Methods and devices for driving micromirrors

Abstract

A micromirror of a micromirror array in an illumination system of a microlithographic projection exposure apparatus can be tilted through a respective tilt angle about two tilt axes. The micromirror is assigned three actuators which can respectively be driven by control signals in order to tilt the micromirror about the two tilt axes. Two control variables are specified, each of which is assigned to one tilt axis and which are both assigned to unperturbed tilt angles. For any desired combinations of the two control variables, as a function of the two control variables, one of the three actuators is selected and its control signal is set to a constant value, in particular zero. The control signals are determined so that, when the control signals are applied to the other two actuators, the micromirror adopts the unperturbed tilt angles as a function of the two control variables.

Claims

1. A method, comprising: providing a micromirror array arranged in a microlithographic illumination system, the micromirror array comprising more than two micromirrors; and switching the micromirrors from a first illumination setting to a second illumination setting, wherein: the second illumination setting is different from the first illumination setting; when the micromirrors are in the first setting, after impinging on the micromirror array, light impinges on an illumination field; when the micromirrors are in in the second setting, after impinging on the micromirror array, light impinges on the illumination field; and switching from the first illumination setting to the second illumination setting takes less than 50 milliseconds for each of the micromirrors.

2. The method of claim 1, wherein the micromirror array comprises more than 1000 micromirrors.

3. The method of claim 2, wherein: each micromirror is tiltable through a respective tilt angle about two tilt axes; and for at least some of the micromirrors, switching the micromirror from the first illumination setting to the second illumination setting comprises changing the tilt angle of the micromirror.

4. The method of claim 2, wherein for at least some of the micromirrors: the micromirror is assigned three actuators; and each of the three actuators is driven by control signals to tilt the micromirror about two tilt axes when changing the micromirror from the first illumination setting to the second illumination setting.

5. The method of claim 1, wherein: each micromirror is tiltable through a respective tilt angle about two tilt axes; and for at least some of the micromirrors, switching the micromirror from the first illumination setting to the second illumination setting comprises changing the tilt angle of the micromirror.

6. The method of claim 1, wherein for at least some of the micromirrors: the micromirror is assigned three actuators; and each of the three actuators is driven by control signals to tilt the micromirror about two tilt axes when changing the micromirror from the first illumination setting to the second illumination setting.

7. The method of claim 6, further comprising, for at least some of the micromirrors: specifying two control variables, each of the two control variables being assigned to one tilt axis, and both of the two control variables being assigned to unperturbed tilt angles; for any desired combinations of the two control variables, as a function of the two control variables, selecting one of the three actuators whose control signal is set to a constant value; determining the control signals so that, when the control signals are applied to the other two actuators, the micromirror adopts the unperturbed tilt angles as a function of the two control variables; and applying the control signals to the actuators.

8. The method of claim 1, further comprising using the microlithographic illumination system to illuminate a mask.

9. The method of claim 8, further comprising using a projection objective to project an image of the mask into a resist.

10. An illumination system, comprising: a micromirror array comprising more than two micromirrors; and drive electronics configured to drive each of the micromirrors, wherein: for at least some of the micromirrors, the drive electronics are configured to switch the micromirror from a first illumination setting to a second illumination setting in less than 50 milliseconds; the second illumination setting is different from the first illumination setting; for each of the at least some micromirrors, the illumination system is configured so that during use: when the micromirrors are in the first setting, after impinging on the micromirror array, light impinges on an illumination field; and when the micromirrors are in the second setting, after impinging on the micromirror array, light impinges on the illumination field; and the illumination system is a microlithographic illumination system.

11. The illumination system of claim 10, wherein the micromirror array comprises more than 1000 micromirrors.

12. The illumination system of claim 11, wherein: the drive electronics are configured to tilt each micromirror through a respective tilt angle about two tilt axes; and for at least some of the micromirrors, the drive electronics are configured to change the tilt angle of the micromirror to switch the micromirror from the first illumination setting to the second illumination setting.

13. The illumination system of claim 11, wherein for at least some of the micromirrors: the micromirror is assigned three actuators; and the drive electronics are configured to send control signals to each of the three actuators so that the actuators tilt the micromirror about two tilt axes when changing the micromirror from the first illumination setting to the second illumination setting.

14. The illumination system of claim 10, wherein: the drive electronics are configured to tilt each micromirror through a respective tilt angle about two tilt axes; and for at least some of the micromirrors, the drive electronics are configured to change the tilt angle of the micromirror to switch the micromirror from the first illumination setting to the second illumination setting.

15. The illumination system of claim 10, wherein for at least some of the micromirrors: the micromirror is assigned three actuators; and the drive electronics are configured to send control signals to each of the three actuators so that the actuators tilt the micromirror about two tilt axes when changing the micromirror from the first illumination setting to the second illumination setting.

16. The illumination system of claim 15, wherein, for at least some of the micromirrors, the illumination system is configured to: specify two control variables, each of the two control variables being assigned to one tilt axis, and both of the two control variables being assigned to unperturbed tilt angles; for any desired combinations of the two control variables, as a function of the two control variables, select one of the three actuators whose control signal is set to a constant value; determine the control signals so that, when the control signals are applied to the other two actuators, the micromirror adopts the unperturbed tilt angles as a function of the two control variables; and apply the control signals to the actuators.

17. An apparatus, comprising: a projection objective having an object plane and an image plane; and an illumination system configured to illuminate the object plane of the projection objective, wherein: the illumination system comprises: a micromirror array comprising more than two micromirrors; and drive electronics configured to drive each of the micromirrors; for at least some of the micromirrors, the drive electronics are configured to switch the micromirror from a first illumination setting to a second illumination setting in less than 50 milliseconds; the second illumination setting is different from the first illumination setting; for each of the at least some micromirros, the illumination system is configured so that during use: when the micromirrors are in the first setting, after impinging on the micromirror array, light impinges on an illumination field; and when the micromirrors are in the second setting, after impinging on the micromirror array, light impinges on the illumination field; the illumination system is a microlithographic illumination system; and the apparatus is a microlithographic projection exposure apparatus.

18. The apparatus of claim 17, wherein the micromirror array comprises more than 1000 micromirrors.

19. The apparatus of claim 18, wherein: the drive electronics are configured to tilt each micromirror through a respective tilt angle about two tilt axes; and for at least some of the micromirrors, the drive electronics are configured to change the tilt angle of the micromirror to switch the micromirror from the first illumination setting to the second illumination setting.

20. The apparatus of claim 18, wherein for at least some of the micromirrors: the micromirror is assigned three actuators; and the drive electronics are configured to send control signals to each of the three actuators so that the actuators tilt the micromirror about two tilt axes when changing the micromirror from the first illumination setting to the second illumination setting.

21. The apparatus of claim 17, wherein: the drive electronics are configured to tilt each micromirror through a respective tilt angle about two tilt axes; and for at least some of the micromirrors, the drive electronics are configured to change the tilt angle of the micromirror to switch the micromirror from the first illumination setting to the second illumination setting.

22. The apparatus of claim 17, wherein for at least some of the micromirrors: the micromirror is assigned three actuators; and the drive electronics are configured to send control signals to each of the three actuators so that the actuators tilt the micromirror about two tilt axes when changing the micromirror from the first illumination setting to the second illumination setting.

23. The apparatus of claim 22, wherein, for at least some of the micromirrors, the illumination system is configured to: specify two control variables, each of the two control variables being assigned to one tilt axis, and both of the two control variables being assigned to unperturbed tilt angles; for any desired combinations of the two control variables, as a function of the two control variables, select one of the three actuators whose control signal is set to a constant value; determine the control signals so that, when the control signals are applied to the other two actuators, the micromirror adopts the unperturbed tilt angles as a function of the two control variables; and apply the control signals to the actuators.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of the disclosure may be found in the following description of embodiments with the aid of the drawings, in which:

(2) FIG. 1 shows a simplified meridian section through the illumination system of a microlithographic projection exposure apparatus having a multi-mirror array;

(3) FIG. 2 shows a simplified perspective representation of a multi-mirror array, in which the individual micromirrors have a square outer contour;

(4) FIG. 3 shows a simplified perspective representation of a micromirror with a circular outer contour, and drive electronics for driving it;

(5) FIG. 4 shows a schematic representation which illustrates the relationship between the orientation and effect of the actuators and the tilting of the micromirror;

(6) FIG. 5 shows a diagram of the control signals applied to the actuators (top) and a force action resulting therefrom on the micromirror (bottom) according to a device known from the prior art;

(7) FIG. 6 shows a diagram of the control signals applied to the actuators (top) and a force action resulting therefrom on the micromirror (bottom) using the method according to the disclosure for driving the micromirror;

(8) FIG. 7 shows a schematic representation of a control and regulation algorithm for driving the micromirror.

DESCRIPTION OF PREFERRED EMBODIMENTS

(9) FIG. 1 shows an illumination system 10 of a microlithographic projection exposure apparatus in a highly simplified meridian section. The illumination system 10 is used for suitably illuminating a mask 12, which carries lithographic structures to be imaged. Usually, maximally uniform illumination of the mask 12 with projection light is desired so that the structures on the mask 12 can be transferred as uniformly as possible onto a wafer coated with a resist. Besides the total intensity striking a mask point, another factor which importantly influences the imaging properties of a microlithographic projection exposure apparatus is the illumination angle distribution of the projection light. This is intended to mean the distribution, between the different incidence angles at which the light strikes the mask point, of the total intensity of the light striking a mask point. In particular, it is desirable to adapt the illumination angle distribution to the type of structures to be illuminated, in order to achieve maximally optimal imaging.

(10) To this end the illumination system 10 includes a multiplicity of optical elements in its beam path, which in FIG. 1 are mostly represented only in a highly simplified way or not at all. The projection light generated by a laser 14 or another light source is initially expanded by first optics 16 and directed by a plane mirror 18 onto a microlens array 20. The plane mirror 18 is primarily used to keep the external dimensions of the illumination system 10 compact.

(11) Following the beam path further, the projection light strikes a so-called multi-mirror array 22 which will be explained below with reference to FIG. 2. The multi-mirror array 22 includes a multiplicity of micromirrors 24 which can be tilted, preferably individually, by a drive instrument 26. The upstream microlens array 20 focuses individual light sub-beams of the projection light onto the micromirrors 24.

(12) With the aid of the drive instrument 26, the individual micromirrors 24 can be tilted so that the light sub-beams of the projection light pass, via second optics 28, through a pupil surface 30 at freely selectable positions. A fly's eye integrator 32 arranged near this pupil surface 30 generates a multiplicity of secondary light sources in the pupil surface 30, which, via a third optics 34, uniformly illuminate an intermediate field plane 35 in which adjustable stop elements 37 are arranged. The third optics 34 generate an assignment between angles in the pupil surface 30 and positions in the intermediate field plane 35. The latter is imaged by an objective 36 onto a mask plane, in which the mask 12 is arranged. The intensity distribution in the pupil surface 30 therefore determines the illumination angle distribution not only in the intermediate field plane 35 but also in the mask plane.

(13) By different tilting of the individual micromirrors 24 of the multi-mirror array 22, different illumination angle distributions can therefore be set up very flexibly. With suitable driving of the micromirrors 24, the illumination angle distribution can even be modified during an exposure.

(14) FIG. 2 shows a simplified perspective representation of the multi-mirror array 22, in which the individual micromirrors 24 are plane and have a square contour. In order to direct an incident light sub-beam, which is generated by the microlens array 20 upstream in the beam path, onto any desired positions within the pupil surface 30, each micromirror 24 is mounted tiltably about two tilt axes x and y. The tilting per se about the tilt axes x, y can be controlled by actuators, and each micromirror 24 desirably is, if possible, assigned its own set of actuators so that the micromirrors 24 can be driven individually. Therefore, each micromirror 24 with the associated actuators thus forms a mirror unit 38 which is repeated over the multi-mirror array 22.

(15) The greater the number of mirror units 38 in a multi-mirror array 22 is, the more finely the intensity distribution can be resolved in the pupil surface 30. Multi-mirror arrays 22 having several thousand micromirrors 24, tiltable about two tilt axes x, y, may be envisaged. Such multi-mirror arrays 22 may, for example, be fabricated in MEMS technology.

(16) FIG. 3 shows a highly schematised perspective representation of an embodiment of a mirror unit 38 in which, unlike in the embodiment shown in FIG. 2, the micromirror 24 has a circular contour. Drive electronics, which are part of the drive instrument 26 and by which this micromirror 24 can be driven, are denoted by 39.

(17) The main component of the mirror unit 38 is the micromirror 24, which has a plane mirror support whose mirror surface 40 carries a coating which reflects the projection light being used, for example VUV light with a wavelength of 193 nm. The mirror surface 40 may be assigned a surface normal 42, with respect to which the incidence angle and emergence angle of the projection light striking the micromirror 24 can be defined. In the case of a curved mirror surface 40, an average surface normal 42 may be defined for this purpose.

(18) The micromirror 24 is mounted tiltably by a universal suspension (not shown) about the two tilt axes x and y, which are represented by dashes in FIG. 3. The universal suspension, which allows two degrees of freedom in rotation, exerts a restoring moment on the micromirror 24 by resilient solid-state articulations used for supporting it, and thus keeps it in a stable central position.

(19) A mirror electrode 44, which is produced for example by vapour depositing a metallic layer, is applied on the rear side of the micromirror 24. A first control electrode E.sub.1, a second control electrode E.sub.2 and a third control electrode E.sub.3, which are configured as circular disc segments with a vertex angle of 120, are applied opposite this mirror electrode 44, and therefore the entire micromirror 24, on the substrate of the mirror unit 38. For each mirror unit 38 of the multi-mirror array 22, the leads of the three control electrodes E.sub.1, E.sub.2 and E.sub.3 and the mirror electrode 44 are fed out from the MEMS unit and connected to the associated drive electronics 39.

(20) By applying various voltages U.sub.1, U.sub.2 and U.sub.3 between the mirror electrode 44 and the control electrodes E.sub.1, E.sub.2 and E.sub.3, the mirror electrode 44 is pulled by the individual control electrodes E.sub.1, E.sub.2 and E.sub.3 owing to electrostatic attraction. This attractive force between the two electrodes is converted by the universal suspension into tilting of the micromirror 24 about the two tilt axes x and y. The control electrodes E.sub.1, E.sub.2 and E.sub.3 therefore function as actuators for tilting the micromirror 24.

(21) The respective tilt angle is essentially dictated by the interaction of the various voltages U.sub.1, U.sub.2 and U.sub.3 and the restoring moments established by the solid-state articulations of the universal suspension. Other forces which act on the micromirror 24, for example gravitational forces, may be neglected in this embodiment since the micromirror 24 is intended to be very small here. Forces due to effects such as for example housing vibrations, air flows or thermal effects may, however, have a considerable influence on the real setting of the micromirror 24.

(22) In order to achieve the simplest possible driving of the mirror unit 38, in the present embodiment control variables SG.sub.x and SG.sub.y which are assigned, preferably linearly, to the desired unperturbed tilt angles .sub.x and .sub.y about the tilt axes x and y are transmitted to the drive electronics 39. In order to convert these control variables SG.sub.x, SG.sub.y into the voltages U.sub.1, U.sub.2 and U.sub.3, the drive electronics 39 include a converter 46, a multiplexer 48 and two signal amplifiers in the form of two controllable high-voltage output stages 50 and 52. The converter 46 receives the two control variables SG.sub.x and SG.sub.y on two input lines and, via a memory 45 and/or a calculation unit 47, determines the values of the three voltages U.sub.1, U.sub.2 and U.sub.3 which are applied to the control electrodes E.sub.1, E.sub.2 and E.sub.3. As a function of the control variables SG.sub.x, SG.sub.y, according to a method explained below with the aid of FIGS. 4 to 6, one control electrode E.sub.1, E.sub.2 or E.sub.3 is respectively selected, for example the first control electrode E.sub.1, and its voltage U.sub.1 relative to the mirror electrode 44 is set to zero by the multiplexer 48, i.e. it is placed at the same potential as the mirror electrode 44. Via two control lines, which lead from the converter 46 to the high-voltage output stages 50 and 52, the converter 46 then sets the other two voltages U.sub.2 and U.sub.3 to values which cause desired tilting of the micromirror 24. The multiplexer 48, which receives these two voltages U.sub.2 and U.sub.3 and is in turn driven by the converter 46, sets the selected control electrode E.sub.1 to zero and applies the associated voltages U.sub.2 and U.sub.3 to the other two control electrodes E.sub.2 and E.sub.3.

(23) In this way, at each instant only two signal amplifiers are involved for driving the three actuators, in order to achieve desired tilting of the micromirror 24 about the two tilt axes x, y. Owing to the multiplicity of mirror units 38 in a multi-mirror array 22, this greatly reduces the outlay on hardware which is desired for driving the micromirrors 24.

(24) If for example electromagnetic actuators are used instead of the electrostatic control electrodes E.sub.1, E.sub.2 or E.sub.3 in another embodiment, then the control signals, which are formed here by the various voltages U.sub.1, U.sub.2 and U.sub.3, may for example be generated by constant-current sources instead of the high-voltage output stages 50 and 52. In particular, the signals specified by the converter 46 may also be transmitted in purely digital form to the signal amplifiers being used, as is possible in the case of digital-analogue converters with an integrated power output stage.

(25) If the actuators being used involve a particular mutual signal, then instead of setting the control signal of the selected actuator to zero, a control signal which is constant over a plurality of mirror units 38 of the multi-mirror array 22 may also be applied by the multiplexer 48. In this way, the number of signal amplifiers per mirror unit 38 is reduced on average over the multi-mirror array 22 in this case as well.

(26) A calculation method by which the three control signals, which are applied to the actuators of the mirror unit 38, can be determined will be described below with the aid of FIGS. 4 to 6.

(27) The starting point of the method is the two control variables SG.sub.x and SG.sub.y, which are transmitted for example from the output of a control and regulation algorithm to the converter 46 and are assigned to desired angles, i.e. unperturbed tilt angles .sub.x and .sub.y of the micromirror 24 about the respective tilt axis x, y. For given control variables SG.sub.x and SG.sub.y, the method is therefore desirably capable of determining as precisely as possible the voltages U.sub.1, U.sub.2 and U.sub.3 which cause the micromirror 24 to tilt into the corresponding unperturbed tilt angles .sub.x and .sub.y.

(28) To a first approximation in the case of electrostatic actuators, the torques with which the control electrodes E.sub.1, E.sub.2 and E.sub.3 act on the micromirror 24 may be assumed to be proportional to the square of the respective voltage U.sub.1, U.sub.2 and U.sub.3. The restoring moments caused by the solid-state articulations of the universal suspension, which are in equilibrium with these torques, are approximately proportional to the tilting of the micromirror 24 so long as movement takes place in the elastic range of the solid-state articulations. The proportionality constants of the restoring moments, which are also referred to as rotational spring constants, may be set differently in the direction of the tilt axes x and y. With the aid of these rotational spring constants, which are indicated here by their reciprocal value as c.sub.x and c.sub.y for the sake of simpler formula notation, it is therefore possible to formulate the following simple model for the dependency of the unperturbed tilt angles .sub.x and .sub.y on the applied voltages U.sub.1, U.sub.2 and U.sub.3:

(29) $\begin{array}{cc}\left(\begin{array}{c}{}_x\\ {}_y\end{array}\right)=\left(\begin{array}{c}{c}_x{e}_{1x}\\ c_y{e}_{1y}\end{array}\right).Math.U_1^2+\left(\begin{array}{c}{c}_x{e}_{2x}\\ c_y{e}_{2y}\end{array}\right).Math.U_2^2+\left(\begin{array}{c}{c}_x{e}_{3x}\\ c_y{e}_{3y}\end{array}\right).Math.U_3^2& \left(1\right)\end{array}$

(30) Here, e.sub.1=(e.sub.1x,e.sub.1y).sup.T, e.sub.2=(e.sub.2x,e.sub.2y).sup.T and e.sub.3=(e.sub.3x,e.sub.3y).sup.T are proportionality factors in the coordinate system of the tilt axes x,y, which, through multiplication by the squared voltages U.sub.1.sup.2, U.sub.2.sup.2 and U.sub.3.sup.2, give the torque which is caused by the individual control electrodes E.sub.1, E.sub.2 and E.sub.3. These proportionality factors are therefore also influenced for example by different orientations or configurations of the control electrodes E.sub.1, E.sub.2 and E.sub.3 and the mirror electrode 44, but also by manufacturing tolerances during their production. Vectors respectively rotated through 120, the length of which corresponds to the force action of the electrodes, may be set as e.sub.1, e.sub.2 and e.sub.3 for the case assumed here in which the control electrodes E.sub.1, E.sub.2 and E.sub.3 are positioned ideally with threefold symmetry and are identical.

(31) By combining the coefficients and rearrangement, Equation (1) can be rewritten more simply as:

(32) $\begin{array}{cc}\left(\begin{array}{c}{}_x\\ {}_y\end{array}\right)=\left[\begin{array}{ccc}{p}_{1x}& p_{2x}& p_{3x}\\ p_{1y}& p_{2y}& p_{3y}\end{array}\right].Math.\left(\begin{array}{c}{U}_1^2\\ U_2^2\\ U_3^2\end{array}\right)=:T\left(\begin{array}{c}{U}_1^2\\ U_2^2\\ U_3^2\end{array}\right)& \left(2\right)\end{array}$

(33) The entries of the matrix T, which represent the model parameters p.sub.1x, p.sub.1y, p.sub.2x, p.sub.2y, p.sub.3x, p.sub.3y of the mirror unit 38, may be obtained either from design data or by a measurement method. An example of such a measurement method will be explained in more detail below.

(34) If there is not a quadratic dependency of the torque on the respective voltages U.sub.1, U.sub.2 and U.sub.3 owing to a different embodiment, for example of the form of electrode, the vector with the squared voltages may at any time be replaced by arbitrary functions f.sub.i(U.sub.i) in the model above.

(35) Equation System (2) has infinitely many solutions, which may partly be restricted by using voltages U.sub.1, U.sub.2 and U.sub.3 greater than or equal to zero for the sake of simplicity, since the electrostatic attraction effect between two electrodes is independent of the polarity of the voltage being used and the high-voltage output stages 50, 52 can therefore be configured for a voltage range with only one polarity.

(36) If one of the voltages U.sub.1, U.sub.2 and U.sub.3 is now set equal to zero, then Equation System (2) becomes uniquely solvable since there are now only two unknowns to be determined. For particular tilting of the micromirror 24 about the two tilt axes x and y, however, it is not possible to set any voltage U.sub.1, U.sub.2 or U.sub.3 to zero. For this reason, in a first step it is desirable to select the control electrode E.sub.1, E.sub.2 and E.sub.3 whose voltage U.sub.1, U.sub.2 or U.sub.3 can be set to zero.

(37) As may be seen in particular from FIG. 4, the control variables SG.sub.x and SG.sub.y span a control variable space which is assigned to the space of the unperturbed tilt angles .sub.x and .sub.y about the tilt axes x and y. In principle this assignment or coordinate transformation may be made in any desired way, the control variables SG.sub.x and SG.sub.y being assigned preferably independently of one another and linearly to their respective tilt angle. In the present embodiment, an identical assignment between the control variables SG.sub.x, SG.sub.y and the unperturbed tilt angles .sub.x, .sub.y is assumed. The coordinate axes of the two spaces therefore correspond to each other, as is indicated in FIG. 4. In the control variable space, various combinations of control variables SG.sub.x, SG.sub.y can now be plotted as different control variable vectors SGV.

(38) Furthermore, as is indicated in FIG. 4 by the control electrodes E.sub.1, E.sub.2 and E.sub.3 and effective tilt vectors w.sub.1, w.sub.2 and w.sub.3 assigned to them, the effects of the control electrodes E.sub.1, E.sub.2 and E.sub.3, which they have on the micromirror 24, may also be taken into account in this control variable space. The respective effective tilt vector w.sub.1, w.sub.2 or w.sub.3 of a control electrode E.sub.1, E.sub.2 or E.sub.3 is in this case given by the control variables SG.sub.x, SG.sub.y that are assigned to those unperturbed tilt angles .sub.x, .sub.y which the micromirror 24 adopts when only this control electrode E.sub.1, E.sub.2 or E.sub.3 is driven with a type of standard voltage.

(39) Except for multiplication by a standard voltage and the representation in the control variable space, the effective tilt vectors w.sub.1, w.sub.2 or w.sub.3 therefore correspond to the entries, or more precisely the columns, of the matrix T, which represent the model parameters p.sub.1x, p.sub.1y, p.sub.2x, p.sub.2y, p.sub.3x, p.sub.3y of the mirror unit 38 in Equation (2). In the embodiment having control electrodes E.sub.1, E.sub.2 and E.sub.3 arranged with threefold symmetry, an alignment angle between the first control electrode E.sub.1 and the tilt axis y, which is due for example to manufacturing tolerances, is therefore also taken into account.

(40) If a desired combination of perturbed tilt angles .sub.x and .sub.y, or more precisely the control variables SG.sub.x, SG.sub.y assigned to them, is now plotted as a control variable vector SGV in the diagram of FIG. 4, then this may also be represented by a linear combination of the three effective tilt vectors w.sub.1, w.sub.2 or w.sub.3 of the three control electrodes E.sub.1, E.sub.2 and E.sub.3.

(41) According to the prior art, the equation system of Equation (2) has previously been solved as shown in FIG. 5, with the additional constraint condition that the total force F.sub.z which acts on the mirror element 24 is kept constant. This means that the sum U.sub.1.sup.2+U.sub.2.sup.2+U.sub.3.sup.2 is desirably of equal value for each control variable vector SGV. This has given for example the voltage profiles of U.sub.1 (continuous), U.sub.2 (dashed) and U.sub.3 (dotted) shown at the top in FIG. 5 for one complete rotation of a given control variable vector SGV about the origin of the diagram in FIG. 4, which corresponds to moving the surface normal 42 of the micromirror 24 on a conical surface with a given vertex angle.

(42) In the present embodiment, however, the constraint condition of keeping constant the total force F.sub.z on the micromirror 24 is omitted, and instead one of the three control electrodes E.sub.1, E.sub.2 or E.sub.3 is selected and its voltage U.sub.1, U.sub.2 or U.sub.3 is set to zero. Admittedly, this cannot exclude the possibility that the micromirror 24 will execute minor excursion movements in the direction perpendicular to the tilt axes. Such excursion movements, however, are generally not detrimental to the optical function since the excursion movements in the case of plane micromirrors 24 do not affect the directions in which the projection light is being deviated.

(43) To this end, the orientation of the control variable vector SGV with respect to the effective tilt vectors w.sub.1, w.sub.2 or w.sub.3 of the three control electrodes E.sub.1, E.sub.2 and E.sub.3 is determined. In this case, the equation

(44) $\begin{array}{cc}=\arctan \left(\frac{\mathrm{SGy}}{\mathrm{SGx}}\right)& \left(3\right)\end{array}$
may be used in order to determine the angle , while taking the respective quadrant into account.

(45) If the angle lies in the angle range [,120+], i.e. the control variable vector SGV lies between the effective tilt vector w.sub.1 of the first control electrode E.sub.1 and the effective tilt vector w.sub.2 of the second control electrode E.sub.2, then the control signal of the third control electrode E.sub.3 i.e. U.sub.3 is set=0 and the control variable vector SGV is generated as a linear combination of the effective tilt vectors w.sub.1 and w.sub.2. For the solution of the linear equations system, this gives:

(46) $\begin{array}{cc}\begin{array}{c}\left(\begin{array}{c}{}_x\\ {}_y\end{array}\right)=\left[\begin{array}{ccc}{p}_{1x}& p_{2x}& p_{3x}\\ p_{1y}& p_{2y}& p_{3y}\end{array}\right].Math.\left(\begin{array}{c}{U}_1^2\\ U_2^2\\ 0\end{array}\right)\\ =\left[\begin{array}{cc}{p}_{1x}& p_{2x}\\ p_{1y}& p_{2y}\end{array}\right].Math.\left(\begin{array}{c}{U}_1^2\\ U_2^2\end{array}\right)\\ =T^{}\left(\begin{array}{c}{U}_1^2\\ U_2^2\end{array}\right)\end{array}& \left(4\right)\end{array}$

(47) This equation can be solved uniquely by

(48) $\begin{array}{cc}\left(\begin{array}{c}{U}_1\\ U_2\end{array}\right)=+\sqrt{T^{-1}\left(\begin{array}{c}{}_x\\ {}_y\end{array}\right)}& \left(5\right)\end{array}$
when a positive solution is selected for the root. The root in Equation (5) is to be understood as taking the root component by component.

(49) If the angle lies in the angle range [120+,240+], then, as may be seen in FIG. 4, U.sub.1=0 is set and the other two equations are determined according to

(50) $\begin{array}{cc}\left(\begin{array}{c}{U}_2\\ U_3\end{array}\right)=+\sqrt{T^{-1}\left(\begin{array}{c}{}_x\\ {}_y\end{array}\right)}\mathrm{with}{T}^{}=\left[\begin{array}{cc}{p}_{2x}& p_{3x}\\ p_{2y}& p_{3y}\end{array}\right]& \left(6\right)\end{array}$

(51) For within [240+,360+], U.sub.2=0 is correspondingly set and U.sub.1 and U.sub.3 are determined according to

(52) $\begin{array}{cc}\left(\begin{array}{c}{U}_1\\ U_3\end{array}\right)=+\sqrt{T^{-1}\left(\begin{array}{c}{}_x\\ {}_y\end{array}\right)}\mathrm{with}{T}^{}=\left[\begin{array}{cc}{p}_{1x}& p_{3x}\\ p_{1y}& p_{3y}\end{array}\right]& \left(7\right)\end{array}$

(53) In the solutions above, the two unperturbed tilt angles .sub.x and .sub.y can now generally be replaced by assignment functions .sub.i=f(SG.sub.i) using the control variables SG.sub.x, SG.sub.y. A method of calculating the three voltages U.sub.1, U.sub.2 and U.sub.3 from the control variables SG.sub.x and SG.sub.y is therefore obtained for all control variable vectors SGV.

(54) The upper part of FIG. 6 illustrates the profile of the voltages U.sub.1 (continuous), U.sub.2 (dashed) and U.sub.3 (dotted) and shows that with the method used here, inter alia lower maximum voltages are used in order to achieve particular tilting, since the control electrode E.sub.1, E.sub.2 or E.sub.3 whose effective tilt vector w.sub.1, w.sub.2 or w.sub.3 contains a component that would oppose the control variable vector SGV is respectively set to zero. The working range of the high-voltage output stages 50, 52 can therefore be selected to be smaller, so that smaller quantisation stages for the individual voltages and concomitantly smaller errors can be achieved. The lower part of FIG. 6 also shows the variation in the total force F.sub.z, which occurs in the method described here and leads to the excursion movements already mentioned above.

(55) As already indicated above, a measurement method may be used for determining the model parameters p.sub.1x, p.sub.1y, p.sub.2x, p.sub.2y, p.sub.3x, p.sub.3y, i.e. the entries of the matrix T, in order to take into account process variations in the production of the mirror units 38. In such a measurement method, various voltages U.sub.1, U.sub.2 and U.sub.3 are applied and the tilt angles .sub.x and .sub.y resulting therefrom are measured. In order to demonstrate this, Equation System (2) may be rewritten as

(56) $\begin{array}{cc}\left(\begin{array}{c}{}_x\\ {}_y\end{array}\right)=\left[\begin{array}{cccccc}{U}_1^2& U_2^2& U_3^2& 0& 0& 0\\ 0& 0& 0& U_1^2& U_2^2& U_3^2\end{array}\right]\underset{\stackrel{.fwdarw.}{p}}{\underset{}{\left(\begin{array}{c}{p}_{1x}\\ p_{2x}\\ p_{3x}\\ p_{1y}\\ p_{2y}\\ p_{3y}\end{array}\right)}}.& \left(8\right)\end{array}$

(57) This notation now illustrates that the original entries p.sub.1x, p.sub.1y, p.sub.2x, p.sub.2y, p.sub.3x, p.sub.3y of the matrix T, in the form of a column vector {right arrow over (p)}, represent the unknowns of an equation system with two equations.

(58) The model parameters p.sub.1x, p.sub.1y, p.sub.2x, p.sub.2y, p.sub.3x, p.sub.3y could not be determined with only one measurement, since the equation system of Equation (8) would not be sufficiently determined. With N measurement points, N3 being desired, i.e. there are N assignments of the three voltages U.sub.1, U.sub.2 and U.sub.3 to the two tilt angles .sub.x and .sub.y, Equation (8) can however be set up N times:

(59) 0$\begin{array}{cc}\underset{\stackrel{.fwdarw.}{}}{\underset{}{\left(\begin{array}{c}{}_{x1}\\ {}_{y1}\\ \mathrm{.Math.}\\ {}_{\mathrm{xN}}\\ {}_{\mathrm{yN}}\end{array}\right)}}+\stackrel{.fwdarw.}{e}=\underset{\underset{H}{}}{\left[\begin{array}{cccccc}{U}_{11}^2& U_{21}^2& U_{31}^2& 0& 0& 0\\ 0& 0& 0& U_{11}^2& U_{21}^2& U_{31}^2\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ U_{1N}^2& U_{2N}^2& U_{3N}^2& 0& 0& 0\\ 0& 0& 0& U_{1N}^2& U_{2N}^2& U_{3N}^2\end{array}\right]}\underset{\stackrel{.fwdarw.}{p}}{\underset{}{\left(\begin{array}{c}{p}_{1x}\\ p_{2x}\\ p_{3x}\\ p_{1y}\\ p_{2y}\\ p_{3y}\end{array}\right)}}& \left(9\right)\end{array}$

(60) The vector {right arrow over (e)} stands for the measurement inaccuracy inherent in each measurement. If the voltages U.sub.11 to U.sub.3N are now selected so that the matrix H has full rank, then the unknown model parameters p.sub.1x, p.sub.1y, p.sub.2x, p.sub.2y, p.sub.3x, p.sub.3y can be determined from Equation System (9).

(61) The parameter vector {right arrow over (p)} is in this case estimated by
{right arrow over (p)}=(H.sup.TH).sup.1H.sup.T{right arrow over ()}(10)
for example with a least-squares estimator or another estimator, in order to eliminate as far as possible the error of the parameter vector, or more precisely the influence of the measurement inaccuracies, by the larger number of measurements.

(62) Instead of modelling the relationship between the applied voltages U.sub.1, U.sub.2 and U.sub.3 and the unperturbed tilt angles .sub.x, .sub.y resulting therefrom in a calculation model, a somewhat different method of determining the voltages U.sub.1, U.sub.2 and U.sub.3 consists in simply reading it from a so-called look-up table which has been determined beforehand.

(63) To this end, N.sup.2 unperturbed tilt angles .sub.x, .sub.y within the angle ranges of the two tilt axes x, y are activated in a measurement run, and these are stored together with the voltages U.sub.1, U.sub.2 and U.sub.3 used for this in a table, preferably in an electronic memory. The N.sup.2 measurement points are expediently distributed uniformly on an NN grid inside the angle ranges of the two tilt axes x, y. The activation of the individual tilt angles may for example be carried out with the aid of a regulation algorithm, to which the measured tilt angles .sub.x, .sub.y are in turn supplied. The individual tilt angles of the measurement run may, however, also be activated only with a control algorithm in which the real tilt angles are merely measured and stored with the associated voltages U.sub.1, U.sub.2 and U.sub.3 in the table.

(64) For each combination of control variables SG.sub.x, SG.sub.y and the look-up table, with the aid of a given assignment between the control variables SG.sub.x, SG.sub.y and the unperturbed tilt angles .sub.x, .sub.y, the associated voltages U.sub.1, U.sub.2 and U.sub.3 can be read out during operation and applied to the control electrodes E.sub.1, E.sub.2 and E.sub.3. Since the values of the voltages U.sub.1, U.sub.2 and U.sub.3 are available only at the positions of the NN tilt angles .sub.x, .sub.y, intermediate values may be calculated by interpolation, for example bilinearly or bicubically.

(65) These procedures just explained may also be combined, in order to set one of the voltages U.sub.1, U.sub.2 or U.sub.3 to zero as explained above by already setting one of the voltages U.sub.1, U.sub.2 or U.sub.3 to zero when compiling the look-up table, or more precisely when activating the N.sup.2 tilt angles .sub.x, .sub.y. The outlay on signal amplifiers can also be kept small by this approach.

(66) Since the mirror units 38 in genuine systems are always subject to certain perturbations z, a control and regulation algorithm 54 which adjusts real actual values of the micromirror 24, according to specified target tilt angles, will be explained below.

(67) To this end, FIG. 7 shows a diagram of the control and regulation system 54 as part of the drive instrument 26, the various components of which may be embodied individually as devices. Preferably, however, the functions of the control and regulation algorithm 54 are undertaken by digital algorithms, which are carried out for example in a digital signal processor (DSP). For this reason, comments below about various components are also intended to refer to embodiments in the form of algorithms. Various embodiments may optionally contain only individual parts of these control and regulation components.

(68) The regulation section represented by dashes, which acts on the perturbation z, includes the mirror unit 38 including the micromirror 24 and the associated drive electronics 39. If a linear, preferably identical assignment has been selected for assigning the control variables SG.sub.x, SG.sub.y to the unperturbed tilt angles .sub.x, .sub.y of the micromirror 24 about the two tilt axes x, y, then, owing to the drive electronics 39, the considerations about the control and regulation components remain free from the complex dependencies of the unperturbed tilt angles .sub.x, .sub.y on the three control signals of the actuators, which are applied here in the form of voltages U.sub.1, U.sub.2 and U.sub.3 to the control electrodes E.sub.1, E.sub.2 and E.sub.3 of the mirror unit 38. The logic of the control and regulation components is therefore kept straightforward, which inter alia simplifies their layout.

(69) At the input of the control and regulation algorithm 54, a trajectory determination unit 56 receives the target angle, through which the micromirror 24 is finally intended to be tilted, from a superordinate system or the user. From these target tilt angles, the trajectory determination unit 56 then determines a sequence of a setpoint tilt angles which converts the actual tilt angles, through which the micromirror 24 is instantaneously tilted, into the target tilt angles. This allows, for example, smooth activation of the target tilt angles. Calibration data, which can be used in order to adapt the actual tilt angles with respect to superordinate systems, may furthermore be transmitted to the trajectory determination unit 56.

(70) The sequence of setpoint tilt angles is transmitted to a regulator 58 that determines or corrects the control variables SG.sub.X, SG.sub.Y, which are transmitted to the drive electronics 39 of the mirror unit 38. To this end the regulator 58 uses a regulation difference e, which is given by the setpoint tilt angles at the instant in question and negative feedback of the actual tilt angles measured by a monitoring system 60. A regulator 58 configured as a simple PID regulator may be parameterised according to the regulation characteristics of the regulation section.

(71) A predictive controller 62 is furthermore provided in the present embodiment, which contains an inverse system dynamics model of the regulation section and thus anticipates the reaction of the micromirror 24 to a change in the control variables SG.sub.X, SG.sub.Y. Such a solution is recommendable in particular owing to the multiplicity of individual mirror units 38, since the regulation frequency of the closed control loop via the regulator 58, dictated essentially by the limited bandwidth of the monitoring system 60, may be relatively low.

(72) The predictive controller 62 therefore includes the predictable reaction of the control section, and the regulator 58 corrects the control variables SG.sub.X, SG.sub.Y specified by the predictive controller 62 in order to compensate for the perturbation z acting on the control section and errors of the drive electronics 39.

(73) The control variables SG.sub.X, SG.sub.Y thus determined and optionally corrected are then converted by the drive electronics 39 into control signals according to the method presented above, and these are applied to the actuators of the mirror unit 38.

(74) All the described methods and devices for driving a micromirror 24 in a multi-mirror array 22 may also be employed in illumination systems for the use of EUV light, i.e. light with a wavelength in the range of a few nanometers, for example 13.6 nm.

(75) The above description of the preferred embodiments has been given by way of example. From the disclosure given, those skilled in the art will not only understand the present disclosure and its attendant advantages, but will also find apparent various changes and modifications to the structures and methods disclosed. The applicant seeks, therefore, to cover all such changes and modifications as fall within the spirit and scope of the disclosure, as defined by the appended claims, and equivalents thereof.