Patent Grant
7348574
1. Field of the Invention
The present invention relates to a position measurement system and a lithographic apparatus.
2. Description of the Related Art
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 that instance, 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., comprising 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. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, 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.
In order to accurately transfer the pattern onto the target portion of the substrate, the relative position of the pattern and the target portion should be known. Therefore, the lithographic apparatus is in general equipped with one or more measurement systems to determine the position of, e.g., the substrate or the patterning device. Examples of such measurement systems are interferometer systems or encoder systems. Both systems can be designated as incremental systems. Using such a position measurement system, the position of an object can be determined relative to a chosen reference as an integer number of increments (or periods) of a predefined length. Using an interferometer, this increment may, e.g., correspond to a quarter of the wavelength of the interferometer laser. In case of an encoder system, the increment may, e.g., correspond to a quarter of the period of the encoder grating.
In order to improve the resolution of such an incremental measurement system, methods are developed to provide an interpolation within one increment (or period).
Such a position measurement system usually comprises an incremental measurement unit comprising a first part comprising a sensor and a second part co-operating with the sensor of the first part. In case of an interferometer system, the second part may comprise a mirror for reflecting a beam originating from the interferometer laser to the sensor. In case of an encoder system, the second part may comprise a one- or two-dimensional grating co-operating with the sensor (in this case, the sensor usually comprises an encoder head). Because of the limited size of, e.g., the mirror or the grating, the operating range of the measurement system is limited. In order to increase the operating range, the measurement system can be equipped with more that one sensor arranged on different locations along a required operating range ensuring that the position measurement can be performed over the entire required operating range. In such a multi-sensor measurement system, problems may arise during the transition of the position measurement by a first sensor to the position measurement by a second sensor. Conventionally, one (or more) measurement values of the first sensor are used to initialize the second sensor during the transition (such initialization may be required because the initial measurement by the second sensor may not be related to a reference). Because this initialization is based upon measurements of both the first sensor and the second sensor, measurements that may contain a measurement error, this initialization may result in an increased measurement error for the second sensor. During a next transition (either a transition of a measurement by the second sensor to a measurement by a third sensor or a transition of a measurement by the second sensor to a measurement by the first sensor) a further increase in the measurement error may occur. As such, the accuracy of a multi-sensor measurement system used in a conventional way may deteriorate due to transition from a measurement by one sensor to a measurement by another sensor.
Embodiments of the invention include an improved position measurement system. In embodiments of the invention, the accuracy of the position measurement system is improved during a take over process between two sensors of the measurement system.
According to an embodiment of the invention, there is provided a position measurement system for measuring a position of an object, comprising:
wherein the position measurement system is constructed and arranged to initialize the second incremental measurement unit on the basis of the first number and the second fraction.
According to a further embodiment of the invention there is provided a lithographic apparatus comprising:
wherein the apparatus further comprises a position measurement system according to the present invention.
Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:
a and 2b schematically depict a multi-sensor incremental position measurement system;
a-3c schematically depict a take over process in an incremental position measurement system;
a-4c schematically depict a take over process according to the present invention;
a-5c schematically depict a take over process in an interferometer system;
a-6e schematically depict a take over process in a measurement system comprising multiple gratings and multiple sensors.
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, for directing, shaping, or controlling radiation.
The support structure supports, i.e., bears the weight of, the patterning device. It 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 support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure may be a frame or a table, for example, which may be fixed or movable as required. The support structure 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.”
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 such 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.
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.
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.”
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).
The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and/or two or more mask tables). In such “multiple stage” machines the additional tables may be used in parallel, or preparatory steps may be carried out on one or more tables while one or more other tables are being used for exposure.
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 are well known in the art for increasing 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 liquid is located between the projection system and the substrate during exposure.
Referring to
The illuminator IL may comprise an adjuster AD for adjusting 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 comprise 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.
The radiation beam B is incident on the patterning device (e.g., mask MA), which is held on the support structure (e.g., mask table MT), and is patterned by the patterning device. Having traversed the mask MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and 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 positioner PM and another position sensor (which is not explicitly depicted in
The depicted apparatus could be used in at least one of the following modes:
1. In step mode, the mask table MT and the substrate table WT 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 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 mask table MT and the substrate table WT 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 relative to the mask table 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 (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 mask table MT is kept essentially stationary holding a programmable patterning device, 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, 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 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.
Combinations and/or variations on the above described modes of use or entirely different modes of use may also be employed.
In order to project a pattern onto a predefined target portion of the substrate, the lithographic apparatus requires an accurate measurement system for determining the position of the substrate table and the patterning device. Interferometer systems and encoder systems are found to be suitable for accurately determining the position of an object (e.g., a substrate table or a mask table). Both measurement systems can be designated as incremental position measurement systems. In both systems, the position of an object can be determined relative to a chosen reference as an integer number of distance steps (or periods or increments) of a predefined length. Within one increment or distance step, the position can be determined by means of interpolation in order to improve the resolution of the measurement. As such, an output signal Xout of the position measurement system, representing the position of an object (e.g., an X-position) can be described by the following equation (1):
Xout=IC+(N+φ+ε)·p (1)
wherein
p=distance step of the measurement system
IC=initialization constant
N=integer number representing a number of distance steps p
φ=fraction between 0 and 1
ε=measurement error.
Fraction φ in equation (1) is also referred to as the phase of the position measurement.
In general, an incremental position measurement comprises an incremental measurement unit comprising a first part comprising a sensor and a second part co-operating with the sensor of the first part. In case of an interferometer system, the second part may comprise a reflective surface (e.g., a mirror) for reflecting a beam originating from the interferometer laser to the sensor. In case of an encoder system, the second part may comprise a one- or two-dimensional grating co-operating with the sensor. Either the first part or the second part can be mounted to the object of which the position is to be determined (as an example, the object may be an object table for holding a substrate or a patterning device of a lithographic apparatus).
In general, an incremental position measurement system does not provide an absolute position measurement but provides information about a distance traveled between a first position and a second, by counting the number of distance steps p that are detected during the displacement from the first position to the second and by an interpolation within one period. Therefore, in order to provide an output signal Xout representing the position of an object, e.g., relative to a reference or in order to define a reference position such as a zero reference, a calibration may be required. As an example, starting from a known position of the object (e.g., a position relative to a frame), the initialization constant IC can be set during a calibration sequence such that the output signal of the measurement system correspond to that known position. Alternatively, the initialization constant IC may also be used to define a zero reference for the measurements. It should also be noted that the calibration may be based on another position measurement.
The measurement range of the position measurement system is, in general, limited by the size of the second part, i.e., the reflective surface in case of an interferometer system or the grating in case of an encoder system. In case the operating range of the object of which the position is to be determined is larger that the measurement range, one can opt to increase the size of the second part (e.g., increase the length of the reflective surface or the grating) or one can choose to position multiple sensors along the required operating range. The latter is illustrated in
a, 3b and 3c schematically illustrate the take over process from one sensor to another in a more detailed manner.
This can be achieved as follows: When the measurement system is brought online in the initial position, the sensor 30.1 may produce an output signal X1out
X1out
Equation (2) comprises an initialization constant IC0. Initially, the initialization constant may have an arbitrary value or can be set equal to zero. Initially, N10, representing the number of periods traveled between two positions, can be set to zero or may have any arbitrary value. φ10 represents the phase determined by the measurement system in the initial position. Referring to
In order to provide an output signal corresponding to X0, a value ICa can be added to the initial value of the initialization constant IC0:
ICa=X0−X1out
By doing so, the output signal corresponds to X0. Once the measurement system is calibrated, a measurement of the X-position within the measurement range of the sensor 30.1 can be performed. In case the object 20 is to be displaced beyond the measurement range of the sensor 30.1, a take over of the position measurement by sensor 30.2 may be required. Such a take over can be performed in a position as schematically indicated in
Designating the X-position by Xt in the position as indicated, the output signal of sensor 30.1 in this position (X1out
X1out
IC0 in equation (4) represents the initialization constant of the sensor 30.1 after calibration.
When sensor 30.2 is brought online in the position as depicted in
X2out
As indicated, the output signal comprises an initialization constant IC2 initially having an arbitrary value prior to the initialization. Also N2t may initially have an arbitrary value. In general, X2out
ICa=Xt−X2out
Once initialized, the position measurement can be obtained from the output signal of sensor 30.2. As such, a take over process between sensor 30.1 and sensor 30.2 can be established. As a result, a position measurement of the object 20 may be performed by sensor 30.2 in a position as indicated in
The process as described in
At first, a first measurement sensor is calibrated based upon, e.g., a reference position. In order to take over the position measurement from the first sensor, a second sensor is initialized using the output signal from the first sensor in a position wherein both sensors are able to perform a position measurement.
When the object 20 is in a position as depicted in
Conventionally, such a take over from a position measurement using sensor 30.2 back to a position measurement using sensor 30.1 is done in a similar manner as the take over from a position measurement using sensor 30.1 to a position measurement using sensor 30.2, i.e., in order to take over the position measurement from the sensor 30.2, sensor 30.1 is initialized using the output signal from the sensor 30.2 in a position wherein both sensors are able to perform a position measurement.
It should be noted that such an approach may have an important impact on the positional accuracy of the measurement. This can be illustrated as follows:
Assuming a first sensor arranged to measure the position of an object, the sensor being initialized in a reference position as described above. The output signal of the sensor can in general be described by equation (1) and contains a certain measurement error ε·p (note that the measurement error may also be described as a separate error rather than as a fraction of the period p). Because the initialization constant IC (see eq. (3)) is based upon a measurement, this constant also comprises a measurement error ε·p. (It is assumed that the measurement error ε·p made by a sensor on different positions or by different sensors in an array of sensors is substantially equal for all measurements and that those errors are independent of each other).
As a result, a position measurement with the first sensor at an arbitrary position after initialization may have a measurement error that is larger than ε·p because the initialization constant is subject to a measurement error ε·p and the actual measurement is subject to a measurement error ε·p . Characterizing the error of the measurements by the standard deviation σε, the standard deviation of the position measurement of the first sensor substantially equals σε·√{square root over (2)} (because the addition (or subtraction) of two signals which are independent and having a standard deviation a and b results in a standard deviation equal to √{square root over (a2+b2)}).
During the take over process of the position measurement by a second sensor, the second sensor is initialized using the position measurement of the first sensor. The initialization constant of the second sensor can be determined according to equation (6). The initialization constant according to equation (6) is a function of the measurement of the first sensor (having an standard deviation of σε·√{square root over (2)}) and the initial measurement of the second sensor (having a standard deviation σε). As a result, the initialization constant of the second sensor may have a standard deviation equal to σε·√{square root over (3)}. As a result, a position measurement with the second sensor at an arbitrary position after initialization may result in a further increase in the measurement error because of the initialization that is subject to a standard deviation of σε·√{square root over (3)} and because of the actual measurement that is subject to an standard deviation of σε. In case both errors are independent, the standard deviation of the output signal of the second sensor equals σε·√{square root over (4)}.
In case the same procedure is repeated during a subsequent take over take over from a position measurement using the second sensor back to a position measurement using the first sensor, the standard deviation of the first sensor may have increased to σε·√{square root over (6)}. As can be seen, in case a larger number of take over processes are to be expected, the take over process may cause a built up of take over errors and may result in significant reduction in the accuracy of the measurement.
It should be noted that the built up of take over errors can be mitigated to some extend by calculating the initialization constant on the basis of an average of multiple measurement samples. However, in order for this method to be effective, the averaging should be performed over a comparatively large period in time because in general, the dominant part in the measurement error ε·p may be low frequent. As an example, the frequency spectrum may comprise an important so-called 1/f component implying that the size of the error in the frequency domain is proportional to one over the frequency f. Significantly reducing the take over error by averaging would require sampling over several tenth of a second. In most cases this would cause an unacceptable throughput penalty.
In the measurement system according to the present invention, a different approach is adopted during the take over process in order to reduce or mitigate the built up of take over errors.
The approach adopted in the present invention uses the insight that the measurement systems as described can be considered deterministic with respect to the measured phase φ: a repeated object position, measured with a specific sensor, will result in the same phase φ or, the measured phase φ can be considered to represent an absolute position within one period p (apart from the measurement error). In case the relative position between different sensors of an array of sensors remains substantially constant, one can easily acknowledge that the difference between the measured phase of one sensor and the measured phase of an other sensor also remains substantially constant in a repeated object position. This can be illustrated as follows:
a schematically depicts an object 40, a grating 44 mounted to the object (the grating is represented as an array of alternating black and white squares (44.1, 44.2, 44.3 and 44.4) having a period p).
When the object 40 is displaced to a position as depicted in
Xa=IC2+(N2φ2+ε)·p (7)
wherein IC2 denotes an initialization constant. Subscript 2 in eq. 7 refers to variables/constants of sensor 46.2. φ2 in equation (7) corresponds to the phase measurement of sensor 46.2 in the X-position as depicted in
X2=IC1+(N1+φ1+ε)·p (8)
IC1, N1 and φ1 are known and are related to the X-position as shown in
The difference Δ between the output signal of sensor 46.1 (representing the X-position X2) and the output signal of sensor 46.2 (Xa) can therefore be written as:
Δ=X2−Xa=(IC1−IC2)+(N1−N2)·p+(φ1−φ2)·p+ε″·p (9)
Note that Equation 9 introduces an error ε″·p for the difference Δ that may be larger than the error error ε·p of the output signals Xa and X2. The standard deviation of the difference Δ can be represented by σε·√{square root over (2)}, wherein σε corresponds to the standard deviation the error ε·p of the output signals Xa and X2 Equation 9 provides a relationship between the variables N1, N2, φ1 and φ2 and the initialization constants IC1 and IC2. It may further be observed that, the phase difference ((φ1−φ2) is substantially constant for a given position and determined by the geometry of the measurement system. As a consequence, a repeated object position can result in the same phase measurements φ1 and φ2 and in the same phase difference (φ1−φ2).
The difference Δ can be applied to initialize the sensor 46.2 in order for sensor 46.2 to take over the position measurement of the object. This may be obtained by adding the difference Δ to the output signal Xa, e.g., by setting the initialization constant IC2 to the initial value of IC2+Δ. (note that this corresponds to the conventional approach as described above). Once sensor 46.2 is initialized, an X-position of the object as indicated in
In the measurement system according to the present invention, a previously established relation between the sensors 46.1 and 46.2 (as described by equation 9) is used to initialize the sensor 46.1 in the following manner (rather than adding the difference Δ to the output signal Xa, e.g., by setting the initialization constant IC2 to the initial value of IC2+Δ):
In order to calibrate sensor 46.1 such that its output signal represents the position of the object 40, IC1, N1 and φ1 are required (see equation 8). Because the phase measurement φ1 is deterministic, it can be obtained from the measurement system. IC1 can also be considered known from the initial calibration of the sensor 46.1. As such, the only unknown to be determined is N1. According to the present invention, N1 is calculated from the previously established relationship between the sensor parameters (e.g., equation (9)). This calculation may, e.g., be accomplished by rounding off to the nearest integer value. By doing so, the measurement errors can be eliminated, provided that they are smaller than half a period p (which is usually the case). As a result, sensor 46.1 can be calibrated substantially without introducing an additional error. It should be noted that the take over from sensor 46.2 back to sensor 46.1 can be performed in a different position than the position in which the relationship according to equation 9 is determined. Equation 9, in general, provides a relation between N1, N2, φ1 and φ2 that can be summarized as:
(N1−N2)+(φ1−φ2)=C (10)
wherein C is a constant.
Equation 10 can, e.g., be applied to determine N1 when N2, φ1 and φ2 are known or to determine N2 when N1, φ1 and φ2 are known according to the following equations 11a and 11b:
N1=round(C+N2−(φ1−φ2)) (11a)
N2=round(−C+N1+(φ1−φ2)) (11b)
wherein ‘round( )’ is used to designate the well-known round off function to the nearest integer.
As such, a subsequent take over from a position measurement using sensor 46.1 to a position measurement using sensor 46.2 can be performed in a similar manner, substantially without introducing an additional measurement error. It will be clear that in case more than two sensors are present, similar relationships can be determined between, e.g., a second sensor and a third sensor in order to perform a take over from a position measurement using the second sensor to a position measurement using the third sensor.
It should be noted that the round-off process may also be applied during the initialization process of the second sensor. This can be illustrated as follows: Assuming the first sensor 46.1 being calibrated at a known object position such that IC1, N1 and φ1 are known. When sensor 46.2 is brought online, IC2, N2 should be determined. φ2 is available from measurement of sensor 46.2.
In order to initialize N2, one may set IC2 equal to zero and initialize N2 using equation 11b. When the value of N2, as found is used to generate an output signal, the output signal shall, in general, not correspond to the actual position, due to the round off function that is applied to obtain N2. In order for the output signal to correspond to the actual position, IC2 can be calibrated by equating it to the actual position (e.g., corresponding to the output signal of the first sensor 46.1) minus the output signal of sensor 46.2 (after introduction of the calculated N2).
The measurement system may comprise a control unit for processing the output signals of the sensors of the array of sensors. The control system can be arranged to select and/or process one or more of the output signals in order to generate an output signal suitable for use in e.g. a position controller. When a relationship between the sensor parameters N1, N2, φ1 and φ2 is established (see e.g., equations 9 or 10), it can be applied, for example, in the control unit of the measurement system or in a separate unit in order to perform the take over process according to the present invention. The control unit of the measurement system may further be arranged to perform the round off process in order to determine the integer number representing a number of periods traveled from the reference position of the sensor to be initialized.
It should be noted that the take over process according to the present invention may also be applied in a homodyne or a heterodyne interferometer measurement system. Such a measurement system may also require a take over from a position measurement using a first sensor to a position measurement using a second sensor.
a schematically depicts an interferometer measurement system for measuring the Y-position of an object 50 (e.g., a substrate table of a lithographic apparatus) relative to a reference frame 60. The measurement system comprises an array of sensors 62 comprising a first sensor 62.1 and a second sensor 62.2 mounted on the reference frame 60. A mirror (in general a reflective surface) 64 is mounted to the object 50 in order to reflect laser beams 66 and 68 to the sensors 62.1 and 62.2. The Y-position of the object can be determined by the interferometer measurement system by counting a number of periods (each period corresponding, for example, to a quarter of the wavelength of the laser beam) that is detected and by interpolation within one period. By using an array of sensors, the objects Y-position can be determined over a range of motion in the X-direction that is larger than the length of the mirror in the X-direction.
It should be noted that the laser beams 66 and 68 may originate from the same laser source or from a different laser source. In the latter case, the Y-measurement performed with sensor 62.1 may have a different period (or increment) than the period of a Y-measurement performed with sensor 62.2.
In general, when a different period is applicable for two sensors, the take over process according to the present invention can be applied in a similar manner. In such an arrangement, the relationship established between the parameters N1, N2, φ1 and φ2 (representing the measurement of the phase and the integer number of periods passed of the sensors) may be expanded to include the period p1 of the first sensor and the period p2 of the second sensor. This can be done as follows. Assuming an incremental position measurement system such as an interferometer system or an encoder system (e.g., a Y-measurement) comprising a first (index 1) and a second (index 2) sensor operating with a different period, the output signal Yout
Yout
Yout
wherein
p1, p2=period of the incremental measurement system of the resp. sensors
and can be used to derive the following relationship between the parameters N1, N2, φ1, φ2, p1 and P2:
(N1·p1−N2·p2)+(φ1·p1−φ2·p2)=C′ (14)
wherein C′ is a constant.
Note that, regarding the error as indicated in eq. 13, the considerations as made for eq. 9 are valid, i.e., the standard deviation of the difference Δ′ may be larger than the standard deviation of the output signals of eq. 12. Equation 14 can be applied to determine N1 when N2, φ1 and φ2 are known or to determine N2 when N1, φ1 and φ2 are known according to the following equations 15a and 15b:
wherein ‘round( )’ is used to designate the well-known round off function to the nearest integer.
Using equations 15a and 15b, the take over process as used in the present invention can be perform when the sensors involved are operating with a different period.
The take over process according to the present invention may also be applied in a measurement system comprising multiple gratings and multiple sensors.
It should be noted that the described invention may also be applied to monitor certain drift components in the measurement system such as the distance from sensor to sensor or the length of the grating. The take over process according to the present invention applies a previously established relationship between parameters obtained from different sensors (see e.g., eq. 10 or 14). This relationship can, e.g., be established during calibration of the measurement system. In case of a relative slowly drifting measurement system, the relationship between the sensor parameters may change over time. This change can be monitored because the relationship between the sensor parameters can be determined each time a take over process is performed resulting in a actualized value of C. Comparing the actualized value to the initially established value provides information on the drift of the measurement system over time. By monitoring C as a function of time and correcting for it, the take over process according to the present invention can also be applied in relative slow drifting systems.
It should be noted that the present invention may equally be applied in a measurement system arranged to measure a position in more than one degree of freedom. As an example, the present invention can be applied in a 2D encoder measurement system. Such a system may comprise a plurality of sensors constructed and arranged to co-operate with a two-dimensional grating in order to determine the position of an object in both X-direction and Y-direction. In order to perform the take over process according to the present invention, a relationship as described in eq. 9 or 10 can be established for both directions.
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. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.
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.
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, 355, 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.
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.
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.
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 claims set out below.
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