Lithographic Apparatus Controller System

Abstract

The controller system is configured to control the plant and includes a feedforward controller for providing a feedforward signal to the plant based on a reference state signal, and a feedback controller system for providing a feedback signal to the plant based on a difference between the reference state signal and a plant state signal representative of an actual state of the plant. The feedback controller system includes an integrator, a trajectory generator, and a selector. The feedback controller system is configured to operate in a first control mode or a second control mode as a function of the reference state, where in the first control mode, the feedback controller system operates the selector to select a trajectory generator output signal generated by the trajectory generator, and in the second control mode, the feedback controller system operates the selector to select an integrator output signal generated by the integrator.

Description

[Technical field]

[0001] The present invention relates to a controller system, a stage comprising such a controller system, and a lithographic apparatus comprising such a controller system. [Background technology]

[0002] A lithographic apparatus is a machine built to apply a desired pattern onto a substrate. Lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus can project a pattern (often referred to as a "design layout" or "design") from, for example, a patterning device (e.g., mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., wafer).

[0003]

[0003] As semiconductor manufacturing processes continue to advance, the dimensions of circuit elements have been continually scaled down, while the amount of functional elements, such as transistors, per device has been steadily increasing for decades, following a trend colloquially known as "Moore's Law". To accommodate Moore's Law, the semiconductor industry is pursuing technologies that allow it to create smaller and smaller features. To project a pattern onto a substrate, a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the features that are patterned on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. To form smaller features on a substrate than a lithographic apparatus using radiation with a wavelength of, for example, 193 nm, a lithographic apparatus using extreme ultraviolet (EUV) radiation with a wavelength in the range of 4 nm to 20 nm, for example, 6.7 nm or 13.5 nm, may be used.

[0004]

[0004] The lithographic apparatus may perform repetitive movements when projecting a pattern onto a substrate, for example performing a scanning movement to scan a portion of the substrate. Acceleration and deceleration may be performed between the scanning movements to change the speed or direction of the movement. The movements, such as the movements of a stage of the lithographic apparatus, may be controlled by a controller. The controller may implement, for example, proportional control, integrator control, and differentiator control. Summary of the Invention

[0005]

[0005] In view of the above, it is an object of the present invention to provide a lithographic apparatus having a high throughput.

[0006]

[0006] According to one embodiment of the present invention, a feedforward controller configured to provide a feedforward signal to a plant based on a reference state signal; a feedback controller system configured to provide a feedback signal to the plant based on a difference between a reference state signal and a plant state signal representative of an actual state of the plant; A controller system configured to control a plant is provided, comprising: The feedback controller system includes an integrator, a trajectory generator, and a selector configured to selectively output one of a trajectory generator output signal generated by the trajectory generator and an integrator output signal generated by the integrator as a feedback signal to a plant; the feedback controller system is configured to operate in a first control mode or a second control mode as a function of the reference state signal; The feedback controller system is configured to, in a first control mode, operate the selector to select a trajectory generator output signal generated by the trajectory generator; The feedback controller system is configured to operate, in a second control mode, the selector to select the integrator output signal generated by the integrator.

[0007]

[0007] According to a further embodiment of the present invention, there is provided a stage comprising a controller system according to the present invention configured to control a position of the stage, the reference state signal being a position setpoint of the stage.

[0008] According to yet another embodiment of the present invention there is provided a lithographic apparatus comprising a controller system according to the present invention. [Brief description of the drawings]

[0009]

[0009] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which:

[0010] [Figure 1] 1 depicts a schematic overview of a lithographic apparatus according to one embodiment of the invention; [Diagram 2] 2 illustrates a detailed view of a portion of the lithographic apparatus of FIG. 1; [Diagram 3] 1 illustrates diagrammatically a position control system as part of a positioning system that may be used in an embodiment of the present invention; [Figure 4] 1 illustrates a controller system. [Diagram 5] 5 illustrates a timing diagram showing the time response obtained from the controller system of FIG. 4. [Figure 6] 1 illustrates a controller system according to one embodiment. [Figure 7] 7 illustrates a timing diagram showing the time response obtained from the controller system described in FIG. 6. [Figure 8] A block diagram is shown, on the basis of which the switching stability of the controller system according to FIG. 6 is explained. [Figure 9]A block diagram is shown, on the basis of which the switching stability of the controller system according to FIG. 6 is explained. [Figure 10] The Lur'e system representation is illustrated, based on which the switching stability of the controller system described in FIG. 6 is explained. [Figure 11] A complex plane diagram is illustrated based on which the switching stability of the controller system described in FIG. 6 is explained. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011]

[0010] In this document, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including ultraviolet (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and EUV (extreme ultraviolet, e.g., having a wavelength in the range of about 5 to 100 nm).

[0012]

[0011] The terms "reticle", "mask" or "patterning device" as used herein may be broadly construed as referring to a general purpose patterning device that can be used to impart a patterned cross-section to an incoming radiation beam that corresponds to a pattern to be produced on a target portion of a substrate. The term "light valve" may also be used in this context. Besides the classical mask (transmissive or reflective mask, binary mask, phase-shifting mask, hybrid mask, etc.), examples of other such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0013] 1 illustrates a lithographic apparatus LA, which includes an illumination system (also called illuminator) IL configured to condition a radiation beam B (e.g. UV radiation, DUV radiation or EUV radiation), a mask support (e.g. mask table) MT constructed to support a patterning device (e.g. mask) MA and coupled to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g. wafer table) WT configured to hold a substrate (e.g. resist coated wafer) W and coupled to a second positioner PW constructed to accurately position the substrate support according to certain parameters, and a projection system (e.g. refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0014]

[0013] In operation, the illumination system IL receives a radiation beam from the radiation source SO, for example via the beam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic and / or other types of optical components, or any combination thereof, for directing, shaping and / or controlling the radiation. The illuminator IL may be used to condition the radiation beam B such that its cross-section has a desired spatial and angular intensity distribution in a plane of the patterning device MA.

[0015]

[0014] The term "projection system" PS as used herein should be interpreted broadly to encompass various types of projection systems including refractive optical systems, catadioptric optical systems, anamorphic optical systems, magnetic optical systems, electromagnetic optical systems, and / or electrostatic optical systems, or any combination thereof, as appropriate to the exposure radiation used and / or other factors such as the use of an immersion liquid or the use of a vacuum. Where the term "projection lens" is used herein, it may be considered synonymous with the more general term "projection system" PS.

[0016]

[0015] The lithographic apparatus LA may be of a type in which at least a part of the substrate may be covered with a liquid having a relatively high refractive index, e.g. water, so as to fill a space between the projection system PS and the substrate W. This is also called immersion lithography. More information about immersion techniques is given in US Pat. No. 6,952,253, which is incorporated herein by reference.

[0017] The lithographic apparatus LA may be of a type having two or more substrate supports WT (also referred to as "dual stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel and / or a substrate W located on one substrate support WT may be used for exposing a pattern on the substrate W while a preparation step for a subsequent exposure of the substrate W is performed on the other substrate support WT.

[0018]

[0017] In addition to the substrate support WT, the lithographic apparatus LA may include a measurement stage. The measurement stage is arranged to hold a sensor and / or a cleaning device. The sensor may be arranged to measure a property of the projection system PS or a property of the radiation beam B. The measurement stage may hold a number of sensors. The cleaning device may be arranged to clean a part of the lithographic apparatus, for example a part of the projection system PS or a part of the system for providing immersion liquid. When the substrate support WT is remote from the projection system PS, the measurement stage may move below the projection system PS.

[0019]

[0018] In operation, the radiation beam B is incident on a patterning device MA, e.g. a mask, which is held on a mask support MT and is patterned by a pattern (design layout) present on the patterning device MA. Having traversed the mask MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of a substrate W. By means of the second positioner PW and a position measurement system IF, the substrate support WT can be moved accurately, e.g. to position various target portions C at focused and aligned positions in the path of the radiation beam B. Similarly, the first positioner PM, and possibly further position sensors (not explicitly shown in Fig. 1), can be used to accurately position the patterning device MA with respect to the path of the radiation beam B. The patterning device MA and substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the illustrated substrate alignment marks P1, P2 occupy dedicated target portions, the substrate alignment marks may be located in spaces between the target portions. When the substrate alignment marks P1, P2 are located between target portions C, they are known as scribe-line alignment marks.

[0020]

[0019] To clarify the invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes, namely, the x-axis, the y-axis, and the z-axis. Each of the three axes is orthogonal to the other two axes. Rotation about the x-axis is called the Rx rotation. Rotation about the y-axis is called the Ry rotation. Rotation about the z-axis is called the Rz rotation. The x-axis and the y-axis define a horizontal plane, whereas the z-axis is vertical. The Cartesian coordinate system is not limiting to the invention and is used only for clarity. Alternatively, another coordinate system, such as a cylindrical coordinate system, may be used to clarify the invention. The orientation of the Cartesian coordinate system may be different, for example, such that the z-axis has a component along the horizontal plane.

[0021]

[0020] Figure 2 shows a more detailed view of a part of the lithographic apparatus LA of Figure 1. The lithographic apparatus LA may comprise a base frame BF, a balance mass BM, a metrology frame MF, and a vibration isolation system IS. The metrology frame MF supports the projection system PS. The metrology frame MF may also support part of the position measurement system PMS. The metrology frame MF is supported by the base frame BF via the vibration isolation system IS. The vibration isolation system IS is arranged to prevent or reduce vibrations from propagating from the base frame BF to the metrology frame MF.

[0022]

[0021] The second positioner PW is arranged to accelerate the substrate support WT by providing a driving force between the substrate support WT and the balance mass BM. The driving force accelerates the substrate support WT in a desired direction. Due to conservation of momentum, the driving force is also applied to the balance mass BM with the same magnitude, but in a direction opposite to the desired direction. Typically, the mass of the balance mass BM is significantly larger than the mass of the second positioner PW and the moving parts of the substrate support WT.

[0023]

[0022] In one embodiment, the second positioner PW is supported by the balance mass BM. For example, the second positioner PW then comprises a planar motor for levitating the substrate support WT above the balance mass BM. In another embodiment, the second positioner PW is supported by the base frame BF. For example, the second positioner PW then comprises a linear motor and the second positioner PW then comprises a bearing, such as a gas bearing, for levitating the substrate support WT above the base frame BF.

[0024]

[0023] The position measurement system PMS may comprise any type of sensor suitable for determining the position of the substrate support WT. The position measurement system PMS may comprise any type of sensor suitable for determining the position of the mask support MT. The sensor may be an optical sensor, such as an interferometer or an encoder. The position measurement system PMS may comprise a combined interferometer and encoder system. The sensor may be another type of sensor, such as a magnetic sensor, a capacitive sensor or an inductive sensor. The position measurement system PMS may determine the position relative to a reference, for example the metrology frame MF or the projection system PS. The position measurement system PMS may determine the position of the substrate table WT and / or the mask support MT by measuring the position or by measuring a time derivative of the position, such as the velocity or acceleration.

[0025]

[0024] The position measurement system PMS may comprise an encoder system. Encoder systems are known, for example, from US Patent Application No. 2007 / 0058173 A1, filed 7 September 2006, which is incorporated herein by reference. The encoder system comprises an encoder head, a grating and a sensor. The encoder system may receive a primary radiation beam and a secondary radiation beam. Both the primary radiation beam and the secondary radiation beam may originate from the same radiation beam, i.e. the original radiation beam. At least one of the primary radiation beam and the secondary radiation beam is produced by diffracting the original radiation beam with a grating. If both the primary radiation beam and the secondary radiation beam are produced by diffracting the original radiation beam with a grating, the primary radiation beam must have a different diffraction order than the secondary radiation beam. The different diffraction orders are, for example, +1, -1, +2 and -2. The encoder system optically combines the primary radiation beam and the secondary radiation beam into a combined radiation beam. A sensor in the encoder head determines the phase or phase difference of the combined radiation beam. The sensor generates a signal based on the phase or phase difference. The signal represents the position of the encoder head relative to the grating. One of the encoder head and the grating may be located on the substrate structure WT. The other of the encoder head and the grating may be located on the metrology frame MF or the base frame BF. For example, multiple encoder heads are located on the metrology frame MF while a grating is located on the top surface of the substrate support WT. In another example, a grating is located on the bottom surface of the substrate support WT and an encoder head is located below the substrate support WT.

[0026]

[0025] The position measurement system PMS may comprise an interferometer system. An interferometer system is known, for example, from US Pat. No. 6,020,964, filed 13 July 1998, which is incorporated herein by reference. The interferometer system may comprise a beam splitter, a mirror, a reference mirror and a sensor. The radiation beam is split into a reference beam and a measurement beam by the beam splitter. The measurement beam propagates to the mirror and is reflected by the mirror back to the beam splitter. The reference beam propagates to the reference mirror and is reflected by the reference mirror back to the beam splitter. At the beam splitter, the measurement beam and the reference beam are combined into a combined radiation beam. The combined radiation beam is incident on a sensor. The sensor determines the phase or frequency of the combined radiation beam. The sensor generates a signal based on the phase or frequency. The signal represents the displacement of the mirror. In an embodiment, the mirror is coupled to the substrate support WT. The reference mirror may be coupled to the metrology frame MF. In one embodiment, the measurement and reference beams are combined into a combined radiation beam by an additional optical component rather than a beam splitter.

[0027]

[0026] The first positioner PM may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the mask support MT over a small range of movement with high accuracy relative to the long-stroke module. The long-stroke module is arranged to move the short-stroke module over a large range of movement with relatively low accuracy relative to the projection system PS. By the combination of the long-stroke module and the short-stroke module, the first positioner PM can move the mask support MT over a large range of movement with high accuracy relative to the projection system PS. Similarly, the second positioner PW may comprise a long-stroke module and a short-stroke module. The short-stroke module is arranged to move the substrate support WT over a small range of movement with high accuracy relative to the long-stroke module. The long-stroke module is arranged to move the short-stroke module over a large range of movement with relatively low accuracy relative to the projection system PS. By the combination of the long-stroke module and the short-stroke module, the second positioner PW can move the substrate support WT over a large range of movement with high accuracy relative to the projection system PS.

[0028]

[0027] The first positioner PM and the second positioner PW each comprise an actuator for moving the mask support MT and the substrate support WT, respectively. The actuator may be a linear actuator for providing a driving force along a single axis, for example the y-axis. A plurality of linear actuators may be applied for providing a driving force along a plurality of axes. The actuator may be a planar actuator for providing a driving force along a plurality of axes. For example, the planar actuator may be arranged to move the substrate support WT with six degrees of freedom. The actuator may be an electromagnetic actuator comprising at least one coil and at least one magnet. The actuator is arranged to move the at least one coil relative to the at least one magnet by applying a current to the at least one coil. The actuator may be a moving magnet actuator, which has at least one magnet coupled to the substrate support WT or to the mask support MT. The actuator may be a moving coil actuator, which has at least one coil coupled to the substrate support WT or to the mask support MT. The actuator may be a voice coil actuator, a reluctance actuator, a Lorentz actuator, or a piezo actuator, or any other suitable actuator.

[0029]

[0028] The lithographic apparatus LA comprises a position control system PCS, which is illustrated diagrammatically in Fig. 3. The position control system PCS comprises a setpoint generator SP, a feedforward controller FF and a feedback controller FB. The position control system PCS provides a drive signal to an actuator ACT. The actuator ACT may be an actuator of the first positioner PM or may be an actuator of the second positioner PW. The actuator ACT drives a plant P, which may comprise a substrate support WT or a mask support MT. An output of the plant P is a position quantity, such as a position or a velocity or an acceleration. The position quantity is measured by a position measurement system PMS. The position measurement system PMS generates a signal, which is a position signal representative of a position quantity of the plant P. The setpoint generator SP generates a signal, which is a reference signal representative of a desired position quantity of the plant P. For example, the reference signal represents a desired trajectory of the substrate support WT. The difference between the reference signal and the position signal forms an input of the feedback controller FB. Based on the input, the feedback controller FB provides at least a part of the drive signal for the actuator ACT. The reference signal may form an input of a feedforward controller FF, based on which the feedforward controller FF provides at least a portion of the drive signal for the actuator ACT. The feedforward controller FF may utilize information about the dynamic properties of the plant P, such as mass, stiffness, resonant modes, and natural frequencies.

[0030]

[0029] Figure 4 illustrates a block schematic diagram of a controller system CS. The control system is configured to control a plant PL. The plant PL may be formed by any plant to be controlled, such as any actuator, system, subsystem, process, etc. For example, the plant may be formed by a movable object, such as a stage, for example a substrate stage or a reticle stage, or any other positioning device. Correspondingly, the reference state signal may be formed by a position signal representative of a desired position of the movable object.

[0031]

[0030] The controller system CS comprises a feedback controller system FB for generating a feedback signal FBS and a feedforward controller FF for generating a feedforward signal FFS. The feedforward and feedback signals are summed and provided as input to the plant PL. For example, in the case of a stage, the feedforward and feedback signals may be actuator drive signals driving the positioning actuators of the stage. Thus, the general term "plant" in relation to FIG. 4 may be understood as comprising the actuator ACT referred to in relation to FIG. 3. The feedback controller system FB operates in a feedback loop configuration, where the feedback signal is derived from the output of the plant, i.e. the plant state signal PSS. The plant state signal is subtracted from a setpoint signal, i.e. a reference state signal RSS, which represents the desired state of the plant. The difference between the reference state signal and the plant state signal, i.e. the error signal e, is provided as input to the feedback controller system. The feedforward controller uses the reference state signal as input to provide a feedforward signal FFS to the plant. The combination of feedforward and feedback makes it possible to address dynamic behavior and precision.

[0032]

[0031] It should be noted that the illustrated control system may further provide a second feedforward signal FFS2 to the output of the plant, whereby the output of the plant may be corrected, for example, for non-ideal behavior in response to the feedforward signal. For example, if the plant is formed by a stage, the finite stiffness of the stage may result in deformations in response to the feedforward signal, which may be at least partially corrected by the second feedforward signal FFS2.

[0033] The feedback controller system may comprise a PID controller comprising a proportional gain (P), an integrator (I), and a differentiator (D).

[0034]

[0033] The lithographic apparatus may perform repetitive movements when projecting a pattern onto a substrate, for example performing a scanning movement to scan a portion of the substrate. The scanning movement may be performed at a constant stage speed. Acceleration and deceleration may be performed between the scanning movements, for example to change the direction of the movement.

[0035]

[0034] Figure 5 illustrates a graphical display of the integrator output signal versus time T in response to changes in acceleration. As shown in Figure 5, as acceleration changes, the integrator tends to give an overshoot in the opposite direction.

[0036] FIG. 6 illustrates a block schematic diagram of a controller system CS according to one embodiment.

[0037]

[0036] Similar to the controller system described with reference to Fig. 4, the controller system CS illustrated in Fig. 6 comprises a feedback controller system FB generating a feedback signal FBS and a feedforward controller FF generating a feedforward signal FFS. The feedback controller system FBS comprises a feedback controller FB. The feedforward signal and the feedback signal are added and provided as input to the plant PL. For example, in the case of a stage, the feedforward signal and the feedback signal can be an actuator drive signal driving a positioning actuator of the stage. The feedback controller system FBS operates in a feedback loop configuration, where the feedback signal is derived from the output of the plant, i.e. the plant state signal PSS. The plant state signal is subtracted from a setpoint signal, i.e. a reference state signal RSS representing a desired state of the plant. The difference between the reference state signal and the plant state signal, i.e. the error signal e, is provided as input to the feedback controller system. The feedforward controller uses the reference state signal as input to provide a feedforward signal FFS to the plant. The combination of feedforward and feedback makes it possible to address dynamic behavior and precision.

[0038]

[0037] Similar to the controller system described with reference to Fig. 4, the illustrated controller system further provides a second feedforward signal FFS2 to the output of the plant, whereby the output of the plant can be corrected for, for example, a non-ideal behavior in response to the feedforward signal. For example, if the plant is formed by a stage, the finite stiffness of the stage leads to deformations in response to the feedforward signal and can be at least partially corrected by the second feedforward signal FFS2.

[0039]

[0038] The feedback controller system FBS illustrated in Fig. 6 comprises a feedback controller FB and an integrator INT. The feedback controller system further comprises a trajectory generator TG for generating a trajectory, which may be formed by a time series of trajectory generator output values. Furthermore, the feedback controller system comprises a selector. The selector comprises a dual selector input, one of the selector inputs being coupled to the output of the trajectory generator, while the other of the selector inputs is coupled to the output of the integrator INT of the feedback controller system. The trajectory generator may generate a desired response as desired from any suitable trajectory generator output signal, e.g. an integrator, examples of which are described in more detail below. Thus, the selector selects one of these inputs to be output at the selector output of the selector. The selector output outputs the output of the integrator or the output of the trajectory generator accordingly. The feedback controller further comprises a mode controller MC for operating the selector as a function of a reference state signal, which is input to the mode controller. As a function of the reference state signal, the feedback controller system operates in a first control mode or in a second control mode. In a first control mode, the feedback controller system operates the selector to select a trajectory generator output signal generated by the trajectory generator while omitting (discarding) the integrator output signal. Thus, in the first control mode, the feedback controller system adds the trajectory generator output signal to the feedback controller output signal. In a second control mode, the feedback controller system operates the selector to select an integrator output signal generated by the integrator. Thus, in the second control mode, the feedback controller system adds the integrator output signal to the feedback controller output signal while omitting (discarding) the trajectory generator output signal. The selector is controlled by the mode controller to operate in the first or second control mode as a function of the reference state signal.

[0040]

[0039] The feedback controller system is configured by a selector to replace the integrator output signal by the trajectory generator output signal. The feedback controller system performs the selection as a function of the reference state signal. The function can be any suitable function. For example, the function can comprise a threshold for deriving a time derivative, a second time derivative or a third time derivative of the reference state signal, a single, double or triple time differentiator. Any other suitable function indicative of physical knowledge of the type of disturbance acting on the plant may be used.

[0041]

[0040] Thus, in response to the reference state signal, for example in response to its changes over time, the selector selects the integrator output signal f I,FB The trajectory generator output signal f I,FF As a result, in situations where the integrator may, for example, lag, delay, or otherwise adversely affect a fast and accurate response, the integrator output signal may be replaced by the trajectory output signal.

[0042]

[0041] In one embodiment, the trajectory represents the second time derivative of the reference state signal. For example, if the reference state signal is a position, the second time derivative of the reference state signal is an acceleration. Thus, as the acceleration (as such) exhibits a relatively fast change, a trajectory can be derived from the reference state signal generated by the reference state signal generator, for example, when the stage transitions from accelerating to moving at a constant velocity. Scaling may be performed to specify that the start value of the trajectory corresponds to the actual value of the integrator output at the moment of transition to the first mode, while the end value of the trajectory corresponds to the expected value of the integrator output when the constant velocity is reached. The second time derivative of the reference state signal may represent a dynamic situation in which a (relatively slow) integrator may adversely affect the performance of the controller system, so that in this situation the controller system output may be replaced by the trajectory generator output, whereby an advantageous trajectory can be derived from the second time derivative of the reference state signal.

[0043]

[0042] An example of a trajectory is shown in Fig. 7. Fig. 7 illustrates the acceleration signal versus time, i.e. the second time derivative of the stage position versus time. Initially, the stage acceleration is zero, so the stage is moving, for example, at a constant velocity. Then, at time t1, the stage acceleration in the y direction, ACC-y, increases from 0 towards a constant level, causing the stage velocity to change. For example, the stage velocity changes from V towards zero, and then towards -V, i.e. moving in the opposite direction. At time ts, the acceleration decreases towards zero. Once zero is reached, the stage moves at a constant velocity -V, i.e. in the opposite Y direction. The next scan movement at a constant scan velocity can start. Fig. 7 similarly illustrates the stage acceleration ACC-x in the x direction. Fig. 7 further illustrates the closed loop integrator system response signal during the acceleration phase before the exposure scan phase. The response f 1,FB represents the response of a prior art integrator system. At time t1, the integrator responds to the change in acceleration with an integrator signal that is initially in the opposite direction, as represented by the "undershoot" in FIG. 7. After such a damped ringing phenomenon subsides, a constant integrator output signal is provided following the constant change in acceleration. Then, at time ts, as the acceleration decreases toward zero, the change in acceleration results in a corresponding change in the integrator output signal, also exhibiting damped ringing, resulting in a response that initially tends toward the opposite direction. After a stabilization period, the integrator output signal returns toward zero, and a constant speed scan movement can commence. The response f 1,FF represents the proposed integrator system with first and second control modes.

[0044] In one embodiment, the switching time t s Before this, the controller system is in the second control mode, whereby the selector selects the integrator output signal f I,FBAs shown in FIG. 7, at time t1, the integrator output signal tends to trend in the opposite direction, i.e., to provide some damped ringing, resulting in an "overshoot" in the opposite direction, which may be identified, for example, by an "undershoot." s At ts, the controller system switches from the second control mode to the first control mode, i.e., transitions from a selector outputting an integrator output signal to a selector outputting a trajectory generator output signal. If the selector had not switched to the first control mode, the integrator output signal would have been selected, in which case the same "undershoot" behavior would have been observed, similar to the behavior at t1 and similar to the behavior illustrated in FIG. 5. However, at ts, instead of selecting the integrator output signal, the selector selects the trajectory generator output signal. The trajectory generator outputs a scaled acceleration trajectory, i.e., a scaled second time derivative of the position setpoint signal, i.e., the second time derivative of the reference state signal. As a result, delays, overshoots / undershoots, or damped ringing may be avoided, and instead a more desirable trajectory may be provided by the trajectory generator. As a result, at time ts, s The settling time counted from the scanning time may be reduced and the lithographic apparatus may be more quickly ready for the next scanning movement. Thus, the throughput of the lithographic apparatus may be improved. In general, faster settling times may be achieved in any other application.

[0045] A smooth transition when changing from the first control mode to the second control mode and vice versa may be achieved as follows: A trajectory generator is configured to generate a trajectory from a first value to a second value in the first control mode. When transitioning from the second control mode to the first control mode, the trajectory generator is configured to set the first value equal to an integrator output of the integrator.

[0046]

[0045] When transitioning from the first control mode to the second control mode, in one embodiment, the integrator output signal is set to a second value. Thus, when the integrator is selected during the transition from the first mode to the second mode, it starts at a value equal to the second value of the trajectory to provide a smooth transition from the first control mode to the second control mode. In one embodiment, the second value is set to a value of the integrator output signal that corresponds to the state of the controller system when the second time derivative of the reference state signal is zero. Thus, when the integrator is set to t s Once stabilized after t, the second value of the trajectory is s Thus, when transitioning to the second control mode, the integrator restarts at the steady state value that would have been reached, thus providing stable behavior after transitioning from the first control mode to the second control mode.

[0047] Alternatively, the second value may be set to zero.

[0048]

[0047] To activate the first control mode when the second time derivative of the reference state signal changes, for example, when the acceleration changes while the reference state signal is a position, the feedback controller system is configured to operate in the first control mode when the absolute value of the third time derivative of the reference state signal exceeds a predetermined threshold. Correspondingly, the feedback controller system is configured to transition from the first control mode to the second control mode when the absolute value of the third time derivative of the reference state signal transitions below the predetermined threshold. The reference state signal can be provided to the feedback controller so that the feedback controller determines whether to select the first or second control mode.

[0049]

[0048] The feedback controller system may comprise a PD control, i.e. proportional-differential control, and the proportional-differential signal generated by the proportional-differential control is output to the feedback signal. In the second control mode, the integrator is selected to add the integrator output signal, thus forming a PID (proportional-integral-differential) feedback controller system, while in the first control mode, the trajectory signal generated by the trajectory generator is complemented to form a PD feedback controller system, promoting faster response in dynamic situations as mentioned above.

[0050]

[0049] The controller system as described above may be provided to the stage. The controller system may be configured to control the position of the stage. The reference state signal may be a position setpoint signal of the stage. Thus, the position of the stage may be controlled, whereby the controller system may transition between the second control mode and the first control mode and vice versa, depending on the position setpoint signal of the stage.

[0051]

[0050] The controller system may be included in a lithographic apparatus, such as the lithographic apparatus described with reference to Fig. 1. The controller system included in the lithographic apparatus may be configured to control the position of a stage of the lithographic apparatus, and the reference state signal is a position setpoint of the stage.

[0052]

[0051] As explained above with reference to Fig. 7, the stage may alternate between a movement with a constant velocity (e.g. for scanning purposes) and a movement with deceleration and acceleration parts, whereby the velocity of the stage is reversed, for example, to resume the scan, for example at a reverse velocity. Other movements are possible as well. The lithographic apparatus may comprise a reference state signal generator for generating a reference state signal. The reference state signal may cause the stage to alternate between a scanning movement with a constant stage velocity and deceleration / acceleration, whereby the stage changes velocity. The reference state signal may be input to the feedback controller system to determine whether the feedback controller system operates in a first control mode or a second control mode depending on the reference state signal. For example, the feedback controller system may alternate between the first control mode and the second control mode. For example, the feedback controller system may operate in the first control mode when the absolute value of the time derivative of the acceleration of the stage exceeds a predefined threshold, and may operate in the second control mode during the scanning movement of the stage. During the scanning movement of the stage, the velocity of the stage is, for example, constant or zero, and thus the acceleration of the stage is zero. At zero acceleration, including an integrator in the feedback controller system can promote high accuracy and thus high precision of the positioning of the stage. During periods when the acceleration of the stage changes at a certain rate over time, i.e. the absolute value of the third derivative of the position setpoint, i.e. the third derivative of the reference state signal, exceeds a certain level, the somewhat slow response of the integrator can adversely affect the response time of the controller system. For example, this can be the case when the third time derivative of the reference state signal, i.e. the third time derivative of the position setpoint signal, exceeds zero in an absolute sense. Thus, the third time derivative of the reference state signal, i.e. the third time derivative of the position setpoint signal, is smaller or larger than zero. A fast settling, as can be achieved in the first control mode, can be advantageous when moving to a scanning movement, i.e. a movement by which irradiation of (part of) the substrate is performed and where high precision of the positioning of the substrate is desired.Thus, the feedback controller system may operate in the first control mode when the absolute value of the time derivative of the stage acceleration exceeds a predetermined threshold prior to the transition of the stage to a scanning movement.

[0053] A discussion of the closed-loop stability of the above-described control system is summarized below with reference to FIGS.

[0054]

[0053] In the proposed control strategy, switching is performed between the plant in a closed loop with two types of feedback controller systems, namely PID and PD closed loop scenarios. Although the two closed loop scenarios can be made stable by the current linear time-invariant (LTI) frequency domain design approach, switching between the two scenarios would theoretically be unstable. To ensure stable switching behavior in this design, the following stability analysis approach is adopted. Note that the feedback-related items in the control scheme of Figure 6 can be abstracted into the following block scheme:

[0055] FIG. 8 shows an abstraction of the feedback control scheme assuming an arbitrary switching sequence in time.

[0056]

[0055] The switch of Fig. 6 is represented in Fig. 8 by a function σ(μ), where μ(t) is a time-dependent exogenous signal that can take the value 0 or 1. If μ(t)=1, then the integrator CI(s) is in the loop. Hence, the plant P(s) is in a closed loop with a PID controller. If μ(t)=0, then the integrator CI(s) is out of the loop and thus, the plant is in a closed loop with a PD controller.

[0057] The block scheme of FIG. 8 may be represented by the Lur'e system shown in FIGS.

[0058]

[0057] The sensitivity transfer corresponds to the PD control scenario if P SPD(s)=-P(s) / (P(s)CPD(s)+1) is the process.

[0059]

[0058] Figure 10: Lur'e system representation of the scheme of Figure 6. Left: (σ(μ)e,e) plane, where domains show PID and PD scenarios and sectors correspond to switching between them.

[0060]

[0059] Then the following theorem can be formulated: Theorem 1: The Lur'e system of FIGS. 9 and 10 is globally asymptotically stable for any switching sequence μ(t) if:

[0061] 1. The PSPD(s) has a pole in the left half of the complex plane.

[0062] 2.

[0061]

number

[0062]

[0063] 3.

[0063]

number

[0064]

[0064] This proof follows the line of reasoning applied to the proof of Theorem 1 in [Reference 3].

[0065] To prove that the scheme in Fig. 6 is stable under integral state reinitialization, we use the stability result of Theorem 1 in the Lur'e system shown in Fig. 9. That is, based on Theorem 1, 1) PD to PID transition with CI(s) having initial condition fI,FF(ts+δt), 2) and transition from PID to PD We can conclude that the stability of the trajectory segment is such that fI,FF(ts+δt) is the same as fI,FF(ts+δt)=fI,FF(ts+δt). Naturally, the same property applies to the next trajectory segment following the above sequences 1 and 2. It also applies to any other externally provided initial condition value fI,FF(ts+δt) (and PSPD with the end state value of the previous time segment as the initial state condition). Then, we can conclude that the entire connected trajectory segments forming the trajectory response of the closed loop system as shown in FIG. 6 exhibits the property of global asymptotic stability.

[0066] It can be verified that the conditions of Theorem 1 are satisfied for the considered application. That is, items 1 and 2 of Theorem 1 are satisfied by using a standard LTI-based PD controller design. Item 3 of Theorem is a simple graphical frequency domain check. In FIG. 11, the check is performed for the considered application (example corresponds to the z-axis). Note that item 3 of Theorem 1 is satisfied with a significant margin.

[0067]

[0067] [Reference 1] Bode's sensitivity integral - Wikipedia

[0068] [Reference 2] On the Theory of Stability of Control Systems. Prikladnaya Matematika / Mekhanika (in Russian) Lur'e, AI, Postnikov, VN

[0069] [Reference 3]Synthesis of Variable Gain Integral Controllers for Linear Motion Systems. IEEE Transaction on Control systems technology vol. 23 No 1, January 2015, Bram Hunnekens, Nathan van de Wouw, Marcel Heertjes, Henk Nijmeijer.

[0068]

[0070] Therefore, the I-action with FF mode interconnected with the PD controller and the plant is globally stable with set-point based triggered switching.

[0069]

[0071] In another embodiment, in situations where scan-direction dependent disturbance forces are present, for example during the acceleration and / or deceleration phases of the stage, it may be beneficial for the feedback controller system to be configured to operate in a third control mode as a function of the reference state signal, the feedback controller system being configured in the third control mode to initially set the integrator output signal generated by the integrator to zero, to select the trajectory generator output signal generated by the trajectory generator, and to add the integrator output signal generated by the integrator. In this control mode, the trajectory generator outputs a scaled acceleration trajectory as described above, while the integrator output further compensates for the scan-direction dependent disturbance forces.

[0070]

[0072] Although specific reference is made in this text to the use of lithographic apparatus in the manufacture of ICs, it will be appreciated that the lithographic apparatus described herein may have other applications, including the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0071]

[0073] Although particular reference is made herein to embodiments of the invention in relation to lithographic apparatus, embodiments of the invention may also be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes objects such as wafers (or other substrates) or masks (or other patterning devices). These apparatus may be generally referred to as lithography tools. Such lithography tools may use vacuum or ambient (non-vacuum) conditions.

[0072]

[0074] Although particular reference may be made above to the use of embodiments of the invention in relation to optical lithography, it will be appreciated that the invention is not limited to optical lithography and may be used in other applications, such as, for example, imprint lithography, where the context permits.

[0073]

[0075] Where the context permits, embodiments of the invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read-only memory (ROM), random-access memory (RAM), magnetic storage media, optical storage media, flash memory devices, electrical, optical, acoustic or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Furthermore, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such description is merely for convenience, and that such actions may in fact result from a computing device, processor, controller, or other device executing the firmware, software, routines, instructions, etc., which, in performing the actions, may cause actuators or other devices to interact with the material world.

[0074]

[0076] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The above description is intended to be illustrative, not limiting.

Claims

1. 1. A controller system configured to control a plant, comprising: A feedforward controller configured to provide a feedforward signal to the plant based on a reference state signal; a feedback controller system configured to provide a feedback signal to the plant based on a difference between the reference state signal and a plant state signal representative of an actual state of the plant; Equipped with The feedback controller system includes an integrator, a trajectory generator, and a selector configured to selectively output one of a trajectory generator output signal generated by the trajectory generator and an integrator output signal generated by the integrator as a feedback signal to the plant; the feedback controller system is configured to operate in a first control mode or a second control mode as a function of the reference state signal; the feedback controller system is configured to operate the selector to select the trajectory generator output signal generated by the trajectory generator in the first control mode; The feedback controller system is configured to, in the second control mode, operate the selector to select the integrator output signal generated by the integrator.

2. The controller system of claim 1 , wherein the plant is a movable object and the reference state signal is a position setpoint of the movable object.

3. The controller system of claim 1 or 2, wherein the trajectory generator is configured, in the first control mode, to generate a trajectory representing a second time derivative of the reference state signal.

4. The controller system of claim 3 , wherein the trajectory generator is configured to generate a trajectory that represents a scaled second time derivative of the reference state signal.

5. 5. The controller system of claim 1, wherein the trajectory generator is configured to generate a trajectory from a first value to a second value in the first control mode, and wherein the trajectory generator is configured to set the first value equal to the integrator output of the integrator upon transition from the second control mode to the first control mode.

6. 6. The controller system of claim 5, wherein the feedback controller system is configured to set the integrator output signal to the second value upon transition from the first control mode to the second control mode.

7. 7. The controller system of claim 5 or 6, wherein the second value is set to a value of the integrator output signal that corresponds to a state of the controller system when a second time derivative of the reference state signal is zero.

8. The controller system of claim 5 or 6, wherein the second value is set to zero.

9. 9. The controller system of claim 1, wherein the feedback controller system is configured to operate in the first control mode when an absolute value of a third time derivative of the reference state signal exceeds a predetermined threshold.

10. 10. The controller system of claim 9, wherein the feedback controller system is configured to transition from the first control mode to the second control mode when the absolute value of the third time derivative of the reference state signal transitions below the predetermined threshold.

11. The controller system of claim 1 , further comprising a proportional-derivative control, wherein a proportional-derivative signal generated by the proportional-derivative control is output to the feedback signal.

12. 12. The controller system of claim 1, wherein the feedback controller system is configured to operate in a third control mode as a function of the reference state signal, the feedback controller system being configured in the third control mode to initially set the integrator output signal generated by the integrator to zero, to select the trajectory generator output signal generated by the trajectory generator, and to add the integrator output signal generated by the integrator.

13. 13. A stage comprising a controller system according to claim 1 configured to control a position of the stage, the reference state signal being a position setpoint of the stage.

14. A lithographic apparatus comprising a controller system according to any one of the preceding claims.

15. The lithographic apparatus of claim 14, wherein the controller system is configured to control a position of a stage of the lithographic apparatus, and the reference state signal is a position setpoint of the stage.

16. 16. The lithographic apparatus of claim 15, further comprising a reference state signal generator configured to generate the reference state signal, the reference state signal generator configured to generate the reference state signal to cause the stage to alternate between a scanning movement at a constant stage velocity and deceleration / acceleration at which the stage changes velocity, and the feedback controller system configured to operate in the first control mode when an absolute value of a time derivative of the acceleration of the stage exceeds a predetermined threshold prior to the stage transitioning to the scanning movement, and to operate in the second control mode during the scanning movement of the stage.

Images