The method of claim 1, wherein the optical system is a microlithographic projection exposure apparatus.

14. The method of claim 13, further comprising selecting the calibration parameter depending on a reticle used in the projection exposure apparatus.

15. The method of claim 14, wherein the average temperature is estimated during the operation of the microlithographic projection exposure apparatus.

16. The method of claim 13, wherein the average temperature is estimated during the operation of the microlithographic projection exposure apparatus.

17. The method of claim 13, determining the calibration parameter based at least one measurement or simulation of a variable for the illumination setting currently set in the optical system, wherein the at least one variable depends on a thermal state of the optical element.

18. The method of claim 17, further comprising determining the calibration parameter based at least one measurement or simulation of a variable for the illumination setting currently set in the optical system, wherein the at least one variable depends on a thermal state of the optical element.

19. The method of claim 13, further comprising determining the calibration parameter based at least one measurement or simulation of a variable for the illumination setting currently set in the optical system, wherein the at least one variable depends on a thermal state of the optical element.

20. A method of estimating an average temperature of an incidence surface of optical element of an optical system, the optical elementconfigured to have electromagnetic radiation incident thereon during use of the optical system, the method comprising: measuring a temperature of the incidence surface using at least one temperature sensor arranged at a distance from the incidence surface; determining a calibration parameter based on an illumination setting in the optical system; and using the calibration parameter to estimate the average temperature of the incidence surface based on the temperature measurement.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In the figures:

[0041] FIG. 1 shows a schematic illustration of the possible structure of a microlithographic projection exposure apparatus designed for operation in the EUV;

[0042] FIG. 2 shows a diagram which shows, by way of example, different time profiles of a calibration parameter caused by different illumination settings and ascertained and used in a method according to the disclosure;

[0043] FIG. 3 shows a diagram which shows the time profile of the respective measurement signal for different sensor positions, in comparison with the real average temperature at the surface of an optical element;

[0044] FIG. 4 shows a schematic illustration for explaining the possible structure of a mirror with which the method according to the disclosure can be realized in exemplary fashion; and

[0045] FIGS. 5A-5D show diagrams for explaining a problem encountered in a conventional method for ascertaining the thermal state of a mirror.

DETAILED DESCRIPTION

[0046] FIG. 1 shows a schematic illustration of a projection exposure apparatus 1 which is designed for operation in the EUV and in which the disclosure is realizable by way of example. The description of the basic structure of the projection exposure apparatus 1 and its components should not be construed as limiting here.

[0047] One embodiment of an illumination system 2 of the projection exposure apparatus 1 has, in addition to a light or radiation source 3, an illumination optical unit 4 for illuminating an object field 5 in an object plane 6. In an alternative embodiment, the light source 3 may also be provided as a module separate from the rest of the illumination system. In this case, the illumination system does not comprise the light source 3.

[0048] Here, a reticle 7 arranged in the object field 5 is exposed. The reticle 7 is held by a reticle holder 8. The reticle holder 8 is displaceable by way of a reticle displacement drive 9 for example in a scanning direction. For purposes of elucidation, a Cartesian xyz-coordinate system is shown in FIG. 1. 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 perpendicularly to the object plane 6.

[0049] 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 by way of a wafer displacement drive 15 for example longitudinally with respect to the y-direction. The displacement, firstly, of the reticle 7 by way of the reticle displacement drive 9 and, secondly, of the wafer 13 by way of the wafer displacement drive 15 may be implemented so as to be mutually synchronized.

[0050] The radiation source 3 is an EUV radiation source. The radiation source 3 emits, for example, 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 of between 5 nm and 30 nm. The radiation source 3 can be for example a plasma source, a synchrotron-based radiation source or a free electron laser (FEL). The illumination radiation 16 emanating from the radiation source 3 is focused by a collector 17 and propagates through an intermediate focus in an intermediate focal plane 18 into the illumination optical unit 4. The illumination optical unit 4 comprises a deflection mirror 19 and, disposed downstream thereof in the beam path, a first facet mirror 20 (having schematically indicated facets 21) and a second facet mirror 22 (having schematically indicated facets 23).

[0051] The projection lens 10 comprises a plurality of mirrors Mi (i= 1, 2, ...), which are consecutively numbered in accordance with their arrangement in the beam path of the projection exposure apparatus 1. In the example illustrated in FIG. 1, the projection lens 10 comprises six mirrors M1 to M6. Alternatives with four, eight, ten, twelve or any other number of mirrors Mi are similarly possible. The penultimate mirror M5 and the last mirror M6 each have a through 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.

[0052] During operation of the microlithographic projection exposure apparatus 1, the electromagnetic radiation incident on the optical effective surface of the mirrors is partly absorbed and, as explained in the introduction, results in heating and an associated thermal expansion or deformation, which can in turn result in an impairment of the imaging properties of the optical system. The temperature of the mirrors can now be suitably controlled via a suitable correction mechanism (e.g., pre-heaters).

[0053] With reference to FIG. 2 to FIG. 4, embodiments of a method according to the disclosure will be described below for correspondingly estimating the heating state of the mirror in question and for possibly correspondingly controlling a suitable correction mechanism such as pre-heaters, for example. The concept according to the disclosure for determining the heating state can be applied here to any desired mirror of the microlithographic projection exposure apparatus 1 from FIG. 1.

[0054] FIG. 4 shows, in a purely schematic illustration, the possible arrangement of a temperature sensor 420 at an optical element 400 in the form of a mirror. According to FIG. 4 (however, without the disclosure being limited thereto), the temperature sensor 420 is located in a borehole introduced as an access channel 411 into the mirror substrate 410 from the back side of the mirror. “405” denotes a reflection layer system and “401” denotes the optical effective surface or incidence surface of the mirror for electromagnetic radiation.

[0055] What the embodiments described below have in common is that a calibration parameter used to estimate an average temperature present on the incidence surface of an optical element or mirror on the basis of a sensor-based temperature measurement is not chosen to be constant and fixed for all use scenarios or operating states in the optical system, but is chosen differently depending on the illumination setting currently set in the optical system (possibly additionally dependent on the reticle used in each case). If the calibration parameter is denoted by “q”, the sought-after average temperature at the incidence surface of the optical element or mirror is denoted by “T”, and the temperature measured with the aid of sensors is denoted by “Ts”, then the following applies:

[00001]$\begin{array}{cc}T=q\cdot T_s& \text{­­­(1)}\end{array}$

[0056] According to a first embodiment, the calibration parameter for the illumination setting currently set in the optical system can be determined on the basis of a reference calibration parameter previously ascertained for a reference illumination setting. If a single measurement of the temperature taking place at a single point in time is initially taken as a starting point in this case, and if the sought-after average temperature T at the incidence surface and the associated sensor-based measured temperature T.sub.s are assumed as known for the reference illumination setting, then the reference illumination setting (corresponding to the use scenario known in advance) and the illumination setting currently set in the optical system (corresponding to the unknown use scenario) can be related to one another, as described hereinafter, wherein, for example, use can be made of the resultant power behind the reticle for both use scenarios.

[0057] If this power for the reference illumination setting or the use scenario known in advance is denoted by

[00002]$P_{AR}^R$

and this power for the currently set illumination setting or the unknown use scenario is denoted by

[00003]$P_{AR}^U,$

then the following arises under the assumption of a linear relationship:

[00004]$\begin{array}{cc}\frac{T^U}{T^R}=\frac{P_{AR}^U}{P_{AR}^R}=\mu & \text{­­­(2)}\end{array}$

[0058] This results in the calibration parameter for the currently set illumination setting or the unknown use scenario as follows:

[00005]$\begin{array}{cc}{q}^U=q^R\cdot \mu \cdot \frac{T_S^R}{T_S^U}& \text{­­­(3)}\end{array}$

[0059] Consequently, different calibration parameters q.sup.U arise depending on the currently set illumination setting or use scenario.

[0060] In this respect, FIG. 2 shows merely exemplary possible time profiles of the calibration parameter q.sup.U for three different use scenarios (denoted by UC1, UC2 and UC3, respectively). A value of the calibration parameter q.sup.U < 1 emerges at all times for the use scenario UC1. For the use scenario UC2, the value of the calibration parameter q.sup.U deviates from the value one only within a comparatively short period of time after the optical system has been put into operation. In the use scenario UC3, q.sup.U < 1 applies for comparatively short times, q.sup.U > 1 for comparatively large times, and the calibration parameter q.sup.U (corresponding to an “overshoot”) temporarily increases relatively strongly on a medium time scale.

[0061] In embodiments of the disclosure, the temperature measurement with at least one temperature sensor 420 can also be carried out to ascertain a time profile. In this way, it is possible to take account of the fact that, depending on the position of the temperature sensor, a temperature change occurring at the incidence surface of the optical element or mirror becomes “visible” on the temperature sensor with various degrees of quickness, which is to say the respective temperature sensor “sees” the temperature change belatedly.

[0062] To this end, FIG. 3 shows a diagram in which the time profile of the respective measurement signal is plotted for two different sensor positions, in comparison with the actual average temperature at the incidence surface of the optical element. According to FIG. 3, the sought-after average temperature T at the incidence surface rises for instance immediately after the optical system is switched on, whereas sensors located at different distances from the incidence surface deliver correspondingly delayed measurement signals. Using the heat conduction equation

[00006]$\begin{array}{cc}\frac{\partial T\left(\stackrel{.fwdarw.}{r},t\right)}{\partial T}-\alpha \cdot \Delta T\left(\stackrel{.fwdarw.}{r},t\right)=f\left(\stackrel{.fwdarw.}{r},t\right)& \text{­­­(4)}\end{array}$

with the thermal conductivity α and the source f(r,t),it is possible to specify for instance the following dependence of the respective sensor-based measured temperature T.sub.s on the distance r.sub.z of the temperature sensor from the incidence surface merely as an example for an analytical relationship - without the disclosure being limited thereto - under simplified boundary conditions (for example the assumption of an infinitely large optical element with surfaces parallel to the xy-plane and the assumption of a homogeneous light load):

[00007]$\begin{array}{cc}\frac{T_S}{T}=q\approx e^{\frac{-r_z{}^2}{4\alpha t}}-\sqrt{\frac{\pi r_z{}^2}{4\alpha t}}\left[1-erf\left(\sqrt{\frac{r_z{}^2}{4\alpha t}}\right)\right]& \text{­­­(5)}\end{array}$

[0063] As a result, the temperature T.sub.s measured by a temperature sensor on account of its position can thus be determined as a function of time and used for a determination of the calibration parameter for reliable characterization of the heating state of the optical element or mirror, already for the aforementioned start-up phase immediately after switching on the optical system.

[0064] In further embodiments, a numerical determination of the calibration parameter q.sup.U can be carried out, in which case, in addition to knowledge of the currently used illumination setting and reticle, a model for the optical system that is as realistic as possible is used as a basis. On the basis thereof, the temperature distribution setting-in in the optical element can be predicted and the temperature T.sub.s which a temperature sensor would measure at its respective position can be calculated. On the basis thereof, the calibration parameter q.sup.U can be determined using equation (1).

[0065] If the currently used illumination setting is not specifically known, it may also be possible to select from a previously created library (lookup table) of illumination settings that illumination setting which comes closest to the desired setting or the currently used illumination setting.

[0066] In further embodiments, a temperature measurement or temperature simulation can be replaced by a wavefront measurement or wavefront simulation in order to use the wavefront (e.g., determined in the region of the wafer plane) to draw conclusions about the thermal change in the optical element or mirror. In this case, too, the currently used illumination setting can be classified by comparing the deformation ascertained on the basis of the measured wavefront with the deformation of illumination settings calculated in advance, in order in this way to determine the calibration parameter q.sup.U.

[0067] 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.