Method for determining absolute position of movable object, interferometer system, projection system and lithographic apparatus

Abstract

There is described a method of determining an absolute position of a first movable object using an interferometer system, the method comprising: providing a first beam and a second beam having a first light frequency from a first light source; providing, from a second light source, a further first beam and a further second beam having a second (tunable) light frequency; the first and further first beams are directed along a first axis to a reflective surface of the first object to obtain a first interferometer signal, and the second and further second beams are directed along a second axis to a reflective surface of a second object to obtain a second interferometer signal while varying the tunable frequency, the method includes detecting a first interferometer signal and a further first interferometer signal, detecting a second interferometer signal and a further second interferometer signal, determining a first count offset and / or a further first count offset using a nonlinear equation, and determining an absolute position of the first object.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to European application 22182093.9 filed on June 30, 2022, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The invention relates to a method for determining the absolute position of a movable object using an interferometer system. The invention also relates to an interferometer system and a projection system for an optical lithography system and / or a lithography apparatus comprising such an interferometer system. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a substrate, usually on a target portion of the substrate. For example, a lithographic apparatus may be used in the manufacture of integrated circuits (ICs). In this case, a pattern forming device, alternatively referred to as a mask or mask, may be used to produce a circuit pattern to be formed on a single layer of the IC. This pattern may be transferred to a target portion (e.g., including a portion of a die, one or several dies) on a substrate (e.g., a silicon wafer). Typically, the transfer of the pattern is performed by imaging the pattern onto a layer of radiation-sensitive material (resist) disposed on the substrate. Typically, a single substrate will contain a grid of adjacent target portions that are patterned successively. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing the entire pattern to the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the substrate synchronously parallel or antiparallel to a given direction (the "scanning" direction) while the radiation beam scans the pattern. It is also possible to transfer a pattern from a pattern forming device to a substrate by imprinting the pattern onto the substrate.

[0005] In an embodiment of the lithographic apparatus, an interferometer system is used to determine the position of movable objects with high accuracy. Examples of such movable objects are substrate supports and movable optical elements, such as mirrors of a projection optics box.

[0006] Another disadvantage of most known interferometers is that they are only able to determine the relative displacement of the movable object relative to a reference position. In order to determine the absolute position of the movable object relative to the reference position, a separate zeroing sensor can be provided. The zeroing sensor is used to determine the absolute starting position of the movable object. Once this absolute starting position is known, the interferometer can determine the relative displacement of the movable object relative to this absolute starting position in order to calculate the absolute position of the movable object.

[0007] The zeroing sensor is usually installed at a specific position where the absolute starting position of the movable object can be determined. Therefore, the absolute position of the movable object can be determined only when the movable object is located in a relatively small measuring range of the zeroing sensor. The measuring range of the zeroing sensor is typically close to the zeroing sensor, for example, within a few centimeters above and below the zeroing sensor. Each time the interferometer is used to start the measurement of the movable object, the movable target must be brought back to the relatively small measuring range of the zeroing sensor of the position measurement system. This may be the case not only when the lithography equipment is turned on, but also when, for example, the movable object slightly leaves the field of view of the interferometer (for example, when traveling behind another movable object).

[0008] WO2019149515A1 discloses a method for determining the absolute position of a movable object relative to a reference object using an interferometer system. The interferometer system includes a measurement axis and a reference axis, the measurement axis includes a reflective measurement surface on the object, and the reference axis includes a reflective reference surface on the reference object. In this method, a first beam and a second beam originating from a first light source are guided through the measurement axis and the reference axis, respectively. Similarly, another first beam and another second beam originating from a second light source are guided through the measurement axis and the reference axis, respectively. The optical frequency of the second light source is tunable so that the optical frequency of the second light source can be changed during measurement.

[0009] WO2019149515A1 provides an algorithm in which specific measurement values ​​of the interferometer signal obtained from the measurement in the measurement axis and the reference axis are selected to determine the absolute position of the movable object. This algorithm requires that the length of the reference axis is stable, i.e. does not change during the measurement. In addition, the calculation is relatively complex and may require some specific selection criteria for the measurement data, which may complicate the application of the method.

[0010] In another known method for determining the absolute position of the movable object, it is necessary that the tuning frequency of the tunable light source is high in order to make the measurement less sensitive to movements of the movable object.

[0011] While both methods are capable of determining the absolute position of a movable object using an interferometer system, the requirement for a stable length reference axis and / or a fast frequency modulated light source combined with the relatively complex computations limits the practical application of these methods in interferometer systems. Summary of the invention

[0012] It is an object of the present invention to provide an improved method of determining the absolute position of a movable object using an interferometer system. In particular, it is an object of the present invention to provide a method of determining the absolute position of a movable object using an interferometer that does not require a fast frequency modulated light source and / or a fixed reference axis. A further object is to provide an interferometer system in which such a method can be implemented.

[0013] According to one aspect of the present invention, there is provided a method for determining an absolute position of a first movable object using an interferometer system, the method comprising:

[0014] providing a first beam and a second beam having a first light frequency from a first light source;

[0015] providing an additional first beam and an additional second beam having a second optical frequency from a second optical source, wherein the second optical frequency is a tunable optical frequency;

[0016] directing the first beam and the further first beam along a first measuring axis to a first reflecting surface of the first movable object to obtain a first interferometer signal and a further first interferometer signal, respectively,

[0017] while changing the tunable optical frequency of the second light source, directing the second beam and the further second beam along a second measuring axis to a second reflecting surface of a second object to obtain a second interferometer signal and a further second interferometer signal, respectively,

[0018] detecting the first interferometer signal and the further first interferometer signal at at least one first detector,

[0019] detecting the second interferometer signal and the further second interferometer signal at at least one second detector,

[0020] A first count shift and / or a further first count shift is determined based on the first interferometer signal, the further first interferometer signal, the second interferometer signal and the further second interferometer signal using a non-linear equation, wherein the non-linear equation is based on the following relationship:

[0021] λ ls2 / λ ls1 = C ma1, ls1 / C ma1, ls2 = C ma2, ls1 / C ma2, ls2 ,

[0022] in,

[0023] λ ls2 is the second wavelength of the second light source,

[0024] λ ls1 is the first wavelength of the first light source,

[0025] C ma1, ls1 is the total number of counts about the first measurement axis and the first beam,

[0026] C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam,

[0027] C ma2, ls1 is the total number of counts about the second measurement axis and the second beam,

[0028] C ma2, ls2 is the total number of counts about the second measurement axis and the further second beam, and

[0029] The absolute position of the first movable object is determined based on the first count shift and the first interferometer signal or based on the further first count shift and the further first interferometer signal.

[0030] According to one aspect of the present invention, there is provided an interferometer system for determining an absolute position of a first movable object, the interferometer system comprising:

[0031] a first light source arranged to provide a first beam and a second beam having a first light frequency;

[0032] a second light source arranged to provide a further first beam and a further second beam having a second light frequency, wherein the second light source is arranged to provide a tunable second light frequency,

[0033] a first measurement axis for directing the first beam and the further first beam to a first reflecting surface of the first movable object to obtain a first interferometer signal and a further first interferometer signal, respectively,

[0034] a second measuring axis for directing the second beam and the further second beam to a second reflecting surface of a second object to obtain a second interferometer signal and a further second interferometer signal, respectively,

[0035] at least one first detector for detecting the first interferometer signal and the further first interferometer signal,

[0036] at least one second detector for detecting the second interferometer signal and the further second interferometer signal,

[0037] processing means, wherein the processing means is arranged to determine a first count shift and / or a further first count shift based on the first interferometer signal, the further first interferometer signal, the second interferometer signal and the further second interferometer signal using a non-linear equation, wherein the non-linear equation is based on the following relationship:

[0038] λ ls2 / λ ls1 = C ma1, ls1 / C ma1, ls2 = C ma2, ls1 / C ma2, ls2 ,

[0039] in,

[0040] λ ls2 is the second wavelength of the second light source,

[0041] λ ls1 is the first wavelength of the first light source,

[0042] C ma1, ls1 is the total number of counts about the first measurement axis and the first beam,

[0043] C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam,

[0044] C ma2, ls1 is the total number of counts about the second measurement axis and the second beam,

[0045] C ma2, ls2 is the total number of counts about the second measurement axis and the further second beam, and

[0046] The absolute position of the first movable object is determined based on the first count shift and the first interferometer signal or based on the further first count shift and the further first interferometer signal.

[0047] According to an aspect of the present invention, there is provided a projection system for an optical lithography system and / or a lithography apparatus comprising such an interferometer system. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which corresponding reference numerals indicate corresponding parts, and in which:

[0049] Figure 1 A lithographic apparatus is schematically depicted;

[0050] Figure 2A first embodiment of an interferometer system according to the invention is shown; and

[0051] Figure 3 A second embodiment of an interferometer system according to the invention is shown. . DETAILED DESCRIPTION

[0052] Figure 1 A lithographic apparatus according to an embodiment of the invention is schematically depicted. The apparatus comprises an illumination system IL, a support structure MT, a substrate table WT and a projection system PS.

[0053] The illumination system IL is configured to condition the radiation beam B. The support structure MT (e.g. a mask table) is configured to support a patterning device MA (e.g. a mask) and is connected to a first positioner PM configured to accurately position the patterning device according to certain parameters. The substrate table WT (e.g. a wafer stage) is configured to hold a substrate W (e.g. a resist-coated wafer) W and is connected to a second positioner PW configured to accurately position the substrate according to certain parameters. The projection system PS is 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.

[0054] The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping or controlling radiation.

[0055] The term "radiation beam" as used herein encompasses all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365 nm, 355 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm to 20 nm), as well as particle beams, such as ion beams or electron beams.

[0056] The support structure MT supports the pattern forming device MA, i.e. bears the weight of the pattern forming device MA. The way in which the support structure MT holds the pattern forming device MA depends on the orientation of the pattern forming device MA, the design of the lithographic equipment, and other conditions, such as, for example, whether the pattern forming device MA is kept in a vacuum environment. The support structure MT can use mechanical, vacuum, electrostatic or other clamping techniques to hold the pattern forming device MA. The support structure MT can be, for example, a frame or a table, which can be fixed or movable as required. The support structure MT can ensure that the pattern forming device MA is in a desired position, for example relative to the projection system PS.

[0057] The term “patterning device” as used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam B with a pattern in its cross-section so as to create a pattern in a target portion C of the substrate W. It should be noted that the pattern imparted to the radiation beam B may not exactly correspond to the desired pattern in the target portion C of the substrate W (for example if the pattern includes phase-shifting features or so called assist features). Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device (such as an integrated circuit) to be created in the target portion C.

[0058] The pattern forming device MA can be transmissive or reflective. Examples of the pattern forming device include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary masks, alternating phase shift masks, and attenuated phase shift masks, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incident radiation beam B in different directions. The tilted mirrors impart a pattern in the radiation beam B reflected by the mirror matrix.

[0059] The term "projection system" as used herein should be broadly interpreted as covering any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems or any combination thereof, as appropriate to the exposure radiation used or other factors such as the use of immersion liquid or the use of a vacuum.

[0060] As depicted here, the device is transmissive (eg, employing a transmissive mask). Alternatively, the device may be reflective (eg, employing a programmable mirror array of the type mentioned above, or employing a reflective mask).

[0061] The lithographic apparatus may be of a type having two (dual stage) or more substrate tables WT (and / or two or more mask tables). In such a "multi-stage" machine, the extra tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure. In addition to one or more substrate tables WT, the lithographic apparatus may have a measurement stage which is arranged to be located at a position when the substrate table WT leaves a position under the projection system PS. Instead of supporting a substrate W, the measurement stage may be provided with sensors to measure properties of the lithographic apparatus. For example, the projection system may project an image onto a sensor on the measurement stage to determine image quality.

[0062] The lithographic apparatus may also be of a type in which at least a portion of the substrate W may be covered by a liquid having a relatively high refractive index, such as water, so as to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, such as the space between the pattern forming device MA and the projection system PS. Immersion techniques are well known in the art for increasing the numerical aperture of the projection system. The term "immersion" as used herein does not mean that structures such as the substrate W must be immersed in liquid, but "immersion" only means that liquid is located between the projection system PS and the substrate W during exposure.

[0063] refer to Figure 1 , the illumination system IL receives a radiation beam B from a radiation source SO. The radiation source SO and the lithographic apparatus may be separate entities (for example when the radiation source SO is an excimer laser). In such a case, the source is not considered to constitute a part of the lithographic apparatus, and the radiation beam B is transferred from the radiation source SO to the illumination system IL by means of a beam delivery system BD comprising, for example, suitable directional mirrors and / or a beam expander. In other cases, for example when the radiation source SO is a mercury lamp, the radiation source SO may be an integral part of the lithographic apparatus. The radiation source SO and the illuminator IL and, if necessary, the beam delivery system BD may be referred to together as a radiation system.

[0064] The illumination system IL may comprise an adjuster AD for adjusting the angular intensity distribution of the radiation beam B. Typically, at least the outer radial extent and / or the inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illumination system may be adjusted. Furthermore, the illumination system IL may comprise various other components, such as an integrator IN and a condenser CO. The illumination system IL may be used to adjust the radiation beam B to have a desired uniformity and intensity distribution in its cross-section.

[0065] The radiation beam B is incident on the patterning device MT which is held on the support structure MT and is patterned by the patterning device MA. Having traversed the patterning device MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g. an interferometer device, a linear encoder, or a capacitive sensor), the substrate table WT can be accurately moved, for example in order to position a different target portion C in the path of the radiation beam B. Similarly, the first positioner PM and a further position sensor ( Figure 1The support structure MT is used to accurately position the pattern forming device MA relative to the path of the radiation beam B (not explicitly shown in the figure). Typically, the movement of the support structure MT can be achieved with the help of a long-stroke module and a short-stroke module that form part of the first positioner PM. The long-stroke module can provide coarse positioning of the short-stroke module over a large range of movement. The short-stroke module can provide fine positioning of the support structure MT with respect to the long-stroke module over a small range of movement. Similarly, the movement of the substrate table WT can be achieved using a long-stroke module and a short-stroke module that form part of the second positioner PW. The long-stroke module can provide coarse positioning of the short-stroke module over a large range of movement. The short-stroke module can provide fine positioning of the substrate table WT relative to the long-stroke module over a small range of movement. In the case of a stepper (as opposed to a scanner), the support structure MT may be connected only to a short-stroke actuator, or may be fixed. The pattern forming device MA and the substrate W may 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, they may be located in spaces between multiple target portions C (these are referred to as scribe lane alignment marks). Similarly, where more than one die is disposed on the patterning device MA, the mask alignment marks M1, M2 may be located between these dies.

[0066] The depicted device can be used in at least one of the following modes:

[0067] In a first mode (the step mode), the support structure MT and the substrate table WT are held substantially stationary while the entire pattern imparted to the radiation beam B is projected at once onto a target portion C (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C that is imaged in a single static exposure.

[0068] In a second mode (the so called scan mode), the support structure MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam B is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning movement determines the height of the target portion C (in the scanning direction).

[0069] In a third mode, the support structure MT holding the programmable patterning device is held substantially stationary and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation may be readily applied to maskless lithography using a programmable patterning device, such as a programmable mirror array of the type described above.

[0070] Combinations and / or variations on the above-described modes of use or entirely different modes of use may also be employed.

[0071] Figure 2 An embodiment of an interferometer system 100 according to the invention is shown. The interferometer system 100 is arranged to determine the absolute position of a first movable object 200 and the absolute position of a second movable object 300. The interferometer system 100 may be a single pass or a multi-pass interferometer system.

[0072] The first movable object 200 and the second movable object 300 are for example components of a projection system PS and / or a movable substrate support WT of a lithographic apparatus, such as mirrors. The first movable object 200 comprises a first reflective measurement surface 201 and the second movable object 300 comprises a second reflective measurement surface 301.

[0073] The interferometer system 100 is a heterodyne interferometer system, which includes a first light source 101 to provide a light beam, such as a laser beam having a fixed first optical frequency. The first light source 101 is, for example, a stable HeNe laser source. The light beam of the first light source 101 is split into a first beam and a second beam by, for example, a non-polarizing beam splitter. The first beam is directed to an interferometer optical device 110 of a first measurement axis 102. The interferometer optical device 110 is arranged to split the first beam into a first measurement beam and a first reference beam. The first measurement beam is along a path having a measurement path length L x1 The measurement path of the first measuring beam is guided to the first reflecting measuring surface 201 on the first movable object 200. After the first measuring beam is reflected by the first reflecting measuring surface 201, the first measuring beam is recombined with the first reference beam in the interferometer optics 110 to form a first interferometer signal. The first interferometer signal is guided to the detector 103b connected to the optical sensor device 103.

[0074] The second beam of the laser beam is directed to the interferometer optics 111 of the second measurement axis 104. The interferometer optics 111 is arranged to split the second beam into a second measurement beam and a second reference beam. The second beam measurement is performed along a path having a measurement path length L x2 The second measurement beam is guided to the second reflective measurement surface 301 by a second measurement path of the first light source 101. After the second measurement beam is reflected by the second reflective measurement surface 301, the second measurement beam is recombined with the second reference beam in the interferometer optics 111 to form a second interferometer signal. The second interferometer signal is guided to a detector 103c connected to the light sensor device 103. A portion of the light beam of the first light source 101 is guided to a detector 103a connected to the light sensor device 103. This portion of the light beam will not be guided into the first measurement axis 102 or the second measurement axis 104.

[0075] The detector 103a propagates the portion of the light beam to a light emitting diode of the light sensor device 103. The detector 103b propagates the recombined first beam and the first reference beam to another light emitting diode of the light sensor device 103. The detector 103c propagates the recombined second beam and the second reference beam to yet another light emitting diode of the light sensor device 103. The measurement results of the light emitting diodes are fed to the processing device 106 via the light sensor device 103. The processing device 106 generates a first measurement phase value ph based on the input of the first interferometer signal at the detector 103b. ma1, ls1 Alternatively, the processing device 106 may generate the first measured phase value ph based on the input from the detector 103b and the input from the detector 103a. ma1, ls1 , to compensate for the disturbance of the laser beam between the first light source 101 and the interferometer optical device 110. The processing device 106 generates a second measured phase value ph based on the input of the second interferometer signal at the detector 103c ma2, ls1 Alternatively, the processing device 106 may generate the first reference phase value ph based on the input from the detector 103c and the input from the detector 103a. ma2, ls1 , to compensate for the disturbance of the laser beam between the first light source 101 and the interferometer optical device 111. The first measured phase value ph ma1, ls1 is related to the distance or displacement of the measured object 200, that is, to the first measurement path length L x1 The second measured phase value ph ma2, ls1 With the second measurement path length L x2 related.

[0076] The interferometer system 100 includes a second light source 107. The second light source 107 has a tunable optical frequency. In the illustrated embodiment, the second light source 107 is configured to provide a second laser beam having a tunable optical frequency (e.g., from a tunable laser source). The second laser beam is split into an additional first beam and an additional second beam. Similar to the first beam, the additional first beam is directed to the interferometer optical device 110 of the first measurement axis 102. The interferometer optical device 110 is arranged to split the additional first beam into an additional first measurement beam and an additional first reference beam. The additional first measurement beam is along a path having a measurement path length L x1 The measurement path of the further first measurement beam is guided to the first reflective measurement surface 201 on the first movable object 200. After the further first measurement beam is reflected by the first reflective measurement surface 201, the further first measurement beam is recombined with the further first reference beam in the interferometer optics 110 to form a further first interferometer signal. The further first interferometer signal is guided to a detector 103b connected to the light sensor device 103.

[0077] The further second beam is directed to the interferometer optics 111 of the second measurement axis 104. The interferometer optics 111 is arranged to split the further second beam into a further second measurement beam and a further second reference beam. The further second measurement beam is directed along a second measurement path having a second measurement path length L x2 The second measurement path of the further second measurement beam is guided to the second reflective measurement surface 301. After the further second measurement beam is reflected by the second reflective measurement surface 301, the further second measurement beam is recombined with the further second reference beam in the interferometer optics 111 to form a further second interferometer signal. The further second interferometer signal is guided to a detector 103 c connected to the light sensor device 103.

[0078] A portion of the second light beam of the second light source 107 is directed to a detector 103a connected to the light sensor device 103. This portion of the second light beam does not interact with the first reflection measurement surface 201 or the second reflection measurement surface 301.

[0079] The detector 103a propagates the portion of the second light beam to a light emitting diode of the light sensor device 103. The detector 103b propagates the recombined further first beam and the further first reference beam to another light emitting diode of the light sensor device 103. The detector 103c propagates the recombined further second beam and the further second reference beam to yet another light emitting diode of the light sensor device 103. The measurement results of the light emitting diodes are fed into the processing device 106 via the light sensor device 103. The processing device 106 generates a further first measurement phase value ph based on the input of the further first interferometer signal at the detector 103b. ma1, ls2 Alternatively, the processing means 106 may generate the further first measured phase value ph based on the input from the detector 103b and the input from the detector 103a. ma1, ls2 , to compensate for the disturbance of the second laser beam between the second light source 107 and the interferometer optical device 110. The processing device 106 generates a further second phase value ph based on the input of the further second interferometer signal at the detector 103c ma2, ls2 Alternatively, the processing means 106 may generate the further second measured phase value ph based on the input from the detector 103c and the input from the detector 103a. ma2, ls2 , to compensate for the disturbance of the second laser beam between the second light source 107 and the interferometer optical device 111. The additional first measured phase value ph ma1, ls2 is related to the distance or displacement of the first movable object 200, that is, to the first measurement path length L x1 The other second measured phase value ph ma2, ls2 is related to the distance or displacement of the second movable object 300, that is, to the second measurement path length L x2 related.

[0080] Therefore, the light beams of the first light source 101 and the second light source 107 are as follows: Figure 2 After being combined in the Rochon prism 108 shown in FIG. 1 , the light beams of the first light source 101 and the second light source 107 follow the same path along the first measurement axis 102 and the second measurement axis 104. In an embodiment, optical components other than the Rochon prism 108 may also be used to combine the light beams of the first light source 101 and the second light source 107.

[0081] In the embodiment shown, the first interferometer signal and the further first interferometer signal are both directed to detector 103b, and the second interferometer signal and the second interferometer signal are both directed to detector 103c. In an alternative embodiment, the first interferometer signal and the further first interferometer signal may be directed to two separate detectors after optical separation of the first interferometer signal and the further first interferometer signal. Correspondingly, the second interferometer signal and the further second interferometer signal may be directed to two separate detectors after optical separation of the second interferometer signal and the further second interferometer signal.

[0082] The processing means 106 are arranged to distinguish between the first measured phase value ph ma1, ls1 , the second measured phase value ph hma2, ls1 , another first measured phase value ph ma1, ls2 and another second measured phase value ph ma2, ls2 .

[0083] The first measured phase value ph ma1, ls1 and another first measured phase value ph ma1, ls2 The second measured phase value ph may change due to the movement of the first movable object 200. hma2, ls1 and another second measured phase value ph ma2, ls2 The value may be changed due to the movement of the second movable object 300 .

[0084] In addition, the first measured phase value ph ma1, ls1 and the second measured phase value ph hma2, ls1 The first measured phase value ph may be changed due to the change of the first optical frequency of the first light source 101. ma1, ls2 and another second measured phase value ph ma2, ls2 The change may be due to the change of the second light frequency of the second light source 107 .

[0085] Due to these changes, the first measured phase value ph ma1, ls1 , the second measured phase value ph ma2, ls1 , the further first measured phase value ph ma1, ls2 and the further second measured phase value ph ma2, ls2The periodic distribution may be followed within the spatial period (i.e. wavelength) of the optical frequency of the corresponding light source. When the corresponding measured phase value runs from one period to another, this may be determined by the processing means 106 and defined as a count. By adding the counts (which may be positive or negative, depending on the direction of movement of the corresponding movable object or the change in the optical frequency of the corresponding light source), the change in position and / or the change in optical frequency during the measurement may be registered as a count number. For example, ΔC ma1, ls1 (t) is the first beam (eg, the first measured phase value ph) measured with respect to the first measurement axis 102 and using the first interferometer signal. ma1, ls1 ) count changes over time.

[0086] The absolute position L1 of the first movable object 200 as measured by the first beam may be described as:

[0087] L ma1, ls1 = λ ls1 × C ma1, ls1,

[0088] Among them, λ ls1 is the first wavelength of the first light source, and C ma1, ls1 is the total number of counts with respect to the first measurement axis 102 and the first beam (ie, the light originating from the first light source 101 ).

[0089] Note that based on the first measured phase value ph ma1, ls1 , the relative position of the first movable object 200 within the wavelength (i.e., spatial period) can also be determined. This relative position can be added to the count quantity C ma1, ls1 , for example as a real number between 0 and 1, to improve the accuracy, ie precision, of determining the absolute position of the first movable object 200, for example by interpolation.

[0090] The absolute position L1 of the first movable object 200 using the measurement with the further first beam can be described as:

[0091] L ma1, ls2 = λ ls2 × C ma1, ls2,

[0092] Among them, λ ls2 is the second wavelength of the second light source, and C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam. The further first measurement phase value ph ma1, ls2 It can also be used to determine the relative position of the first movable object 200 within the wavelength (spatial period).

[0093] The absolute position L2 of the second movable object 300 using the measurements using the second beam and the further second beam can be described as:

[0094] L ma2, ls1 = λ ls1 × C ma2, ls1, and

[0095] L ma2, ls2 = λ ls2 × C ma2, ls2,

[0096] Among them, C ma2, ls1 is the total number of counts about the second measurement axis and the second beam, and C ma2, ls2 is the total number of counts about the second measurement axis and the additional second beam. It should also be noted here that the second measurement phase value ph hma2, ls1 and another second measured phase value ph ma2, ls2 It can also be used to determine the relative position of the second movable object 200 within the wavelength (spatial period).

[0097] When the starting position of the first movable object 200 is unknown, the total number C ma1, ls1 is also unknown. The total number of counts C ma1, ls1 can be described as:

[0098] C ma1, ls1 (t) = ΔC ma1, ls1 (t) + offset ma1, ls1

[0099] Here, the total number of counts C of the first beam on the first measurement axis 102 is ma1, ls1 The first count offset is defined as unknown. ma1, ls1 Add the measured change in counts ΔC ma1, ls1 (t).

[0100] Similarly, count the total number C ma1, ls2 (t), C ma2, ls1 (t) and C ma2, ls2 (t) can be described as:

[0101] C ma1, ls2 (t) = ΔC ma1, ls2 (t) + offset ma1, ls2

[0102] C ma2, ls1 (t) = ΔC ma2, ls1 (t) + offsetma2, ls1

[0103] C ma2, ls2 (t) = ΔC ma2, ls2 (t) + offset ma2, ls2

[0104] Among them, offset ma1, ls2 is a further first offset of the counts of the further first beam on the first measuring axis 102, ma2, ls1 is a second offset of counts of the second beam on the second measurement axis, and offset ma2, ls2 is a further second offset in counts of a further second beam on the second measuring axis.

[0105] In order to make the counts of the first light source 101 and the second light source 107 consistent, the following equation is applied:

[0106] L ma1, ls1 (t) = λ ls1 (t) × C ma1, ls1 (t) = L ma1, ls2 (t) = λ ls2 (t) × C ma1, ls2 (t)

[0107] L ma2, ls1 (t) = λ ls1 (t) × C ma2, ls1 (t) = L ma2, ls2 (t) = λ ls2 (t) × C ma2, ls2 (t),

[0108] in:

[0109] L ma1, ls1 (t) is a first position determined on the first measurement axis using the first beam, λ ls1 is the first wavelength of the first light source, C ma1, ls1 is the total number of counts about the first measurement axis and the first beam,

[0110] L ma1, ls2 (t) is the first position determined on the first measurement axis using the further first beam, λ ls2 is the second wavelength of the second light source, C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam,

[0111] L ma2, ls1(t) is a second position determined on the second measurement axis using the second beam, and C ma2, ls1 is the total number of counts about the second measurement axis and the second beam,

[0112] L ma2, ls1 (t) is the second position determined on the second measurement axis using the further second beam, and C ma2, ls2 is the total number of counts regarding the second measurement axis and the further second beam.

[0113] This results in:

[0114] λ ls2 (t) / λ ls1 (t) = C ma1, ls1 (t) / C ma1, ls2 (t), and

[0115] λ ls2 (t) / λ ls1 (t) = C ma2, ls1 (t) / C ma2, ls2 (t).

[0116] And therefore:

[0117] λ ls2 (t) / λ ls1 (t) = C ma1, ls1 (t) / C ma1, ls2 (t) = C ma2, ls1 (t) / C ma2, ls2 (t),

[0118] By using the relationship between these ratios, a nonlinear equation can be defined, based on which the absolute position of the first movable object 200 and / or the second movable object 300 can be determined. This nonlinear equation can be, for example:

[0119] C ma1, ls2 (t) × C ma2, ls1 (t) = C ma2, ls2 (t) × C ma1, ls1 (t).

[0120] An advantage of this non-linear equation is that it does not require a stable first light frequency of the first light source 101. Furthermore, it is not required that one of the objects 200, 300 is a static object held in a fixed static position.

[0121] Since the total number of counts for measuring axis i and light source j can be described as:

[0122] C mai, lsj (t) = ΔC mai, lsj (t) + offset mai, lsj

[0123] So the nonlinear equation can also be described as:

[0124]

[0125] The processing device 106 of the interferometer system 100 is arranged to calculate the first count offset offset using this nonlinear equation ma1, ls1 and / or the additional first count offset ma1, ls2 The processing device 106 will solve the equation to find the offset for the four unknown parameters. ma1, ls1 、offset ma1, ls2 、offset ma2, ls1 and offset ma2, ls2 Once the first count offset is known ma1, ls1 and / or the additional first count offset ma1, ls2 , the absolute position of the first movable object 200 can be calculated.

[0126] Finding a solution to the nonlinear equation may include obtaining a first estimate of a solution using the reduced data set, and using the first estimate as input for solving the nonlinear equation for the full data set.

[0127] For the nonlinear equation with four unknown parameters (i.e., four count offsets), in order to be solvable with high accuracy, it is necessary that the frequency difference between the first optical frequency and the second optical frequency is not constant, i.e., at least one of the first light source 101 and the second light source 107 needs to have a changed first optical frequency or a changed second optical frequency, respectively. In addition, the length ratio L of the two measuring axes 102, 104 is ma1 / L ma2 This requires that at least one of the first movable object 200 and the second movable object 300 will move during the measurement.

[0128] In an embodiment, both the first optical frequency of the first light source 101 and the second optical frequency of the second light source 107 can be changed during the measurement. For example, both the first light source 101 and the second light source 107 can be tunable lasers. In the case where both the first optical frequency and the second optical frequency are tuned (i.e. changed) during the measurement, it is advantageous that the first light source 101 and the second light source 107 have a large tuning range and / or the tuning of the first optical frequency and the second optical frequency is opposite with respect to each other, for example 180° out of phase with respect to each other. This will provide measurement data that is more suitable for solving the nonlinear equation.

[0129] In the case where both the first movable object 200 and the second movable object 300 are moved during measurement, it is desirable that the first movable object 200 and the second movable object 300 perform different movements, such as movements in opposite directions.

[0130] Furthermore, in order to simplify the solution of the nonlinear relationship, a priori information can be used as input. For example, in the case where one of the first movable object 200 and the second movable object 300 does not move during measurement and one of the light sources 101, 107 has a fixed light frequency, then the count offsets associated with the corresponding measurement axis and light source from a previous solution can be stored and used as boundary conditions for solving the nonlinear equations in order to reduce the number of free estimators.

[0131] Furthermore, when the average center frequency ratio between the first optical frequency of the first light source 101 and the second optical frequency of the second light source 107 is known for at least some averaging period, this information can also be used to reduce the number of free estimators. This can reduce the complexity of the equations to be solved to linear equations.

[0132] Previous count offset information that can be used to solve the non-linear equation can also be derived from pre-calibrated measurement axes.These previously calibrated count offsets can, for example, be stored in a memory of the processing device 106 for later use.

[0133] Once the first count is offset ma1, ls1 and the first count offset ma1, ls2 If the first measuring axis 102 is known, then for the second counting offset ma2, ls1 Determination and additional second count offset offset ma2, ls2 can be simplified to a linear equation with only 2 unknown parameters.

[0134] Due to λ ls2 (t) / λ ls1(t) = C ma1, ls1 (t) / C ma1, ls2 (t) is known, so the second count offset is ma2, ls1 and another second count offset ma2, ls2 It can be calculated as follows:

[0135] λ ls2 (t) / λ ls1 (t) = λratio(t) = (ΔC ma2, ls1 (t) + offset ma2, ls1 ) / (ΔC ma2, ls2 (t) + offset ma2, ls2 ).

[0136] This can be written as a set of linear equations in matrix notation, where i is the index indicating the number of rows, with two unknown variables offset ma2, ls1 and offset ma2, ls2 :

[0137] H = [λratio(t i ) - 1]

[0138] b = [ ΔC ma2, ls2 (t i ) - λratio(t i )·ΔC ma2, ls1 (t i ) ]

[0139] Then the second count offset is solved by least squares fitting ma2, ls1 and another second offset ma2, ls2 :

[0140] [offset ma2, ls1 ; offset ma2, ls2 ] = (H T H) -1 H T b;

[0141] This equation can be solved by a linear least squares fitting method to generate the second measurement axis 104 and the second count offset offset ma2, ls1 and another second offset ma2, ls2 The zero count offset.

[0142] For this set of linear equations to be solvable, λratio(t) must contain at least 2 unique, i.e., different, values. Typically, the measurement data used to solve these equations will be redundant and contain hundreds or thousands of data points in order to improve fit accuracy and reduce error sensitivity to measurement noise.

[0143] exist Figure 2 In an embodiment, the interferometer system 100 includes two measurement axes 102, 104. It is possible that the interferometer system includes more than two measurement axes. In such an interferometer system, the third measurement axis and additional measurement axes can be used to add redundancy to the absolute zeroing equation by optimizing the nonlinear count offset problem for different combinations of interferometer axes simultaneously or sequentially. Once λratio(t) can be derived, the count offset equation for any other axis can be solved using the above linear equation.

[0144] Using the above method, the absolute number of counts for a measurement axis 102, 104 for a particular wavelength can be determined based on the count offset of the respective measurement axis 102, 104. This means that the measurement is considered "traceable" to the wavelength of the respective light source 101, 107. Basically, this count offset is the parameter of interest for determining the absolute position that can be measured by the interferometer system 100.

[0145] However, in order to be able to determine the absolute position in meters at a certain point in time, the wavelength of at least one of the light sources 101, 107 should be known or the length of at least one of the measuring axes should be known. If any of the two parameters, the wavelength of the first or second beam or the length of the first or second measuring axis, is known in meters, all other parameters can also be determined in meters.

[0146] By using measurements against a calibrated light source (e.g., a calibrated laser, such as a comb laser or another stable reference laser), the wavelength of the light source can be made traceable with respect to the meter. In another embodiment, analysis of the intensity transmitted through a gas with a known transmission spectrum (i.e., a gas reference chamber or a spectrum analyzer) can be used to determine the wavelength with respect to the meter. Other possibilities include locking the laser frequency to a known laser gain curve, such as is achieved in a Zeeman split frequency stabilized laser. Alternatively, at least one interferometer axis can include a pre-calibrated cavity length.

[0147] Once the absolute length in meters of one measurement axis 102, 104 is known and the length ratio between the two interferometer axes 102, 104 is known, the length of the other measurement axis 104, 102 can be traced back to the length of the first measurement axis 102, 104. When the interferometer system 100 includes more than two measurement axes, the lengths of these additional measurement axes can also be determined when the length of one of the measurement axes is known and the length ratio between the interferometer axes is known. The length of one interferometer axis can be determined using a previous or external calibration, while the length ratio can be determined based on the solution of the nonlinear equation described above.

[0148] Figure 3 An embodiment of an interferometer system 100 having more than two measuring axes is shown. Figure 3 The interferometer system comprises a stable first light source 101 and a second light source 107 having a tunable optical frequency. The tunable second light source 107 may have a relatively large tuning range to facilitate determination of the length ratio between different measurement axes.

[0149] Corresponds to Figure 2 An embodiment of Figure 3 The interferometer system of FIG. 1 comprises a first measurement axis 102 and a second measurement axis 104. The first measurement axis 102 and the second measurement axis 104 are used to measure the position of the first movable object 200 using the first reflection measurement surface 201 and the second reflection measurement surface 301. The first reflection measurement surface 201 and the second reflection measurement surface 301 are arranged at opposite sides of the first movable object 200. When the first movable object 200 is in a position such that the first measurement path length L x1 When moving in the direction of increase, the second measurement path length L x2 The first measurement axis 102 and the second measurement axis 104 will be reduced, and vice versa. The measurement data obtained by these opposite movements on the first measurement axis 102 and the second measurement axis 104 will improve the robustness of the nonlinear algorithm. The movable object 200 can be movable over a relatively long stroke. Such movement over a relatively long stroke can facilitate accurate determination of the count offset of the corresponding measurement axis (in this case, the first measurement axis 102 and the second measurement axis 104).

[0150] In addition to the first measurement axis 102 and the second measurement axis 104, the interferometer system 100 also includes a reference axis 400 and an additional measurement axis 510. The reference axis 400 is arranged to measure the position of a reference surface 401 (e.g. a reference path length Lref) via an interferometer optics 411 using the light of the first light source 101 and the light of the second light source 107. The reference surface 401 is arranged at a fixed position. The reference interferometer signal related to the light of the first light source 101 and the further reference interferometer signal related to the light of the second light source 107 obtained from the measurement on the reference axis 400 are directed to the detector 103d for further processing in the processing device 106. This reference axis 400 in combination with the first light source 101 having a stable optical frequency can be used to memorize the count offset of the reference axis 400. The memorized count offset can be used to facilitate solving the nonlinear equation to determine the count offset of the measurement axes (such as the first measurement axis 102, the second measurement axis 104 and the additional measurement axis 510).

[0151] An additional measurement axis 510 is provided to determine the position of an additional movable object 500, for example an additional measurement path length Lx3. To measure this position, the light of the first light source 101 and the light of the second light source 107 are directed via interferometer optics 511 to an additional reflective measurement surface 501 arranged on the additional movable object 500. An additional interferometer signal related to the light of the first light source 101 and an additional reference interferometer signal related to the light of the second light source 107 obtained from the measurement on the additional measurement axis 510 are directed to the detector 103e for further processing in the processing device 106.

[0152] If the additional movable object 500 is movable over a relatively small travel, such as, for example, a mirror of a projection system, the measurement data obtained from the additional measurement axis 510 may not be well suited for solving the nonlinear equation. However, since both the first movable object 200 and the additional movable object 500 are arranged in the same interferometer system 100 using the same light source 101, 107 for measurements on the first measurement axis 102, the second measurement axis 104, the reference axis 400 and the additional measurement axis 510, the nonlinear equation can be solved primarily using the data measured on the first measurement axis 102, the second measurement axis 104 and / or the reference axis 400. Once the count offset of at least one of the first measurement axis 102 and the second measurement axis 104 has been determined, the count offset of the additional measurement axis 510 can also be determined from the linear equation discussed above.

[0153] The interferometer system 100 may include more additional measurement axes to measure the positions of more movable objects within, for example, a lithographic apparatus.

[0154] Embodiments of interferometer systems are described in which some optical paths are defined in free space and some optical paths are defined by optical fibers. In alternative embodiments, the optical paths in free space may also be provided by optical fibers, and the optical paths defined by optical fibers may be arranged in free space.

[0155] Although it is specifically mentioned herein that the lithographic apparatus is used in the manufacture of integrated circuits, it should be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns of magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc. It will be understood by those skilled in the art that in the context of such alternative applications, any term "wafer" or "die" used herein may be considered to be synonymous with the more general term "substrate" or "target portion", respectively. The substrates mentioned herein may be processed in, for example, a coating and developing system or track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), a measurement tool, and / or an inspection tool before or after exposure. Where applicable, the disclosure herein may be applied to such substrate processing tools and other substrate processing tools. In addition, the substrate may be processed more than once, for example to produce a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0156] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, such as imprint lithography, and is not limited to optical lithography where the context permits. In imprint lithography, the topography in a patterning device defines the pattern produced on a substrate. The topography of the patterning device may be imprinted into a layer of resist supplied to the substrate, whereby the resist is cured by application of electromagnetic radiation, heat, pressure, or a combination thereof. After the resist is cured, the patterning device is removed from the resist, leaving a pattern therein.

[0157] Although specific embodiments of the present invention have been described above, it will be appreciated that the present invention may be practiced in ways other than those described. For example, the present invention may take the form of a computer program comprising one or more sequences of machine-readable instructions describing the methods disclosed herein, or a data storage medium (e.g., a semiconductor memory, a magnetic disk, or an optical disk) in which the computer program is stored.

[0158] The above description is intended to be illustrative and not limiting. Therefore, it will be appreciated by those skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set forth below. Other aspects of the invention are set forth in the following numbered aspects.

[0159] 1. A method of determining an absolute position of a first movable object using an interferometer system, the method comprising:

[0160] providing a first beam and a second beam having a first light frequency from a first light source;

[0161] providing an additional first beam and an additional second beam having a second optical frequency from a second optical source, wherein the second optical frequency is a tunable optical frequency;

[0162] directing the first beam and the further first beam along a first measuring axis to a first reflecting surface of the first movable object to obtain a first interferometer signal and a further first interferometer signal, respectively,

[0163] while changing the tunable optical frequency of the second light source, directing the second beam and the further second beam along a second measuring axis to a second reflecting surface of a second object to obtain a second interferometer signal and a further second interferometer signal, respectively,

[0164] detecting the first interferometer signal and the further first interferometer signal at at least one first detector,

[0165] detecting the second interferometer signal and the further second interferometer signal at at least one second detector,

[0166] A first count shift and / or a further first count shift is determined based on the first interferometer signal, the further first interferometer signal, the second interferometer signal and the further second interferometer signal using a non-linear equation, wherein the non-linear equation is based on the following relationship:

[0167] λ ls2 / λ ls1 = C ma1, ls1 / C ma1, ls2 = C ma2, ls1 / C ma2, ls2 ,

[0168] in,

[0169] λ ls2 is the second wavelength of the second light source,

[0170] λ ls1 is the first wavelength of the first light source,

[0171] C ma1, ls1 is the total number of counts about the first measurement axis and the first beam,

[0172] C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam,

[0173] C ma2, ls1 is the total number of counts about the second measurement axis and the second beam,

[0174] C ma2, ls2 is the total number of counts about the second measurement axis and the further second beam, and

[0175] The absolute position of the first movable object is determined based on the first count shift and the first interferometer signal and / or based on the further first count shift and the further first interferometer signal.

[0176] 2. The method according to aspect 1, wherein the step of determining the first count offset and / or the further first count offset comprises solving the nonlinear equation:

[0177]

[0178] in:

[0179] ΔC ma1, ls2 (t) is the change in counts with time for the first measurement axis and the further first beam measured using the further first interferometer signal,

[0180] offset ma1, ls2 is a further first count offset about said first measurement axis and said further first beam,

[0181] ΔC ma2, ls1 (t) is the change in counts with time about the second measurement axis and the second beam measured using the second interferometer signal,

[0182] offset ma2, ls1 is a second count offset about the second measurement axis and the second beam,

[0183] ΔC ma2, ls2 (t) is the change in counts over time for the second measurement axis and the further second beam measured using the further second interferometer signal,

[0184] offset ma2, ls2 is a further second count offset about said second measurement axis and said further second beam,

[0185] ΔC ma1, ls1 (t) is the change in counts with time about the first measurement axis and the first beam measured using the first interferometer signal, and

[0186] offset ma1, ls1 is the first count offset with respect to the first measurement axis and the first beam.

[0187] 3. A method according to aspect 1 or 2, wherein the absolute position L1 of the first movable object can be calculated as:

[0188] L1(t) = λ ls1 (t)× (ΔC ma1, ls1 (t) + offset ma1, ls1 ),or

[0189] L1(t) = λ ls2 (t)× (ΔC ma1, ls2 (t) + offset ma1, ls2 ).

[0190] 4. A method according to any one of the preceding aspects, wherein solving the nonlinear equation comprises: obtaining a first estimate using a reduced data set, and using the first estimate as input for solving the nonlinear equation for the full data set.

[0191] 5. A method according to any one of the preceding aspects, wherein the second object is movable.

[0192] 6. The method of clause 5, wherein the method comprises determining the absolute position of the second object, wherein determining the absolute position of the second object comprises:

[0193] determining a second count offset and / or a further second count offset, and

[0194] The absolute position of the second movable object is determined based on the second count shift and the second interferometer signal and / or based on the further second count shift and the further second interferometer signal.

[0195] 7. A method according to aspect 6, wherein the second count offset and / or the further second count offset is determined as:

[0196] (ΔC ma2, ls1 (t) + offset ma2, ls1 ) / (ΔC ma2, ls2 (t) + offset ma2, ls2 ) = λ ls2 / λ ls1 ,

[0197] where λ is known from the calculation about the first measuring axis ls2 / λ ls1 ,

[0198] ΔC can be determined from the second interferometer signal ma2, ls1 (t), and

[0199] ΔC can be determined from the further second interferometer signal ma2, ls2 (t).

[0200] 8. A method according to clause 7, wherein the absolute position L2 of the second movable object can be calculated as:

[0201] L2(t) = λ ls1 (t)× (ΔC ma2, ls1 (t) + offset ma2, ls1 ),,or

[0202] L2(t) = λ ls2 (t)× (ΔC ma2, ls2 (t) + offset ma2, ls2 ).

[0203] 9. A method according to any of clauses 5 to 8, wherein the method comprises moving the first movable object in a first direction and moving the second object in a second direction, wherein the first direction and the second direction are opposite to each other.

[0204] 10. The method according to any of the preceding aspects, wherein the first optical frequency is a tunable optical frequency.

[0205] 11. The method of clause 10, wherein tuning the frequencies of the first optical frequency and the second optical frequency is performed in opposite directions.

[0206] 12. The method according to any one of the preceding aspects, wherein:

[0207] directing the first beam along the first measurement axis comprises splitting the first beam into a first measurement beam and a first reference beam, wherein the first measurement beam is directed along a first measurement path to the first reflective measurement surface, and after the first measurement beam is reflected by the first reflective measurement surface, the first measurement beam and the first reference beam are recombined to form the first interferometer signal,

[0208] directing the further first beam along the first measurement axis comprises splitting the further first beam into a further first measurement beam and a further first reference beam, wherein the further first measurement beam is directed along the first measurement path to the first reflecting measurement surface and, after the further first measurement beam is reflected by the first reflecting measurement surface, the further first measurement beam and the further first reference beam are recombined to form the further first interferometer signal,

[0209] directing the second beam along the second measurement axis comprises splitting the second beam into a second measurement beam and a second reference beam, wherein the second measurement beam is directed along a second measurement path to the second reflective measurement surface, and after the second measurement beam is reflected by the second reflective measurement surface, the second measurement beam and the second reference beam are recombined to form the second interferometer signal, and

[0210] Guiding the additional second beam along the second measurement axis comprises splitting the additional second beam into an additional second measurement beam and an additional second reference beam, wherein the additional second measurement beam is guided along the second measurement path to the second reflecting measurement surface, and after the additional second measurement beam is reflected by the second reflecting measurement surface, the additional second measurement beam and the additional second reference beam are recombined to form the additional second interferometer signal.

[0211] 13. An interferometer system for determining an absolute position of a first movable object, the interferometer system comprising:

[0212] a first light source arranged to provide a first beam and a second beam having a first light frequency;

[0213] a second light source arranged to provide a further first beam and a further second beam having a second light frequency, wherein the second light source is arranged to provide a tunable second light frequency,

[0214] a first measurement axis for directing the first beam and the further first beam to a first reflecting surface of the first movable object to obtain a first interferometer signal and a further first interferometer signal, respectively,

[0215] a second measuring axis for directing the second beam and the further second beam to a second reflecting surface of a second object to obtain a second interferometer signal and a further second interferometer signal, respectively,

[0216] at least one first detector for detecting the first interferometer signal and the further first interferometer signal,

[0217] at least one second detector for detecting the second interferometer signal and the further second interferometer signal,

[0218] processing means, wherein the processing means is arranged to determine a first count shift and / or a further first count shift based on the first interferometer signal, the further first interferometer signal, the second interferometer signal and the further second interferometer signal using a non-linear equation, wherein the non-linear equation is based on the following relationship:

[0219] λ ls2 / λ ls1 = C ma1, ls1 / C ma1, ls2 = C ma2, ls1 / C ma2, ls2 ,

[0220] in,

[0221] λ ls2 is the second wavelength of the second light source,

[0222] λ ls1 is the first wavelength of the first light source,

[0223] C ma1, ls1 is the total number of counts about the first measurement axis and the first beam,

[0224] C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam,

[0225] C ma2, ls1 is the total number of counts about the second measurement axis and the second beam,

[0226] C ma2, ls2 is the total number of counts about the second measurement axis and the further second beam, and

[0227] Wherein the processing means is arranged to determine the absolute position of the first movable object based on the first count shift and the first interferometer signal or based on the further first count shift and the further first interferometer signal.

[0228] 14. An interferometer system according to aspect 13, wherein the processing means is arranged to determine the first count shift and / or the further first count shift comprises solving the non-linear equation:

[0229]

[0230] in:

[0231] ΔC ma1, ls2 (t) is the change in counts with time for the first measurement axis and the further first beam measured using the further first interferometer signal,

[0232] offset ma1, ls2 is the further first count offset with respect to the first measurement axis and the further first beam,

[0233] ΔC ma2, ls1 (t) is the change in counts with time about the second measurement axis and the second beam measured using the second interferometer signal,

[0234] offset ma2, ls1 is a second count offset about the second measurement axis and the second beam,

[0235] ΔC ma2, ls2 (t) is the change in counts over time for the second measurement axis and the further second beam measured using the further second interferometer signal,

[0236] offset ma2, ls2 is a further second count offset about said second measurement axis and said further second beam,

[0237] ΔC ma1, ls1 (t) is the change in counts with time about the first measurement axis and the first beam measured using the first interferometer signal, and

[0238] offset ma1, ls1 is the first count offset with respect to the first measurement axis and the first beam.

[0239] 15. An interferometer system according to clause 13 or 14, wherein the processing means is arranged to calculate the absolute position L1 of the first movable object as:

[0240] L1(t) = λ ls1 (t)× (ΔC ma1, ls1 (t) + offsetma1, ls1 ),or

[0241] L1(t) = λ ls2 (t)× (ΔC ma1, ls2 (t) + offset ma1, ls2 ).

[0242] 16. An interferometer system according to any one of aspects 13 to 15, wherein solving the nonlinear equation includes: obtaining a first estimate of the solution using a reduced data set, and using the first estimate as input for solving the nonlinear equation for the full data set.

[0243] 17. An interferometer system according to any one of clauses 13 to 16, wherein the second object is movable.

[0244] 18. An interferometer system according to clause 17, wherein the processing means is arranged to determine the absolute position of the second object, comprising:

[0245] determining a second count offset and / or a further second count offset, and

[0246] The absolute position of the second movable object is determined based on the second count shift and the second interferometer signal and / or based on the further second count shift and the further second interferometer signal.

[0247] 19. An interferometer system according to clause 18, wherein the second count offset and / or the further second count offset is determined as:

[0248] (ΔC ma2, ls1 (t) + offset ma2, ls1 ) / (ΔC ma2, ls2 (t) + offset ma2, ls2 ) = λ ls2 (t) / λ ls1 (t),

[0249] where λ is known from the calculation about the first measuring axis ls2 (t) / λ ls1 (t),

[0250] ΔC can be determined from the second interferometer signal ma2, ls1 (t), and

[0251] ΔC can be determined from the further second interferometer signal ma2, ls2 (t).

[0252] 20. An interferometer system according to aspect 19, wherein the absolute position L2 of the second movable object can be calculated as:

[0253] L2(t) = λ ls1 (t) × (ΔC ma2, ls1 (t) + offset ma2, ls1 ),or

[0254] L2(t) = λ ls2 (t)× (ΔC ma2, ls2 (t) + offset ma2, ls2 ).

[0255] 21. An interferometer system according to any one of aspects 17 to 20, wherein the method comprises moving the first movable object in a first direction and moving the second object in a second direction, wherein the first direction and the second direction are opposite to each other.

[0256] 22. An interferometer system according to any one of clauses 13 to 21, wherein the first optical frequency is a tunable optical frequency.

[0257] 23. The interferometer system of clause 22, wherein tuning of the frequencies of the first optical frequency and the second optical frequency is performed in opposite directions.

[0258] 24. An interferometer system according to any one of clauses 13 to 23, wherein:

[0259] the first measurement axis being arranged to split the first beam into a first measurement beam and a first reference beam, to direct the first measurement beam along a first measurement path to the first reflecting measurement surface, and to recombine the first measurement beam with the first reference beam to form the first interferometer signal after the first measurement beam is reflected by the first reflecting measurement surface,

[0260] the first measurement axis being arranged to split the further first beam into a further first measurement beam and a further first reference beam, to guide the further first measurement beam along the first measurement path to the first reflecting measurement surface, and to recombine the further first measurement beam with the further first reference beam to form the further first interferometer signal after the further first measurement beam is reflected by the first reflecting measurement surface,

[0261] the second measurement axis being arranged to split the second beam into a second measurement beam and a second reference beam, to direct the second measurement beam along a second measurement path to the second reflecting measurement surface, and to recombine the second measurement beam with the second reference beam to form the second interferometer signal after the second measurement beam is reflected by the second reflecting measurement surface, and

[0262] The second measurement axis is arranged to split the further second beam into a further second measurement beam and a further second reference beam, to guide the further second measurement beam along the second measurement path to the second reflecting measurement surface, and to recombine the further second measurement beam with the further second reference beam to form the further second interferometer signal after the further second measurement beam is reflected by the second reflecting measurement surface.

[0263] 25. A projection system for an optical lithography system, comprising the interferometer system according to any of clauses 13 to 24.

[0264] 26. A lithographic apparatus comprising an interferometer system according to any of clauses 13 to 24.

[0265] 27. The lithographic apparatus of clause 26, wherein the first movable object is part of a projection system of the lithographic apparatus.

Claims

1. A method of determining an absolute position of a first movable object using an interferometer system, the method comprising: providing a first beam and a second beam having a first light frequency from a first light source; providing an additional first beam and an additional second beam having a second optical frequency from a second optical source, wherein the second optical frequency is a tunable optical frequency; directing the first beam and the further first beam along a first measuring axis to a first reflecting surface of the first movable object to obtain a first interferometer signal and a further first interferometer signal, respectively, while changing the tunable optical frequency of the second light source, directing the second beam and the further second beam along a second measuring axis to a second reflecting surface of a second object to obtain a second interferometer signal and a further second interferometer signal, respectively, detecting the first interferometer signal and the further first interferometer signal at at least one first detector, detecting the second interferometer signal and the further second interferometer signal at at least one second detector, A first count shift and / or a further first count shift is determined based on the first interferometer signal, the further first interferometer signal, the second interferometer signal and the further second interferometer signal using a non-linear equation, wherein the non-linear equation is based on the following relationship: l ls2 / l ls1 = C ma1, ls1 / C ma1, ls2 = C ma2, ls1 / C ma2, ls2 , in, λ ls2 is the second wavelength of the second light source, λ ls1 is the first wavelength of the first light source, C ma1, ls1 is the total number of counts about the first measurement axis and the first beam, C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam, C ma2, ls1 is the total number of counts about the second measurement axis and the second beam, C ma2, ls2 is the total number of counts about the second measurement axis and the further second beam, and The absolute position of the first movable object is determined based on the first count shift and the first interferometer signal and / or based on the further first count shift and the further first interferometer signal.

2. The method according to claim 1, wherein: The step of determining the first count offset and / or the further first count offset comprises solving the non-linear equation: (ΔC ma1, ls2 (t)+ offset ma1, ls2 ) × (ΔC ma2, ls1 (t)+ offset ma2, ls1 ) = (ΔC ma2, ls2 (t)+offset ma2, ls2 ) × (ΔC ma1, ls1 (t)+ offset ma1, ls1 ) in: ΔC ma1, ls2 (t) is the change in counts with time for the first measurement axis and the further first beam measured using the further first interferometer signal, offset ma1, ls2 is a further first count offset about said first measurement axis and said further first beam, ΔC ma2, ls1 (t) is the change in counts with time about the second measurement axis and the second beam measured using the second interferometer signal, offset ma2, ls1 is a second count offset about the second measurement axis and the second beam, ΔC ma2, ls2 (t) is the change in counts over time for the second measurement axis and the further second beam measured using the further second interferometer signal, offset ma2, ls2 is a further second count offset about said second measurement axis and said further second beam, ΔC ma1, ls1 (t) is the change in counts with time about the first measurement axis and the first beam measured using the first interferometer signal, and offset ma1, ls1 is the first count offset with respect to the first measurement axis and the first beam.

3. The method according to claim 1 or 2, wherein: The absolute position L1 of the first movable object can be calculated as: L1(t) = λ ls1 (t)×(ΔC ma1, ls1 (t)+ offset ma1, ls1 ), or L1(t) = λ ls2 (t)× (ΔC ma1, ls2 (t)+ offset ma1, ls2 )。 4. A method according to any one of the preceding claims, wherein: Solving the nonlinear equation includes obtaining a first estimate using a reduced data set and using the first estimate as input for solving the nonlinear equation for the full data set.

5. A method according to any one of the preceding claims, wherein: The second object is movable.

6. The method according to claim 5, wherein: The method includes determining the absolute position of the second object, wherein determining the absolute position of the second object includes: determining a second count offset and / or a further second count offset, and The absolute position of the second movable object is determined based on the second count shift and the second interferometer signal and / or based on the further second count shift and the further second interferometer signal.

7. The method according to claim 6, wherein: The second count offset and / or the further second count offset is determined as: (ΔC ma2, ls1 (t)+ offset ma2, ls1 ) / (ΔC ma2, ls2 (t)+ offset ma2, ls2 ) =λ ls2 / λ ls1 , where λ is known from the calculation about the first measuring axis ls2 / λ ls1 , ΔC can be determined from the second interferometer signal ma2, ls1 (t), and ΔC can be determined from the further second interferometer signal ma2, ls2 (t).

8. The method according to claim 7, wherein: The absolute position L2 of the second movable object can be calculated as: L2(t) = λ ls1 (t)×(ΔC ma2, ls1 (t)+ offset ma2, ls1 ), or L2(t) = λ ls2 (t)× (ΔC ma2, ls2 (t)+ offset ma2, ls2 )。 9. The method according to any one of claims 5 to 8, wherein: The method includes moving the first movable object in a first direction and moving the second object in a second direction, wherein the first direction and the second direction are opposite to each other.

10. The method according to any one of the preceding claims, wherein: The first optical frequency is a tunable optical frequency.

11. The method according to claim 10, wherein: Tuning of the frequencies of the first optical frequency and the second optical frequency is performed in opposite directions.

12. A method according to any one of the preceding claims, wherein: directing the first beam along the first measurement axis comprises splitting the first beam into a first measurement beam and a first reference beam, wherein the first measurement beam is directed along a first measurement path to the first reflective measurement surface, and after the first measurement beam is reflected by the first reflective measurement surface, the first measurement beam and the first reference beam are recombined to form the first interferometer signal, directing the further first beam along the first measurement axis comprises splitting the further first beam into a further first measurement beam and a further first reference beam, wherein the further first measurement beam is directed along the first measurement path to the first reflecting measurement surface and, after the further first measurement beam is reflected by the first reflecting measurement surface, the further first measurement beam and the further first reference beam are recombined to form the further first interferometer signal, directing the second beam along the second measurement axis comprises splitting the second beam into a second measurement beam and a second reference beam, wherein the second measurement beam is directed along a second measurement path to the second reflective measurement surface, and after the second measurement beam is reflected by the second reflective measurement surface, the second measurement beam and the second reference beam are recombined to form the second interferometer signal, and Guiding the additional second beam along the second measurement axis comprises splitting the additional second beam into an additional second measurement beam and an additional second reference beam, wherein the additional second measurement beam is guided along the second measurement path to the second reflecting measurement surface, and after the additional second measurement beam is reflected by the second reflecting measurement surface, the additional second measurement beam and the additional second reference beam are recombined to form the additional second interferometer signal.

13. An interferometer system for determining an absolute position of a first movable object, the interferometer system comprising: a first light source arranged to provide a first beam and a second beam having a first light frequency; a second light source arranged to provide a further first beam and a further second beam having a second light frequency, wherein the second light source is arranged to provide a tunable second light frequency, a first measurement axis for directing the first beam and the further first beam to a first reflecting surface of the first movable object to obtain a first interferometer signal and a further first interferometer signal, respectively, a second measurement axis for directing the second beam and the further second beam to a second reflecting surface of a second object to obtain a second interferometer signal and a further second interferometer signal, respectively, at least one first detector for detecting the first interferometer signal and the further first interferometer signal, at least one second detector for detecting the second interferometer signal and the further second interferometer signal, processing means, wherein the processing means is arranged to determine a first count shift and / or a further first count shift based on the first interferometer signal, the further first interferometer signal, the second interferometer signal and the further second interferometer signal using a non-linear equation, wherein the non-linear equation is based on the following relationship: l ls2 / l ls1 = C ma1, ls1 / C ma1, ls2 = C ma2, ls1 / C ma2, ls2 , in, λ ls2 is the second wavelength of the second light source, λ ls1 is the first wavelength of the first light source, C ma1, ls1 is the total number of counts about the first measurement axis and the first beam, C ma1, ls2 is the total number of counts about the first measurement axis and the further first beam, C ma2, ls1 is the total number of counts about the second measurement axis and the second beam, C ma2, ls2 is the total number of counts about the second measurement axis and the further second beam, and Wherein the processing means is arranged to determine the absolute position of the first movable object based on the first count shift and the first interferometer signal or based on the further first count shift and the further first interferometer signal.

14. The interferometer system of claim 13, wherein: The processing means is arranged to determine the first count shift and / or the further first count shift comprises solving the non-linear equation: (ΔC ma1, ls2 (t)+ offset ma1, ls2 ) × (ΔC ma2, ls1 (t)+ offset ma2, ls1 ) = (ΔC ma2, ls2 (t)+offset ma2, ls2 ) × (ΔC ma1, ls1 (t)+ offset ma1, ls1 ) in: ΔC ma1, ls2 (t) is the change in counts with time for the first measurement axis and the further first beam measured using the further first interferometer signal, offset ma1, ls2 is the further first count offset with respect to the first measurement axis and the further first beam, ΔC ma2, ls1 (t) is the change in counts with time about the second measurement axis and the second beam measured using the second interferometer signal, offset ma2, ls1 is a second count offset about the second measurement axis and the second beam, ΔC ma2, ls2 (t) is the change in counts over time for the second measurement axis and the further second beam measured using the further second interferometer signal, offset ma2, ls2 is a further second count offset about said second measurement axis and said further second beam, ΔC ma1, ls1 (t) is the change in counts with time about the first measurement axis and the first beam measured using the first interferometer signal, and offset ma1, ls1 is the first count offset with respect to the first measurement axis and the first beam.

15. An interferometer system according to claim 13 or 14, wherein: The processing means is arranged to calculate the absolute position L1 of the first movable object as: L1(t) = λ ls1 (t)×(ΔC ma1, ls1 (t)+ offset ma1, ls1 ), or L1(t) = λ ls2 (t)× (ΔC ma1, ls2 (t)+ offset ma1, ls2 )。 16. An interferometer system according to any one of claims 13 to 15, wherein: Solving the nonlinear equation includes obtaining a first estimate of the solution using a reduced data set, and using the first estimate as input for solving the nonlinear equation for the full data set.

17. An interferometer system according to any one of claims 13 to 16, wherein: The second object is movable.

18. The interferometer system of claim 17, wherein: The processing means is arranged to determine the absolute position of the second object, comprising: determining a second count offset and / or a further second count offset, and The absolute position of the second movable object is determined based on the second count shift and the second interferometer signal and / or based on the further second count shift and the further second interferometer signal.

19. The interferometer system of claim 18, wherein: The second count offset and / or the further second count offset is determined as: (ΔC ma2, ls1 (t)+ offset ma2, ls1 ) / (ΔC ma2, ls2 (t)+ offset ma2, ls2 ) =λ ls2 (t) / λ ls1 (t), where λ is known from the calculation about the first measuring axis ls2 (t) / λ ls1 (t), ΔC can be determined from the second interferometer signal ma2, ls1 (t), and ΔC can be determined from the further second interferometer signal ma2, ls2 (t).

20. The interferometer system of claim 19, wherein: The absolute position L2 of the second movable object can be calculated as: L2(t) = λ ls1 (t)×(ΔC ma2, ls1 (t)+ offset ma2, ls1 ), or L2(t) = λ ls2 (t)× (ΔC ma2, ls2 (t)+ offset ma2, ls2 )。 21. An interferometer system according to any one of claims 17 to 20, wherein: The method includes moving the first movable object in a first direction and moving the second object in a second direction, wherein the first direction and the second direction are opposite to each other.

22. An interferometer system according to any one of claims 13 to 21, wherein: The first optical frequency is a tunable optical frequency.

23. The interferometer system of claim 22, wherein: Tuning of the frequencies of the first optical frequency and the second optical frequency is performed in opposite directions.

24. An interferometer system according to any one of claims 13 to 23, wherein: the first measurement axis being arranged to split the first beam into a first measurement beam and a first reference beam, to direct the first measurement beam along a first measurement path to the first reflecting measurement surface, and to recombine the first measurement beam with the first reference beam to form the first interferometer signal after the first measurement beam is reflected by the first reflecting measurement surface, the first measurement axis being arranged to split the further first beam into a further first measurement beam and a further first reference beam, to guide the further first measurement beam along the first measurement path to the first reflecting measurement surface, and to recombine the further first measurement beam with the further first reference beam to form the further first interferometer signal after the further first measurement beam is reflected by the first reflecting measurement surface, the second measurement axis being arranged to split the second beam into a second measurement beam and a second reference beam, to direct the second measurement beam along a second measurement path to the second reflecting measurement surface, and to recombine the second measurement beam with the second reference beam to form the second interferometer signal after the second measurement beam is reflected by the second reflecting measurement surface, and The second measurement axis is arranged to split the further second beam into a further second measurement beam and a further second reference beam, to guide the further second measurement beam along the second measurement path to the second reflecting measurement surface, and to recombine the further second measurement beam with the further second reference beam to form the further second interferometer signal after the further second measurement beam is reflected by the second reflecting measurement surface.

25. A projection system for an optical lithography system, comprising an interferometer system according to any one of claims 13 to 24.

26. A lithographic apparatus comprising an interferometer system according to any one of claims 13 to 24.

27. The lithographic apparatus of claim 26, wherein: The first movable object is part of a projection system of the lithographic apparatus.

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