JP2007129101A - Method for calculating correction information, method for controlling movable stage, and exposure apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To control a movable stage with high precision in all sections including a measuring section and a non-measuring section. <P>SOLUTION: Information corresponding to the actual position of a movable stage for a plurality of target positions in the measuring sections (L-R) of the movable stage is measured, and a correction function is calculated by interpolating the information, based on respective measurement error information. A line passing the end points L and R of the correction function in the measuring section and having the slants a<SB>L</SB>and a<SB>R</SB>of tangents at the end points is considered as the correction function at an extrapolation part, and correction information in the measuring section and at the extrapolation part is calculated, based on the correction function in the measuring section and at the extrapolation part. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a correction information calculation method for calculating correction information used for controlling movement of a movable stage, a control method for a movable stage using the correction information calculation method, and an exposure apparatus using the control method for the movable stage. .

  In a photolithography process for manufacturing a semiconductor element or the like, a mask and a wafer on which a pattern is formed are moved synchronously by a stage device, and shots on the wafer are sequentially exposed with slit-like light. -A scanning exposure apparatus is used. The position of the movable stage on which the mask or wafer of the stage device is held is irradiated with laser light from the laser interferometer to the movable mirror provided in the movable stage, and the reflected light and predetermined reference light are caused to interfere with each other. This is performed by measuring the position change, and the movement of the movable stage is controlled based on the measurement result. Here, the movement of the movable stage (hereinafter sometimes referred to as the mask stage) of the mask stage device that holds the mask with respect to the movable stage (hereinafter also referred to as the wafer stage) of the wafer stage device that holds the wafer causes laser interference. Even if the measurement result of the meter (that is, apparently) is accurately followed, the moving mirror bends or swells (hereinafter sometimes referred to as moving mirror bending), or the movement depends on the movement of the movable stage. If there is a typical error, the actual movement of the mask stage relative to the wafer stage does not follow these errors. If the wafer is exposed through the mask pattern in this state, the error The exposure accuracy deteriorates by the amount.

  Accordingly, it is necessary to measure such an error that cannot be seen by the interferometer (hereinafter, sometimes referred to as an invisible error) and to control the movement of the movable stage while correcting the error so as to cancel it. As a method for correcting the invisible error, for example, a reference wafer (reference shot) is actually exposed (baked) through a reference mask having marks formed in an array, and a transferred image of the mark is designed. There is a method of adding each error with respect to a value as a correction value to a target value for stage movement. In addition, a plurality of marks arranged on the mask are respectively measured by a two-dimensional sensor or the like while moving the movable stage, and each deviation amount from the corresponding design value of each measurement result is set as a target value for moving the stage. There is also a method of adding. Of the correction methods described above, in the method of obtaining correction information by actual exposure, the measurement section can be set only within a range smaller than the exposure section (scan length). Specifically, when the exposure center is taken as the origin, measurement can be performed only in the range of ± [(exposure section) − (slit width)] × 0.5, and this range becomes the measurement range. On the other hand, the range that affects the exposure is ± [(exposure section) + (slit width)] × 0.5. Further, in the case of directly measuring the mark attached to the mask, the maximum range with the mark is the measurement range, and correction information of the portion (section) outside the mark cannot be obtained by measurement. For this reason, extrapolation based on error information collected in the measurement section, that is, estimation of error information of an extrapolation unit (sometimes referred to as a non-measurement section) that is a section outside the measurement section is performed. As a conventional technique for this extrapolation, error information of a measurement interval is interpolated (that is, interpolated) using an appropriate interpolation function, such as a power function or a spline function, and the interpolation function is non-measured interval. The extrapolation was performed using an estimation method in which the error information (values) at both ends of the measurement interval is treated as a representative value outside the measurement interval and a constant value is taken outside the measurement interval.

  However, in the former method, although the fitting to the interpolation formula (power function or spline function) within the measurement section (interpolation) is certain, the fitting of the extrapolated portion is not necessarily certain. In particular, when a higher-order power function is used as an interpolation function, the extrapolation part may have a high frequency that exceeds the follow-up performance of the stage, and the pattern line width uniformity deteriorates. May get worse. Further, in the latter method, the correction information at the boundary between the measurement section (interpolation section) and the outside of the measurement section (extrapolation section) is discontinuous, and the stage cannot follow the correction information at this discontinuous portion, In some cases, the synchronization accuracy between the wafer stage and the mask stage is deteriorated, and the exposure accuracy is deteriorated.

The present invention has been made in view of such a point, and an object thereof is to provide a correction information calculation method capable of controlling the position of a movable stage with high accuracy in all of a measurement section and a non-measurement section. .
JP 2005-166951 A

  According to the present invention, based on measurement error information obtained by measuring information corresponding to the actual position of the movable stage with respect to a plurality of target positions in a predetermined measurement section of the movable stage, the measurement section and the measurement section A correction information calculation method for calculating correction information in an outer non-measurement section, calculating an interpolation function for interpolating these based on the measurement error information, and making the interpolation function a correction function in the measurement section, The correction function in the non-measurement section is defined as a straight line passing through the end point with the slope of the tangent line at the end point of the measurement section in the measurement section or a point in the vicinity of the end point, and the measurement section and the A correction information calculation method for calculating correction information in the measurement section and the non-measurement section based on the correction function in the non-measurement section. It is subjected. In this invention, since the straight line passing through the end point having the inclination of the tangent line at the end point of the measurement section of the correction section in the measurement section or a point near the end point is used as the correction function in the non-measurement section, The correction information changes proportionally with a certain slope, and the correction information is continuous or almost continuous before and after the end point. Therefore, the movable stage can reliably follow the correction information even in the non-measurement section, and the correction information is continuous or almost continuous at the boundary between the measurement section and the non-measurement section. be able to.

  According to the present invention, there is an effect that the movable stage can reliably follow the correction information in all of the measurement section and the non-measurement section.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. First, the overall configuration of an exposure apparatus to which the present invention can be applied will be outlined.

[Exposure equipment]
FIG. 1 is a front view schematically showing the overall configuration of an exposure apparatus according to an embodiment of the present invention. The exposure apparatus shown in FIG. 1 employs a step-and-scan method in which the pattern formed on the reticle R is sequentially transferred onto the wafer W while the reticle stage RST and the wafer stage WST are moved synchronously with respect to the projection optical system PL. It is an exposure apparatus. In FIG. 1, the illumination optical system IL shapes the cross-sectional shape of laser light emitted from a light source such as an ArF excimer laser light source (wavelength 193 nm) into a slit shape extending in a predetermined direction, and uniformizes the illuminance distribution for illumination. Ejected as light. In this embodiment, the case where an ArF excimer laser light source is provided as a light source will be described as an example. In addition, an ultrahigh pressure mercury lamp that emits g-line (wavelength 436 nm) and i-line (wavelength 365 nm), or A KrF excimer laser (wavelength 248 nm), an F ₂ laser (wavelength 157 nm), and other light sources can be used.

  The reticle R is attracted and held on the reticle stage RST, and a movable mirror MRr to which the length measuring beam BMr from the reticle interferometer system IFR is irradiated is fixed to one end of the reticle stage RST. Positioning of the reticle R is performed by a reticle driving device DR that translates the reticle stage RST in the XY plane perpendicular to the optical axis AX and rotates it slightly in the XY plane. When transferring the pattern of the reticle R onto the wafer W, the reticle driving device DR scans the reticle stage RST at a constant speed in a direction orthogonal to a predetermined direction in which the slit extends. Above the reticle stage RST, alignment systems OB1 and OB2 for photoelectrically detecting reticle alignment marks RM formed at two positions around the reticle R are provided. The detection results of the alignment systems OB1 and OB2 are used to position the reticle R with a predetermined accuracy with respect to the optical axis AX of the illumination optical system IL or the projection optical system PL.

  Reticle stage RST is movably held on reticle stage base structure CL1 that forms part of the column structure of the apparatus body, and a motor and the like of reticle drive apparatus DR are also mounted on base structure CL1. Further, a beam interference portion (such as a beam splitter) of the reticle interferometer system IFR that measures a change in the position of the reticle R is also attached to the base structure CL1. Interferometer system IFR projects length measurement beam BMr onto moving mirror MRr attached to one end of reticle stage RST, receives the reflected beam, and measures the positional change of reticle R. The image of the pattern formed on the reticle R is imaged and projected onto the wafer W at a projection magnification of 1/4 or 1/5 via the projection optical system PL disposed immediately below the reticle stage RST. The lens barrel of the projection optical system PL is fixed to a lens base structure CL3 that constitutes a part of the column structure, and the lens base structure CL3 supports the reticle base structure CL1 via a plurality of column structures CL2. is doing.

  The projection optical system PL has a plurality of optical elements such as lenses, and the glass material of the optical elements is selected from optical materials such as quartz and fluorite according to the wavelength of illumination light emitted from the illumination optical system IL. . Note that some of the optical elements provided in the projection optical system PL are configured to be movable in the direction of the optical axis AX and the direction intersecting the optical axis AX, and the posture (angle with respect to the optical axis AX) is adjusted. The optical characteristics such as magnification and aberration of the projection optical system PL can be adjusted by adjusting the position or orientation of these optical elements. The lens base structure CL3 is mounted on the wafer base structure CL4 on which the wafer stage WST that mounts the wafer W and moves two-dimensionally along the XY plane is mounted. Although not shown, wafer stage WST is provided with a wafer holder that vacuum-sucks wafer W and a leveling table that finely moves and tilts the wafer holder in the direction of optical axis AX. The movement coordinate position of wafer stage WST in the movement plane (XY plane) and the minute rotation amount by yawing are measured by wafer interferometer system IFW. The interferometer system IFW projects the laser beam from the laser light source LS onto the movable mirror MRw fixed to the leveling table of the wafer stage WST and the fixed mirror FRw fixed to the bottom of the projection optical system PL. The coordinate position and minute rotation amount (yawing amount) of wafer stage WST are measured by causing the reflected beams from mirrors MRw and FRw to interfere. On the leveling table of wafer stage WST, various alignment systems, focus sensors, and a reference plate FM used for calibration of the leveling sensor and measurement of the baseline amount are also attached. On the surface of the reference plate FM, reference marks that can be detected by the alignment systems OB1 and OB2 are formed together with the mark RM of the reticle R under illumination light having an exposure wavelength.

[Collection of error information in measurement section and calculation of correction function]
The collection and calculation of error information for correcting an invisible error (for example, an error due to moving mirror bending) of the reticle stage RST of the exposure apparatus described above will be described. First, error information in the measurement section is collected. In this embodiment, a reference reticle on which a plurality of marks (patterns) for error measurement are arranged in advance with high accuracy is used, and an exposure apparatus to be corrected is used to actually print on a reference wafer coated with a resist. (Exposure processing) is performed, and a positional deviation amount from a design position of a mark image (resist image, etching image, etc.) exposed and formed on the reference wafer is measured using, for example, a light wave measuring device. Here, a case where the error in the direction orthogonal to the scanning direction of the exposure apparatus is corrected will be described as an example. In addition, the collection of error information in the measurement section may be other than that actually collected by exposure processing as described above. For example, the reticle for measuring the position of the reticle arranged on the reticle is connected to the reticle. Measurement may be performed using the alignment systems OB1, OB2, and the like described above while moving the stage, and the amount of deviation from the design value may be collected. Next, a correction function is calculated based on the collected error information in the measurement section. The calculation of the correction function is performed by substituting each error information into a predetermined model formula (interpolation formula) and obtaining the coefficient of the model formula by the least square method or the like. Refer to Japanese Patent Application Laid-Open No. 2005-166951 for details of the calculation of the correction function and the collection of the error information described above.

[Calculation of correction information]
Hereinafter, a calculation method (extrapolation method) of correction information in the non-measurement section (extrapolation unit) will be described in detail. In the following first to fifth calculation methods, it is considered that moving mirror bending is dominant as a cause of shot distortion, and there is no high frequency included in the moving mirror bending or there are no discontinuous portions. It is based on the assumption.

[First calculation method]
A first calculation method for calculating the correction information of the movable stage will be described with reference to FIG. In the first calculation method, the end point (L, R) of the correction function in the measurement section or the end point ( _L , a _R ) of the tangent at the end point (L, R) in the vicinity of the end point is used as the slope. The straight line passing through is used as a correction function in a non-measurement section (extrapolation unit) outside the measurement section. In FIG. 2, the horizontal axis represents the coordinates (x) of the reticle stage (RS), and the vertical axis represents the correction value (f (x)). Note that the coordinate (x) on the horizontal axis represents an operation variable, which is a coordinate in the scan direction here. In the figure, L indicates an end point on the left side (negative side) of the measurement section, and R indicates an end point on the right side (positive side) of the measurement section. Therefore, the measurement section is in the range of L ≦ x ≦ R, and the extrapolation part as the non-measurement section is in the range of x <L, x> R. Although not shown, the middle point (shot center) of the measurement section is the origin O, and if necessary, the left (negative) end point of the measurement section is the L side end point and the right side (positive side). Are referred to as the R-side end point, the left (negative) extrapolated portion as the L-side extrapolated portion, and the right (positive) extrapolated portion as the R-side extrapolated portion. For example, the exposure section (scan length) is set to 33 mm, and the width of the slit light (hereinafter sometimes referred to as slit width) is set to 8 mm, so that the entire section of this exposure section can be measured (ie, exposure section = measurement section). )), The position of the end point on the L side is L = −16.5 mm, the position of the end point on the R side is R = + 16.5 mm, and the L side extrapolation part and the R side extrapolation part are each 1 / s of the slit width. 2 or 4 mm.

Here, when the correction value (correction function in the measurement section) f (x) is differentiable with x = x ′, the slope a _{x ′ at} x = x ′ can be obtained by the following (Equation 1-1). it can.

The correction functions of the L side extrapolation unit and the R side extrapolation unit are obtained as follows.
(1) the (Equation 1-1) is used to determine the slope _{a R} in _{tilt-a L} a Oyobi R end point (x = R) in the L-side end point (x = L).
(2) Extrapolated value (correction function) g _L (x) of the L-side extrapolation part (x <L range) is
g _{L (x)} is a = a L x + f (L ) -L × a L. f (L) is a correction value obtained as a result of interpolation when x = L.
(3) Extrapolated value (correction function) g _R (x) of the R-side extrapolation section (range x> R) is:
g _{R (x)} is a = a R x + f (R ) -R × a R. f (R) is a correction value obtained as a result of interpolation when x = R.

In FIG. 2, for example, when the correction function f (x) of the measurement section obtained by interpolation using a higher-order power function as an interpolation function is applied to the extrapolation unit, f _L at the L side extrapolation unit and R side In the extrapolation section, as indicated by f _R , the correction value may become extremely large such that the moving mirror cannot be bent, or inflection points may be concentrated on the extrapolation section. In some cases, the correction value cannot be followed. However, as in this embodiment, the correction function g _L (x) in the _L- side extrapolation unit and the correction function g _R (x) in the R-side extrapolation unit are used to correct the target value of the movable stage. On the other hand, by controlling the operation of the movable stage, these correction functions are linear and continuous at the end points (L, R) of the measurement section, so that the movable stage has a sufficient correction value based on this. It is possible to follow, and it is possible to more accurately correct an invisible error of the movable stage in the extrapolation unit. In the first calculation method described above, the slopes a _L and a _R at the L-side end point and the R-side end point are used, but the L-side end point and the R-side end point are inside the L-side end point and the R-side end point. An inclination at a nearby point (an arbitrary point that is not limited to a measurement point) may be adopted, and substantially the same effect can be obtained. In this case, although it is slightly discontinuous at the boundary between the measurement section and the extrapolation section, the amount of change is extremely small, so that there is little problem in controlling the operation of the movable stage.

In addition, when the correction function f (x) in the measurement section cannot be analytically obtained or when error information is handled discretely, the slope of the correction function f (x) using the error information about the end points of the measurement section and the measurement points in the vicinity thereof is used. May be calculated. If the amount of change Δf in the minute section Δx ′ is assumed, the inclination can be obtained by a _{x ′} = Δf / Δx ′. As Δx ′, the sampling interval (measurement pitch) of the correction information can be used, but for the purpose of removing the high frequency, the size of Δx ′ can be appropriately determined. For example, with respect to error information sampled (measured) at a pitch of 1 mm, Δx ′ = 4 mm and the slope of L = 16 mm is a ₁₄ = [f (16) −f (12)] / (16−12). This slope may be used.

[Second calculation method]
A second calculation method for calculating the correction information of the movable stage will be described with reference to FIG. In the first calculation method described above, when the slope at the end points (L, R) of the measurement section is large, the correction value in the extrapolation unit may be large. In order to suppress this, the second calculation method includes a first inclination that is an inclination of a tangent line at an end point of the measurement section of the correction function in the measurement section or a point near the end point, and the correction function in the measurement section. The tangent slope at the end point of the measurement section or a point in the vicinity of the end point is defined as a second slope, and the end point is defined as a slope related to the average of the first slope and the second slope. The straight line passing through is used as a correction function in the non-measurement section (extrapolation section).

In FIG. 3, the horizontal axis, the vertical axis, the meanings of the symbols, and the like are the same as those in FIG. The correction functions of the L side extrapolation unit and the R side extrapolation unit are obtained as follows.
(1) Using the above (Equation 1-1), a slope a _{l1 at} a point (x = l ₁ ) near the inner side of the L-side end point and a point (x = l ₂ ) further inside than the neighboring point seeking a _l2, we obtain the gradient _{a L} of the average. That seek _{a L = (a l1 + a} l2) / 2. Further, by using the above (Equation 1-1), the slopes a _r1 and a at a point (x = r ₁ ) near the inner side of the R-side end point and a point (x = r ₂ ) further inside than the neighboring point seeking _r2, obtains the gradient _{a R} of the average. That is, a _R = (a _r1 + a _r2 ) / 2 is obtained.
(2) Extrapolated value (correction function) g _L (x) of the L-side extrapolation part (x <L range) is
g _{L (x)} is a = a L x + f (L ) -L × a L. f (L) is a correction value obtained as a result of interpolation when x = L.
(3) Extrapolated value (correction function) g _R (x) of the R-side extrapolation section (range x> R) is:
g _{R (x)} is a = a R x + f (R ) -R × a R. f (R) is a correction value obtained as a result of interpolation when x = R.

In FIG. 3, for example, when the correction function f (x) of the measurement section obtained by interpolation using a higher-order power function as an interpolation function is applied to the extrapolation unit, f _L at the L side extrapolation unit and R side In the extrapolation section, as indicated by f _R , the correction value may become extremely large such that the moving mirror cannot be bent, or inflection points may be concentrated on the extrapolation section. In some cases, the correction value cannot be followed. Further, in the first calculation method, when the inclination at the end points (L, R) of the measurement section is large, the correction value in the extrapolation unit is also large. However, as in the second calculation method, the correction function in the extrapolation unit is calculated using the average of the slopes of the points near the inner end of the end point of the measurement section and the points further inside the neighboring points. By calculating, it is possible to suppress an increase in the slope of the correction function in the extrapolation part due to the averaging effect, and it becomes possible for the movable stage to sufficiently follow the correction value based on this, An invisible error of the movable stage in the insertion portion can be corrected more accurately. In the second calculation method described above, in order to obtain the correction function of the L-side extrapolation unit, the slopes a _l1 , a at a point near the inside of the L-side end point and a point further inside than the nearby point _Although the average of _l2 is used, the average of the slopes at the two points of the L-side end point and the point inside the L-side end point may be used. You may make it use the average of each inclination in three or more points including this L side end point or not including this L side end point. The same applies to the R-side extrapolation part.

[Third calculation method]
A second calculation method for calculating movable stage correction information will be described with reference to FIG. In the first and second calculation methods described above, when the slopes at the end points (L, R) of the measurement section and in the vicinity thereof are large, the correction value in the extrapolation unit may be large. In order to further suppress this, the third calculation method uses a function obtained by rotating the correction function in the measurement section by 180 degrees around the end point of the measurement section of the correction function in the measurement section. The correction function in the insertion section).

In FIG. 4, the horizontal axis, the vertical axis, the meanings of the symbols, and the like are the same as those in FIGS. The correction functions of the L side extrapolation unit and the R side extrapolation unit are obtained as follows.
(1) The extrapolated value (correction function) g _L (x) of the L-side extrapolation section (x <L range) is
g _L (x) = − f (x−2L) + 2f (L). f (L) is a correction value obtained as a result of interpolation when x = L.
(2) The extrapolated value (correction function) g _R (x) of the R-side extrapolation section (x> R range) is
g _R (x) = - a f (x-2R) + 2f (R).

  Since the correction function in the measurement section (that is, the interpolation section) is based on the actual measurement value, it cannot contain a high frequency that the movable stage cannot follow. In the third calculation method, the correction function of the interpolation unit is rotated by 180 degrees, and this is used as the correction function of the extrapolation unit. In addition to being able to follow, the correction function of the interpolation part and the correction function of the extrapolation part are continuous even at the end points (L, R) of the measurement section, so that the movable stage reliably follows the correction value. Thus, the invisible error of the movable stage in the extrapolation portion can be corrected more accurately.

[Fourth calculation method]
A fourth calculation method for calculating the correction information of the movable stage will be described. This fourth calculation method is a method using a low-pass filter to remove high frequencies, and the measurement error information related to the target position closest to the end of the measurement section of the measurement error information in the measurement section is converted into the non-measurement section. Correction information in the measurement section and non-measurement section (extrapolation section) is calculated based on the measurement error information and the extrapolation error information, and the measurement error information and the extrapolation error. The information is interpolated by a predetermined interpolation formula using a Sinc function and a Hanning window function, thereby obtaining correction information at arbitrary positions in the measurement section and the non-measurement section. In the first to third calculation methods described above, the correction value is expressed as a continuous function, but here, the correction value is handled discretely. Further, in the first to third calculation methods, only the extrapolation unit is handled, but here, the interpolation is also performed at the same time.

(1) Preparation First, with respect to the horizontal axis x, data (error information) measured in the measurement interval in the measurement pitch p _s [mm] is expressed as f (kp _s ), k = 1, 2,. f (kp _s ) is a positional shift amount obtained from the printing result. Hereinafter, the discrete measurement data is referred to as a map. The horizontal axis of this map is represented as X _j = X ₀ + jp _s , j = 0, 1, 2,..., M−1 when there are M data. X ₀ is the minimum value of the horizontal axis of the map. f (kp _s ) can be expressed as f (X _j ). Using this map, a correction value (estimated value of measurement data) at a certain x (continuous value) is calculated. If the closest sample point is X = kp _s , a correction value at a certain x is obtained by using 2α + 1 f (X _j ) in the vicinity thereof. α is the number of data to which the filter is applied.

(2) Preparation of map for obtaining correction value Assuming that the extrapolated portions are L _min <x <L and R <x <R _max ,
_{X j = X 0 + jp s} , j = -β, - (β-1), - (β over 2), ..., 1,2, ... , M, M + 1, M + 2, ..., M + β-2, M + β-1
_{X -β = X 0 -βp s <} L min - (α + 1) p s
X _{M + β-1} = X ₀ + (M + β-1) p _s > R _max + α p _s
Stretch both ends of the map so that there are measurements in In the stretched map portion, the nearest data with a value is entered. That is,
f (X _j ) = f (X ₀ ), j = −β, − (β−1), − (β−2),.
f (X _j ) = f (X _M−1 ), j = M, M + 1, M + 2,..., M + β−2, M + β−1
It becomes. Note that β is the number of data to be increased in the extrapolation unit.
(3) A correction value is obtained using a map with both ends extended.
The following (Expression 4-1) to (Expression 4-7) are applied to the map with both ends extended. By varying the parameters _{p t} of Sinc function (Equation 4-1) in (Equation 4-1) is a low-pass filter. Thus, by the maximum frequency to be corrected to apply p _t such that 1 / 2p _t, can ends to create a smooth correction value.

Note that, in (Equation _4-5), when _{the 1 / 2p t = 1 / 2p} s is satisfied becomes interpolation, the low pass filter when not satisfied. By using such an interpolation formula, it is possible to obtain a smooth correction value in all the sections including the boundary between the measurement section and the extrapolation section, and the correction value is almost constant in the extrapolation section. The movable stage can reliably follow the correction value, and the invisible error of the movable stage in the extrapolation unit can be corrected more accurately.

[Fifth calculation method]
A fifth calculation method for calculating the correction information of the movable stage will be described with reference to FIG. In the fifth calculation method, the extrapolation unit is asymptotically approximated to a constant value so that the synchronization accuracy is not deteriorated. The measurement error information relating to the target position closest to the end of the measurement section of the measurement error information Applying the rate of change obtained from the measurement error information related to the next closest target position, the extrapolation error related to the extrapolation position closest to the end of the measurement section among the plurality of extrapolation positions in the non-measurement section Information, and sequentially applying a rate of change smaller than the rate of change to calculate extrapolation error information at an extrapolation position after the next extrapolation position of the extrapolation position, and measurement error information and Based on the extrapolation error information, correction information for the measurement section and the non-measurement section is obtained. In the fourth calculation method, correction values are handled discretely as in the third calculation method described above. Here, as in the fourth calculation method, not only the extrapolation unit but also the interpolation is performed simultaneously.

In FIG. 5, the horizontal axis, the vertical axis, the meaning of symbols, and the like are the same as those in FIGS.
(1) In the extrapolation unit, extrapolation positions Xj, j = 1, 2, 3,... Are set at the same measurement pitch as the measurement section, and correction values f (X _j ) at these extrapolation positions are set as follows: It is determined by (Formula 5-1).
f (X _j ) = f (X _j−1 ) + α ^j (f (X _j−1 ) −f (X _j−2 )) (Formula 5-1)
Here, α is an attenuation rate, and is selected from the range of α <1, and here, α = ½. X ₀ is a measurement point one inner side from the end points (L, R) of the measurement section, and f (X ₀ ) is a correction value corresponding to the measurement error at the measurement point. X ₁ is an end point (L, R) of the measurement section, and f (X ₁ ) is a correction value corresponding to a measurement error at the end point.
(2) Perform extrapolation of the L-side extrapolation section (x <L range). X ₁ = L, subscripts j = 0, 1, 2, 3,... Are added in the direction of decreasing x, and extrapolated by (Equation 5-1).
(3) Perform extrapolation of the R-side extrapolation part (range x> R). As X ₁ = R, subscripts j = 0, 1, 2, 3,... Are assigned in the direction of decreasing x and extrapolated by (Equation 5-1).

Thus, the L-side extrapolation, slope between X ₀ and L (X ₁₎ (rate of change) is applied, the correction value of the first extrapolated position X ₂ is calculated, L (X ₁ ) And X ₂ , a correction value of the next extrapolation position X ₃ is calculated by applying a half of the inclination (change rate) between X ₂ and X _2. / 2 is applied, and correction values for the extrapolated positions are sequentially calculated. The same applies to the R-side extrapolation part. By calculating the correction value in the extrapolation part (extrapolation position) in this way, the correction value is gradually approaching a constant value by applying a small change rate toward the outside. Therefore, the correction value does not include high frequencies or the correction value becomes extremely large, and the movable stage can reliably follow the correction value, so that the movable stage can be seen in the extrapolation section. Error can be corrected more accurately. Although the correction value is discontinuous before and after each extrapolation position in the extrapolation unit, the control of the movable stage is greatly influenced by appropriately selecting the attenuation factor α (1/2 in this example). It is not considered to give. However, when this discontinuity becomes a problem, for example, smoothing may be performed by applying the low-pass filter or the like in the fourth calculation method described above.

  The embodiment described above is described in order to facilitate understanding of the present invention, and is not described in order to limit the present invention. Therefore, each element disclosed in the above embodiment is intended to include all design changes and equivalents belonging to the technical scope of the present invention. For example, in the above-described embodiment, the case where the present invention is applied to the control of the operation of the reticle stage has been described. However, the present invention can also be applied to the control of the operation of the wafer stage.

It is a front view which shows typically the whole structure of the exposure apparatus which concerns on embodiment of this invention. It is a figure for demonstrating the 1st calculation method of the correction information of embodiment of this invention. It is a figure for demonstrating the 2nd calculation method of the correction information of embodiment of this invention. It is a figure for demonstrating the 3rd calculation method of the correction information of embodiment of this invention. It is a figure for demonstrating the 5th calculation method of the correction information of embodiment of this invention.

Explanation of symbols

  R ... reticle, RST ... reticle stage, W ... wafer, WST ... wafer stage.

Claims (8)

Based on measurement error information obtained by measuring information corresponding to the actual position of the movable stage with respect to a plurality of target positions in a predetermined measurement section of the movable stage, the measurement section and a non-measurement section outside the measurement section A correction information calculation method for calculating correction information in
Based on the measurement error information, to calculate an interpolation function for interpolating these, the interpolation function as a correction function in the measurement section,
The correction function in the non-measurement section is a straight line that passes through the end point of the correction function in the measurement section and the tangent slope at the end point of the measurement section or a point near the end point.
A correction information calculation method comprising: calculating correction information in the measurement section and the non-measurement section based on the correction function in the measurement section and the non-measurement section. Based on measurement error information obtained by measuring information corresponding to the actual position of the movable stage with respect to a plurality of target positions in a predetermined measurement section of the movable stage, the measurement section and a non-measurement section outside the measurement section A correction information calculation method for calculating correction information in
Based on the measurement error information, to calculate an interpolation function for interpolating these, the interpolation function as a correction function in the measurement section,
A first slope that is a slope of a tangent at an end point of the measurement section of the measurement section or a point near the end point of the correction section, and an end point of the correction section of the measurement section or the vicinity of the end point A straight line passing through the end point having a slope of a tangent line at a point inside the point as a second slope and a slope related to the average of the first slope and the second slope as the slope is defined as a correction function in the non-measurement section. ,
A correction information calculation method comprising: calculating correction information in the measurement section and the non-measurement section based on the correction function in the measurement section and the non-measurement section. Based on measurement error information obtained by measuring information corresponding to the actual position of the movable stage with respect to a plurality of target positions in a predetermined measurement section of the movable stage, the measurement section and a non-measurement section outside the measurement section A correction information calculation method for calculating correction information in
Based on the measurement error information, to calculate an interpolation function for interpolating these, the interpolation function as a correction function in the measurement section,
A function obtained by rotating the correction function in the measurement section 180 degrees around the end point of the measurement section of the correction function in the measurement section is a correction function in the non-measurement section,
A correction information calculation method comprising: calculating correction information in the measurement section and the non-measurement section based on the correction function in the measurement section and the non-measurement section. Based on measurement error information obtained by measuring information corresponding to the actual position of the movable stage with respect to a plurality of target positions in a predetermined measurement section of the movable stage, the measurement section and a non-measurement section outside the measurement section A correction information calculation method for calculating correction information in
The measurement error information related to the target position closest to the end of the measurement section of the measurement error information in the measurement section is extrapolation error information at a plurality of extrapolation positions in the non-measurement section,
Correction information at an arbitrary position in the measurement section and the non-measurement section is obtained by interpolating the measurement error information and the extrapolation error information with a predetermined interpolation formula using a Sinc function and a Hanning window function. A correction information calculation method. Based on measurement error information obtained by measuring information corresponding to the actual position of the movable stage with respect to a plurality of target positions in a predetermined measurement section of the movable stage, the measurement section and a non-measurement section outside the measurement section A correction information calculation method for calculating correction information in
Applying the rate of change obtained from the measurement error information related to the target position closest to the end of the measurement section of the measurement error information and the measurement error information related to the next target position, a plurality of non-measurement sections in the non-measurement section Extrapolation error information related to the extrapolation position closest to the end of the measurement section among the extrapolation positions is calculated,
Thereafter, by applying a change rate smaller than the change rate sequentially, extrapolation error information at an extrapolation position after the next extrapolation position of the extrapolation position is calculated,
A correction information calculation method for calculating correction information for the measurement section and the non-measurement section based on the measurement error information and the extrapolation error information.   Correction information at an arbitrary position in the measurement section and the non-measurement section is obtained by interpolating the measurement error information and the extrapolation error information with a predetermined interpolation formula using a Sinc function and a Hanning window function. The correction information calculation method according to claim 5. A method for controlling a movable stage having a mirror for optically measuring the position of the movable stage,
Correction information is obtained using the correction information calculation method according to any one of claims 1 to 6,
A method for controlling a movable stage, wherein the movement of the movable stage is controlled while being corrected using the correction information. An exposure apparatus that sequentially exposes and transfers a pattern of the mask onto the substrate while moving the mask and the substrate synchronously,
A mask stage for moving the mask;
A substrate stage for moving the substrate;
A control device that controls at least one of the mask stage and the substrate stage as the movable stage using the movable stage control method according to claim 7;
An exposure apparatus comprising:

Images