A method for determining a linear motor commutation angle

Abstract

A method for determining a commutation angle of a permanent magnetic linear motor comprising a coil array and a mover physically connected to a moving body, the method comprising: applying to the coil array a first set of currents, adapting a phase offset of the first set of currents until the moving body reaches a first stationary condition with a first settled phase offset and a first actuation force, determining an estimated second actuation force, applying to the coil array and varying a second set of currents thereby transitioning the actuation force from the first actuation force to the estimated second actuation force via one or more intermediate force setpoints, further adapting the phase offset of the second set of currents until the moving body reaches a second stationary condition with a second settled phase offset, determining the commutation angle based on the first and the second settled phase offset.

Description

A METHOD FOR DETERMINING A LINEAR MOTOR COMMUTATION ANGLE CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 24164356.8 which was filed on 19 March 2024 and which is incorporated herein in its entirety by reference. FIELD

[0002] The present invention relates to a method for determining a commutation angle of a permanent magnetic linear motor, to a current controller for controlling the permanent magnetic linear motor to execute the method, to a permanent magnetic linear motor system configured to execute the method to determine a commutation angle thereof, and to an integrated circuit manufacturing apparatus comprising the permanent magnetic linear motor system. BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as “design layout” or “design”) of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., a wafer).

[0004] As semiconductor manufacturing processes continue to advance, the dimensions of circuit elements have continually been reduced while the amount of functional elements, such as transistors, per device has been steadily increasing over decades, following a trend commonly referred to as ‘Moore’s law’. To keep up with Moore’s law the semiconductor industry is chasing technologies that enable to create increasingly smaller features. To project a pattern on a substrate a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which are patterned on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm and 13.5 nm. A lithographic apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within a range of 4 nm to 20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus which uses, for example, radiation with a wavelength of 193 nm.

[0005] Actuators, for example permanent magnetic linear motors, are used in lithographic apparatus for moving a motion stage or a moving body. A permanent magnetic linear motor, for example a Lorentz linear actuator, may comprise an array of permanent magnets and an array of coils, wherein coil currents are applied in a way, for example as a function of a mover position with respect to a stator, that the permanent magnetic linear motor mover is driven by a desired force in a desired direction. The said determination and / or application of desired coil currents of a permanent magneticlinear motor is called commutation. It is desired to accurately commutate the permanent magnetic linear motor in order to efficiently move the motion stage or the moving body as desired. SUMMARY

[0006] It is an object of the invention to provide an improved method to determine a commutation angle of a permanent magnetic linear motor to enable an accurate commutation and an efficient operation of the permanent magnetic linear motor. It is a further object of the invention to provide a method to determine a commutation angle of a permanent magnetic linear motor and the method is robust to disturbance forces. Another object of the invention is to provide a method to determine a commutation angle of a permanent magnetic linear motor and the method reduces disturbances to surrounding structures of the motor. One or more of the objects of the invention is reached by the method for determining a commutation angle of a permanent magnetic linear motor for moving a moving body, the permanent magnetic motor comprising a coil array and a magnet array, according to the first aspect of the invention, as defined in claim 1, the method comprising successive steps of: a) applying to the coil array a first set of currents thereby generating an actuation force on the moving body, b) adapting a phase offset of the first set of currents until the moving body reaches a first stationary condition with a first settled phase offset and a first actuation force, c) determining an estimated second actuation force having a magnitude substantially the same as the first actuation force and an estimated direction, d) applying to the coil array a second set of currents thereby generating an actuation force on the moving body, varying a phase offset and a magnitude of the second set of currents thereby transitioning the actuation force from the first actuation force to the estimated second actuation force via one or more intermediate force setpoints, e) further adapting the phase offset of the second set of currents until the moving body reaches a second stationary condition with a second settled phase offset and a second actuation force, f) determining the commutation angle based on the first settled phase offset and the second settled phase offset.

[0007] The method determines the commutation angle based on two settled phase offsets at two stationary conditions with the first and the second actuation force. By doing so, an accurate commutation angle can be determined without knowing the exact disturbance force value. The step of estimating a second actuation force sets an endpoint for the actuation force transitioning and also acts as a starting point to further adapt the phase offset in order to reach the second stationary condition in a more efficient way. The actuation force transitions from the first actuation force to an estimated second actuation force via one or more intermediate force setpoints instead of switching abruptly from the first actuation force to the estimated second actuation force. By doing so, the two settled phaseoffsets can be determined while less disturbances and excitations are introduced to the surrounding structures of the actuator, and an improved determination of the commutation angle is achieved.

[0008] In an embodiment, the estimated direction of step c) is determined based on the first actuation force and an estimated disturbance force exerted on the moving body. The disturbance force may be gravity of the moving body. The disturbance force may also be for example friction and gravity of other components connected with the moving body.

[0009] In another embodiment, the actuation force transitions from the first actuation force to the estimated second actuation force in a predefined transition time. The transition time may be defined to balance an external disturbance caused by the method and a time spent on the method.

[0010] In a further embodiment, the one or more intermediate force setpoints are defined in such a way that the trajectory of a magnitude and / or a direction of the one or more intermediate force setpoints is a function of time.

[0011] In an alternative embodiment, the trajectory of the magnitude and / or the direction of the one or more intermediate force setpoints is a polynomial as a function of time, the polynomial having a degree of one, two or higher.

[0012] In yet an alternative embodiment, the trajectory of the magnitude of a component of the one or more intermediate force setpoints is a polynomial as a function of time, the polynomial having a degree of one, two or higher.

[0013] In some embodiments, the actuation force transitions from the first actuation force to the estimated second actuation force in a discrete way or in a continuous way.

[0014] According to a second aspect, there is provided a current controller configured to control the first and / or the second set of currents for executing the method according to any of the embodiments described above. The current controller may be configured to operate in a first control mode during use for step b) and / or e), to adapt the phase offsets of the first and second sets of currents for reaching the stationary conditions based on a measured position or a measured parameter indicative of a position of the mover or moving body.

[0015] The current controller may also be configured to operate in a second control mode during use for step d), to control the phase offset and the magnitude of the second set of currents based on a measured position or a measured parameter indicative of a position of the mover or the moving body.

[0016] According to a third aspect, there is provided a permanent magnetic linear motor system comprising a permanent magnetic motor having a stator and a mover which is physically connected to a moving body, the permanent magnetic motor comprising a coil array and a magnet array, and the permanent magnetic linear motor system further comprises a current controller described above, wherein the permanent magnetic linear motor system is configured to execute the method according to any of the embodiments described above.

[0017] According to a fourth aspect, there is provided a lithographic apparatus, a substrate inspection apparatus or a wafer metrology apparatus comprising the permanent magnetic linear motor system described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which: - Figure 1 depicts a schematic overview of a lithographic apparatus; - Figure 2(a) depicts a side view of a three-phase moving-coil Lorentz linear actuator; - Figure 2(b) depicts Lorentz forces acting on each of the three coils of Figure 2(a) when an equal and constant current is applied to each of the three coils, i.e., no commutation is applied; - Figure 3(a) depicts a three-phase Lorentz linear actuator of one degree-of-freedom movement in vertical direction with a vertical disturbance force Fz, wherein the coil array and the magnet array is aligned. - Figure 3(b) depicts a three-phase Lorentz linear actuator of 1 degree-of-freedom movement in vertical direction with a vertical disturbance force Fz, wherein the coil array and the magnet array are misaligned with a vertical displacement of Δz. - Figure 4 depicts a flow chart for executing a magnetic alignment method according to some embodiments. - Figure 5(a-c) depicts free-body diagrams of a moving body M driven by the actuator of Figure 3(b), under conditions when the vertical component Fz of the actuation force Falign is smaller (5(a)), larger (5(b)) or equal to (5(c)) the vertical disturbance force Fz. - Figure 6 depicts a free-body diagram of the moving body M and shows how an estimated second actuation force Fest is determined. - Figure 7 depicts an actuation force Ftranstransitioning from a first force setpoint Ftrans[0] to a last force setpoint Ftrans[4]. - Figure 8 depicts an example of a current controller operating in the first control mode according to some embodiments. - Figure 9 depicts an example of a current controller operating in the second control mode according to some embodiments. - Figure 10 depicts an actuation force Ftranstransitioning discretely via three intermediate force setpoints as a function of time. - Figure 11 depicts exemplary trajectories of the phase, magnitude and horizontal force component of the intermediate force setpoints as a function of time, wherein the phase of the intermediate force setpoints is a linear function of time, and the force transitioning is discrete. - Figure 12 depicts another exemplary trajectories of the phase, magnitude and horizontal force component of the intermediate force setpoints as a function of time, wherein the horizontal forcecomponent of the intermediate force setpoints is a linear function of time, and the force transitioning is discrete. - Figure 13 depicts yet another trajectories of the phase, magnitude and horizontal force component of the intermediate force setpoints as a function of time, wherein the phase of the intermediate force setpoints is a polynomial function of time with a degree of two, and the force transitioning is discrete. - Figure 14 depicts yet another trajectories of the phase, magnitude and horizontal force component of the intermediate force setpoints as a function of time, wherein the phase of the intermediate force setpoints is a polynomial function of time with a degree of two, and the force transitioning is continuous. - Figure 15 depicts a free-body diagram of the moving body M after the force transition, and the phase offset is further adapted to reach a second stationary condition. - Figure 16(a) depicts a sectional view of a tubular linear actuator of one degree-of-freedom movement in vertical direction z with a vertical disturbance force Fz. - Figure 16(b) depicts a cross section 16B-16B of Figure 16(a). - Figure 16(c) depicts a cross section of the tubular linear actuator of Figure 16(a), the cross section 16C-16C is taking along a plane perpendicular to direction z as shown in Figure 16(b). - Figure 17 depicts another arrangement of a Lorentz linear actuator of one degree-of-freedom movement in vertical direction with a vertical disturbance force Fz, - Figure 18 depicts the actuator of Figure 3(a) when a disturbance force Fx is exerted on the mover in direction -x. DETAILED DESCRIPTION

[0019] In the present document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g. having a wavelength in the range of about 5-100 nm).

[0020] The term “reticle”, “mask” or “patterning device” as employed in this text may be broadly interpreted as referring to a generic patterning device that can be used to endow an incoming radiation beam with a patterned cross-section, corresponding to a pattern that is to be created in a target portion of the substrate. The term “light valve” can also be used in this context. Besides the classic mask (transmissive or reflective, binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include a programmable mirror array and a programmable LCD array.

[0021] Figure 1 schematically depicts a lithographic apparatus LA. The lithographic apparatus LA includes an illumination system (also referred to as illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation or EUV radiation), a mask support (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a firstpositioner PM configured to accurately position the patterning device MA in accordance with certain parameters, a substrate support (e.g., a wafer table) WT constructed to hold a substrate (e.g., a resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support in accordance with certain parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0022] In operation, the illumination system IL receives a radiation beam from a radiation source SO, e.g., via a 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 radiation. The illuminator IL may be used to condition the radiation beam B to have a desired spatial and angular intensity distribution in its cross section at a plane of the patterning device MA.

[0023] The term “projection system” PS used herein should be broadly interpreted as encompassing various types of projection system, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, and / or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system” PS.

[0024] The lithographic apparatus LA may be of a type wherein at least a portion of the substrate may be covered by 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 – which is also referred to as immersion lithography. More information on immersion techniques is given in US6952253, which is incorporated herein by reference.

[0025] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also named “dual stage”). In such “multiple stage” machine, the substrate supports WT may be used in parallel, and / or steps in preparation of a subsequent exposure of the substrate W may be carried out on the substrate W located on one of the substrate support WT while another substrate W on the other substrate support WT is being used for exposing a pattern on the other substrate W.

[0026] In addition to the substrate support WT, the lithographic apparatus LA may comprise 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 multiple sensors. The cleaning device may be arranged to clean part of the lithographic apparatus, for example a part of the projection system PS or a part of a system that provides the immersion liquid. The measurement stage may move beneath the projection system PS when the substrate support WT is away from the projection system PS.

[0027] In operation, the radiation beam B is incident on the patterning device, e.g., mask, MA which is held on the mask support MT, and is patterned by the pattern (design layout) present on patterning device MA. Having traversed the mask MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and a position measurement system IF, the substrate support WT can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B at a focused and aligned position. Similarly, the first positioner PM and possibly another position sensor (which is not explicitly depicted in Figure 1) may be used to accurately position the patterning device MA with respect to the path of the radiation beam B. Patterning device MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 as illustrated occupy dedicated target portions, they may be located in spaces between target portions. Substrate alignment marks P1, P2 are known as scribe-lane alignment marks when these are located between the target portions C.

[0028] To clarify the invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes, i.e., an x-axis, a y-axis and a z-axis. Each of the three axis is orthogonal to the other two axis. A rotation around the x-axis is referred to as an Rx-rotation. A rotation around the y- axis is referred to as an Ry-rotation. A rotation around about the z-axis is referred to as an Rz-rotation. The x-axis and the y-axis define a horizontal plane, whereas the z-axis is in a vertical direction. The Cartesian coordinate system is not limiting the invention and is used for clarification only. Instead, 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.

[0029] The first positioner PM and the second positioner PW each are provided with an actuator to move respectively the mask support MT and the substrate support WT. The actuator may be a linear actuator to provide a driving force along a single axis, for example the y-axis. Multiple linear actuators may be applied to provide driving forces along multiple axis. The actuator may be a planar actuator to provide a driving force along multiple axis. For example, the planar actuator may be arranged to move the substrate support WT in 6 degrees of freedom. The actuator may be an electro- magnetic 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 an electrical current to the at least one coil. The actuator may be a moving-magnet type actuator, which has the at least one magnet coupled to the substrate support WT respectively to the mask support MT. The actuator may be a moving-coil type actuator which has the at least one coil coupled to the substrate support WT respectively 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.

[0030] In some applications of a permanent magnetic linear motor, for example a Lorentz linear actuator, an absolute position measurement system may not be provided due to restrictions like spaceand / or cost. In such cases, the absolute position of the mover with regard to the stator is not known, i.e., the position of the magnet array with regard to the coil array is not known. Without knowledge of the absolute position, it is very difficult to efficiently use the actuator or even, in the worst-case scenario, it is not possible to move the actuator at all. Magnetic alignment is a method that calibrates the position offset of the magnet array with regard to the coil array to enable an efficient operation of the actuator.

[0031] According to an embodiment, Figure 2(a) depicts a side view of a three-phase moving-coil Lorentz linear actuator 201 comprising a coil array 202 and a permanent magnet array 203. In this exemplary configuration, the coil array consists of three coils 2021-2023, and the permanent magnet array consists of seven permanent magnets. Note that other number of coils and magnets may be chosen, for instance, for a different actuation force or for a different moving range. In this exemplary configuration, the coil array is connected to a mover 204 and the permanent magnet array is connected to a stator 205. Preferably, each coil surrounds a ferromagnetic part, a so-called tooth 206, which is part of a ferromagnetic element, a so-called back-iron 207. This configuration greatly enhances the magnetic field that is created by the current through the coil. A moving body <now shown> is connected to the back-iron 207 and moved by the actuator. Similarly, the permanent magnet array is connected to a ferromagnetic element, a back-iron 208. The coils behave like a magnet when a current flows through them. When a set of currents flows clockwise in the coils, as seen from the bottom of Figure 2(a), a North pole will be created on top of the coil center, and thus the coils will interact with the permanent magnets 203. The actuation force acting on each of the three coils depends on its position with respect to the magnets in x-direction and is almost ideal sinusoidal function of the position. Figure 2(b) depicts Lorentz forces acting on each of the three coils when an equal and constant current is applied to each of the three coils.

[0032] In Figure 2(a), coil 2022 creates the maximum force in +x direction, as it is located exactly in the middle of two permanent magnets. Hence the coil 2022 is attracted by the permanent magnet South pole on its right and is repulsed by the North pole on its left. If the mover moves to the right until the center of coil 2022 is directly below a permanent magnet, no force in x direction result from any current. If coil 2022 moves even further to the right, the sign of the force reverses. In Figure 2(a), coils 2021 and 2023 are closer to a permanent magnet compared to coil 2022 and will produce smaller forces. The three forces acting on the coils have a phase shift to each other of 120° or 2π / 3 radials and the period of the sinus is dependent on the mechanical pitch Xmof the magnets in the motor. The mechanical pitch is determined by the mechanical design of the motor. For the exemplary design in Figure 2(a), the forces acting on the coils are: F1(x) = ki1sin^F2(x) = ki2sin^

[0033] Here, k is the ratio between the amplitude of the current through one coil to the force produced by it, x is the position of the coil array relative to position x=0 as in Figure 2(a), and i1, i2 and i3 are the currents applied in coil 2021, 2022 and 2023 respectively. If i1=i2=i3, then F1(x)+F2(x)+F3(x)=0. Obviously, it is useless to excite a motor in this manner, since this excitation would result in a net force of 0 N. Instead, sending the largest current through the coil will deliver the largest force. For the example of Figure 2(a), coil 2022 would then get the largest current, decreasing to zero with a move towards the center of the South pole on its right. An even larger move would even require a switch of the sign of the current. Commutation is the application of varying currents to the coils of an actuator with regard to the coils’ positions, such that a required actuation force is achieved. To achieve a position independent total force, usually the following currents are sent through the coils, wherein the currents are also position dependent:

[0034] Here, itdenotes the current waveform amplitude. Using these currents, the net force of the three-phase actuator becomes: Ft(x) = F1(x) + F2(x) + F3(x) (7)Ft(x) =3 2kit = kmit (8)

[0035] with kmdenoting the motor constant and it=Fdesired / km. Hence, the total force is proportional 3 to itby km=2 k, and is independent of the coil array position x.

[0036] In a permanent magnetic linear motor, for example a Lorentz linear actuator, the commutation position is defined as the position of the permanent magnet array with regard to the coil array for which the maximum force is generated. In the example of Figure 2(a), the commutation position is zero at position x=0 (the middle of coil 2022 is exactly in the middle of two permanent magnets). Normally the position of the mover or the moving body may be measured using, for example, interferometry or an encoder-based position measurement system, but the absolute position of the permanent magnet array with regard to the coil array may not be measured. During initialization of such an actuator, the commutation position is not known. Therefore, an extra angleϕcommutation, depending on the horizontal position of the mover (the middle of coil 2022) with respect to the stator (the middle between a north and a south pole), is added to the measured mover position x in the equations of the forces:

[0037] For maximum force generation also an extra angle ϕ̂commutationneeds to be added to the equation of the currents:

[0038] Here, ϕ̂commutationis the calibrated commutation angle and the highest efficiency in a motor is reached when ϕ̂commutationequals ϕcommutation. Moreover, the motor force (and thus also the efficiency of the motor) is a sinusoidal function of the difference between ϕcommutation and ϕ̂commutation, combining equations (9-14) results in:

[0039] With kmdenoting the motor constant and it=Fdesired / km, wherein Fdesiredis the desired actuation force generated by the motor. Note that in a worst-case scenario, it is impossible to move the mover, this occurs when there is a mismatch between ϕ̂commutationand ϕcommutationof π / 2 radials, i.e., the force is applied perpendicular to the direction of the movement, and in this scenario the mover reaches a stationary condition in the moving direction, which is x direction in Figure 2(a). As such, using ϕ̂commutation found at the stationary condition, the commutation angle ϕcommutation can be derived and the highest efficiency in the motor can be reached by adding ϕcommutation to the phases of the currents of the motor coils.

[0040] Figure 3 depicts a three-phase linear actuator 301 having one-degree-of-freedom movement in the vertical direction z. The exemplary moving coil actuator comprises a stator 305 and a mover 306 which is connected to a moving body 309. The coil array and the permanent magnet array of Figure 3(a) are aligned similar to Figure 2(a), while a displacement Δz between the coil array and the permanent magnet array is present in Figure 3(b) which needs to be compensated by a commutation angle ϕcommutation. Compared to the actuator in Figure 2(a), gravity of the moving body acts as a disturbance force for the actuator and needs to be compensated by applying a force in the opposite direction of gravity, i.e., upwards in +z, in addition to the default actuation force for a desired movement. In addition to gravity of the moving body, there may be other disturbance forces at least partially in the moving direction, for example friction, air resistance, gravity of other elements connected with the moving body. When a disturbance force in the moving direction is present, we may use the same calculation as described in equations (9-17). However compared to the situation when ignoring any disturbance force, a stationary condition is achieved when the vertical component of the actuation force cancels out the said disturbance force Fz in the moving direction z, i.e.− ϕcommutation) = −Fz. However, the exact magnitude of disturbance forcesis often unknown, thus ϕcommutationmay not be accurately derived from ϕ̂commutationat this stationary condition.

[0041] The invention provides a method for determining a commutation angle ϕcommutationfor which a high efficiency of the motor is reached, with a presence of a disturbance force at least partially in the moving direction. Figure 4 depicts a flow diagram of the method according to some embodiments and the steps are explained in more details below using Figure 5-15.

[0042] According to some embodiments of the invention, Figure 5(a) depicts a free-body diagram of the moving body of Figure 3(b) simplified as a rigid block M. Angle ϕcommutationdenotes an extra angle added in the equations of the forces which depends on the initial vertical position of the mover with respect to the stator, as shown in the equations:

[0043] Wherein Zmdenotes mechanical pitch Zmof the magnets in the motor, andF1(z), F2(z)^and^F3(z) are Lorentz forces generated by coils 3021-3023 respectively. In the situationof Figure 3(a), the coil array and the permanent magnet array are aligned, thus ϕcommutation = 0. Inthe situation of Figure 3(b), the coil array and the permanent magnet array has a displacement of Δz,thus ϕ = 2πΔz commutationZm. In Figure 5(a), a disturbance force Fzis exerted on the moving body M indirection -z. In a first step S1 of Figure 4, a first set of currents are applied to the coil array. A phase offset ϕalign1is added to each of the coil currents in addition to a set of reference phases, wherein the set of reference phases are the default phases when the coil array and the permanent magnet array are π 2 π π 2 aligned as in Figure 3(a), i.e., 2 + 3 π, 2 ^and^ 2 − 3 π. The initial phase offset ϕalign1 may be chosen randomly, empirically or at least partially based on a parameter indicative of a movement, a position, and / or a setpoint of the moving body or rigid block M or the coil array 3021-3023 of Figure 3(b), or any parameters based on which the initial phase offset may be chosen to improve for example, time consumption and adaptation speed of the method of the invention. The first set of currents are expressed as

[0044] With the first set of currents, an actuation force, so called alignment force Falignis generated on the moving body M, wherein Falignhas a vertical component Falign_zand a horizontal componentFalign_x. According to equation (17), Falign_z = |Fdesired| cos(ϕalign1 − ϕcommutation) =|Falign| cos(ϕalign1 − ϕcommutation).

[0045] Further in step S2 of Figure 4, the phase offset ϕalign1 is adapted, while keeping the magnitude of Falign substantially constant, and tracking the movement of the stator by means of a position sensor, until the stator is stationary in the moving direction z. Here the position sensor may be, for example, an interferometer-based position sensor, or an encoder-based position sensor, or any other type of sensors suitable for determining the position or a parameter indicative of the position of the moving body. Figure 5(a) depicts a free-body diagram when the vertical component |Falign_z|<|Fz|, and a motion downwards may be detected by the position sensor. Figure 5(b) depicts a free-body diagram with when |Falign_z|>|Fz|, thus a motion upwards may be detected by the position sensor. Figure 5(c) depicts a first stationary condition, when an actuation force Fstat1 is generated with a firstsettled phase offset ϕstat1 and Fstat1’s vertical component Fstat1_z = |Falign| cos(ϕstat1 −ϕcommutation) = −Fz. Under this condition, the net force is in the horizontal direction +x, whichequals to the horizontal component of Fstat1 and denoted as Fstat1_x.

[0046] According to some embodiments, an exemplary control diagram for executing step S2 of Figure 4 using a current controller in a first control mode is depicted in Figure 8. The current controller comprises a position controller and a commutation block. In this control diagram, zref represents the position setpoint around which the magnetic alignment procedure operates. A position of the moving body z is measured by a position sensor. Furthermore, a position controller converts theposition error z-zrefinto an angle offset ϕalign1using the alignment force as a parameter. A commutation block converts the alignment force with the phase offset ϕalign1into a set of currents applied to the motor coil array for driving the moving body in a desired moving direction to reduce the position error. The phase offset ϕalign1is adapted by adding and adapting a feedforward input ϕFFuntil z=zref is achieved and the moving body achieves a first stationary condition. As such, a first settled phase offset ϕstat1of Figure 5© is achieved. Here, instead of measured positions, the positions zrefand z may also be measured parameters indicative of the position of the moving body, as long as the control scheme converges to a stationary condition based on the measured parameters.

[0047] In a third step S3 of Figure 4, Figure 6 depicts an estimated second actuation force Feston the moving body, wherein Festhas the same amplitude as Falignand Fstat1, and an estimated direction ofϕstat1 + 2ϕest, wherein the angle ϕest may be determined by ϕest = cos−1(m∙g |Falign|), wherein m is the estimated mass of the moving body and g is the gravitational constant. Such estimation is valid when assuming the z-direction disturbance force is dominated by gravity of the moving body. A differentestimated disturbance force value may be used instead of m ∙ g in the estimation of ϕest if thedifferent disturbance force is dominating, or a combination of estimated disturbance forces can beestimated and used. As such,a vertical component Fest_z that approximates to Fstat1_z and a horizontal component Fest_x that approximates to -Fstat1_x. The determination of Fest is to set an end point of a transition of a second actuation force in the next step, which is further explained using Figure 7.

[0048] In a fourth step S4 of Figure 4, Figure 7 depicts a free-body diagram of the moving body of Figure 3(b) when an actuation force Ftrans is generated by applying a second set of currents to the coil array. The second set of currents are controlled in a second control mode that the actuation force Ftrans transitions from a starting force setpoint Ftrans[0]=Fstat1to an ending force setpoint Ftrans[4]=Festvia a number of intermediate force setpoints Ftrans[1], Ftrans[2] and Ftrans[3]. Note that the number of intermediate points may be chosen differently, preferably more than zero. For a better accuracy of the magnetic alignment, a large magnitude of Falignis preferred. However, in this exemplary motor configuration of Figure 3(b), when an actuation force transitions from Fstat1to Festvia no intermediate force setpoint, the transition needs to be fast enough to prevent the moving body from moving downwards due to gravity. During the said transition, the horizontal force transitions from Fstat1_xto Fest_x, with the orientation of force switching from +x to -x. Such a fast orientation switch of a large force may cause a large, broadband disturbance of surrounding structures of the motor. The said disturbance may require long time to settle, which impacts system availability. By adding intermediate force setpoints between Fstat1and Fest, the transition between the starting point and the endpoint may be slowed down and smaller disturbance may be created. Similarly, the speed of transitioning the actuation force from Fstat1to Festimpacts the level of the disturbance. The faster thetransition is, the larger the disturbance is created. A time period may be defined for the transition, for balancing the disturbance level and the time spent on the magnetic alignment procedure.

[0049] According to some embodiments, an exemplary control diagram for executing step S4 of Figure 4 using a current controller in a second control mode is depicted in Figure 9. Similar to Figure 8, zrefrepresents the position setpoint around which the magnetic alignment procedure operates. A position of the moving body z is measured by a position sensor. A position controller converts the position error z – zref into a force F applied to the plant, an alignment force Ftrans with an angle offset ϕtrans are applied, and the commutation block converts the alignment force Ftrans with the angle offset ϕtransinto a set of currents with a certain magnitude and a certain phase offset, and applies the set of currents to the motor coil array for driving the moving body in a desired direction to reduce the position error. Compared to the first control mode where |Falign| is kept constant while only ϕalign1is adapted, in the second control mode, |Ftrans| and ϕtransmay both vary in a chosen manner for optimizing the effect of the disturbance reduction, as long as the vertical component of Ftrans isapproximate to the disturbance force in magnitude, i.e. the relationship cos(ϕstat1 + ϕest −ϕtrans) = (m∙g |Ftrans|) is met, assuming the disturbance force in z direction is dominated by gravity of the moving body. Errors in the estimation of the required alignment force and in the commutation angle due to the estimation error of the disturbance force can be compensated for by the position controller output force F. As such, at every force setpoint, the control mode ensures a stationary condition when converged, i.e. z = zref. Similar to the first control mode, instead of measured positions, the positions zref and z may also be measured parameters indicative of the position of the moving body, as long as the control scheme converges to a stationary condition based on the measured parameters.

[0050] The transition of Ftransvia the intermediate force setpoints Ftrans[k] (k = 1, 2, 3) of Figure 7 may be configured in different manners. One example is provided in Figure 10 according to an embodiment, wherein the transition is a function of time, such that at time points tk,k = 0, 1, 2, 3, 4, Ftrans[tk] are expressed as Ftrans[tk] = Ftrans[k], k=0-4 (24)|Ftrans|, Ftrans_x and ϕtransas a function of time are then expressed as |Ftrans[tk]| = |Ftrans[k]| (25)wherein the transition time T=t4-t0is chosen for balancing the disturbance level and the time spent on the transition.

[0051] In another embodiment, Ftrans[tk] may further be defined such that the trajectory of the direction ϕtrans[tk] of Ftrans[tk] is a polynomial as a function of time, for example with a degree ofone, i.e. ϕtrans[tk] is a linear function of time t, for example ϕtrans[t] = ϕstat1 + t ∙ ϕest, where t =0, 0.5, 1, 1.5, 2s. The trajectories of ϕtrans,^Ftrans, and Ftrans_xwith respect to time are depicted as π π dashed lines in Figure 11, with the assumption of T = 2s, ϕstat1= 6, and ϕest= 3.

[0052] In yet another embodiment, Ftrans[tk] may instead be defined such that the trajectory of the horizontal component of Ftrans[tk], Ftrans_x[tk] is a polynomial as a function of time, for example with adegree of one, i.e. Ftrans_x[t] = Fstat1_x − t ∙ Fstat1_x, t = 0, 0.5, 1, 1.5, 2s. The trajectories of ϕtrans,Ftrans, and Ftrans_xwith respect to time are depicted as dashed lines in Figure 12, with the assumption π π of T = 2s, ϕstat1= 6, and ϕest= 3.

[0053] In yet another embodiment, Ftrans[tk] may instead be defined such that the trajectory of the magnitude of Ftrans[tk], i.e. |Ftrans[tk]| is a polynomial as a function of time, for example with a degree oftwo, i.e. |Ftrans[t]| = (|Fstat1| − m ∙ g)t2 + 2(m ∙ g − |Fstat1|)t + |Fstat1|, t = 0, 0.5, 1, 1.5, 2s. Thetrajectories of and with to time are depicted as dashed lines in Figure 13, with the assumption

[0054] Examples of Figure 11-13 are based on discrete force setpoints Ftrans[tk] with respect to time. According to another embodiment, a smooth transition of Ftrans(t) by continuously tuning the phase offset ϕtrans(^^) and |Ftrans(t)| along a defined trajectory can achieve a similar technical effect. Anexample of such a smooth transition is shown in Figure 14, wherein |Ftrans(^^)| = (|Fstat1| − m ∙g)t2 + 2(m ∙ g − |Fstat1|)t + |Fstat1|, 0s≤t≤2s. The trajectories of ϕtrans,^Ftrans, and Ftrans_x withπ π respect to time are depicted as solid lines with the assumption of T = 2s, ϕstat1=and ϕest= 3.

[0055] Note that a different polynomial function may be chosen for one or more of the trajectories in the given examples of Figure 11-14, for example a polynomial function of a higher degree. Also, relevant parameters, for example the number of intermediate force setpoints, transition time, time intervals between setpoints, transition speed, alignment force magnitude, coil currents magnitude may also be chosen differently. One skilled in the art may choose a different trajectory and / or different values of the one or more said parameters to fine tune the disturbance reduction effect based on, for example, the surrounding structure configurations, the time allowed for such transition, or the required accuracy of the magnetic alignment method.

[0056] In a fifth step S5 of Figure 4, Figure 15(a) depicts a free-body diagram of the moving body of Figure 3(b) when the phase offset ϕalign2^of the second set of currents are further adapted in the first control mode as shown in Figure 8:

[0057] Wherein the adapting ϕalign2 is around ϕalign2 = ϕstat1 + 2ϕest after the second actuationforce reaches the force transition endpoint Fest. Similar to the adapting ϕalign1depicted in Figure 5, the magnitude of actuation force is kept substantially at |Falign|, and the movement of the stator is tracked by means of a position sensor, until the stator is stationary in the moving direction z. Figure 15(b) depicts a second stationary condition, when a second actuation force Fstat2is generated with a secondsettled phase offset ϕstat2, wherein the second actuation force Fstat2 = |Falign| cos(ϕstat2 −ϕcommutation) = −Fz, and the net force Fstat2_x is in the horizontal direction -x. The same currentcontroller may be used again in the first control mode for adapting ϕalign2to achieve the second stationary condition.

[0058] In a sixth step S6 of Figure 4, combining the equations at the two stationary conditions of Figure 5© and Figure 15(b) results in:cos(ϕstat1 − ϕcommutation) = cos(ϕstat2 − ϕcommutation) = cos(ϕcommutation − ϕstat2) (32)Since ϕstat2is deemed different from ϕstat1to achieve a Fstat2_x in the opposite direction of Fstat1_x, assuming the angle ϕcommutationis not zero, which is the case when the initial position of the coil array with respect to the permanent magnet array deviates from position z=0 in Figure 3(a), in which case

[0059] The commutation angle ϕcommutationmay be determined based on the phase offsets ϕstat1^and^ϕstat2of the first and the second sets of settled phases in addition to the set of reference phases ϕi1_0according to equation (29). As such, by adding ϕcommutationto the set of reference phases of the coil currents, the displacement offset between the magnet array and the coil array is compensated, and thus a maximal efficiency of the motor is achieved. The set of currents of the three coils are then:

[0060] Note that the exact value of the disturbance force Fzis not required for determining the commutation angle, which makes the method robust against constant disturbance forces.

[0061] A similar method may also be applied for a moving magnet and / or a tubular actuator for determining a commutation angle. An example is shown in Figure 16(a). Figure 16(a) depicts a sectional view of a tubular linear actuator 1601 having one-degree-of-freedom movement in the vertical direction z. A cross-section 16B-16B of Figure 16(a) is shown in Figure 16(b), wherein the cross-section 16B-16B is taken along a vertical plane (at least in the view of the paper) through the central axis. A cross-sectional top view of the tubular linear actuator 1601 is shown in Figure 16(c), wherein the cross-section 16C-16C is taking along a plane perpendicular to direction z as shown in Figure 16(b). The exemplary moving magnet actuator comprises a stator 1606 comprising a coil array 1602 and a mover 1605 comprising a magnet array 1603, wherein the mover 1605 is connected to a moving body 1609. A disturbance force Fz is exerted on the moving body, of which the exact value is unknown. A similar method as previously described may be applied for the actuator for determining the commutation angle, for example: a) applying to the coil array 1602 a first set of currents thereby generating an actuation force on the moving body 1609, b) adapting a phase offset of the first set of currents until the moving body reaches a first stationary condition with a first settled phase offset and a first actuation force, c) determining an estimated second actuation force having a magnitude substantially the same as the first actuation force and an estimated direction, d) applying to the coil array 1602 a second set of currents thereby generating an actuation force on the moving body 1609, varying a phase offset and a magnitude of the second set of currents thereby transitioning the actuation force from the first actuation force to the estimated second actuation force via one or more intermediate force setpoints, e) further adapting the phase offset of the second set of currents until the moving body 1609 reaches a second stationary condition with a second settled phase offset and a second actuation force, f) determining the commutation angle based on the first settled phase offset and the second settled phase offset.

[0062] The estimated direction may be determined based on an estimated disturbance force, which may be gravity of the moving body assuming gravity is the dominating disturbance force in the moving direction z. The adapting of the phase offset in step a) and step d) may be controlled by a current controller in a first control mode as depicted in Figure 8. The adapting of the phase offset andthe magnitude in step c) may be controlled by the current controller in a second control mode as depicted in Figure 9. The transitioning of the actuation force in step c) via one or more intermediate force setpoints may apply any of the embodiments as described with reference to any of Figure 11-14.

[0063] In yet another embodiment, Figure 17 depicts a linear actuator 1701 similar to Figure 3(a), comprising more coils and more magnets in the coil array 1702 and the magnet array 1703. A similar method described in any preceding embodiments may be applied for 1701 to determine the commutation angle, as long as the current of each coil is chosen according to the physical configuration, for example mechanical pitch Zmof the magnets.

[0064] In yet another embodiment, Figure 18 depicts a linear actuator of Figure 2(a) which suffers from a disturbance force Fx in direction -x, which may be for example friction when the actuator tends to move the moving body 1809 in direction +x. Similar methods as described in any of the preceding embodiments may be applied to the actuator 1801 to determine the commutation angle.

[0065] A permanent magnetic linear motor system may be arranged to comprise a permanent magnetic motor, for example as described using Figure 2, 3, 16, 17 or 18, which has a stator and a mover which is physically connected to a moving body, wherein the permanent magnetic motor comprises a coil array and a magnet array, and the permanent magnetic linear motor system may further comprise a current controller which may operate in two control modes for example as described using Figure 8 and 9, wherein the permanent magnetic linear motor system is configured to execute the following steps to determine a commutation angle: a) a first set of currents is applied to the coil array thereby generating an actuation force on the moving body, b) a phase offset of the first set of currents is adapted until the moving body reaches a first stationary condition with a first settled phase offset and a first actuation force, c) an estimated second actuation force is determined having a magnitude substantially the same as the first actuation force and an estimated direction, d) a second set of currents is applied to the coil array thereby generating an actuation force on the moving body, a phase offset and a magnitude of the second set of currents are varied thereby transitioning the actuation force from the first actuation force to the estimated second actuation force via one or more intermediate force setpoints, e) the phase offset of the second set of currents is further adapted until the moving body reaches a second stationary condition with a second settled phase offset and a second actuation force, f) the commutation angle is determined based on the first settled phase offset and the second settled phase offset.

[0066] The permanent magnetic linear motor system may further be configured to execute the method for determining the commutation angle according to any preceding embodiments.

[0067] An apparatus, for example a lithographic apparatus of Figure 1 may comprise a permanent magnetic linear motor system described in the preceding embodiments for positioning a movingcomponent in the system, for example in the positioner PW for accurately positioning a wafer table WT and / or a mask table MT. The lithography system may use the method described in any preceding embodiments to determine the commutation angle. Similarly, a substrate inspection apparatus or a wafer metrology apparatus may also comprise such a permanent magnetic linear motor system described in the preceding embodiments for positioning a moving component in the apparatus.

[0068] Although specific reference may be made in this text to the use of a lithographic apparatus in the manufacture of Ics, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include 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.

[0069] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may 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 an object such as a wafer (or other substrate) or mask (or other patterning device). These apparatus may be generally referred to as lithographic tools. Such a lithographic tool may use vacuum conditions or ambient (non-vacuum) conditions.

[0070] Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention, where the context allows, is not limited to optical lithography and may be used in other applications, for example imprint lithography.

[0071] Where the context allows, 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, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. and in doing that may cause actuators or other devices to interact with the physical world.

[0072] 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 descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art thatmodifications may be made to the invention as described without departing from the scope of the claims set out below.

Claims

CLAIMS 1. A method for determining a commutation angle of a permanent magnetic linear motor having a stator and a mover which is physically connected to a moving body, the permanent magnetic motor comprising a coil array and a magnet array, the method comprising successive steps of: a) applying to the coil array a first set of currents thereby generating an actuation force on the moving body, b) adapting a phase offset of the first set of currents until the moving body reaches a first stationary condition with a first settled phase offset and a first actuation force, c) determining an estimated second actuation force having a magnitude substantially the same as the first actuation force and an estimated direction, d) applying to the coil array a second set of currents thereby generating an actuation force on the moving body, varying a phase offset and a magnitude of the second set of currents thereby transitioning the actuation force from the first actuation force to the estimated second actuation force via one or more intermediate force setpoints, e) further adapting the phase offset of the second set of currents until the moving body reaches a second stationary condition with a second settled phase offset and a second actuation force, f) determining the commutation angle based on the first settled phase offset and the second settled phase offset.

2. The method of claim 1, wherein the estimated direction of step c) is determined based on the first actuation force and an estimated disturbance force exerted on the moving body.

3. The method of claim 2, wherein the disturbance force is gravity of the moving body.

4. The method of any preceding claim, wherein the actuation force transitions from the first actuation force to the estimated second actuation force in a predefined transition time.

5. The method of claim 4, wherein the transition time is defined to balance an external disturbance caused by the method and a time spent on the method.

6. The method of claim 4 or 5, wherein the one or more intermediate force setpoints are defined in such a way that the trajectory of a magnitude and / or a direction of the one or more intermediate force setpoints is a function of time.

7. The method of claim 6, wherein the trajectory of the magnitude and / or the direction of the one or more intermediate force setpoints is a polynomial as a function of time, the polynomial having a degree of one, two or higher.

8. The method of claim 7, wherein the trajectory of the magnitude of a component of the one or more intermediate force setpoints is a polynomial as a function of time, the polynomial having a degree of one, two or higher.

9. The method of any preceding claim, wherein the actuation force transitions from the first actuation force to the estimated second actuation force in a discrete way or in a continuous way.

10. A current controller configured to control the first and / or the second set of currents for executing the method according to any preceding claim.

11. The current controller of claim 10, wherein the current controller is configured to operate in a first control mode during use for step b) and / or e), to adapt the phase offsets of the first and second sets of currents for reaching the stationary conditions based on a measured position or a measured parameter indicative of a position of the mover or moving body.

12. The current controller of claim 10 or 11, wherein the current controller is configured to operate in a second control mode during use for step d), to control the phase offset and the magnitude of the second set of currents based on a measured position or a measured parameter indicative of a position of the mover or the moving body.

13. A permanent magnetic linear motor system comprising a permanent magnetic motor having a stator and a mover which is physically connected to a moving body, the permanent magnetic motor comprising a coil array and a magnet array, and the permanent magnetic linear motor system further comprises a current controller of claim 10, 11 or 12, wherein the permanent magnetic linear motor system is configured to execute the method according to any one of claims 1-9.

14. A lithographic apparatus, a substrate inspection apparatus or a wafer metrology apparatus comprising the permanent magnetic linear motor system of claim 13.

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