NL2006058A - Stage system calibration method, stage system, and lithographic apparatus comprising such stage system. - Google Patents

Description

STAGE SYSTEM CALIBRATION METHOD, STAGE SYSTEM, AND LITHOGRAPHIC APPARATUS

COMPRISING SUCH STAGE SYSTEM

FIELD

[0001] The present invention relates to a calibration method to calibrate an encoder position measurement system of a stage, to a stage system, and to a lithographic apparatus including such a stage system.

BACKGROUND

[0002] A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning’-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.

[0003] In stage systems, such as lithographic apparatus stage systems, a position sensor may be applied to measure a position of the stage. Recently, encoder position measurement systems are applied for such position measurement. Thereto, use may be made of a grid (also referred to as grating), such as a one or two dimensional grid, grid plate, etc., and a sensor head cooperating with the grid. Due to manufacturing of the grating, it may not be ideal and may incorporate disturbances. Calibration of grid errors in the position measurement system may be performed by a so-called “fishbone” technique, wherein a pattern is projected repetitively onto the substrate at different mutual locations, and afterwards the distances between the patterns are measured to compare them with the intended distances between the patterns. A measured difference relates to an error in the measurement system at the location of the exposure. By determining these differences over the complete working range of the position measurement system, an error compensation value can be determined for a large number of locations on the measurement system, that, when applied, corrects the measurement system errors. Commonly, however not exclusively limited thereto, use is made of overlapping or adjacent patterns, such as line patterns, which may in some setups provide fishbone like patterns. It will be understood that this calibration technique can however apply to any type of patterns.

[0004] The fishbone calibration technique is only able to calibrate errors in the grid plate having a low spatial frequency. That is, errors which change relatively gradually when moving the stage and the grid plate relative to each other and having a spatial frequency in a frequency range related to the repetition pattern according to the fishbone technique or below. Inaccuracies or other effects that lead to errors at a higher spatial frequency may be difficult or impossible to detect by the above fishbone technique.

[0005] Errors at a higher spatial frequency can be obtained by moving the stage relative to the grid using a low-bandwidth controller. The low-bandwidth of the controller will cause feedback corrections to make the stage follow an irregularity in the grid to be slow. By measuring an input signal of the low-bandwidth controller, information is obtained as to the inaccuracies of the grating in a certain frequency range. This calibration however is prone to disturbances not related to the inaccuracies of the grating, such as measurement noise and/or excitations of resonances in the measurement system and/or stage system. Therefore, an accuracy of such calibration may be limited.

SUMMARY

[0006] It is desirable to improve an accuracy of the calibration of the encoder position measurement system of a stage, in particular a lithographic apparatus stage.

[0007] According to an embodiment of the invention, there is provided a calibration method to calibrate an encoder position measurement system of a stage, the encoder position measurement system including a two dimensional encoder grid and a sensor head cooperating with the encoder grid, the method including: a) moving the stage along multiple adjacent first trajectories in a first direction, thereby moving the sensor head relative to the encoder grid; b) during the moving of a), measuring a position of the stage with respect to the encoder grid by the sensor head; c) determining a first raw disturbance data map from an output signal of the sensor head, the first raw disturbance data map corresponding to the first trajectories; d) moving the stage along multiple adjacent second trajectories in a second direction, thereby moving the sensor head relative to the encoder grid, the second direction being at an angle to the first direction; e) during the moving of d), measuring the position of the stage with respect to the encoder grid by the sensor head; f) determining a second raw disturbance data map from the output signal of the sensor head, the second raw disturbance data map corresponding to the second trajectories; g) filtering the first and second raw disturbance data map; h) combining the filtered first and second raw disturbance data map into a combined disturbance data map representative for disturbances in the encoder grid; i) calibrating the encoder position measurement system by applying the combined disturbance data map.

[0008] According to another embodiment of the invention, there is provided a stage system including a moveable stage; an encoder position measurement system to provide a measurement of a position of the stage, the encoder position measurement system having an encoder grid and a sensor head cooperating with the encoder grid; a control system with a controller to control the position of the stage, the control system being provided with output signals of the sensor head, and the control system being configured to perform the calibration method according to embodiments of the invention.

[0009] According to a further embodiment of the invention, there is provided a lithographic apparatus including an illumination system configured to condition a radiation beam; a patterning device support constructed to support a patterning device, the patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam; a substrate support constructed to hold a substrate; and a projection system configured to project the patterned radiation beam onto a target portion of the substrate,

wherein at least one of the supports includes a stage system according to embodiments the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Embodiments of the invention will now be described, byway of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

[0011] Figure 1 depicts a lithographic apparatus according to an embodiment of the invention;

[0012] Figure 2 depicts an encoder position measurement system suitable to be used in the lithographic apparatus of Figure 1 in accordance with an embodiment of the invention;

[0013] Figure 3 depicts a grid plate with first trajectories of an encoder position measurement system in accordance with an embodiment of the invention;

[0014] Figure 4 depicts the grid plate of Figure 3 with second trajectories;

[0015] Figure 5 depicts the grid plate of Figure 3 with both the first and second trajectories;

[0016] Figure 6 depicts a filtering action in a 2 dimensional (2D) frequency domain in accordance with an embodiment of the invention;

[0017] Figure 7 depicts another filtering action in the 2D frequency domain in accordance with an embodiment of the invention;

[0018] Figure 8 depicts the combined filtering action of Figures 6 and 7 in the 2D frequency domain in accordance with an embodiment of the invention;

[0019] Figure 9 depicts a filtering action in the data domain using a 2D kernel in accordance with an embodiment of the invention;

[0020] Figure 10 depicts yet another filtering action in the 2D frequency domain in accordance with an embodiment of the invention;

[0021] Figure 11 depicts an embodiment of expanding data outside an encoder grid in accordance with an embodiment of the invention;

[0022] Figure 12 depicts a schematic flow chart of 2D band-limited extrapolation of data in accordance with an embodiment of the invention.

DETAILED DESCRIPTION

[0023] Figure 1 schematically depicts a lithographic apparatus according to one embodiment of the invention. The apparatus includes an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV radiation or any other suitable radiation), a patterning device support or mask support structure (e.g. a mask table) MT constructed to support a patterning device (e.g. a mask) MA and connected to a first positioning device PM configured to accurately position the patterning device in accordance with certain parameters. The apparatus also includes a substrate table (e.g. a wafer table) WT or "substrate support" constructed to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioning device PW configured to accurately position the substrate in accordance with certain parameters. The apparatus further includes a projection system (e.g. a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g. including one or more dies) of the substrate W.

[0024] The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, to direct, shape, or control radiation.

[0025] The patterning device support holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions, such as for example whether or not the patterning device is held in a vacuum environment. The patterning device support can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The patterning device support may be a frame or a table, for example, which may be fixed or movable as required. The patterning device support may ensure that the patterning device is at a desired position, for example with respect to the projection system. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.”

[0026] The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section so as to create a pattern in a target portion of the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

[0027] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography, and include mask types such as binary, alternating phase-shift, and attenuated phase-shift, 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 so as to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in a radiation beam which is reflected by the mirror matrix.

[0028] The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”.

[0029] As here depicted, the apparatus is of a transmissive type (e.g. employing a transmissive mask). Alternatively, the apparatus may be of a reflective type (e.g. employing a programmable mirror array of a type as referred to above, or employing a reflective mask).

[0030] The lithographic apparatus may be of a type having two (dual stage) or more substrate tables or "substrate supports" (and/or two or more mask tables or "mask supports"). In such “multiple stage” machines the additional tables or supports may be used in parallel, or preparatory steps may be carried out on one or more tables or supports while one or more other tables or supports are being used for exposure.

[0031] The lithographic apparatus may also be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g. water, so as to fill a space between the projection system and the substrate. An immersion liquid may also be applied to other spaces in the lithographic apparatus, for example, between the mask and the projection system. Immersion techniques can be used to increase the numerical aperture of projection systems. The term “immersion” as used herein does not mean that a structure, such as a substrate, must be submerged in liquid, but rather only means that a liquid is located between the projection system and the substrate during exposure.

[0032] Referring to Figure 1, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD including, for example, suitable directing mirrors and/or a beam expander. In other cases the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[0033] The illuminator IL may include an adjuster AD configured to adjust the angular intensity distribution of the radiation beam. Generally, at least the outer and/or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may include various other components, such as an integrator IN and a condenser CO. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross-section.

[0034] The radiation beam B is incident on the patterning device (e.g., mask) MA, which is held on the patterning device support (e.g., mask table) MT, and is patterned by the patterning device. Having traversed the patterning device (e.g. mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioning device PW and position sensor IF (e.g. an interferometric device, linear encoder or capacitive sensor), the substrate table WT can be moved accurately, e.g. so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioning device PM and another position sensor (which is not explicitly depicted in Figure 1) can be used to accurately position the patterning device (e.g. mask) MA with respect to the path of the radiation beam B, e.g. after mechanical retrieval from a mask library, or during a scan. In general, movement of the patterning device support (e.g. mask table) MT may be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which form part of the first positioning device PM. Similarly, movement of the substrate table WT or "substrate support" may be realized using a long-stroke module and a short-stroke module, which form part of the second positioner PW. In the case of a stepper (as opposed to a scanner) the patterning device support (e.g. mask table) MT may be connected to a short-stroke actuator only, or may be fixed. Patterning device (e.g. mask) MA and substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the patterning device (e.g. mask) MA, the patterning device alignment marks may be located between the dies.

[0035] The depicted apparatus could be used in at least one of the following modes: 1. In step mode, the patterning device support (e.g. mask table) MT or "mask support" and the substrate table WT or "substrate support" are kept essentially stationary, while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT or "substrate support" 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 imaged in a single static exposure.

2. In scan mode, the patterning device support (e.g. mask table) MT or "mask support" and the substrate table WT or "substrate support" are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT or "substrate support" relative to the mask table MT or "mask support" 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 (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion.

3. In another mode, the patterning device support (e.g. mask table) MT or "mask support" is kept essentially stationary holding a programmable patterning device, and the substrate table WT or "substrate support" is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, generally a pulsed radiation source is employed and the programmable patterning device is updated as required after each movement of the substrate table WT or "substrate support" or in between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography that utilizes programmable patterning device, such as a programmable mirror array of a type as referred to above.

[0036] Combinations and/or variations on the above described modes of use or entirely different modes of use may also be employed.

[0037] Figure 2 depicts an encoder position measurement system which is suitable to be used in the lithographic apparatus of Figure 1 to measure a position of a stage system including the substrate table and second positioning device PW or including the patterning device support MT and first positioning device PM.

[0038] The measurement system includes a sensor head SH and a grid plate GP, wherein the measurement system is configured to measure a position of the sensor head SH with respect to grid plate GP. The sensor head includes two sensor elements or sensors SE1 ,SE2. In this example, an incremental encoder position measurement system is applied, providing a periodic sensor element output signal when moving the sensor head with respect to the grid plate. Position information may be obtained from periodicity and phase of corresponding sensor element output signals of the sensor head. In the embodiment shown, a sensor head assembly is depicted emitting two measurement beams MB1, MB2 towards the grid plate. Due to an interaction with the pattern on the grid plate (which may be one dimensional or two dimensional), beams are returned towards the sensor head at an angle, as schematically depicted in Figure 2, and detected by the sensor elements or sensors SE1 ,SE2 of the sensor head. Thus, the sensor head provides for two measurements, namely at A and at B on the grid plate GP. Each of the measurements provides for a sensitivity in horizontal as well as in vertical direction. A sensitivity of the left one of the sensor elements SE1 is schematically indicated by vector ea, while a sensitivity of the right one of the sensor elements SE2 is schematically indicated by eb. In a present, practical implementation, an angle of ea and eb with respect to horizontal will be small, smaller than indicated in Figure 2. A measurement of the horizontal position can now be obtained from an addition of ea and eb. A measurement of the vertical position can be obtained from a subtraction of ea and eb, as outlined in the below expressions.

wherein posX and posZ represent a respective horizontal and vertical encoder position information, and ki and k2 are gain factors compensating for the fact that the vectors ea and eb are not exactly directed in the horizontal or vertical direction.

[0039] Figure 3 depicts a two dimensional grid plate GP and, shown relative to the grid plate GP, first trajectories PA1 along which a sensor head of a stage can move to obtain information about disturbances in the grid plate. The sensor head may be cooperating with the grid plate similar to the encoder position measurement system of Figure 2.

[0040] An accuracy of the encoder position measurement system of Figure 3 is in part determined by an accuracy and repetition accuracy of a pattern of a grating on the grid plate GP. The disturbances of the grid plate can be determined by moving the stage along the multiple adjacent first trajectories PA1 in a first direction FD, thereby moving the sensor head relative to the encoder grid i.e. the grid plate. The movement of the stage can be controlled by a control system with a controller having a low-bandwidth which causes feedback corrections to make the stage follow the disturbances in the grid to be slow. By measuring an input signal of the low-bandwidth controller including an output signal of the sensor head or the output signal of the sensor head directly, information is obtained as to the disturbances of the grating in a certain frequency range. This information can be determined and stored in a first raw disturbance data map corresponding to the first trajectories.

[0041] Depending on the measurement location in the control system, the obtained measurement signal may include a set point of the controller. The first raw disturbance data map may then be determined by subtracting the set point from the measurement signal. In case the movement of the stage is performed at constant velocity, the set point may also be removed from the measurement signal by fitting a first order equation through the measurement signal and subtracting the fitted first order equation from the measurement signal.

[0042] The first raw disturbance data map includes the disturbances of interest, i.e. the disturbances in the grating, but also measurement noise and other errors not related to the grating. The measurement noise and the other errors are removed, in an embodiment of the invention, by filtering the first raw disturbance data map thereby improving the calibration accuracy.

[0043] In an embodiment, the filtering includes filtering the first raw disturbance data map in the first direction FD using a first band-pass filter. The band-pass filter filters the first raw disturbance data map to obtain the disturbances in a spatial frequency range of interest. The band-pass filter includes a lower cut-off frequency corresponding to the lowest spatial frequency of interest and a higher cut-off frequency corresponding to the highest spatial frequency of interest. The lowest spatial frequency of interest may be determined by a highest spatial frequency that can be detected by other calibration methods such as the fishbone technique. The highest spatial frequency of interest may be determined by the contribution of components above the highest spatial frequency of interest to the overall measurement error and/or by the signal to noise ratio of components above the highest spatial frequency of interest.

[0044] In another embodiment, the filtering includes filtering of the first raw disturbance data map in a second direction SD being at an angle, in this case substantially perpendicular, to the first direction FD using a first low-pass filter. Measurement noise in the second direction of the first raw disturbance data map is uncorrelated as the measurement noise relates to different first trajectories PA1. The measurement noise will thus manifest itself as white noise, so that filtering in the second direction is able to remove the measurement noise at least partially.

[0045] Figure 4 depicts the two dimensional grid plate GP of Figure 3 showing second trajectories PA2 along which the sensor head of the stage can move to obtain information about disturbances in the grid plate. Similarly to the first trajectories PA1, the information about the disturbances in the grid plate can be determined and stored in a second raw disturbance data map which is also polluted by measurement noise and other errors not related to the disturbances in the grid plate. The second raw disturbance data map is therefore also filtered, in an embodiment of the invention, similarly to the first raw disturbance data map.

[0046] In an embodiment of the invention, filtering includes filtering the second raw disturbance data map in the second direction SD using a second band-pass filter, and in an embodiment, the filtering includes filtering of the second raw disturbance data map in the first direction FD substantially perpendicular to the second direction FD using a second low-pass filter.

[0047] The filtered first raw disturbance data map and the filtered second raw disturbance data map are combined into a combined disturbance data map as schematically shown for the respective first and second trajectories PA1, PA2 in Figure 5. The combined disturbance data map is representative of the disturbances in the grid plate. Subsequently, the encoder position measurement system may be calibrated by applying the combined disturbance data map. Due to the filtering of the raw disturbance data maps, the errors not related to the disturbances in the grid plate are at least partially removed, thereby increasing the accuracy of the calibration.

[0048] It is explicitly mentioned here that the calibration method described above can also be applied using first and second trajectories which are not perpendicular to each to each other, but are at angle to each other. Further, the calibration method described above may also be applied for three or more sets of adjacent trajectories, which sets of adjacent trajectories extend in different directions.

[0049] Figure 6 depicts the filtering of the first raw disturbance data map in both the first and second direction of Figure 3 in the frequency domain. A horizontal axis Fx of the graph corresponds to spatial frequencies in the first direction FD and a vertical axis Fy of the graph corresponds to spatial frequencies in the second direction SD. The low-pass filtering action of the first low-pass filter in the second direction is indicated in the graph by arrow FLF and the band-pass filtering of the first band-pass filter in the first direction is indicated in the graph by arrow FBF. It is noted here that in the frequency domain also negative frequencies are shown, resulting in a point symmetric representation of the filtering action so that also the filtering action is shown for negative frequencies.

[0050] Figure 7 depicts the filtering as described with reference to Figure 4 in the frequency domain in which horizontal axis Fx of the graph corresponds to spatial frequencies in the first direction FD and vertical axis Fy corresponds to spatial frequencies in the second direction SD. The low-pass filtering action of the second low-pass filter in the first direction is indicated in the graph by arrow SLF and the band-pass filtering of the second band-pass filter in the second direction is indicated in the graph by arrow SBF.

[0051] Combining the filtered first and second raw disturbance data maps of Figures 3,4 and 6,7 will result in a frequency range of interest SFR in the frequency domain as shown in Figure 8. In this embodiment, a cut-off frequency of the first low-pass filter FLP is chosen equal to a cut-off frequency of the second low-pass filter SLF, so that combining the filtering actions of Figures 6 and 7 will result in overlapping regions OR (see Figure 8) at the corners of the frequency range of interest SFR in which the data of the filtered first raw disturbance data map and the filtered second raw disturbance data map are combined differently then in the other frequency ranges of the frequency range of interest SFR due to the overlap. A simple addition of the data in the frequency ranges may result in twice the data in the overlapping regions OR.

Combining the data maps may thus include averaging the data in the overlapping regions OR to obtain a data map representative for the disturbances in the encoder grid.

[0052] Filtering in both the first and the second direction as described with respect to Figures 3 and 4 and visualized in Figures 6 and 7 can be implemented by using a kernel KE as shown in Figure 9. Figure 9 depicts a schematic representation of a raw disturbance data map DDM filled with data, indicated by data points DP. Also shown in this raw disturbance data map DDM for explanatory purposes is an outer contour of the grid plate CGP indicating edges of the grid plate. A filtering action may be converted into a kernel KE which is filled with kernel values. Filtering of a data point P01 is done by virtually placing the kernel around the data point so that the center of the kernel coincides with the data point P01, multiplying the kernel values with corresponding data points, and summing the result to obtain a filtered data point P01, i.e. similar to convolution. Filtering other data points is done in a similar way by shifting the kernel KE. It is indicated here that the representation of the kernel and the raw disturbance data map in Figure 9 is used to explain the underlying working principle of the filtering action. A person skilled in the art knows how to implement such a filtering operation in a practical embodiment.

[0053] In an embodiment, the kernel is 2D point symmetric, i.e. a kernel value at a position (x, y) with respect to the center of the kernel is equal to a kernel value at a position (-x, -y). This enables to remove certain spatial frequency disturbances without any phase delay. Furthermore, the 2D spatial frequency ranges to be removed from the raw disturbance data map can be chosen arbitrarily, i.e. with an arbitrary shape in the frequency domain. An example of such arbitrary shape is shown in Figure 10 in which the spatial frequency range of interest SFR is composed, in an embodiment, of frequency areas including the disturbances in the grid plate that are most significant.

[0054] Referring to Figure 9 again, when filtering the data points at an edge of the grid plate, at least a portion of the kernel KE will be located outside the grid plate where no data is available. For computational reasons, the data map may be extended by zeros outside the grid plate, alternatively referred to as zero-padding. As a result, undesired oscillations at the edges of the grid plate may be introduced by the filtering action.

[0055] In an embodiment, the undesired oscillations are prevented by applying a position dependent kernel. Near the edge, the kernel could be modified such that no data from outside the grid plate is required for filtering. This could be done by reducing the kernel width as the distance to the edge decreases (and possibly keeping the kernel symmetric). Alternatively or additionally, an a-symmetric kernel could be designed that depends on a distance of a to be filtered data point to the edge.

[0056] In an embodiment, the undesired oscillations can be reduced by expanding the respective first and second raw disturbance data map to outside the grid plate prior to filtering, thereby generating “extra” data that can be used in filtering near the edges. In that case, the kernel does not necessarily have to be adapted near the edge.

[0057] Figure 11 depicts a way to expand the disturbance data map to outside the grid plate by showing a one-dimensional example of the raw disturbance data of one trajectory. The disturbance data of the trajectory is indicated by DA, and the data DA shows discontinuities at the edges of the data in the form of respective steps ST1 and ST2. These steps ST1, ST2 are introduced by extending the data with zeros, i.e. zero-padding, and will cause undesired oscillations at the edges when filtering is applied. The data can be expanded by zeroth order derivative extrapolation of the data, alternatively referred to as border-padding, which simply continues the data at the edge with a constant value corresponding to the value at the edge, as indicated by dashed lines FED1 and FED2. In an embodiment, not only the value at the edge is continued, but also the first derivative of the data, so that the first derivative of the data and expanded data does not have any discontinuities. An example of expanding the data using the zeroth order and first order derivative is shown by lines SED1 and SED2. The extrapolation can also include the extrapolation of one or more subsequent higher order derivatives, such as the second order or third order derivative. An example of such an extrapolation is shown by lines TED1 and TED2. The more derivatives of the data are extrapolated, the more smooth the transition of the data inside the grid plate to outside the grid plate is, and the less undesired oscillations will occur during filtering.

[0058] Although the 1D example of Figure 11 is quite straightforward, extending the principle to 2D may involve some modifications. In 2D, an expanded data point can be obtained in multiple ways, i.e. by expanding data in different directions which not necessarily result in the same value of the expanded data point. Averaging expansion results from different directions may be an option to at least partially compensate for this problem.

[0059] Figure 12 depicts a signal flow schematically indicating an embodiment of how a disturbance data map can be expanded using 2D band-limited extrapolation. For simplicity reasons the explanation is done referring to a one dimensional signal, but it will be apparent to a person skilled in the art that the principle can also be applied to a two-dimensional case such as the first and second raw disturbance data map of Figures 3,4,6,7,8,9, and 10. For the two-dimensional case it has the advantage that it expands the data in multiple directions at the same time, thereby avoiding any irregularities in the expanded data.

[0060] At the top of Figure 12 is the original disturbance data ODS shown as a schematic block having discontinuities at edges E1, E2 of the block ODS. In a first step, the data at the edges is extended with zeros, i.e. zero-padding, then the Fast Fourier Transform FFT is taken from the original disturbance data ODS including the extended zeros, resulting in a frequency spectrum FS as shown in the second graph. Subsequently, the frequency spectrum FS is low-pass filtered by a low-pass filter LPF, thereby resulting in a filtered frequency spectrum FFS as shown in the third graph, the filtered frequency spectrum having a smaller bandwidth than the frequency spectrum FS of the original disturbance data ODS. It is noted that although the low-pass filter LPF is shown with a slope, other low-pass filters are also possible.

[0061] Subsequently, the inverse Fast Fourier Transform iFFT is taken of the filtered frequency spectrum FFS, thereby resulting in an altered original disturbance data set IODS (see fourth graph) which is mainly altered at the discontinuities, so that “extra” data is generated outside the grid plate. Edges E1 and E2 of the original disturbance data ODS have been shown in the graph for comparison reasons. In the last step, the data of the altered original disturbance data between the edges E1 and E2 is replaced by the original disturbance data ODS, so that the result is that the data is expanded outside the grid plate thereby reducing the discontinuities or the magnitude of the discontinuities.

[0062] In an embodiment, the steps as described can be repeated in an iterative manner, so that the signal at the end of a previous cycle forms the basis for the Fast Fourier Transform of a next cycle, but in the last step of the cycle, the original disturbance data ODS is returned into the data set, so that an iteration only changes/improves the parts IODS’ and IODS” outside the grid plate.

[0063] In an embodiment, a cut-off frequency of the low-pass filter can be increased with increasing number of performed iterations so that the total amount of necessary iterations can be reduced to obtain a certain reduction in undesired oscillations.

[0064] The disturbance data maps may contain errors which are constant and thus predictable, but do not relate to the disturbances in the grid plate. These errors may for instance be introduced by cogging of an actuator moving the stage or the relative position of a spatially varying magnetic field relative to the stage causing deformations of the stage and thereby errors in the position measurement. These errors are usually periodic, but not sinusoidal. However, the periodic errors can be described as a sum of sinusoidal signals (so-called harmonics), of which at least one can manifest itself in the spatial frequency range of interest.

[0065] These errors can be removed by fitting them through the disturbance data map and subtracting them from the data map. However, fitting is only possible when the stage has moved with a constant velocity, and most of the time this is not the case, especially not at the edges where the stage is accelerated or decelerated. It is therefore desirable to fit the raw disturbance data map in a direction perpendicular to the direction of the trajectories corresponding to the raw disturbance map. As the movement along the trajectory is the same for each trajectory, the accelerations and decelerations of each movement do not affect the fitting in the direction perpendicular to the direction of the movement.

[0066] In an embodiment, the predictable errors may be removed by averaging measurement results, i.e. output signals of a sensor head, from all trajectories in one direction, and subtracting the averaged measurement result corresponding to the trajectories from each individual measurement result of the trajectories. This same principle can be used to remove a nominal signal from a data map, e.g. a set-point.

[0067] In the shown embodiments, the grid plate has a rectangular shape. It is explicitly mentioned here that the grid plate can have any arbitrary shape, e.g. an oval, circular, square, triangular, or L shape.

[0068] It is further explicitly stated here that a disturbance data map according to the invention can be determined for every measurement signal of a sensor head. As shown with respect to Figure 2, the sensor head may output multiple sensor head output signals, each for a different measurement direction. In case of the sensor head of Figure 2, two sensor head output signals are provided, one for a horizontal position of the stage and one for a vertical position of the stage. A disturbance data map can then be determined for each position quantity using the method according to the invention.

[0069] It is also explicitly mentioned here that the first and second direction are preferably substantially parallel to a main surface of the encoder grid, i.e the grid plate. In an embodiment, the first and second direction are both substantially perpendicular to a radiation beam of the lithographic apparatus for transferring a pattern from a patterning device to a substrate.

[0070] In an embodiment, the encoder position measurement system may comprise a further sensor head. The sensor head and the further sensor head may both measure the position of the stage in the same degree of freedom (DOF). For example, for a stage moveable in 6 DOF’s, 8 position measurements can be taken. Only 6 position measurements are needed to completely determine the position of the stage in the three translations x, y, z, and the three rotations Rx, Ry and Rz.. This gives a sensor redundancy which can be used to separate motion disturbances that occurred during calibration, from actual position-dependent disturbances which are e.g. caused by grid errors.

[0071] Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, 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 for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein may be considered as synonymous with the more general terms “substrate” or “target portion", respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology tool and/or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools, e.g. substrate diagnosis and/or substrate measurement tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer 1C, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0072] Although specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substrate whereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured.

[0073] The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g. having a wavelength of or about 365,248,193,157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g. having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams.

[0074] The term “lens”, where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components.

[0075] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. For example, the invention may take the form of a computer program containing one or more sequences of machine-readable instructions describing a method as disclosed above, or a data storage medium (e.g. semiconductor memory, magnetic or optical disk) having such a computer program stored therein.

[0076] The descriptions above are intended to be illustrative, not limiting. Thus, it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the clauses set out below. Other aspects of the invention are set out as in the following numbered clauses: 1. A calibration method to calibrate an encoder position measurement system of a stage, the encoder position measurement system comprising a two dimensional encoder grid and a sensor head configured to cooperate with the encoder grid, the method comprising: moving the stage along multiple adjacent first trajectories in a first direction so as to move the sensor head and the encoder grid relative to each other; during the moving, measuring the position of the stage using the encoder position measurement system; determining a first raw disturbance data map from an output signal of the sensor head, the first raw disturbance data map corresponding to the first trajectories; moving the stage along multiple adjacent second trajectories in a second direction, so as to move the sensor head and the encoder grid relative to each other; during the moving of the stage along multiple adjacent second trajectories, measuring the position of the stage using the encoder position measurement system; determining a second raw disturbance data map from the output signal of the sensor head, the second raw disturbance data map corresponding to the second trajectories; filtering the first and the second raw disturbance data map; combining the filtered first and the second raw disturbance data map into a combined disturbance data map representative of disturbances in the encoder grid; calibrating the encoder position measurement system using the combined disturbance data map.

2. The calibration method of clause 1, wherein filtering the first and the second raw disturbance data map comprises filtering the first raw disturbance data map in the first direction using a first band-pass filter, and filtering the second raw disturbance data map in the second direction using a second band-pass filter.

3. The calibration method of clause 1, wherein filtering the first and the second raw disturbance data map comprises filtering the first raw disturbance data map in the second direction using a first low-pass filter, and filtering the second raw disturbance data map in the first direction using a second low-pass filter.

4. The calibration method of clause 1, wherein filtering the first and the second raw disturbance data map comprises filtering the first and second raw disturbance data map in both the first and second direction with a respective 2D point symmetric kernel.

5. The calibration method of clause 1, wherein the first and second raw disturbance data map are expanded outside the encoder grid prior to filtering.

6. The calibration method of clause 5, wherein the first and the second raw disturbance data map are expanded outside the encoder grid by extrapolating the zeroth order derivative of data at edges of the encoder grid.

7. The calibration method of clause 6, wherein the first and the second raw disturbance data map are expanded outside the encoder grid extrapolating one or more subsequent higher order derivatives of the data as well.

8. The calibration method of clause 5, wherein the first and the second raw disturbance data map are expanded outside the encoder grid by 2D band-limited extrapolation which comprises: extending the respective first and the second raw disturbance data map with zeros; performing a Fast Fourier Transform on the respective extended first and second raw disturbance data map; multiplying the Fast Fourier Transform of the respective first and the second raw disturbance data map by a spectrum of a low-pass transfer function; performing an inverse Fast Fourier Transform on the respective modified first and second raw disturbance data map obtained after the multiplying to generate data outside the encoder grid; and replacing the data obtained after performing the inverse Fast Fourier Transform at a location of the encoder grid with the data of the original respective first and the second raw disturbance data map.

9. The calibration method of clause 8, wherein the 2D band-limited extrapolation is performed multiple times in an iterative manner, wherein data obtained after the replacing of a previous iteration forms the basis for the Fast Fourier Transform on the respective extended first and second raw disturbance data map of a next iteration..

10. The calibration method of clause 9, wherein a cut-off frequency of the low-pass transfer function spectrum increases with increasing number of performed iterations.

11. The calibration method of clause 1, wherein filtering the first and the second raw disturbance data map comprises filtering the respective first and the second raw disturbance data map with a position dependent kernel, wherein the kernel is adapted at edges of the encoder grid to stay within the respective first and second disturbance data map.

12. The calibration method of clause 1, wherein filtering the first and the second raw disturbance data map comprises: determining a parameterised model of predictable errors which are not related to the disturbances in the encoder grid; fitting the predictable errors through the first raw disturbance data map in the second direction; fitting the predictable errors through the second raw disturbance data map in the first direction; filtering the respective first and second raw disturbance data map by removing the respective fitted predictable errors from the respective first and second raw disturbance data map.

13. The calibration method of clause 1, wherein filtering the first and the second raw disturbance data map comprises: averaging all output signals of the sensor head corresponding to the first trajectories; subtracting the averaged signal corresponding to the first trajectories from each individual output signal corresponding to the first trajectories; averaging all output signals of the sensor head corresponding to the second trajectories; subtracting the averaged signal corresponding to the second trajectories from each individual output signal corresponding to the second trajectories.

14. The calibration method of clause 1, wherein moving of the stage along the first and second trajectories is performed using a low-bandwidth controller.

15. The calibration method of clause 1, wherein the bandwidth of the controller is below a frequency range of interest of the disturbances of the encoder grid.

16. The calibration method of clause 1, wherein the encoder position measurement system comprises a further sensor head, wherein the sensor head and the further sensor head both measure the position of the stage in the same degree of freedom.

17. A stage system comprising: a moveable stage; an encoder position measurement system configured to provide a measurement of a position of the stage, the encoder position measurement system having an encoder grid and a sensor head configured to cooperate with the encoder grid; a controller configured to control the position of the stage, the controller being provided with output signals of the sensor head, and the controller being configured to perform the calibration method according to clause 1.

18. A lithographic apparatus comprising: a patterning device support constructed to support a patterning device, the patterning device being capable of imparting a radiation beam with a pattern in its cross-section to form a patterned radiation beam; a substrate support constructed to hold a substrate; and a projection system configured to project the patterned radiation beam onto a target portion of the substrate, wherein at least one of the supports comprises a stage system according to clause 16.

Claims (1)

A lithography device comprising: an exposure device adapted to provide a radiation beam; a carrier constructed to support a patterning device, the patterning device being capable of applying a pattern in a section of the radiation beam to form a patterned radiation beam; a substrate table constructed to support a substrate; and a projection device adapted to project the patterned radiation beam onto a target area of the substrate, characterized in that the substrate table is adapted to position the target area of the substrate in a focal plane of the projection device.