The invention relates generally to an interferometer system for position measurement and more specifically to an interferometer system and method for improving the accuracy of interferometric measurements.
A laser interferometer is often used to accurately measure relative displacement between two members in a projection exposure system used to manufacture semiconductor devices. The laser interferometer is used as a measuring apparatus for measuring the coordinates of a wafer stage or mask stage for highly accurate positioning of a semiconductor wafer or reticle relative to stationary projection optics.
A prior art laser interferometer system is shown in FIGS. 1 and 2. The interferometer system typically measures a change in position in measurement mirrors 2X and 2Y attached to a movable stage S relative to stationary reference mirrors 1X and 1Y. One or more laser sources (not shown) generate(s) a beam B of light and direct it toward respective beam splitters BX and BY. The beam splitters BX and BY split the beams B into two beams 3 and 4. Beam 3 is the portion of each beam B that is reflected by the beam splitter and directed toward respective reference mirrors 1X and 1Y. The beams 3 reflect off the reference mirrors 1X and 1Y and pass through the beam splitters to give beams C. Beam 4 is the portion of each beam B that passes through the beam splitters and is directed toward respective measurement mirrors 2X and 2Y, and is then reflected by the measurement mirrors back to the respective beam splitters. The reflected beams 4 are reflected by the respective beam splitters where they are combined with reflected beams 3 into the combined beams C.
The combined beams C are then directed into respective sensors SX and SY, where they are analyzed to compare the distances represented by beams 3 and 4. If the measurement mirror 2X moves relative to the reference mirror 1X, the intensity of the combined beam periodically increases and decreases as the reflected light from the two paths alternately interferes constructively and destructively. This constructive and destructive interference is caused by the two beams moving in and out of phase. Each half wavelength of movement of the measurement mirror results in a total optical path change of one wavelength and thus, one complete cycle of intensity change. The number of cycle changes indicates the number of wavelengths that the measurement mirror has moved. Therefore, by counting the number of times the intensity of the light cycles between darkest and lightest, the change in position of the measurement mirror can be estimated as an integral number of wavelengths.
Theoretically, if the measurement mirrors 2X and 2Y are perfectly planar, and the stage to which they are mounted moves perfectly along the x axis, the 2Y mirror surface should not change its position along the y axis during x axis movements of the stage, and the beams 3 and 4 should stay perfectly in phase as received by the sensor SY. In reality, among other disturbances that may cause interference between beams 3 and 4 at the sensor SY in this situation, the mirror 2Y is never perfectly planar (of course the same holds true for mirror 2X). In practice, these mirrors generally have a polishing error of xcex/10 or more which equates, for present semiconductor uses, to up to 60 nm deformations measured from the theoretical plane of the mirror surface.
An example of such a deformation is shown in the 2X mirror in FIG. 2, where the solid line shows the actual deformation of mirror 2X, and the phantom line 2XI shows the ideal perfectly flat surface, with the deformation indicated by d. The shift of the reflection point from the ideal plane, caused by the bowing of the mirror by distance d, brings about a measurement error, since the interferometer is no longer measuring from the actual reflection point on the ideal planar surface. This error or deformation can be corrected by a pre-measurement of the reflection surface of the measurement mirror 2X. A shift of the reflection point caused by deformation of the mirror in the x-z plane is typically averaged because the stage stroke along the z axis is small enough, compared with the beam size, to be less significant than the errors induced by bowing.
U.S. Pat. No. 5,790,253 to Kamiya describes an interferometer system for correcting linearity errors of a moving mirror and stage. Thus, Kamiya can correct for the deformation in the mirror along the long axis of the mirror, which is referred to in the art as correcting xe2x80x9cmirror bowxe2x80x9d. To correct for mirror bow, Kamiya measures the curvature data of the moving mirror prior to its installation on the stage and stores the data as mapping data. Kamiya takes discrete curving error measurement along the length of the mirror after it has been mounted on the stage. Finally, a main controller creates continuous curvature error data after installation of the mirror on the wafer based on the relationship between the data generated before and after mounting the mirror on the stage. The continuous curvature error data is then used as correction data for more accurately placing the stage.
U.S. Pat. No. 5,363,196 to Cameron also describes an interferometer system for correcting mirror bow of a moving mirror mounted to a stage. Cameron provides two interferometer laser metering devices, either one of which is capable of providing measurement data of the angle of rotation of the stage in the x-y plane, for use by computer controlled servo devices that control the x-y movement of the stage. In a calibration mode, the servo devices may receive data of specific measurements defining the respective values of undesired departures from flatness or straightness of the moving mirror surfaces that are mounted to the stage. The departure data is stored in memory, and may be used by the computer controlled servo devices to compensate for the undesired departures in linearity of the mirrors, during the actual movement and processing phases of the stage. Cameron also discloses that, if desired, an additional interferometer may be provided along each of the x and y axes to measure twist in the moving mirrors. However, because of the long, narrow aspect ration of both of the moving mirrors, Cameron indicates that determination of twist may not be worth pursuing.
Sueyoshi, in Japanese HE19-210648, discloses a method and device for measuring a plane shape at a desired pitch by detecting positional information on the plane along three specified points that are separated by predetermined distances. For example, three x direction interferometers are aligned in the y direction and spaced at predetermined distances along the y direction. A similar arrangement is provide for y direction interferometers. These arrangements are then used to take measurements for a determination of mirror bowing in the x and y reflective mirrors, respectively.
As manufacturers of integrated circuits attempt to increase circuit density and reduce circuit feature size, interferometers are required to provide more precise measurement data. As the circuit density increases, the tolerance for error in alignment of the stage system decreases, so that a shift of the reflection point caused by deformation of a mirror in the x-z or y-z plane also becomes more significant. Additionally, if the stage tilts, a lateral shift of the reflection point occurs which will not be detected by a system for correction of mirror bowing. The result is an error in the position measurement of the stage that results in misalignment of circuit patterns on the wafer (mounted on the stage) relative to one another.
There is, therefore, a need for an interferometer system that measures and corrects for deformation of moving mirrors as well as tilt of the mirrors and tilt of the stage with respect to the z axis.
The invention provides a measuring system that measures and corrects for deformation and tilt of substantially planar surfaces with respect to a vertical axis. The measurement system generally includes first, second, third and fourth sensors, each capable of generating data indicative of a distance between the sensors, respectively, and corresponding locations on a reflective surface of the reflective object. A controller is provided for receiving inputs from the first, second, third and fourth sensors and determining a tilt of the reflective surface with respect to a z axis. A support on which the reflective object is mounted has a generally planar surface that is generally perpendicular to the z axis but which may tilt with respect thereto. The reflective object is mounted to the support so that said reflective surface is in a plane substantially parallel with the z axis and longitudinally extends substantially parallel to an axis normal to the z axis.
The first and second sensors are aligned substantially parallel to the axis normal to the z axis along which the reflective surface extends longitudinally and are separated by a distance a. The third and fourth sensors are aligned substantially parallel to the axis normal to the z axis along which the reflective surface extends longitudinally and are separated by the distance a. The first and third sensors are aligned substantially parallel to the z axis and are separated by the distance a, and the second and fourth sensors are aligned substantially parallel to the z axis and are separated by the distance a.
The controller determines a tilt of the reflective surface at a location ka along the longitudinally extending direction of the reflective surface according to the following formula:
xcex94(ka)="PHgr"((k+1)a)xe2x88x92"PHgr"(ka)
where:
xcex94(ka) is a measure of a displacement of the reflective surface out of the plane substantially parallel with the z axis, at location ka;
"PHgr"(ka) is a measure of tilt of the reflective surface measured by the second and fourth sensors; and
"PHgr"((k+1)a) is a measure of tilt of the reflective surface measured by the first and third sensors.
In a preferred embodiment, the first, second, third and fourth sensors comprise first, second, third and fourth measuring laser beams L1, L2, L3 and L4 that are emitted from an interferometric measurement system. The beams L1 AND L2 are aligned along an imaginary line parallel to the y axis, and the beams L3 and L4 are aligned along another imaginary line parallel to the y axis and separated from the imaginary line joining L1 and L2 by a distance a. Further, the beams L2 and L4 are aligned along an imaginary line parallel to the z axis, and the beams L1 and L3 are aligned along another imaginary line parallel to the z axis and separated from the imaginary line joining L2 and L4 by the distance a. Thus, the distances between L1 AND L2, L1 and L3, L2 and L4, and L3 and L4 are all equal to a. A reflective surface or mirror can be located at position ka along the y axis with respect to the system, and can alternately be located at position ka+a along the y axis with respect to the system.
The measurement values obtained by the system through the beams L1, L2, L3 and L4 when the mirror is at position y=ka are determined according to the following equations:
L2(ka)=s(ka)+xcex4(ka)xe2x88x92(a/2)xcex8(ka)xe2x80x83xe2x80x83(4)
L4(ka)=t(ka)+xcex4(ka)+(a/2)xcex8(ka)xe2x80x83xe2x80x83(5)
L1(ka)=s(ka+a)+xcex4(ka)xe2x88x92(a/2)xcex8(ka)xe2x80x83xe2x80x83(6)
L3(ka)=t(ka+a)+xcex4(ka)+(a/2)xcex8(ka)xe2x80x83xe2x80x83(7)
where:
xcex8(x) is a measure of the tilt of the support or stage on which the mirror is mounted;
s(x) is the x coordinate of the shape of the mirror surface at z=0;
t(x) is the x coordinate of the shape of the mirror surface at z=xe2x88x92a;
xcex4(x) is a measurement of the displacement of the stage along the x axis direction that can be due to factors such as vibration, control error and the like; and
a is a distance between measurement beams as defined above.
In order to simplify terms, J1 is defined as the difference between equations (5) and (4), and J2 is defined as the difference between equations (7) and (6) as follows:
J1(ka)xe2x89xa1(L4(ka)xe2x88x92L2(ka))/a=(t(ka)xe2x88x92s(ka))/a+xcex8(ka)="PHgr"(ka)+xcex8(ka)xe2x80x83xe2x80x83(8)
where (t(x)xe2x88x92s(x))/a is defined as the mirror tilt "PHgr"(x); and
J2(ka)xe2x89xa1(L3(ka)xe2x88x92L1(ka))/a=(t((k+1)a)xe2x88x92s((k+1)a))/a+xcex8(ka)="PHgr"((k+1)a)+xcex8(ka)xe2x80x83xe2x80x83(9)
Next, the difference between terms J2 and J1 is calculated by subtracting equation (8) from equation (9) to give the mirror tilt at position y=ka:
xcex94(ka)=J2(ka)xe2x88x92J1(ka)="PHgr"((k+1)a)xe2x88x92"PHgr"(ka)xe2x80x83xe2x80x83(10)
After determination of initial tilt values near an end of the mirror, the mirror is incrementally moved with respect to the sensors, preferably by at least one motor, to continue measuring displacement of the mirror out of the intended plane with respect to the z axis. The measurements are performed at each incremental location. In the preferred embodiment, the mirror is thus moved incrementally in the y axis direction and measurement values are obtained by the system through the beams L1, L2, L3 and L4 at position y=ka+a according to the equations (4)-(7) above, where y now equals ka+a. This process is repeatedly performed while incrementally moving the mirror in the y axis direction by a distance a for each iteration. By storing these values in a controller, the mirror tilt can readily be determined at any of the incremental positions along the mirror by a simple summation of the differential tilt values obtained from an initial end of the mirror, where the first tilt measurement was made, sequentially up to the actual location on the mirror where it is desired to determine the mirror tilt.
In general, the measurement values determined by the interferometer system at y=(kxe2x88x921)a, (kxe2x88x922)a, . . . a, 0 can be described as:
xcex94((kxe2x88x921)a)="PHgr"(ka)xe2x88x92"PHgr"((kxe2x88x921)a)
xcex94((kxe2x88x922)a)="PHgr"((kxe2x88x921)a)xe2x88x92"PHgr"((kxe2x88x922)a)
. . . 
xcex94(0)="PHgr"(a)xe2x88x92"PHgr"(0)
Since the tilt measurement values are differential values defined with respect to the previously measured value, a tilt value for a given location can be determined by summing the sequence of values preceding and including that location. A summation of the general equations given above gives:                                           ∑                          m              =              0                                      k              -              1                                ⁢                      Δ            ⁢                          xe2x80x83                        ⁢                          (              ma              )                                      =                              Φ            ⁡                          (              ka              )                                -                      Φ            ⁡                          (              0              )                                                          (        11        )            
Therefore, a mirror tilt value at position ka is given by the equation:                               Φ          ⁡                      (            ka            )                          =                              Φ            ⁡                          (              0              )                                +                                    ∑                              m                =                0                                            k                -                1                                      ⁢                          Δ              ⁡                              (                ma                )                                                                        (        12        )            
Thus, the mirror tilt of the mirror at position ka can be readily determined using equation (12). This value is then added, by the controller, to the interferometer position measurement value that is inputted to the controller, to more accurately position the stage by including the lateral offset due to the mirror tilt.
Additionally, the measurement system preferably includes a second reflective surface and a second set of four sensors, preferably four measuring laser beams incorporated into an interferometric measurement system that measures the second substantially planar reflective surface that is oriented orthogonally to the first reflective surface. Measurements from the second set of sensors are also inputted to the controller for a determination of tilt of the second reflective surface. The determination is made according to the same procedure used to determine tilt of the first reflective surface.
The invention also provides a method of measuring the tilt of a substantially planar surface that includes (1) providing a measurement system having the capability of measuring distances between first, second, third and fourth adjacent locations on the substantially planar surface and respective first, second, third and fourth adjacent locations on the measurement system, where the distances measured are along imaginary lines substantially perpendicular to the substantially planar surface; (2) positioning the substantially planar surfaces such that the measurement system is near an end of the substantially planar surface; (3) measuring distances between the pairs of first, second, third and fourth locations; (4) subtracting the distance between the second locations from the distance between the fourth locations and dividing the difference by a distance between the second and fourth locations on the substantially planar surface to give a term J1; (5) subtracting the distance between the first locations from the distance between the third locations and dividing the difference by the distance between the first and third locations on the substantially planar surface to give a term J2; and (6) determining a tilt of the substantially planar surface at the location of the substantially planar surface according to the following formula:
xcex94(ka)=J2(ka)xe2x88x92J1(ka)="PHgr"((k+1)a)xe2x88x92"PHgr"(ka)
where:
xcex94(ka) is a measure of a displacement out of the substantially planar surface;
"PHgr"(ka) is a measure of tilt of the substantially planar surface with respect to the vertical axis measured between the second and fourth locations;
"PHgr"((k+1)a) is a measure of tilt of the substantially planar surface with respect to the vertical axis measured between the first and third locations; and
a is a distance between the first and second locations on the substantially planar surface.
The method preferably further includes (1) incrementally moving the substantially planar surface in a direction parallel to an axis normal to the vertical axis and away from the end of the surface by the distance a; (2) measuring distances between the first, second, third and fourth locations on the measurement system and the respective four new locations on the substantially planar surface; (3) subtracting the distance between the second locations from the distance between the fourth locations and dividing the difference by a distance between the second and fourth locations on the substantially planar surface to give a term J1; (4) subtracting the distance between the first locations from the distance between the third locations and dividing the difference by the distance between the first and third locations on the substantially planar surface to give a term J2; and (5) determining a tilt of the substantially planar surface at the new location incrementally removed from a previously measured location according to the following formula:
xe2x80x83xcex94(ka+a)=J2(ka+a)xe2x88x92J1(ka+a)="PHgr"((k+2)a)xe2x88x92"PHgr"(k+1)a)
where:
xcex94(ka+a) is a measure of a displacement out of the substantially planar surface;
"PHgr"((k+1)a) is a measure of tilt of the substantially planar surface with respect to the vertical axis measured between the second and fourth locations on the measurement system and the new locations on the substantially planar surface; and
"PHgr"((k+2)a) is a measure of tilt of the substantially planar surface with respect to the vertical axis measured between the first and third locations on the measurement system and the new locations on the substantially planar surface.
Incremental measurements are continued by incrementally repeating the previously described incremental procedure, until an opposite end of the substantially planar surface is reached and no further incremental measurements can be taken, or until a predetermined length of the substantially planar surface has been measured.
As described above, a determination of the tilt of the substantially planar surface with respect to the vertical axis for any predetermined position ka can be determined according to the following formula:       Φ    ⁢          (      ka      )        =            Φ      ⁢              (        0        )              +                  ∑                  m          =          0                          k          -          1                    ⁢              Δ        ⁢                  (          ma          )                    
where:
"PHgr"(ka) is a measure of tilt of the substantially planar surface with respect to the vertical axis at position ka;
"PHgr"(0) is a measure of tilt of the substantially planar surface near the end of the substantially planar surface where an initial measurement was taken; and
xcex94(ma) is a measure of displacement out of the substantially planar surface, at locations where m=0, 1, 2, . . . kxe2x88x921.
The above is a brief description of some deficiencies in the prior art and advantages of the invention. Other features, advantages, and embodiments of the invention will be apparent to those skilled in the art from the following description, drawings and claims.