EUV mirror system, method for operating an EUV mirror system, projection lens for a microlithographic projection exposure system, computer program product

Abstract

An EUV mirror system comprising an EUV mirror, a support structure (31), and a control unit (34), wherein the EUV mirror has a mirror body (38) and an optical surface (32) formed on the mirror body (38), and wherein the support structure (31) supports the EUV mirror. The EUV mirror system comprises a cooling system for cooling a system component (31, 38) of the EUV mirror system, wherein the cooling system comprises a pump (33) and a cooling channel (37). The pump is configured to convey a cooling fluid along the cooling channel (37). An input variable representing a heat load acting on the system component (31, 38) is supplied to the control unit (34). The control unit (34) processes the input variable and a thermal model of the system component (31, 38) to determine a target value for the volume flow of the cooling fluid.The control unit (34) derives a control command for the cooling system from the setpoint for the volume flow, so that the volume flow is changed and a predetermined maximum change rate (75) of the volume flow is not exceeded. The cooling system is controlled by the control command. The invention also relates to a method for operating an EUV mirror system, a projection lens for a microlithographic projection exposure system, and a computer program product.

Description

The invention relates to an EUV mirror system, a method for operating an EUV mirror system, a projection objective for a microlithographically projected exposure apparatus and a computer program product.Microlithographic projection exposure apparatuses are used for the production of integrated circuits having particularly small structures. A photomask illuminated with very short-wave, extreme ultraviolet radiation (EUV radiation) is imaged onto a lithography object in order to transfer the mask structure to the lithography object.The projection exposure apparatus comprises a plurality of EUV mirrors which have an optical surface on which the radiation is reflected. The mirrors have a precisely defined shape and are precisely positioned in order that the image of the photomask on the lithography object has a sufficient quality.During operation of the projection exposure apparatus, heat is supplied to the mirror body of an EUV mirror, with the result that the mirror body is heated. The heat supply results, among other things, from the fact that the EUV radiation impinging on the mirror body is not completely reflected, but rather is absorbed to a greater extent. A supporting structure carrying the mirror body is also heated, for example, by heat exchange with the mirror body or by the supply of infrared radiation. Temperature changes of a body generally involve thermal deformation. This is undesirable in the case of EUV mirrors of a microlithographically projected exposure apparatus, because the wavefront of the EUV radiation reflected at the optical surface changes when the geometric shape of the mirror changes. Thermal deformation is also undesirable in the supporting structure of the mirrors, because the position of the supported mirrors changes therewith. This usually leads to a reduction in the imaging quality.A cooling system can be used to keep the temperature of a system component of the EUV mirror system, in particular the temperature of the mirror body and / or the temperature of the supporting structure as constant as possible. A pump of the cooling system can be used to convey a cooling liquid along a cooling channel formed in the system component. The cooling liquid cools the system component by transferring heat from the system component to the cooling liquid in the cooling channel. A higher volume flow of the cooling liquid leads to an increased cooling capacity and vice versa. If the volumetric flow of the cooling liquid is kept constant, this has the advantage that turbulences of the cooling liquid within the cooling channel can be reduced. Turbulence of the cooling liquid within the cooling channel is undesirable because it can transfer as vibrations to the mirror body, which usually also leads to a reduction in the imaging quality.The thermal load acting on the mirror body can change over time, for example if no EUV radiation strikes the EUV mirror in dark phases or if the power of other heat sources changes. If the heat supply changes while the volumetric flow of the cooling liquid remains constant, an undesired temperature change of the mirror body occurs.It is possible to monitor the temperature of the mirror body with a temperature sensor and to control the cooling power by changing the volume flow of the cooling liquid on the basis of a detected temperature change. However, this has the disadvantage that the change in the volume flow can only take place with a time delay, namely after the temperature of the mirror body has already changed. The change in the volume flow must also take place quickly in this case, so that the undesired temperature change does not become too great. A rapid change in the volume flow in turn has the disadvantage that undesired turbulences can arise. In this way, it cannot be achieved satisfactorily that the temperature of the mirror body is kept as constant as possible and at the same time undesirable turbulence of the cooling liquid is avoided.The object of the invention is to provide an EUV mirror system, a method for operating an EUV mirror system, a projection objective for a microlithographically projected exposure apparatus and a computer program product, with which these disadvantages are reduced. The object is achieved with the features of the independent claims. Advantageous embodiments are specified in the dependent claims.An EUV mirror system according to the invention comprises an EUV mirror, a supporting structure, a cooling system for cooling a system component of the EUV mirror system and a control unit. The EUV mirror has a mirror body and an optical surface formed on the mirror body. The support structure supports the EUV mirror. The cooling system includes a pump and a cooling channel. The pump is configured to convey a cooling liquid along the cooling channel. The control unit is supplied with an input variable which represents a thermal load acting on the system component. The control unit processes the input variable and a thermal model of the system component in order to determine a setpoint value for the volumetric flow of the cooling liquid. The control unit derives a control command for the cooling system from the setpoint value for the volume flow, so that the volume flow is changed and so that a predefined maximum rate of change of the volume flow is not exceeded. The cooling system is controlled with the control command, so that the cooling system influences the volume flow on the basis of the control command.The invention proposes not only reacting to an already occurring temperature change of the system component, but also to link to a change of a thermal load acting on the system component. The influence of the change on the temperature of the system component is predicted with a thermal model and the volumetric flow of the cooling liquid is set on the basis of the prediction. The thermal load acting on a system component can change abruptly, for example when the EUV radiation is switched off for a change of the wafer or of the photomask. Conventional regulation can result in a correspondingly rapid change in the volume flow. The invention has recognized that it becomes possible with the time obtained by the prediction to temporally stretch the change in the volume flow without an excessive temperature change of the system component occurring. This leads to the proposal according to the invention to preset a maximum rate of change for the volume flow and to actuate the cooling system such that this maximum rate of change is not exceeded. This makes it possible to react to a change in the thermal state of the mirror body without undesired oscillations of the mirror body being excited.In one embodiment, the system component is the mirror body of the EUV mirror. The cooling channel may extend within the mirror body. In another embodiment, the system component is the support structure that supports the EUV mirror. The cooling channel may extend within the support structure. The invention also includes embodiments in which the mirror body is provided with a cooling channel and the supporting structure is provided with a cooling channel and in which the volume flow in the cooling channel of the mirror body and the volume flow in the cooling channel of the supporting structure are adjusted according to the invention.The heat source of the heat load acting on the mirror body may be the EUV radiation impinging on the optical surface of the mirror, which is partially absorbed. The change in the thermal load acting on the mirror body can then result from the fact that no EUV radiation impinges on the optical surface of the mirror body during a dark phase.Another heat source may be a heating device with which thermal energy is supplied to the mirror body. The heating device can be designed, for example, to conduct suitable electromagnetic radiation, in particular infrared radiation, onto the mirror body. The heating device can uniformly heat the mirror body, for example in a preheating phase before the operation of the projection exposure apparatus. It is also possible for the heating device to be designed as a sector heater which heats only specific regions of the mirror body (sectorial). A sector heater can be used, for example, to supply heat to those regions of the mirror body which are heated only to a lesser extent by EUV radiation.A change in the thermal load acting on the mirror body can then result from the heating device being switched on or off, the heating device changing between uniform and sectorial heating of the mirror body, or the power of the electromagnetic radiation which the heating device conducts on the mirror body changing. The support structure carrying the mirror body, which is in a heat exchange with the mirror body, can form a further heat source. The change in the heat load acting on the mirror body can then result from the change in the heat which is absorbed or emitted by the supporting structure itself.A change in the heat load acting on the supporting structure can result, for example, from the fact that the thermal radiation reflected at other system components changes or from the fact that the quantity of heat emitted by another system component changes. If, for example, the EUV radiation is switched off, this has the consequence that the mirror body emits less heat. It is also possible for the power of a heating device directed onto the supporting structure to change.The input representative of a thermal load acting on the system component may be a binary value about the activity of a heat source. For example, the value 0 may mean that the heat source does not transfer heat energy to the system component and the value 1 may mean that the heat source transfers heat energy to the system component. In another embodiment, the input is a value of the amount of thermal energy transferred from the heat source to the system component. The input variable can be a time-dependent and / or a value for a specific point in time. For example, the input variable can comprise information about a future point in time at which a thermal load acting on the system component changes, i.e. at which, for example, the EUV radiation impinging on the optical surface of the mirror will be omitted. The input variable can also comprise a plurality of such values.The thermal model of the mirror body may be chosen to establish a relationship between the thermal load acting on the system component and the temperature of the system component so that future temperature values of the mirror body may be predicted. In the thermal model, for example, the density, thermal conductivity and / or specific heat capacity of the material of the system component can be taken into account. The thermal model may be obtained, for example, by a machine learning method. The thermal model may take into account a heat transfer between the mirror body and the support structure.In one embodiment, the control unit processes the input variable and the thermal model in order to determine a future temperature value of the system component on the assumption that the volume flow of the coolant is kept constant at its current value. In other words, the control unit then predicts the future profile of the temperature of the mirror body at a constant volume flow. The temperature value can be above or below a current temperature of the mirror body or correspond to this. On the basis of the difference between the future temperature value thus determined and a setpoint value for the temperature of the system component, the control unit can determine a setpoint value for the cooling power which is necessary in order to keep the temperature of the mirror body constant. The control unit then determines the setpoint value profile for the volume flow on the basis of the setpoint value for the cooling capacity of the cooling system. For this purpose, the control unit can use information such as the nature of the cooling liquid or a relationship between the rotational speed of the pump and the volumetric flow rate of the cooling liquid, for example. There are several variants for the practical implementation of the process. The control unit can be designed, for example, to carry out the relevant calculations online in each case before a new control command is transmitted. It is also possible to store relationships determined once in a table and to generate the control commands on the basis of values read from the table.The maximum rate of change refers to the change in the volume flow with which the volume flow is guided to the setpoint value. Starting from an actual value of the volume flow, a transition phase follows in which the volume flow changes. At the end of the transition phase, the volume flow corresponds to the setpoint value. During the transition phase, there is no time when the rate of change of the volumetric flow is greater than the predetermined maximum rate of change. The transition phase extends over a time period which can be, for example, between 10 s and 500 s, preferably between 30 s and 300 s. The duration of the transition phase ensures that a sufficiently smooth control trajectory can be predefined, along which the volume flow is controlled from the actual value to the setpoint value of the volume flow without undesired oscillations of the mirror body being excited.The maximum rate of change of the volume flow can be predefined in such a way that, on the one hand, the setpoint value of the volume flow is reached as quickly as possible, while, on the other hand, the transition phase is so long that no substantial oscillations of the system component are excited. The maximum rate of change can also result from the form of a predefined control trajectory for the transition from the actual value of the volume flow to the setpoint value of the volume flow. The control trajectory is advantageous if it does not contain any frequencies which lead to undesired oscillations of the mirror body. It is also advantageous if the control trajectory fulfills the system dynamics, so that the volume flow is physically able to satisfy the control trajectory. Which value for the maximum rate of change results from these requirements can be determined, for example, by experiments or by simulations. The predefined maximum rate of change of the volume flow can be, for example, less than 30% / min, preferably less than 20% / min, further preferably less than 10% / min.In one embodiment, the transition from the actual value of the volume flow to the setpoint value of the volume flow is carried out at a constant rate of change which corresponds to the predefined maximum rate of change. The predefined maximum rate of change then defines a type of ramp along which the volume flow is transferred from the actual value to the new setpoint value. Embodiments are also possible in which the rate of change changes during the transition. Here, the transition may include portions in which the rate of change is less than the predetermined maximum rate of change, but may not include portions in which the rate of change exceeds the predetermined maximum rate of change. The transition can be effected in such a way that the second derivative of the rate of change does not exceed a predefined maximum value either. This makes it possible to make a further contribution to avoiding flux-induced oscillations.In one specific embodiment, a control trajectory is predefined for the transition from the actual value of the volume flow to the setpoint value of the volume flow. The control trajectory may be non-linear. If the control trajectory is non-linear, this has the advantage that sudden changes in the volume flow can be avoided, in particular at the beginning and at the end of the regulation. The control trajectory may correspond to a sigmoid or S curve, for example. If the volume flow follows the control trajectory, then the predefined maximum rate of change of the volume flow is not exceeded. For example, the control trajectory is selected such that its steepest point corresponds to a change in the volume flow which is less than or equal to the predefined maximum rate of change. The control trajectory can be chosen to take into account a dead time required until the cooling system has set the setpoint for the volume flow. For example, the dead time may originate from the inertia of the pump or the cooling liquid. In other words, the boundary conditions of the maximum rate of change and the dead time may limit the selection of possible control trajectories.From an intended transition between the actual value of the volume flow and the setpoint value of the volume flow, control commands for the pump of the cooling system can be derived, so that the pump is controlled in accordance with the desired transition. For example, the rotational speed of the pump can be regulated on the basis of the control trajectory and the volume flow can thus be influenced accordingly. The cooling liquid may be water or other cooling fluids customary in industry.The mirror system may include a temperature sensor to determine a temperature measurement from the system component. The temperature sensor can be formed on the system component. The temperature measurement value can be supplied to the control unit. For this purpose, the temperature sensor can be connected to the control unit via an information line. The temperature measurement value can be processed in the control unit in order to detect and compensate control errors. The control error can result, for example, from the difference between a predicted temperature value and a temperature measurement value.The control unit can comprise a storage block in which, inter alia, the thermal model and the maximum rate of change of the volumetric flow can be stored. It is also possible for relationships between specific changes in a heat load and associated control commands for the pump to be stored in tabular form in the storage block.The cooling system may affect the flow rate by changing the speed of the pump. For this purpose, the pump can be controlled by the control unit via a control line with the control command, for example. It is also possible for the cooling system to comprise valves or slide valves controlled by the control unit in order to influence the volume flow.The cooling system may include a first cooling channel formed in the mirror body and a second cooling channel formed in a support structure supporting the mirror body. The cooling system may also include a first cooling structure of a plurality of cooling channels formed in the mirror body and a second cooling structure of a plurality of cooling channels formed in a support structure supporting the mirror body. The second cooling passage may be connected to the first cooling passage. The invention can also be used to keep the temperature of the supporting structure supporting the mirror body as constant as possible.The invention further relates to a projection objective having a plurality of EUV mirrors, with which a photomask is imaged into an image plane. One or more EUV mirrors of the projection objective can be configured as a component of an EUV mirror system according to the invention. The invention further relates to a microlithographically projected exposure apparatus having such a projected objective.The invention also relates to a method for operating a mirror system having an EUV mirror, wherein the EUV mirror has a mirror body and an optical surface formed on the mirror body, and having a supporting structure carrying the EUV mirror. A pump of a cooling system conveys a cooling liquid along a cooling channel formed within a system component of the EUV system in order to cool the system component. An input variable is supplied to a control unit, which represents a thermal load acting on the system component. In the control unit, the input variable and a thermal model of the system component are processed in order to determine a setpoint value for the volume flow of the cooling liquid, wherein the control unit derives a control command for the cooling system from the setpoint value for the volume flow, such that the volume flow is changed and a predefined maximum rate of change of the volume flow is not exceeded, and wherein the cooling system is controlled with the control command.The invention also relates to a computer program product or a set of computer program products, comprising program parts which, when loaded into a computer or into interconnected computers which are connected to a device according to the invention, are designed for carrying out the method according to the invention.The disclosure comprises developments of the EUV mirror system having features which are described in connection with the method according to the invention. The disclosure comprises developments of the method with features which are described in connection with the EUV mirror system according to the invention.The invention is described below by way of example with reference to the attached drawings on the basis of advantageous embodiments. The following are shown: FIG. 1 : an embodiment of a projection exposure apparatus according to the invention; FIG. 2 : shows a schematic illustration of an EUV mirror system according to the invention; FIG. 3 : shows a schematic illustration of a further EUV mirror system according to the invention; FIG. 4 : shows a schematic plot of the temperature of a mirror body of the EUV mirror system over time with a constant volume flow of the cooling liquid; FIG. 5 : shows a schematic plot over time of a control trajectory according to the invention; FIG. 6 : shows a temperature profile of the mirror body sought according to the invention over time; FIG. 7 : shows a schematic illustration of a further embodiment of a mirror system according to the invention; FIG. 8 : shows a schematic illustration of a further EUV mirror system according to the invention.FIG. 1 schematically illustrates a microlithographically EUV projection exposure apparatus. The projection exposure apparatus comprises an exposure beam source 14, an illumination system 10 and a projection objective 22, which are operated together in a vacuum chamber 23. A negative pressure is applied in the vacuum chamber 23 during operation of the EUV projection exposure apparatus.The exposure beam source 14 generates electromagnetic radiation in the EUV range, i.e. in particular with a wavelength between 5 nm and 30 nm. The exposure radiation emanating from the exposure beam source 14 is focused by a collector 15 into an intermediate focal plane 16. Exposure radiation passing out of the intermediate focus plane 16 is guided by the illumination system 10 into an object plane 12, so that an object field in the object plane 12 is illuminated with uniform radiation intensity.The illumination system 10 comprises a deflection mirror 17 with which the exposure radiation is deflected onto a first facet mirror 18. A second facet mirror 19 is arranged downstream of the first facet mirror 18. The facets of the first facet mirror 18 are imaged into the object plane 12 by the second facet mirror 19.A photomask 13 is arranged in the object plane 12, which is imaged into an image plane 21 via a plurality of mirrors M 1-M 6 of the projection objective 22. A pattern formed on the photomask 13 is transferred to a radiation sensitive layer of a wafer 20 disposed in the image plane 21. The photomask 13 hangs on a first scanning device 24, the wafer 20 rests on a second scanning device 25, so that the wafer 20 can be exposed in a scanning process in which the photomask 13 and the wafer 20 are moved synchronously with one another.FIG. 2 shows a mirror device in which a mirror body 38 of a mirror M 1-M 6 is held on a supporting structure 31 via actuators 30. The position of the mirror body 38 relative to the supporting structure 31 can be changed via the actuators 30 in order to align and position the mirror body 38. An optical surface 32 is formed on the mirror body 38, at which EUV radiation is reflected. In the projection exposure apparatus from FIG. 1, each of the mirrors M 1-M 6 of the projection lens 22 is designed as a mirror device according to FIG. 2. It is also possible to equip only a part of the mirrors M 1-M 6 in this way.A cooling channel 37 is formed in the interior of the mirror body 38, which in this embodiment extends along a serpentine path through the mirror body 38. The cooling channel 37 belongs to a cooling system in which a cooling liquid is conveyed along a closed cooling circuit by a pump 33.In the embodiment shown, the cooling circuit extends from the pump 33 via a feed line 35 to the cooling channel 37 and via a return line 36 back to a storage container 41, from which the cooling liquid is drawn in by means of the pump 33. The supply line 35 is connected to the mirror body 38 via an input connection 39, and the return line 36 is connected to the mirror body 38 via an output connection 40. The lead 35 and the return 36 have sufficient flexibility so that adjustment and alignment of the mirrors is not obstructed. The cooling liquid absorbs heat arising from the absorbed EUV radiation and removes it from the mirror body 38.The mirror system comprises a control unit 34 which controls the operation of the mirror system as a function of different input variables, wherein, inter alia, the thermal state of the mirror body 38 is influenced by control commands. One aspect of this is that the control unit 34 actuates the pump 33 of the cooling system with control commands, so that the pump 33 influences the volume flow of the cooling liquid on the basis of the control command by changing its rotational speed.When the cooling performance of the cooling system corresponds to the supplied heat performance, the temperature of the mirror body 38 remains constant. If a heat load is omitted while the state of the cooling system remains unchanged, the mirror body 38 cools down, FIG. 4 shows a schematic plot of the temperature 61 of the mirror body, plotted over a time axis 60, for this case. More specifically, in the present example, the thermal load acting on the mirror body by the EUV radiation is eliminated at the time T 0, so that overall less heat is supplied to the mirror body. Because the volumetric flow of the cooling liquid remains unchanged, a future temperature value 71 at a future point in time T 1 is below the temperature value 70 at the point in time T 0 of the omission of the heat load. In other words, the cooling system cools the mirror body after the heat load has ceased, which leads to an undesired temperature change 72.In order to counteract this, in the present exemplary embodiment, the control unit 34 processes information about the fact that a thermal load will drop at the time T 0 as an input variable and predicts the future temperature value 71 on the basis of a thermal model. The thermal model is stored in a memory block 43. The control unit 34 then determines a setpoint value for the cooling capacity of the cooling system on the basis of the predicted temperature value 71. The setpoint value for the cooling power is determined, so that the temperature of the mirror body 38 is kept as constant as possible. In this example, the cooling performance needs to be reduced to compensate for the omission of the heat load. The control unit 34 then establishes a relationship between the setpoint value for the cooling capacity and a setpoint value for the volumetric flow of the cooling liquid resulting therefrom, in order to determine a control command for the pump 33. In this example, the volumetric flow of the cooling liquid must be reduced in order to reduce the cooling capacity.In the present exemplary embodiment, the ascertained control command has the effect that the rotational speed 62 of the actuated pump 33 follows a control trajectory 73. FIG. 5 shows a schematic plot of the control trajectory 73 plotted over a time axis 60. The control trajectory 73 is, in this example, a non-linear S-curve, on the basis of which the rotational speed 62 of the pump 33 is reduced over time. Because the control trajectory is non-linear, sudden changes in the rotational speed 62 of the pump 33 are avoided, in particular at the beginning and at the end of the regulation, and thus undesirable turbulences of the cooling liquid are prevented. The control trajectory 73 already starts the reduction of the rotational speed 62 of the pump 33 in a time period 74 shortly before the time T 0 of the omission of the heat load. This is possible because the control unit 34 has processed as input the information that the thermal load will drop at the time T 0. This makes it possible to select a flatter S curve as the control trajectory and to maintain a predefined maximum rate of change 75 that results from a predefined maximum rate of change of the volumetric flow in order to avoid undesired turbulence. In other words, the time period 74 is used to start the regulation already before the time T 0. The control trajectory 73 also takes into account the inertia of the pump, i.e. a dead time of the cooling system, with the time period 74.FIG. 6 shows an idealised plot of the temperature 61 of the mirror body with regulation of the volume flow according to the invention, plotted over a time axis 60. By regulating the volume flow on the basis of the control trajectory 73, the temperature 61 remains constant over time, with the result that no undesired temperature change occurs.FIG. 3 shows a schematic illustration of a further EUV mirror system according to the invention, in which the cooling channel 37 extends through the supporting structure 31. In this case, the control unit 34 influences the thermal state of the supporting structure 31 with the control commands.FIG. 7 shows a schematic illustration of a mirror system with feedback. The feedback consists in that a temperature sensor 51 determines a temperature measurement value from the mirror body and transmits it to the control unit 34 via an information line 52. The control unit 34 recognizes a control error from the temperature measurement value and adjusts the determined control trajectory 73 to compensate for the control error.FIG. 8 shows a schematic illustration of a further EUV mirror system according to the invention, having a first cooling channel 37 which is formed in the mirror body 38, a second cooling channel 80 which is formed in a supporting structure 31 carrying the mirror body, and a third cooling channel 81 which is formed in a further supporting structure 31 carrying the mirror body. The first cooling passage 37 is connected to the third cooling passage 81. A second pump 83 is associated with the second cooling channel 80. The second pump 83, like the pump 33, is controlled with control commands which are determined by the control unit 34.

Claims

EUV mirror system having an EUV mirror and a supporting structure (31), wherein the EUV mirror has a mirror body (38) and an optical surface (32) formed on the mirror body (38) and wherein the supporting structure (31) carries the EUV mirror, having a cooling system for cooling a system component (31, 38) of the EUV mirror system, wherein the cooling system comprises a pump (33) and a cooling channel (37), wherein the pump (33) is configured to convey a cooling liquid along the cooling channel (37), and having a control unit (34), wherein the control unit (34) is supplied with an input variable which represents a thermal load acting on the system component (31, 38), wherein the control unit (34) processes the input variable and a thermal model of the system component (31, 38), in order to determine a setpoint value for the volume flow of the cooling liquid, wherein the control unit (34) derives a control command for the cooling system from the setpoint value for the volume flow, such that the volume flow is changed and that a predefined maximum rate of change (75) of the volume flow is not exceeded, and wherein the cooling system is controlled with the control command.The EUV mirror system of claim 1, wherein the system component is the mirror body (38) and wherein the cooling channel (37) extends within the mirror body (38).The EUV mirror system according to claim 1, wherein the system component is the support structure (31) and wherein the cooling channel (37) extends within the support structure (31).The EUV mirror system according to any of the preceding claims, wherein the thermal model of the system component (31, 38) provides a relationship between the thermal load acting on the system component (31, 38) and the temperature (61) of the system component (31, 38), and wherein the thermal model is applied to predict a future temperature value (71) of the system component (31, 38).The EUV mirror system according to any one of the preceding claims, wherein the control unit (34) determines the setpoint value for the volume flow from a setpoint value for the cooling capacity of the cooling system.The EUV mirror system according to any of the preceding claims, wherein the input variable represents a future change of a thermal load acting on the system component (31, 38).The EUV mirror system according to any of the preceding claims, wherein the thermal model takes into account a heat transfer between the mirror body (38) and the support structure (31).The EUV mirror system according to any of the preceding claims, wherein the cooling system influences the volume flow on the basis of the control command, such that the volume flow follows a control trajectory (73).The EUV mirror system of claim 8, wherein the control trajectory (73) is non-linear.The EUV mirror system according to claim 8 or 9, wherein the steepest point (75) of the control trajectory (73) corresponds to a change in the volume flow which is smaller than or equal to the predefined maximum change rate (75).The EUV mirror system according to any of the preceding claims, wherein a heat source of the heat load acting on the mirror body (38) is an EUV radiation impinging on the optical surface (32) of the mirror and / or a heating device and / or the supporting structure (31).The EUV mirror system according to any one of the preceding claims, characterized bya temperature sensor (51) for determining a temperature measurement value from the system component (31, 38), wherein the temperature measurement value is supplied to the control unit (34) for determining a control error.Projection objective of a microlithography projection exposure apparatus, having a plurality of EUV mirrors (M1-M6), by means of which a photomask is imaged into an image plane, wherein one or more of the EUV mirrors (M1-M6) are part of an EUV mirror system according to one of Claims 1 to 12.Method for operating an EUV mirror system with an EUV mirror, wherein the EUV mirror has a mirror body (38) and an optical surface (32) formed on the mirror body (38), and with a supporting structure (31) which carries the EUV mirror, in which a cooling liquid is conveyed by a pump (33) of a cooling system along a cooling duct (37) formed within a system component (31, 38) of the EUV mirror system in order to cool the system component (31, 38), in which an input variable is fed to a control unit (34) which represents a thermal load acting on the system component (38), in which the control unit (34) processes the input variable and a thermal model of the system component (31, 38) in order to determine a setpoint value for the volume flow of the cooling liquid, in which the control unit (34) derives a control command for the cooling system from the setpoint value for the volume flow, so that the volume flow is changed and so that a predefined maximum rate of change (75) of the volume flow is not exceeded, and in which the cooling system is controlled with the control command.A computer program product or set of computer program products comprising program portions which, when loaded into a computer or interconnected computers connected to an EUV mirror system according to any one of claims 1 to 13, are adapted to perform the method according to claim 14.

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