Displacement correction apparatus, exposure system, exposure method and a computer program product

An exposure system includes, (a) an exposure apparatus, and (b) a displacement correction apparatus having a curvature information storage unit configured to store curvature information of a reticle; a displacement information calculation unit configured to calculate displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curvature information; and a correction information calculation unit configured to calculate correction information for correcting a projection lens of the exposure apparatus based on the displacement.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority from the prior Japanese Patent Applications No. P2003-089376, filed on Mar. 27, 2003; the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to technology for correcting displacement of a reticle (mask) used in lithography process. More specifically, the invention relates to a displacement correction apparatus, an exposure system, an exposure method and a displacement correction program.

2. Description of the Related Art

In a manufacturing process of semiconductors such as LSIs, lithography processes are performed a plurality of times. In general, in the lithography processes, reduction projection exposure is performed stepwise on a semiconductor wafer with an exposure apparatus, such as an aligner or a stepper using a reticle. In an inspection process after manufacturing of reticles, the absolute position of the shape and pattern of a reticle is measured so as to be standardized, and then the reticles are inspected.

However, the reticle is slightly curved in the XYZ directions. Therefore, when the curved reticle is fixed (adsorbed) on a reticle stage of the stepper by use of a vacuum chuck or the like, displacement is generated due to curvature of elements of the reticle. This displacement behaves like curved elements of a projection lens of the stepper.

Conventionally, in the inspection process after the manufacturing of reticles, the absolute position of a curved reticle, that is, a reticle in which the curved elements occur, has been measured. Therefore, secondary distortion, which occurs when the reticle with the curved elements is fixed on the reticle stage, has not been taken into consideration. Hence, especially in an exposure process where a plurality of reticles is used, errors remain attributable to the displacement of the reticles fixed on the reticle stage, thus manufacturing yield is reduced.

SUMMARY OF THE INVENTION

A feature of the present invention inheres in a displacement correction apparatus including (a) a curvature information storage unit configured to store curvature information of a reticle; (b) a displacement information calculation unit configured to calculate displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curvature information; and (c) a correction information calculation unit configured to calculate correction information for correcting a projection lens of the exposure apparatus based on the displacement.

Another feature of the present invention inheres in an exposure system including (a) an exposure apparatus, and (b) a displacement correction apparatus having a curvature information storage unit configured to store curvature information of a reticle; a displacement information calculation unit configured to calculate displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus based on the curvature information; and a correction information calculation unit configured to calculate correction information for correcting a projection lens of the exposure apparatus based on the displacement.

An additional feature of the present invention inheres in an exposure method including (a) measuring curvature information of a reticle; (b) calculating displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus, using the curvature information; (c) calculating correction information for correcting projection lens of the exposure apparatus, using the displacement; (d) correcting the projection lens by using the correction information; and (e) exposing the reticle fixed on the reticle stage to a wafer, using the projection lens corrected.

A further feature of the present invention inheres in a computer program product for executing an application of an exposure system, the computer program product providing (a) instructions for reading curvature information of a reticle from a curvature information storage unit; (b) instructions for calculating displacement generated in the reticle being fixed on a reticle stage of an exposure apparatus, based on the curvature information; (c) instructions for calculating correction information for correcting a projection lens of the exposure apparatus, using the displacement; and (d) instructions for storing the correction information in a correction information storage unit.

DETAILED DESCRIPTION OF THE INVENTION

FIRST EMBODIMENT

An exposure system100according to a first embodiment of the present invention includes a displacement correction apparatus1and an exposure apparatus (aligner or stepper)4as shown inFIG. 1. The displacement correction apparatus1includes a central processing unit (CPU)10, a curvature information measurement device3, a curvature information storage unit8, a correction information storage unit9, a main memory15, an auxiliary memory16, a program storage unit17, an input unit18, and an output unit19.

The curvature information measurement device3measures curvature information of a reticle5indicated by the solid line inFIG. 2and by the dashed line inFIG. 3. As schematically exaggerated inFIG. 2, the reticle5indicated by the solid line has small curvature elements relative to an ideal plane. As schematically, and exaggeratingly, shown inFIG. 3, the curved reticle5indicated by the dashed line is fixed on a reticle stage55of the exposure apparatus4shown inFIG. 1by use of a vacuum chuck or the like such that a surface with a pattern, an illustration of which is omitted, faces downwardly. At this time, a point P1, the position coordinates of which are (xrm, yrm, zrm), on the surface of the curved reticle5that is indicated by the dashed line moves to a point P2, the position coordinates of which are (xrm-dx, yrm-dy, zrm-dz), on the surface of the reticle5when the reticle5is fixedly positioned on the reticle stage55as indicated by the solid line. Accordingly, small displacement (dx, dy, dz) is generated.

At a plurality of arbitrary points (six or more points) on the surface of the curved reticle5, shown inFIG. 3as indicated by the dashed line, which are defined by the coordinate system of the reticle stage55, the curvature information measurement device3measures, for each point, a height (first height) zrmfrom the surface of the reticle5to an arbitrary first reference plane6defined by the coordinate system of the reticle stage55. Here, as the “reference plane,” a surface of an ideal flat plate (ideal plane). set for the reticle is selected. For example, as the ideal plane, it is possible to select a surface of an unillustrated Newton gauge with a radius of curvature of about 20 to 270 mm or more, a flatness of about 30 nm or less (three Newton rings or less), and a surface accuracy of about λ/20 to λ/10 where λ is a wavelength of light from a light source of the curvature information measurement device3. If the upper surface of the reticle stage55can be actually selected as the ideal plane, the upper surface of the reticle stage55can be used as the first reference plane6. Consequently, the following are obtained as the “curvature information” on the curved reticle5: a plurality of the first heights zrmfrom the surface of the reticle5to the first reference plane6; and position coordinates (xrm, yrm) on the surface of the reticle5at which the respective first heights zrmare measured. The curvature information is stored in the curvature information storage unit8. Note that the arbitrary points being measured by the curvature information measurement device3are determined based on an instruction input from the input unit18, the type of curvature information measurement device3, and the like. A laser interferometer, a microsensor or the like can be used as the curvature information measurement device3.

The CPU10shown inFIG. 1includes a curvature information measurement control module11, a displacement information calculation unit12, a correction information calculation unit13, a correction control module14and an exposure control module14a.The curvature information measurement control module11outputs an instruction for the curvature information measurement device3to measure the curvature information of the curved reticle5shown inFIGS. 2 and 3and an instruction to store the measurement results in the curvature information storage unit8.

The displacement information calculation unit12shown inFIG. 1includes a first insertion module12a,a shape simulation module12band a first displacement information calculation module12c.The first insertion module12areads the curvature information on the curved reticle5and inserts coefficients a1into f1of a curved surface approximating polynomial (1) below, e.g. the quadratic polynomial below, of the curved reticle5, as follows: the position coordinates (xrm, yrm) on the surface of the reticle5at which the first heights zrmare measured are substituted for x, y of each term in the right-hand side of the curved surface approximating polynomial (1); and the first heights zrmat the respective arbitrary points corresponding to the respective position coordinates (xrm, yrm) are substituted for z in the left-hand side thereof.
z=a1x2+b1y2+c1xy+d1x+e1y+f1(1)

Note that, since there are six unknowns a1to f1in the curved surface approximating polynomial (1), it is sufficient if six or more arbitrary points for measurement on the surface of the reticle5are selected upon measuring the curvature information of the curved reticle5. Moreover, apart from the quadratic polynomial shown as the curved surface approximating polynomial (1) of the curved reticle5, an n-th degree polynomial (n≧3) can be used. When an n-th degree polynomial is used, it is sufficient if the first heights zrmare measured at a number of points equal to or more than the number of unknowns that are coefficients of respective terms of the n-th degree polynomial.

The shape simulation module12bsimulates the shape of the surface of the curved reticle5in the following manner: position coordinates (xfr, yfr) of a plurality of arbitrary points in the entire area of the reticle stage55(for example, 25 mm in the X direction×33 mm in the Y direction) are substituted in the curved surface approximating polynomial (1) where the coefficients a1to f1have been inserted; and first heights zfrare calculated. Here, using the position coordinates (xfr, yfr) of the arbitrary points on the surface of the curved reticle5and the first heights zfrat the arbitrary points, a three-dimensional shape of the surface can be simulated as shown inFIG. 4. InFIG. 4, the X axis shows positions of the curved surface in the slit direction, which are defined on the reticle stage55, the Y axis shows positions in the scanning direction, and the Z axis shows positions in the focusing direction. Note that, for the position coordinates of the arbitrary points to be substituted in the curved surface approximating polynomial (1) of the reticle5by the shape simulation module12b,the position coordinates (xrm, yrm) on the surface of the reticle5, which have been measured by the curvature information measurement device3, may be used in common, or different coordinates from the position coordinates (xrm, yrm) may be used.

The first displacement information calculation module12cshown inFIG. 1calculates, based on the position coordinates (xfr, yfr) of the arbitrary points obtained by the shape simulation module12band the first heights zfrat the arbitrary points, displacement (dx, dy) which is generated as shown inFIG. 3because the curvature originally observed on the curved reticle5is flattened. Here, the curvature is flattened when the curved reticle5is fixed on the reticle stage55by use of a vacuum chuck or the like to be forcibly flattened. The first displacement information calculation module12cmay calculate the displacement (dx, dy) based on the actually measured first heights zrmand the position coordinates (xrm, yrm) on the surface of the reticle5at which the first heights zrmare measured, instead of the position coordinates (xfr, yfr) of the arbitrary points obtained by the shape simulation module12band the first heights zfrat the arbitrary points.

Herein, a description will be given of an example of a method of calculating, by the first displacement information calculation module12c,the displacement (dx, dy) between two arbitrary points M1and M2shown inFIGS. 4 and 5. InFIG. 5, an arc M1M2shows a part of the shape of the curved surface of the curved reticle5, and a line segment M1M2shows a part of the shape of the surface of the reticle5which is fixed on the reticle stage55and forcibly flattened.

(a) First, arbitrary coordinate values of a central point O are selected. For example, the curved surface approximating polynomial (1) of the reticle5where the coefficients a1to f1have been inserted is partially differentiated by x, y. Then, a position coordinate x1in the X direction of the arbitrary point M1is substituted in the curved surface approximating polynomial (1) partially differentiated by x, thereby obtaining a tangent in the X direction. Similarly, a position coordinate y1in the Y direction of the arbitrary point M1is substituted for y in the curved surface approximating polynomial (1) partially differentiated by y, thereby obtaining a tangent in the Y direction. Subsequently, a first normal V1which is perpendicular to a plane including the tangents in the XY directions and passing the arbitrary point M1is obtained. Similarly to the case of the arbitrary point M1, a second normal V2is obtained for the arbitrary point M2. A point with coordinate values of (x0, y0, z0) where the first and second normals V1and V2intersect with each other may be set as the central point O shown inFIG. 5. The central point O is a point to be the center of a circle including the arc M1M2as a part of the circular arc thereof.

(b) Next, a radius of curvature R defined by the lengths of line segments OM1and OM2is obtained from the coordinate values (x0, y0, z0) of the central point O, the coordinate values (x1, y1, z1) of the arbitrary point M1, and the coordinate values (x2, y2, z2) of the arbitrary point M2. In addition, coordinate values (x4, y4, z4) of a point T, the intersection point of a perpendicular from the arbitrary point M1on the line segment OM2, are obtained. Using a length h of a line segment M1T and the radius of curvature R, a curvature angle θ between the line segments OM1and OM2is obtained by a trigonometric function. A length L of an arc between the two arbitrary points M1and M2is calculated using the radius of curvature R and the curvature angle θ. Here, if the curvature is extremely small, it can be determined that the curvature angle θ is small. Therefore, the length L of the arc between the two arbitrary points M1and M2can be approximated by L=Rθ.

(c) Thereafter, a length L-u, a difference between the length L of the arc between the two arbitrary points M1and M2and a length u of the line segment between the two arbitrary points M1and M2, is calculated. As shown inFIG. 6where the horizontal axis shows the slit positions and the vertical axis shows the scan positions, the length L-u of the difference is resolved into elements in the X and Y directions using the position coordinates (x1, y1), (x2, y2) of the two arbitrary points M1and M2. The length L-u is thus calculated as the displacement (dx, dy) in the XY directions that are generated, relative to the point M1or M2on the surface of the curved reticle5, when the curved reticle5is fixed on the reticle stage55and forcibly flattened. Similarly, the displacement (dx, dy) as shown inFIG. 6are calculated for each two points among the plurality of arbitrary points.

Note that, althoughFIG. 6shows a case where the displacement (dx, dy) are generated at the arbitrary point M1side, it can be assumed that the displacement (dx, dy) are generated at the arbitrary point M2side. Alternatively, it can be assumed that the displacement (dx, dy) are generated at both of the two arbitrary points M1and M2with half values for each point. In this way, the displacement (dx, dy) can be appropriately set.

The correction information calculation unit13shown inFIG. 1includes a coefficient calculation module13aand a correction information calculation module13b.The coefficient calculation module13areads the calculated displacement (dx, dy) and calculates coefficients k1to k20of a first displacement correction polynomial (2) and a second displacement correction polynomial (3) intersecting at a right angle with dx, which are the below identified cubic polynomials for correcting a projection lens54. The position coordinates of one of the two arbitrary points are substituted for x, y of each term in the respective right-hand sides of the first and second displacement correction polynomials (2) and (3), and displacement (dx, dy) between the two arbitrary points are substituted for dx, dy in the respective left-hand sides thereof.
dx=k1+xk3+yk5+x2k7+xyk9+y2k11+x3k13+x2yk15+xy2k17+y3k19(2)
dy=k2+yk4+xk6+y2k8+xyk10+x2k12+y3k14+xy2k16+x2yk18+x3k20(3)

Here, the coefficients k1to k20are parameters to show distortion (displacement) elements in the projection lens54, a wafer and the reticle stage55. The position coordinates to be substituted for x, y of each term in the right-hand sides may be, for example, appropriately selected mean values of the position coordinates of the two arbitrary points.

The correction information calculation module13bshown inFIG. 1calculates correction information on the projection lens54of the exposure apparatus4shown inFIG. 7using the curved surface approximating polynomial (1) or the coefficients k1to k20of the first and second displacement correction polynomials (2) and (3), and stores the correction information in the correction information storage unit9. The correction information for the projection lens54includes a driving position of the projection lens54, a driving force thereof, and the like. As shown inFIG. 7, the exposure apparatus4includes a light source51for irradiating exposure light; an illumination system including a condenser lens52; the reticle stage55on which the reticle5is fixed; a projection optics system including the projection lens54made up of a plurality of lenses; and a substrate stage57on which a wafer56is fixed. A correction unit53for correcting the driving force and driving position of the projection lens54is connected to the projection lens54.

The correction control module14shown inFIG. 1outputs an instruction for the correction unit53of the exposure apparatus4shown inFIG. 7to correct the driving force and driving position of the projection lens54, using the correction information calculated by the correction information calculation module13b.The exposure control module14aoutputs an instruction to drive the exposure apparatus4to provide on exposure. The exposure apparatus4then irradiates exposure light from the light source51, and, through the condenser lens52, the reticle5fixed on the reticle stage55, and the projection lens54corrected by the correction unit53, transfers a pattern of the reticle5to the wafer56fixed on the substrate stage57. At this time, since the driving force and driving position of the projection lens54have been corrected, the pattern of the reticle5can be transferred to the wafer56without errors such as deviation of the transferred pattern attributable to the displacement of the reticle5.

The curvature information storage unit8shown inFIG. 1stores the curvature information measured by the curvature information measurement device3. The correction information storage unit9stores the correction information calculated by the correction information calculation module13b.The main memory15stores results calculated by the CPU10stepwise. The stored results are read from the main memory15when required. A hard disk, which can store various kinds of information such as QC information of the reticle5, can be used as an auxiliary memory16.

The program storage unit17stores a displacement correction program for executing applications on the displacement correction apparatus1. The displacement correction program includes an instruction to read the curvature information of the curved reticle5stored in the curvature information storage unit8; an instruction to calculate the displacement (dx, dy) generated in fixing of the reticle5on the reticle stage55of the exposure apparatus4by use of the curvature information of the curved reticle; an instruction to calculate the correction information for correcting the projection lens54of the exposure apparatus4, using the displacement (dx, dy); an instruction to store the correction information in the correction information storage unit9; and the like. The displacement correction program is executed by the CPU10. As the input unit18, for example, a keyboard, a mouse, a voice device, or the like can be used. The output unit19may be such as a liquid crystal display (LCD), a CRT display, a printer, or the like.

A description will be given of an example of an exposure method according to the first embodiment of the present invention referring toFIGS. 1 to 8. Note that results calculated in the respective following steps are stored stepwise in the main memory15shown inFIG. 1, and read as needed.

(a) In step S110ofFIG. 8, the curvature information measurement control module11shown inFIG. 1controls the curvature information measurement device3to measure first heights zrmsextending from the surface of the curved reticle5to the first reference plane6at a plurality of arbitrary points (six or more points). As a result, the first heights zrmmeasured from the reticle5to the first reference plane6and position coordinates (xrm, yrm) at which the first heights zrmare measured on the surface of the reticle5are obtained as “curvature information”.

(b) In step S121, the first insertion module12areads the curvature information measured by the curvature information measurement device3, and inserts coefficients a1to f1into the curved surface approximating polynomial (1) of the reticle5by substituting the first heights zrmand the position coordinates (xrm, yrm) on the surface of the reticle5, for which first heights zrmhave been measured for the curved surface approximating polynomial (1) of the reticle5.

(c) In step S122, the shape simulation module12bsimulates the surface shape of the reticle5by calculating first heights zfrcorresponding to the position coordinates (xfr, yfr) at a plurality of arbitrary points in a range of the reticle stage55using the curved surface approximating polynomial (1) of the reticle5to which the coefficients a1to f1have been inserted.

(d) In step S123, the first displacement information calculation module12ccalculates displacement (dx, dy) generated due to the originally observed curvature on the reticle5is being flattened when the curved reticle5is fixed on the reticle stage55, using of the curved surface approximating polynomial (1) of the reticle5to which the coefficients a1to f1have been inserted.

(e) In step S131, the coefficient calculation module13areads the displacement (dx, dy) calculated by the first displacement information calculation module12c,and calculates coefficients k1to k20of the first and second displacement correction polynomials (2) and (3) of the projection lens54by substituting one of position coordinates (x1, y1) and (x2, y2) at respective arbitrary points, and displacement (dx, dy) between each arbitrary points in the first and second displacement correction polynomials (2) and (3).

(f) In step S132, the correction information calculation module13bcalculates correction information of the projection lens54shown inFIGS. 1 and 7, using the coefficients k1to k20of the first and second displacement correction polynomials (2) and (3) calculated by the coefficient calculation module13a,QC information of the reticle5stored in the auxiliary memory16and the like. The correction information of the projection lens54is stored in the correction information storage unit9.

(g) In step S140, the correction control module14controls the correction unit53showed inFIG. 7to correct a driving force and a driving position of the projection lens54, using of the correction information. As a result, errors attributable to the displacement (dx, dy) of the reticle5are corrected.

(h) In step S150, the exposure control module14adrives the exposure apparatus4shown inFIG. 7to irradiate exposure light from the light source51with the corrected projection lens54, and a pattern of the flattened reticle5is transferred to the wafer56on the wafer stage57. At this time, since errors attributable to the displacement of the reticle5have been corrected, exposing can be performed without errors such as a deviation of the transferred pattern attributable to the displacement of the reticle5. The steps of the exposure method according to the first embodiment of the present invention are not limited to the above-described steps S110to S150.

According to the first embodiment of the present invention, the displacement (dx, dy) attributable to the curvature of the reticle5, generated when the curvature is fixed on the reticle stage55and flattened, can be predicted prior to an exposure process. Therefore, errors due to displacement (dx, dy) of the reticle5can be corrected, and manufacturing yield can be improved.

SECOND EMBODIMENT

An exposure system100aaccording to a second embodiment of the present invention includes a displacement correction apparatus1aand an exposure apparatus (aligner or stepper)4as shown inFIG. 9. A description will be given of a system, as the exposure system100aaccording to the second embodiment of the present invention, where flatness information of the reticle stage55is taken into consideration in addition to the curvature information of the reticle5.

As schematically enhanced inFIG. 10, a surface of the reticle stage55is actually slightly inclined relative to an ideal plane and has an unevenness. When the curved reticle5as indicated by the dashed line is fixed on the actual surface of the reticle stage55so as to be adhered thereto, a point P on the reticle5at coordinate positions (xrm, yrm, zrm) moves to coordinate positions (xrm-d′x, yrm-d′y, zrm-d′z) such that the reticle5is adhered to the actual surface of the reticle stage55. In other words, displacement (d′x, d′y, d′z) is shifted from the displacement (dx, dy, dz) shown inFIG. 3by the unevenness and inclination of the surface of the reticle stage55relative to the ideal plane. Here, the displacement (d′x, d′y, d′z) is generated when the shape of the curved reticle5is adhered to the reticle stage55having an uneven and inclined surface. Moreover, the displacement (dx, dy, dz) is generated when the original curvature of the reticle5is flattened. In the above case, the displacement (d′x, d′y) in the XY directions is extremely small. Therefore, the displacement d′z in the height direction at the coordinate positions (xrm, yrm) can be approximated to a deviation of an amount of height change at the coordinate positions (xrm, yrm), from the surface of the flat reticle5to a height (second height) zsmof the actual uneven and inclined surface of the reticle stage55by the addition of a height change from the surface of the curved reticle5, as indicated by the dashed line, to the height (first height) zrmof the surface of the flat reticle5.

The displacement correction apparatus la shown inFIG. 9includes a CPU10a,a curvature information measurement device3, a flatness information measurement device7, a curvature information storage unit8, a flatness information storage unit8a,a correction information storage unit9, a main memory15, an auxiliary memory16, a program storage unit17a,an input unit18and an output unit19, all of which are connected to the CPU10a.

The flatness information measurement device7measures, at a plurality of arbitrary points, the heights (second height) zsmfrom the actual surface of the reticle stage55used in the exposure apparatus4to a second reference plane6set for the reticle stage55. A laser interferometer or the like can be used as the flatness information measurement device7. As the second reference plane6set for the reticle stage55, as shown inFIG. 10, the ideal plane which is the first reference plane6set for the reticle5, can be selected. The respective second heights zsmof the plurality of arbitrary points measured by a flatness information measurement module11x,and the respective position coordinates (xrm, yrm) on the surface of the reticle stage55at which the second heights zsmare measured, are obtained as the “flatness information.” The flatness information is stored in the flatness information storage unit8a.

The CPU10ais different from the CPU10shown inFIG. 1in that the CPU10afurther includes the flatness information measurement module11xand a displacement information calculation unit12x.The flatness information measurement module11xoutputs an instruction for the flatness information measurement device7to measure the flatness information of the reticle stage55, and to store the flatness information in the flatness information storage unit8a.

The displacement information calculation unit12xincludes a first insertion module12a,a shape simulation module12b,a third insertion module12d,a height calculation module12e,a second insertion module12f,and a second displacement information calculation module12g.The first insertion module12areads the curvature information of the curved reticle5. Then, using the first heights zrmfrom the surface of the curved reticle5to the first reference plane6and the position coordinates (xrm, yrm) on the surface of the reticle5at which the first heights zrmare measured, the first insertion module12ainserts the coefficients a1to f1into the curved surface approximating polynomial (1).

The third insertion module12dreads the flatness information on the reticle stage55. Then, the third insertion module12dsubstitutes the second heights zsm, which are measured relative to the second reference plane6, and the position coordinates (xrm, yrm), which are on the surface of the reticle stage55and at which the second heights zsmare measured, in the following quadratic polynomial, a curved surface approximating polynomial (4) of the reticle stage55. In this way, coefficients a2to f2of the curved surface approximating polynomial (4) of the reticle stage55are inserted.
z=a2x2+b2y2+c2xy+d2x+e2y+f2(4)

The shape simulation module12bsimulates the shape of the surface of the curved reticle5by substituting position coordinates (xfr, yfr) of a plurality of arbitrary points in the curved surface approximating polynomial (1) where the coefficients a1to f1have been inserted, and calculating first heights zfrfrom the surface of the curved reticle5to the first reference plane6. Moreover, the shape simulation module12bsimulates the shape of the actual surface of the reticle stage55by substituting the position coordinates (xfr, yfr) of the plurality of arbitrary points in the curved surface approximating polynomial (4) of the reticle stage55where the coefficients a2to f2have been inserted, and calculating second heights zsffrom the surface of the reticle stage55to the second reference plane6.

The height calculation module12ereads the first and second heights zfrand zsfobtained by the shape simulation module12b,and calculates third heights zrsf, each obtained by subtracting the second height zsffrom the first height zfrat the same position coordinates (xfr, yfr). Moreover, the height calculation module12ecan calculate, by reading the curvature information on the curved reticle5measured relative to the first reference plane6and the flatness information on the reticle stage55measured relative to the second reference plane6, the third heights zrsm, each obtained by subtracting the second height zsmfrom the first height zrm, measured at the same position coordinates (xrm, yrm). The calculation may be simplified if the first and second reference planes6are the identical ideal plane.

The second insertion module12fsubstitutes the position coordinates (xrm, yrm) of the arbitrary points in the right-hand side of the following curved surface approximating polynomial (5) of the reticle5where the flatness of the reticle stage55is considered. Then, the second insertion module12fsubstitutes the third heights zsmat the arbitrary points in the left-hand side thereof, thereby inserting coefficients a3to f3into the curved surface approximating polynomial (5) when the flatness of the reticle stage55is considered.
z=a3x2+b3y2+c3xy+d3x+e3y+f3(5)

Note that the second insertion module12fcan insert, by use of the third heights zrsmobtained by subtracting the measured second heights zsmfrom the measured first heights zrmand by the common position coordinates (xrm, yrm) at which the first and second heights zrmand zsmare measured, the coefficients a3to f3of the curved surface approximating polynomial (5) of the reticle5where the flatness of the reticle stage55is considered.

The first displacement information calculation module12ccalculates the displacement (d′x, d′y) in the XY directions, using the curved surface approximating polynomial (5) where the coefficients a3to f3have been inserted and the flatness of the reticle stage55is considered. The displacement (d′x, d′y) is generated because the shape of the curvature which the reticle5originally had is changed by being adhered to the reticle stage55when the reticle5is fixed on the reticle stage55so as to be adhered to the actual surface of the reticle stage55.

The flatness information storage unit8astores the flatness information measured by the flatness information measurement device7. The program storage unit17astores a displacement correction program for executing applications on the displacement correction apparatus1a.The displacement correction program includes an instruction to read the flatness information of the reticle stage55stored in the flatness information storage unit8a;an instruction to calculate the third heights zrsf;, and the like. Since another part of the exposure system100ais substantially the same as the displacement correction apparatus1shown inFIG. 1, repeated explanation is omitted.

A description will be given of an exposure method according to the second embodiment of the present invention referring toFIGS. 9 to 11.

(a) In step S210ofFIG. 11, the curvature information measurement control module11shown inFIG. 9controls the curvature information measurement device3to measure the curvature information of the curved reticle5. Since step S210is substantially the same as step S110shown inFIG. 8, repeated explanation is omitted. As shown inFIG. 10, the flatness information measurement control module11xcontrols the flatness information measurement device7to measure the position coordinates (xrm, yrm) at a plurality of arbitrary points (six or more points) and second heights zsmfrom the surface of the reticle stage55to the second reference plane6at the arbitrary points, as the flatness information.

(b) In step S221, the first insertion module12areads the curvature information of the curved reticle5in step S210, and inserts the coefficients a1to f1by substituting the first heights zrmmeasured relative to the first reference plane6and the position coordinates (xrm, yrm) on the surface of the reticle5at which the first heights zrmare measured in the curved surface approximating polynomial (1). In addition, the third insertion module12dinserts the coefficients a2to f2into the curved surface approximating polynomial of (4) of the reticle stage55by substituting the second heights zsmand the position coordinates (xrm, yrm) on the surface of the reticle stage55at which the second heights zsmare measured in the curved surface approximating polynomial (4), by use of the flatness information of the reticle stage55measured in step S210.

(c) In step S222, the shape simulation module12bcalculates first heights zfrby substituting the position coordinates (xfr,yfr) at a plurality of arbitrary points for the curved surface approximating polynomial (1) in which the coefficients a1to f1have been inserted. Then, the shape simulation module12bsimulates the surface shape curvature of the reticle5. Furthermore, the shape simulation module12bcalculates the second heights zsfby substituting the position coordinates (xfr,yfr) at a plurality of arbitrary points for the curved surface approximating polynomial (4) in which the coefficients a2to f2are inserted. Then, the shape simulation module12bsimulates the actual shape of the surface of the reticle stage55.

(d) In step S223, the third height calculation module12ecalculates third heights zrsf, which are obtained by subtracting the second heights zsffrom the first heights zrsat arbitrary points of the same position coordinates respectively calculated in step S222. In addition, the third height calculation module12ecan calculate third heights zrsmby subtracting the second heights zsmfrom the first heights zrmat the same position coordinates measured in step S210.

(e) In step S224, the second insertion module12finserts the coefficients a3to f3corresponding to the reticle5by substituting the position coordinates (xfr,yfr) corresponding to the third heights zrsfcalculated in step S222for the curved surface approximating polynomial (5) of the reticle5when the flatness of the reticle stage55is considered. Note that in step S224, the first insertion module12amay insert the coefficients a3to f3by substituting the position coordinates (xfr, yfr) corresponding to the measured third heights zrsfby subtracting the second height zsmfrom the first heights zrmwhich are calculated in step S210for the curved surface approximating polynomial (5) of the reticle5, in which the flatness of the reticle stage55is taken into account.

(f) In step S225, the second displacement information calculation module12gcalculates the displacement (d′x, d′y) between a plurality of arbitrary points on the originally curved reticle5when the reticle5is fixedly adhered on the reticle stage55, using the curved surface approximating polynomial (5) of the reticle5with the flatness of the reticle stage55taken into consideration in which the coefficients a3to f3have been inserted. The method for calculating the displacement (d′x, d′y) by the second displacement information calculation module12gis similar to the method for calculating the displacement (dx, dy) in step S123shown inFIG. 8. Thus, repeating the explanation is omitted.

(g) In step S231, the coefficient calculation module13acalculates the coefficients k1to k20of the first and second displacement correction polynomials (2) and (3), the same as step S131shown ofFIG. 8. In addition, in step S232, the correction information is calculated by the correction information calculation module13b,the same as step S132shown ofFIG. 8, and the result is stored in the correction information storage unit9. Since steps S240and S250are substantially the same as steps S140and S150shown inFIG. 8, repeating the explanation is omitted.

The exposure method according to the second embodiment of the present invention is not limited to the steps S210to S250. Various types of processes may be provided as the exposure method according to the second embodiment of the present invention.

According to the second embodiment of the present invention, errors attributable to the displacement of the reticle5can be corrected, and thereby manufacturing yield can be improved, the same as in the first embodiment. Furthermore, since calculating displacement (d′x, d′y) based on the flatness information of the reticle stage55in addition to the curvature information of the reticle5, errors attributable to the displacement of the reticle5, taking the flatness of the reticle stage55into consideration, can be corrected.

THIRD EMBODIMENT

As shown inFIG. 12, an exposure system100caccording to the third embodiment of the present invention includes a displacement correction apparatus1cand two exposure apparatuses4and4a.In the third embodiment of the present invention, a description will be given of the case of performing mix and match exposure. In mix and match exposure, the reticle5is fixed on the reticle stage55of the exposure apparatus4shown inFIG. 7, and the fixed reticle5is exposed (first exposure) to a wafer56. Then, the reticle5ais fixed on the reticle stage55aof the exposure apparatus4ashown inFIG. 12, and the fixed reticle5ais exposed (second exposure) to the wafer56.

The displacement correction apparatus1cincludes a CPU10c,a curvature information measurement device3, a flatness information measurement device7, a curvature information storage unit8, a flatness information storage unit8a,a correction information storage unit9, a main memory15, an auxiliary memory16, a program storage unit17c,an input unit18, an output unit19and a communication control unit20. The CPU10cincludes a curvature information measurement control module11, a flatness information measurement control module11x,a displacement information calculation unit12x,a correction information calculation unit13x,a correction control module14and an exposure control module14a.

The curvature information measurement control module11outputs an instruction for the curvature information measurement device3to measure curvature information of the curved reticle5used by the exposure apparatus4, and the curvature information of the curved reticle5aused by the exposure apparatus4a;and an instruction to store the curvature information in the curvature information storage unit8. The flatness information measurement control module11xoutputs an instruction for the flatness information measurement device7to measure flatness information of the reticle stage55of the exposure apparatus4, and flatness information of the reticle stage55aof the exposure apparatus4a;and an instruction to store the flatness information in the flatness information storage unit8a.The displacement information calculation unit12xalso calculates displacement (d′x, d′y) due to curvature which the reticle5originally had and which is changed when the reticle5ais fixedly adhered to the reticle stage55a,in addition to the displacement (d′x, d′y) of the reticle5.

The correction information calculation unit13xfurther includes a different value calculation module13cin addition to a coefficient calculation module13aand a correction information calculation module13b.The coefficient calculation module13acalculates coefficients k1to k20of the first and second displacement correction polynomials (2) and (3) by substituting the displacement (d′x,d′y) of the reticle5calculated by the displacement information calculation unit12xfor the first and second displacement correction polynomials (2) and (3). Furthermore, the coefficient calculation module13acalculates coefficients k′1to k′20with the third displacement correction polynomial (6) and a fourth displacement correction polynomial (7) intersecting at a right angle to dx, using the displacement (d′x, d′y) of the reticle5acalculated by the displacement information calculation unit12x.The calculation by using position coordinates of one of each two arbitrary points for x, y of each term in the respective right-hand side of the third and fourth displacement correction polynomials (6) and (7) being substituted for correcting the projection lens54a;and displacement (dx, dy) of the one of the arbitrary points is substituted for left-hand side of the third and fourth displacement correction polynomials (6) and (7).
dx=k′1+xk′3+yk′5+x2k′7+xyk′9+y2k′11+x3k′13+x2yk′15+xy2k′17+y3k′19(6)
dy=k′2+yk′4+xk′6+y2k′8+xyk′10+x2k′12+y3k′14+xy2k′16+x2yk′18+x3k′19(7)

The correction control module14outputs an instruction for the correction unit53of the exposure apparatus4ato correct a driving force and a driving position of the projection lens54a.The exposure control module14acontrols the exposure apparatus4to expose a pattern of the reticle5with the projection lens54. Then, the exposure control module14acontrols the exposure apparatus4ato expose a pattern of the reticle5awith the projection lens54a.

The program storage unit17cstores a displacement correction program for executing applications on the displacement correction apparatus1c.The displacement correction program includes as an instruction to calculate the different values k1–k′1, k2–k′2, . . . , k20–k′20. Since another part of the exposure system100cis substantially the same as the exposure system100ashown inFIG. 9, a repeated explanation is omitted.

A description will be given of an example of an exposure method according to the third embodiment of the present invention referring toFIGS. 12 and 13.

(a) In step S310ofFIG. 13, the curvature information measurement control module11shown inFIG. 12controls the curvature information measurement device3to measure curvature information of the curved reticles5and5a.In addition, the flatness information measurement control module11xcontrols the flatness information measurement device7to measure flatness information of the reticle stages55and55a.

(c) In step S331, the coefficient calculation module13acalculates coefficients k1. . . k20of the first and second displacement correction polynomials (2) and (3) respectively, using the displacement (d′x, d′y) of the reticle5calculated in step S325. Furthermore, the coefficient calculation module13acalculates coefficients k′1to k′20of the third and fourth displacement correction polynomials (6) and (7), using the calculated displacement (d′x, d′y) of the reticle5a.

(d) In step S332, the different value calculation module13creads coefficients k1to k20of the first and second displacement correction polynomials (2) and (3), and coefficients k′1to k′20of the third and fourth displacement correction polynomials (6) and (7) calculated in step S331, and calculates the different values k1–k′1, k2–k′2, . . . , k20–k′20.

(e) In step S333, the correction information calculation module13bcalculates the correction information for correcting the projection lens54aof the exposure apparatus4ausing the different values k1–k′1, k2–k′2, . . . , k20–k′20calculated in step S332, and QC information of the reticle5stored in the auxiliary memory16. The correction information calculated is stored in the correction information storage unit9.

(f) In step S340, the correction control module14controls the correction unit53ato correct a driving position and a driving force of the projection lens54of the exposure apparatus4a,using the correction information of the projection lens54acalculated in step S333.

(g) In step S350, the exposure control module14adrives the exposure apparatus4shown inFIG. 7to firstly expose of a pattern of the reticle5fixed on the reticle stage55to the wafer56with the projection lens54. Then, the exposure control module14adrives the exposure apparatus4ato secondary expose of a pattern of the reticle5afixed on the reticle stage55ato the wafer56with the projection lens54acorrected. Since the projection lens54ahas been corrected, the pattern of the reticles5and5acan be transferred without errors attributable to curvature of the reticles5and5a.

According to the third embodiment of the present invention, errors attributable to the displacement (d′x, d′y) generated when the reticles5and5aare fixed on the reticle stages55and55acan be corrected before exposure with the exposure apparatus4a,also when performing mix and match exposure using two exposures4and4aand the reticles5and5afixed on the reticle stages55and55a.Therefore, manufacturing yield can be improved.

FOURTH EMBODIMENT

Instead of the bundle exposure system described in the first to third embodiments, plural apparatuses located a distant location from each other may cooperate through a communication network. As shown inFIG. 14, an exposure system100eaccording to the fourth embodiment includes a centrally located displacement correction apparatus1e,a displacement correction apparatus2alocated at a first factory, a displacement correction apparatus2blocated at a second factory side, a displacement correction apparatus2clocated at a third factory side . . . , and a displacement correction apparatus2nlocated at a n-th factory. The displacement correction apparatus1eand the displacement correction apparatuses2ato2ncan connect each other through a communication network2. As the communication network2, the Internet or an intranet can be used.

As shown inFIG. 15, the displacement correction apparatus2alocated at the first factory includes a CPU10f,a curvature information measurement device3, a flatness information measurement device7, a curvature information storage unit8, a flatness information storage unit8a,a main memory15, a program storage unit17f,an input unit18, an output unit19and a communication control unit20. An exposure apparatus4is connected to the displacement correction apparatus2a.

The CPU10fincludes a curvature information measurement control unit11, a flatness information measurement control module1x,a curvature information transmission module11a,a flatness information transmission module11b,a correction information receiving module14b,a correction control module14and an exposure control module14a.

The curvature information transmission module11atransmits curvature information of a curved reticle used by the exposure apparatus4to the centrally located displacement correction apparatus1ethrough the communication network2shown inFIG. 14. In addition, the flatness information transmission module11btransmits flatness information of a reticle stage of the exposure apparatus4to the centrally located displacement correction apparatus1ethrough the communication network2. The correction information receiving module14breceives correction information from the displacement correction apparatus1ethrough the communication network2. The communication control unit20controls communication relating to the displacement correction apparatus2athrough the communication network2. The program storage unit17fstores a displacement correction program for executing applications on the displacement correction apparatus2a.The displacement correction program includes an instruction to transmit the curvature information of a curved reticle; an instruction to receive the correction information; and the like. Since the configuration of the displacement correction apparatuses2bto2nlocated at the second to n-th factories is similar to the displacement correction apparatus2a,a repeated explanation is omitted.

As shown inFIG. 16, the centrally located displacement correction apparatus1eshown inFIG. 14includes a CPU10e,a correction information storage unit9, a main memory15, an auxiliary memory16, a program storage unit17e,an input unit18, an output unit19and a communication control unit20. The CPU10eincludes a curvature information receiving module11c,a flatness information receiving module11d,a displacement information calculation unit12x,a correction information calculation unit13x,and the correction information transmission module14c.

The curvature information receiving module11creceives curvature information of a curved reticle from the displacement correction apparatuses2ato2nlocated at the first to n-th factories respectively through the communication network2. The flatness information receiving module11dreceives flatness information of a reticle stage from the displacement correction apparatuses2ato2nlocated at the first to n-th factories respectively through the communication network2.

The displacement information calculation unit12xcalculates displacement information of reticles used in exposure processes in the respective first to n-th factories. The correction information calculation unit13xcalculates correction information for correcting projection lens of exposure apparatus in the first to n-th factories, and stores the correction information to the correction information storage unit9. The correction information transmission module14cfeeds back the correction information of the projection lens to the displacement correction apparatuses2ato2nlocated at the first to n-th factories through the communication network2. The program storage unit17estores a displacement correction program for executing applications on the displacement correction apparatus1e.The displacement correction program includes an instruction to receive the curvature information of the curved reticles; an instruction to receive flatness information of reticle stages, and the like.

A description will be given of an example of an exposure method according to the fourth embodiment of the present invention referring toFIGS. 14 to 16. Here, the description will be given referring to the displacement correction apparatus2ashown inFIG. 15. The displacement correction apparatuses2bto2nare omitted as they perform same as the displacement correction apparatus2a.

(a) Same as the step S210shown inFIG. 11, in the displacement correction apparatus2alocated at the first factory shown inFIG. 15, the curvature information measurement control unit11controls the curvature information measurement device3to measure curvature information of a curved reticle, and to store the curvature information in the curvature information storage unit8. In addition, the flatness information measurement control module11xcontrols the flatness information measurement device7to measure flatness information of a reticle stage, and to store the flatness information in the flatness information storage unit8a.

(b) Thereafter, the curvature information transmission module11atransmits the curvature information of the curved reticle using by the exposure apparatus4to the centrally located displacement correction apparatus1eshown inFIG. 14through the communication network2. In addition, the flatness information transmission module11btransits the flatness information of the reticle stage of the exposure apparatus4to the centrally located displacement correction apparatus1ethrough the communication network2.

(c) Next, in the centrally located displacement correction apparatus1eshown inFIG. 14, the curvature information receiving module11creceives the curvature information of the curved reticles from the displacement correction apparatuses2ato2nlocated at the first to n-th factories through the communication network2. The flatness information receiving module11dreceives the flatness information of reticle stages from the displacement correction apparatuses2ato2nlocated at the first to n-th factories through the communication network2.

(d) Same as the steps S221to S232shown inFIG. 11, the displacement information calculation unit12xcalculates displacement of the reticles used in exposure processes in the first to n-th factories. The correction information calculation unit13xcalculates correction information for correcting projection lens of exposure apparatuses in the first to n-th factories, and stores the correction information to the correction information storage unit9.

(e) Next, the correction information transmission module14cfeeds back the correction information of the projection lens to the displacement correction apparatuses2ato2nlocated at the first to n-th factories through the communication network2shown inFIG. 14. In the displacement correction apparatus2alocated at the first factory shown inFIG. 15, the correction information receiving module14breceives the correction information from the displacement correction apparatus1ethrough the communication network2.

(f) Same as the steps S240to S250shown inFIG. 11, the correction control module14controls a correction unit, omitted from illustration of the exposure apparatus4, to correct driving force and driving position of the projection lens, omitted from illustration. Moreover, the exposure control module14acontrols the exposure apparatus4to perform exposure with the corrected projection lens.

According to the fourth embodiment of the present invention, errors attributable to the displacement generated when the reticle is fixed on the reticle stage in a plurality of factories can be corrected respectively, and manufacturing yield can be improved.

OTHER EMBODHIMENTS

In the above-described first to fourth embodiments, a cubic equation, a biquadratic equation, a fifth or n-th degree polynomial can be used as the curved surface approximating polynomial (1) of the reticle, the curved surface approximating polynomial (4) of the reticle stage, the curved surface approximating polynomial (5) of the reticle taking the reticle stage into consideration, instead of a quadratic polynomial. Furthermore, a fourth, fifth, or n-th degree polynomial can be used as the first to fourth displacement correction polynomials (2) and (3), (6) and (7), instead of a third degree polynomial.

Furthermore, in the fourth embodiment of the present invention, the number of the displacement correction apparatuses2ato2nlocated at the first to n-th factories, and the number of exposure apparatuses in the displacement correction apparatuses2ato2nis not limited. Various factories, such a semiconductor device manufacturer, an exposure apparatus manufacturer, and a reticle manufacturer can be respective factories.

Furthermore, in the first to fourth embodiments of the present invention, steps from measuring steps such as the curvature information of the curved reticle5and the flatness information of the reticle stage55, to exposure by the exposure apparatus4need not to be done in succession. For example, the measured curvature information of the curved reticle may be previously stored in the curvature information storage unit8shown inFIG. 1. Then, elements such as the first insertion module12acan read the curvature information and the calculate correction information of the projection lens54, and then store the correction information to the correction information storage unit9. Furthermore, the correction information stored in the correction information storage unit9can be read as needed, such as at the exposure process.

In the second to fourth embodiments of the present invention, the displacement (d′x, d′y) due to unevenness and inclination of the reticle stage55when the reticle5, which is supposed to be completely flat when fixed on the reticle stage55can also be calculated based on just the flatness information of the reticle stage55without the curvature information. However, the curved surface approximating polynomial (1) of the reticle5can be expressed as the following equation (8) that is strictly a function of depth (depth of focus). Therefore, it is preferable to measure depth corresponding to the depth of exposure condition of exposure apparatus.
z(T)=a1(T)x2+b3(T)y2+c3(T)xy+d3(T)x+e3(T)y+f3(T)  (8)