Method and device for determining the heating state of a mirror in an optical system

Abstract

The disclosure provides a method and to an apparatus for determining the heating state of a mirror in an optical system, in particular in a microlithographic projection exposure apparatus. A method for determining the heating state of an optical element includes: measuring values of a first temperature that the optical element has at a first position using a temperature sensor; and estimating a second temperature that the optical element has at a second position, which is located at a distance from the first position, on the basis of the measured values, wherein estimating the second temperature is accomplished while taking into account a temporal change in the previously measured values.

Claims

1. A method of estimating a temperature of an incidence surface of an optical element in a microlithographic projection exposure apparatus, the optical element comprising a substrate supporting the incidence surface, the optical element having a channel extending into the substrate from a side of the optical element facing away from the incidence surface, the channel having a channel surface located a distance from the incidence surface, the method comprising: a) using a temperature sensor to measure values of a temperature of the channel surface, the temperature sensor being in direct contact with the channel surface; and b) based on the values measured in a) and taking into account a temporal change in the values measured in a), estimating the temperature of the incidence surface, wherein during use of the optical element, electromagnetic radiation impinges on the incidence surface, and wherein estimating the temperature of the incidence surface comprises using an equation which comprises the term ${p\left(\frac{\partial T_{\mathrm{Sensor}}}{\partial t}\right)}^q,$ and wherein T.sub.sensor is a temperature value measured by the temperature sensor, t is time, and p and q are fit parameters.

2. The method of claim 1, wherein the optical element is in an illumination system of the microlithographic projection exposure apparatus.

3. The method of claim 1, wherein the channel surface faces away from the incidence surface.

4. The method of claim 1, wherein estimating the temperature during b) comprises taking into account previously ascertained temporal changes in the values measured in a).

5. The method of claim 1, further comprising using the temperature estimated in b) as an input signal to regulate a parameter that characterizes the optical element.

6. The method of claim 1, further comprising using the temperature estimated in b) to control pre-heating of the optical element to at least partially compensate temporal changes in the heating state of the optical element occurring during use of the optical element.

7. The method of claim 1, wherein the optical element is a mirror.

8. The method of claim 7, wherein, during use of the optical element, the electromagnetic radiation that impinges on the incidence surface has an operating wavelength of less than 30 nm.

9. The method of claim 1, wherein, during use of the optical element, the electromagnetic radiation that impinges on the incidence surface has an operating wavelength of less than 30 nm.

10. The method of claim 1, wherein: the channel surface faces away from the incidence surface; and estimating the temperature during b) comprises taking into account previously ascertained temporal changes in the values measured in a).

11. A method of estimating a temperature of an incidence surface of an optical element in a microlithographic projection exposure apparatus, the optical element comprising a substrate supporting the incidence surface, the optical element having a channel extending into the substrate from a side of the optical element facing away from the incidence surface, the channel having a channel surface located a distance from the incidence surface, the method comprising: a) using a temperature sensor to measure values of a temperature of the channel surface, the temperature sensor being in direct contact with the channel surface; and b) based on the values measured in a) and taking into account a temporal change in the values measured in a), estimating the temperature of the incidence surface, wherein during use of the optical element, electromagnetic radiation impinges on the incidence surface), and wherein estimating the temperature of the incidence surface comprises using an equation which comprises the term $p{\int }_{-\infty }^{t}d{\tau \left(\frac{\partial T_{\mathrm{Sensor}}}{\partial t}\right)}^q{e}^{-\infty \left(t-\tau \right)},$ and wherein T.sub.sensor is a temperature value measured by the temperature sensor, t is time, τ is a point in time, α represents a decay constant, and p and q are fit parameters.

12. The method of claim 11, wherein the optical element is in an illumination system of the microlithographic projection exposure apparatus.

13. The method of claim 11, wherein the channel surface faces away from the incidence surface.

14. The method of claim 11, wherein estimating the temperature during b) comprises taking into account previously ascertained temporal changes in the values measured in a).

15. The method of claim 11, further comprising using the temperature estimated in b) as an input signal to regulate a parameter that characterizes the optical element.

16. The method of claim 11, further comprising using the temperature estimated in b) to control pre-heating of the optical element to at least partially compensate temporal changes in the heating state of the optical element occurring during use of the optical element.

17. The method of claim 11, wherein the optical element is a mirror.

18. The method of claim 17, wherein, during use of the optical element, the electromagnetic radiation that impinges on the incidence surface has an operating wavelength of less than 30 nm.

19. The method of claim 11, wherein, during use of the optical element, the electromagnetic radiation that impinges on the incidence surface has an operating wavelength of less than 30 nm.

20. The method of claim 11, wherein: the channel surface faces away from the incidence surface; and estimating the temperature during b) comprises taking into account previously ascertained temporal changes in the values measured in a).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The disclosure is explained in greater detail below on the basis of exemplary embodiments illustrated in the accompanying figures, in which:

(2) FIG. 1 shows a schematic illustration of the possible construction of a microlithographic projection exposure apparatus designed for operation in the EUV;

(3) FIG. 2 shows a schematic illustration for explaining the possible construction of a mirror in which the method according to the disclosure can be realized; and

(4) FIGS. 3A, 3B and 4 show diagrams for demonstrating exemplary improvements of the prediction quality that are attainable with a method according to the disclosure when ascertaining the thermal state of a mirror.

DETAILED DESCRIPTION OF EMBODIMENTS

(5) FIG. 1 shows a schematic illustration of a projection exposure apparatus 100 which is designed for operation in the EUV range and in which the disclosure is able to be realized in an exemplary manner.

(6) According to FIG. 1, an illumination device of the projection exposure apparatus 100 comprises a field facet mirror 103 and a pupil facet mirror 104. The light from a light source unit comprising in the example an EUV light source (plasma light source) 101 and a collector mirror 102 is directed onto the field facet mirror 103. A first telescope mirror 105 and a second telescope mirror 106 are arranged in the light path downstream of the pupil facet mirror 104. A deflection mirror 107 is arranged downstream in the light path, the deflection mirror directing the radiation that is incident thereon onto an object field in the object plane of a projection lens comprising six mirrors 121-126. At the location of the object field, a reflective structure-bearing mask 131 is arranged on a mask stage 130, the mask being imaged with the aid of the projection lens into an image plane in which a substrate 141 coated with a light-sensitive layer (photoresist) is situated on a wafer stage 140.

(7) The method according to the disclosure for determining the heating state of an optical element can be applied for example to any desired mirror of the microlithographic projection exposure apparatus of FIG. 1.

(8) FIG. 2 shows, in a merely schematic and highly simplified illustration, the possible construction of a mirror having a mirror substrate 210 (for example made from ULE™) and a reflection layer system 205 (having for example an alternating sequence of molybdenum (Mo) and silicon (Si) layers), wherein the optical effective surface of the mirror is denoted with “201.”

(9) During operation of the optical system or the microlithographic projection exposure apparatus, the electromagnetic radiation that is incident on the optical effective surface or incidence surface 201 (indicated by the arrow in FIG. 2) is partially absorbed and, as explained in the introductory part, results in heat being generated and in an associated thermal expansion or deformation, which in turn can lead to an impairment of the imaging properties of the optical system.

(10) With reference to FIG. 2 to FIG. 4, a method according to the disclosure will now be described for correspondingly estimating the heating state of the mirror in question and for possibly correspondingly controlling a suitable correction mechanism (such as pre-heaters described in the introductory part).

(11) According to FIG. 2, a temperature sensor 220 is located in a hole that has been introduced as an access channel 211 into the mirror substrate 210 from the mirror's rear side.

(12) In the text below, T.sub.Sensor(t) denotes the temperature measured with the temperature sensor 220, T.sub.real(t) denotes the average mirror temperature that actually leads to the surface deformation, and T.sub.Prediction(t) denotes the temperature that is assumed proceeding from the sensor signal of the temperature sensor 220 and can serve for example for regulating a pre-heater. Active mirror heating using such a pre-heater can take place in phases of comparatively low absorption of EUV useful radiation as described in the introductory part, wherein the active mirror heating is correspondingly decreased as the absorption of the EUV useful radiation increases.

(13) According to the disclosure, the prediction temperature T.sub.Prediction(t) is now determined not directly from the temperature T.sub.Sensor(t) measured by the temperature sensor 220 but with additional consideration of the temporal change of the temperature

(14) $\left(\frac{\partial T_{sensor}}{\partial t}\right).$

(15) In one exemplary embodiment, the following approach for the prediction temperature can be selected:

(16) $\begin{array}{cc}{T}_{\mathrm{Prediction}}\left(t\right)=T_{\mathrm{Sensor}}\left(t\right)+{p\left(\frac{\partial T_{Sensor}}{\partial t}\right)}^q& \left(1\right)\end{array}$

(17) In equation (1), both the temperature measured with the temperature sensor 220 (sensor temperature) and the temperature that is present on the optical effective surface 201 of the mirror (as the value for the prediction temperature, e.g. using an infrared camera) can be determined for the suitable selection of the (fit) parameters p and q in a measurement and calibration setup. Then, the values for which equation (1) best describes the results or value pairs (T.sub.Prediction, T.sub.Sensor) can be used for the parameters p and q.

(18) In further embodiments, value pairs can also be ascertained for suitably establishing the parameters p, q in equation (1) using a simulation (e.g. an FE simulation).

(19) The disclosure is not limited to the previous approach according to equation (1) for the functional relationship between the temperature T.sub.Sensor(t) measured with the temperature sensor 220 and the prediction temperature T.sub.Prediction(t). In further embodiments, other approaches or functional relationships in which in each case the temporal change of the temperature values measured with the temperature sensor 220 is taken into account can also be selected. In particular, the following (integral) approach can also be selected:

(20) $\begin{array}{cc}{T}_{\mathrm{Prediction}}\left(t\right)=T_{\mathrm{Sensor}}\left(t\right)+p{\int }_{-\infty }^{t}d{\tau \left(\frac{\partial T_{sensor}}{\partial t}\right)}^q{e}^{-\propto \left(t-\tau \right)}& \left(2\right)\end{array}$

(21) In the integral term given in equation (2), the value of the temporal gradient of the temperature T.sub.Sensor measured by the surface sensor 220 is set here in each case at the time point τ (as integration variable). According to equation (2), the previous temporal profile of the temporal gradient of the temperature T.sub.Sensor measured with the temperature sensor 220 is summed. In that case, α denotes a further parameter that is present in equation (2) in addition to the parameters p, q and that describes the “forgetting” of respectively earlier contributions in the sense of a decay constant.

(22) Also taking into consideration the previous time profile of the temporal gradient of T.sub.Sensor in accordance with equation (2) makes it possible to take into consideration the (e.g. exponential) temporal profile of the temperature via the additional information provided to this extent and for example to take account of the presence of a comparatively steep increase by way of a correspondingly strong post-regulation (in the sense of overdrive).

(23) FIGS. 3A and 3B serve to demonstrate the improvement in the prediction quality that is attainable in the method according to the disclosure on the basis of a simplified model for the temporal profile of the temperature.

(24) Here, curve “A” describes the temporal profile of the temperature on the optical effective surface 201 or the mirror surface, curve “B” describes the temporal profile of the temperature in the mirror material at a depth of 10 mm, and curve “C” describes the temporal profile of the temperature obtained according to the disclosure based both on the relevant “depth information” (that is to say for example the absolute temperature measured at the relevant depth with a corresponding temperature sensor) and on the “correction contribution” taken into account according to the disclosure (that is to say the temporal change of the temperature that is measured in the depth in a sensor-based manner).

(25) As can be seen from FIGS. 3A and 3B, the curve “C” obtained on the basis of the correction contribution according to the disclosure describes the temperature that is actually present on the mirror surface according to curve “A” significantly better in particular in the “starting phase” than curve “B.” The smaller diagram in FIG. 3B over a larger time period furthermore shows that the curve “C” also ultimately converges to the correct temperature value.

(26) FIG. 4 shows a diagram for illustrating a further improvement of the prediction quality that is possible according to the disclosure with the “history” taken into account for example by using the approach described above on the basis of equation (2).

(27) Curve “D” here describes the temporal profile of the temperature error or of the deviation of the temperature predicted solely from the sensor signal of the temperature sensor 220 from the temperature that is actually present on the mirror surface. Curve “E” describes the temporal profile of the corresponding temperature error in the case in which the prediction temperature is ascertained according to the disclosure while taking into account the temporal gradient of the sensor signal (for example according to equation (1)), and curve “F” describes the temporal profile of the corresponding temperature error with the “history” additionally being taken into account when the prediction temperature is ascertained for example according to the approach of equation (2).

(28) It can be seen that by additionally taking account of the history (that is to say of the previous time profile of the temporal gradient of T.sub.Sensor), a further improvement of the prediction quality is attained.

(29) Even though the disclosure 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, it goes without saying for the person skilled in the art that such variations and alternative embodiments are also 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.