Patent Application
20050173992
The present invention relates generally to a precision assembly including a control system that more precisely calibrates and/or adjusts the position and/or movement of a stage within the precision assembly.
Precision assemblies such as exposure apparatuses are commonly used to transfer images from a reticle onto a semiconductor wafer during semiconductor processing. A typical exposure apparatus includes an illumination source, a reticle stage assembly having a reticle stage that retains a reticle, an optical assembly, a wafer stage assembly having a wafer stage that retains a semiconductor wafer, a measurement system, and a control system. Additionally, one or more of the stage assemblies can include a mover assembly that precisely positions the stage(s).
The size of the images and features within the images transferred onto the wafer from the reticle are extremely small. Accordingly, the precise positioning of the wafer and the reticle relative to the optical assembly is critical to the manufacture of high density, semiconductor wafers. Recently, one or more attraction only-type actuators have been used in the mover assemblies. For example, attraction-only type actuators can include one or more E/I core type actuators. The E/I core type actuator can include a somewhat “E” shaped electromagnet and a somewhat “I” shaped target that is positioned near the electromagnet. Among other configurations, attraction-only type actuators can include CI core type actuators which use a “C” shaped electromagnet.
Each “E” shaped electromagnet can have two wings and a center section. An electrical coil is typically wound around the center section of the “E”. Between the electromagnet and the target is a relatively small gap (also referred to herein as the “gap distance”) which can typically range from between zero and 500 microns. Current directed through the coil creates an electromagnetic field that attracts the target toward the electromagnet, effectively decreasing the gap between the electromagnet and the target. The amount of current to be directed to the electromagnet is based at least partially upon the gap distance. The gap distance can be monitored to increase positioning accuracy of the stage, and to reduce the likelihood of a collision between the electromagnet and the target, which could damage components of the precision assembly.
In light of the above, there is a need for a precision assembly that can determine misalignments between the electromagnets and the targets in the mover assemblies. Further, there is a need for a control system that can account for any such misalignments by more precisely controlling the amount of current that is directed to the electromagnets based at least partially on the presence and/or the extent of such misalignments.
The present invention is directed to a stage assembly that includes a stage, a mover assembly that moves the stage, and a control system. In one embodiment, the mover assembly includes an attraction-only type first actuator having a first electromagnet, and a first target having a first target surface that generally faces the first electromagnet. In this embodiment, the first electromagnet is positioned at a first angle with an absolute value of greater than zero relative to the first target surface. In one embodiment, the first electromagnet can include an E core, and the first target can include an I core. In one embodiment, the control system directs a first current to the first actuator based on the first angle.
Further, the first electromagnet can include a first measurement point that is spaced apart a first physical gap g1 from the first target surface, and a spaced apart second measurement point that is spaced apart a second gap {overscore (g)}1 from the first target surface. The first gap g1 can be different than the second gap {overscore (g)}1. The control system can direct the first current to the first actuator based on g1 and {overscore (g)}1.
In another embodiment, the mover assembly includes an attraction-only type second actuator that cooperates with the first actuator to move the stage. The second actuator includes a second electromagnet and a second target having a second target surface that generally faces the second electromagnet. The second electromagnet can be positioned at a second angle relative to the second target surface which may or may not have an absolute value of greater than zero. In this embodiment, the control system can direct a second current to the second actuator based on the second angle.
In an alternative embodiment, the second electromagnet can include a first measurement point that is spaced apart from the second target surface by a first physical gap g2, and a spaced apart second measurement point that is spaced apart from the second target surface by a second gap {overscore (g)}2. The control system can direct the second current to the second actuator based on g2 and {overscore (g)}2.
The present invention is also directed to a precision assembly, an exposure apparatus, a wafer, a device, a method for positioning a stage, a method for using an exposure apparatus, a method for making a wafer, and a method for making an object.
The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which:
As provided herein, the control system 24 utilizes a commutation formula that includes one or more calibration algorithms that improve the accuracy in the control of one or more of the stage assemblies 18, 20.
A number of Figures include an orientation system that illustrates an X axis, a Y axis that is orthogonal to the X axis and a Z axis that is orthogonal to the X and Y axes. It should be noted that these axes can also be referred to as the first, second and third axes, respectively.
The precision assembly 10 can be particularly useful as a lithographic device that transfers a pattern (not shown) of an integrated circuit from a reticle 26 onto a semiconductor wafer 28. The precision assembly 10 mounts to a mounting base 30, e.g., the ground, a base, or floor or some other supporting structure.
There are a number of different types of lithographic devices. For example, the precision assembly 10 can be used as scanning type photolithography system that exposes the pattern from the reticle 26 onto the wafer 28 with the reticle 26 and the wafer 28 moving synchronously. In a scanning type lithographic device, the reticle 26 is moved perpendicularly to an optical axis of the optical assembly 16 by the reticle stage assembly 18 and the wafer 28 is moved perpendicularly to the optical axis of the optical assembly 16 by the wafer stage assembly 20. Scanning of the reticle 26 and the wafer 28 occurs while the reticle 26 and the wafer 28 are moving synchronously.
Alternatively, the precision assembly 10 can be a step-and-repeat type photolithography system that exposes the reticle 26 while the reticle 26 and the wafer 28 are stationary. In the step and repeat process, the wafer 28 is in a constant position relative to the reticle 26 and the optical assembly 16 during the exposure of an individual field. Subsequently, between consecutive exposure steps, the wafer 28 is consecutively moved with the wafer stage assembly 20 perpendicularly to the optical axis of the optical assembly 16 so that the next field of the wafer 28 is brought into position relative to the optical assembly 16 and the reticle 26 for exposure. Following this process, the images on the reticle 26 are sequentially exposed onto the fields of the wafer 28 so that the next field of the wafer 28 is brought into position relative to the optical assembly 16 and the reticle 26.
However, the use of the precision assembly 10 provided herein is not limited to a photolithography system for semiconductor manufacturing. The precision assembly 10, for example, can be used as an LCD photolithography system that exposes a liquid crystal display device pattern onto a rectangular glass plate or a photolithography system for manufacturing a thin film magnetic head. Further, the present invention can also be applied to a proximity photolithography system that exposes a mask pattern from a mask to a substrate with the mask located close to the substrate without the use of a lens assembly.
The apparatus frame 12 is rigid and supports the components of the precision assembly 10. The apparatus frame 12 illustrated in
The illumination system 14 includes an illumination source 34 and an illumination optical assembly 36. The illumination source 34 emits a beam (irradiation) of light energy. The illumination optical assembly 36 guides the beam of light energy from the illumination source 34 to the optical assembly 16. The beam illuminates selectively different portions of the reticle 26 and exposes the wafer 28. In
The illumination source 34 can be a g-line source (436 nm), an i-line source (365 nm), a KrF excimer laser (248 nm), an ArF excimer laser (193 nm) or a F2 laser (157 nm). Alternatively, the illumination source 34 can generate charged particle beams such as an x-ray or an electron beam. For instance, in the case where an electron beam is used, thermionic emission type lanthanum hexaboride (LaB6) or tantalum (Ta) can be used as a cathode for an electron gun. Furthermore, in the case where an electron beam is used, the structure could be such that either a mask is used or a pattern can be directly formed on a substrate without the use of a mask.
The optical assembly 16 projects and/or focuses the light passing through the reticle 26 to the wafer 28. Depending upon the design of the precision assembly 10, the optical assembly 16 can magnify or reduce the image illuminated on the reticle 26. The optical assembly 16 need not be limited to a reduction system. It could also be a 1× or magnification system.
When far ultra-violet rays such as the excimer laser is used, glass materials such as quartz and fluorite that transmit far ultra-violet rays can be used in the optical assembly 16. When the F2 type laser or x-ray is used, the optical assembly 16 can be either catadioptric or refractive (a reticle should also preferably be a reflective type), and when an electron beam is used, electron optics can consist of electron lenses and deflectors. The optical path for the electron beams should be in a vacuum.
Also, with an exposure device that employs vacuum ultra-violet radiation (VUV) of wavelength 200 nm or lower, use of the catadioptric type optical system can be considered. Examples of the catadioptric type of optical system include the disclosure Japan Patent Application Disclosure No. 8-171054 published in the Official Gazette for Laid-Open Patent Applications and its counterpart U.S. Pat. No. 5,668,672, as well as Japan Patent Application Disclosure No. 10-20195 and its counterpart U.S. Pat. No. 5,835,275. In these cases, the reflecting optical device can be a catadioptric optical system incorporating a beam splitter and concave mirror. Japan Patent Application Disclosure No. 8-334695 published in the Official Gazette for Laid-Open Patent Applications and its counterpart U.S. Pat. No. 5,689,377, as well as Japan Patent Application Disclosure No. 10-3039 and its counterpart U.S. Pat. No. 5,805,357, also use a reflecting-refracting type of optical system incorporating a concave mirror, etc., but without a beam splitter, and can also be employed with this invention. As far as is permitted, the disclosures in the above-mentioned U.S. patents, as well as the Japan patent applications published in the Official Gazette for Laid-Open Patent Applications are incorporated herein by reference.
The reticle stage assembly 18 holds and positions the reticle 26 relative to the optical assembly 16 and the wafer 28. Somewhat similarly, the wafer stage assembly 20 holds and positions the wafer 28 with respect to the projected image of the illuminated portions of the reticle 26. The wafer stage assembly 20 is described in more detail below.
Further, in photolithography systems, when linear motors (see U.S. Pat. Nos. 5,623,853 or 5,528,118) are used in a wafer stage or a mask stage, the linear motors can be either an air levitation type employing air bearings or a magnetic levitation type using Lorentz force or reactance force. Additionally, the stage could move along a guide, or it could be a guideless type stage that uses no guide. As far as is permitted, the disclosures in U.S. Pat. Nos. 5,623,853 and 5,528,118 are incorporated herein by reference.
Alternatively, one of the stages could be driven by a planar motor, which drives the stage by an electromagnetic force generated by a magnet unit having two-dimensionally arranged magnets and an armature coil unit having two-dimensionally arranged coils in facing positions. With this type of driving system, either the magnet unit or the armature coil unit is connected to the stage and the other unit is mounted on the moving plane side of the stage.
Movement of the stages as described above generates reaction forces that can affect performance of the photolithography system. Reaction forces generated by the wafer (substrate) stage motion can be mechanically transferred to the floor (ground) by use of a frame member as described in U.S. Pat. No. 5,528,100 and published Japanese Patent Application Disclosure No. 8-136475. Additionally, reaction forces generated by the reticle (mask) stage motion can be mechanically transferred to the floor (ground) by use of a frame member as described in U.S. Pat. No. 5,874,820 and published Japanese Patent Application Disclosure No. 8-330224 and 8-136475. As far as is permitted, the disclosures in U.S. Pat. Nos. 5,528,100 and 5,874,820 and Japanese Patent Application Disclosure No. 8-330224 are incorporated herein by reference.
The measurement system 22 monitors movement of the reticle 26 and/or the wafer 28 relative to the optical assembly 16 or some other reference. With this information, the control system 24 can control the reticle stage assembly 18 to precisely position the reticle 26 and/or the wafer stage assembly 20 to precisely position the wafer 28. For example, the measurement system 22 can utilize multiple laser interferometers, encoders, and/or other measuring devices.
The control system 24 is connected to the reticle stage assembly 18, the wafer stage assembly 20, and the measurement system 22. The control system 24 receives information from the measurement system 22 and controls one or both of the stage mover assemblies of the reticle stage assembly 18 and the wafer stage assembly 20 to precisely position the reticle 26 and/or the wafer 28. The control system 24 includes one or more processors and circuits for performing the functions described herein. A portion of the control system 24 is described in more detail below.
A photolithography system (e.g. an exposure apparatus) according to the embodiments described herein can be built by assembling various subsystems, including each element listed in the appended claims, in such a manner that prescribed mechanical accuracy, electrical accuracy, and optical accuracy are maintained. In order to maintain the various accuracies, prior to and following assembly, every optical system is adjusted to achieve its optical accuracy. Similarly, every mechanical system and every electrical system are adjusted to achieve their respective mechanical and electrical accuracies. The process of assembling each subsystem into a photolithography system includes mechanical interfaces, electrical circuit wiring connections and air pressure plumbing connections between each subsystem. Needless to say, there is also a process where each subsystem is assembled prior to assembling a photolithography system from the various subsystems. Once a photolithography system is assembled using the various subsystems, a total adjustment is performed to make sure that accuracy is maintained in the complete photolithography system. Additionally, it is desirable to manufacture an exposure system in a clean room where the temperature and cleanliness are controlled.
In this embodiment, the stage assembly 220 includes a stage base 202, a first stage mover assembly 204, a first stage 206, a second stage 208 and a second stage mover assembly 210. The design of the components of the stage assembly 220 can be varied. For example, in
In
The design of the first stage mover assembly 204 can be varied to suit the movement requirements of the stage assembly 220. In one embodiment, the first stage mover assembly 204 includes one or more movers, such as rotary motors, voice coil motors, linear motors utilizing a Lorentz force to generate drive force, electromagnetic actuators, planar motor, or some other force actuators.
In
In the embodiment illustrated in
In
The first mover component 212 can be maintained above the second mover component 214 with vacuum pre-load type air bearings (not shown). With this design, the first stage 206 is movable relative to the stage base 202 with three degrees of freedom, namely along the first axis, along the second axis, and rotatable around the third axis. Alternatively, the first mover component 212 could be supported above the second mover component 214 by other ways, such as guides, a rolling type bearing, or by the magnetic levitation forces and/or the first stage mover assembly 204 could be designed to be movable with six degrees of freedom. Still alternatively, the first stage mover assembly 204 could be designed to include one or more electromagnetic actuators.
The control system 224 directs electrical current to one or more of the conductors in the conductor array. The electrical current through the conductors causes the conductors to interact with the magnetic field of the magnet array. This generates a force between the magnet array and the conductor array that can be used to control, move, and position the first mover component 212 and the first stage 206 relative to the second mover component 214 and the stage base 202. The control system 224 adjusts and controls the current level for each conductor to achieve the desired resultant forces. Stated another way, the control system 224 directs current to the conductor array to position the first stage 206 relative to the stage base 202.
The second stage 208 includes a device holder (not shown) that retains the device 200. The device holder can include a vacuum chuck, an electrostatic chuck, or some other type of clamping device.
The second stage mover assembly 210 moves and adjusts the position of the second stage 208 relative to the first stage 206. For example, the second stage mover assembly 210 can adjust the position of the second stage 208 with six degrees of freedom. Alternatively, for example, the second stage mover assembly 210 can be designed to move the second stage 208 with only three degrees of freedom. The second stage mover assembly 210 can include one or more rotary motors, voice coil motors, linear motors, electromagnetic actuators, or other type of actuators. Still alternatively, the second stage 208 can be fixed to the first stage 206.
In the embodiment illustrated in
In
In
Alternatively, for example, two E/I core actuator pairs 226 can be mounted parallel with the first direction and one actuator pair 226 could be mounted parallel with the second direction. Still alternatively, other arrangements of the E/I core actuator pairs 226 are also possible.
The control system 224 directs current to the E/I core actuator pairs 226 to position the second stage 208.
In one embodiment, the measurement system 22 (illustrated in
Additionally, in
In embodiments that utilize the E/I core actuator pair, the combination of the E core 236 and the conductor 238 is sometimes referred to herein as an electromagnet, while the I core 240 is sometimes referred to herein as a target. Each target includes a target surface 240A that generally faces the corresponding E core.
The electromagnets can be mounted to the first stage 206 (illustrated in
The actuators 228 illustrated in
In this embodiment, the measurement system 222 includes one or more sensors 223 that can measure the gap distance between a portion of the E core 236 and a portion of the I core 240 for each actuator 228. A suitable sensor 223, for example, can include a capacitor sensor. Additionally, gap measurements can be performed by other methods, such as by using shims (not shown) to measure the gap distance between a portion of the E core 236 and a portion of the I core 240.
The first electromagnet 436F includes a first upper arm 444F having a first upper end region 446F, a first middle arm 448F having a first middle end region 450F, and a first lower arm 452F having a first lower end region 454F. The second electromagnet 436S includes a second upper arm 444S having a second upper end region 446S, a second middle arm 448S having a second middle end region 450S and a second lower arm 452S having a second lower end region 454S. Because the orientation of the electromagnets 436F, 436S can vary, the terms “first” and “second” are interchangeable and are for convenience of discussion only, as are the terms “upper” and “lower”. In this embodiment, the targets 440F, 440S are secured to the stage 408. A centerline of the stage 408 is also indicated in
The stage 408 has a stage physical range 458 and a force functional range 460. The stage physical range 458 defines the limitations of movement of the portion of the stage 408 and the targets 440F, 440S that are secured to the stage 408. The stage physical range 458 has a first physical range end 458F, a second physical range end 458S and a physical range midpoint 458M. In this embodiment, the first physical range end 458F is positioned at the first lower end region 454F of the first electromagnet 436F, and is closer to the first target surface 442F than to the second target surface 442S. Somewhat similarly, the second physical range end 458S is positioned at the second upper end region 446S of the second electromagnet 436S, and is closer to the second target surface 442S than to the first target surface 442F. The physical range midpoint 458M is located at the center of the stage physical range 458. The distance between the physical range midpoint 458M and the centerline 456 of the stage 408 at any given time t1, t2, t3 . . . tn is referred to herein as “x”. In
In
g1=g2=g0 (1)
where g0 is the nominal operating E/I gap which is equal to (i) the initial gap distance between the first target surface 442F and the first physical range end 458F, and (ii) the initial gap distance between the second target surface 442S and the second physical range end 458S, when the stage 408 is at the initial position.
Alternatively, the first physical gap g1 and the second physical gap g2 could be defined by a distance between another portion of each of the electromagnets 436F, 436S and the corresponding targets 440F, 440S.
The control system 424 directs current to the E/I core actuator pair 426 to position the targets 440F, 440S, and thus the stage 408, within the stage physical range 458. In the embodiment illustrated in
In the embodiment illustrated in
Thus, F1−F2=ΔF. (2)
F1 and F2 are positive or zero, while the ΔF can be positive, zero, or negative.
Theoretically, when the first force F1 is equal to the second force F2, the net force ΔF generated by the E/I core actuator pair 426 on the stage 408 should equal zero and there would be no acceleration of the stage 408. However, (i) when the first force F1 is greater than the second force F2, the net force ΔF is positive and the E/I core actuator pair 426 moves the stage 408 to the right along the first axis and (ii) when the second force F2 is greater than the first force F1, the net force ΔF is negative and the E/I core actuator pair 426 moves the stage 408 to the left along the first axis. Stated another way, the E/I core actuator pair 426 can be used to move and position the stage 408 left and right along the first axis under the influence of the two actuators 428F, 428S. Additional E/I core actuator pairs (illustrated in
The amount of movement is determined by the magnitudes of force F1 and F2 which in turn, are each a function of the amount of current I1, I2 directed to each of the conductors 438F, 438S and the size of the physical gaps g1, g2. There is a linear relationship between the net force ΔF applied to stage 408 and the acceleration of stage 408. Consequently, if a large acceleration is desired, a large net force ΔF must be applied. To apply a large net force ΔF, the first force F1 must be much larger or much smaller than second force F2.
The specific range of movement of the stage 408 can depend upon the positioning of the electromagnets relative to the targets 440F, 440S. Stated another way, movement of the stage 408 between the electromagnets 436F, 436S is at least partially determined by the positioning and/or angle of the arms 444F, 448F, 452F, 444S, 448S, 452S of the electromagnets 436F, 436S relative to their corresponding target 440F, 440S, as described in greater detail below.
The force functional range 460 is the distance directly between the middle arms 448F, 448S of the electromagnets 436F, 436S of the E/I core actuator pair 426. The force functional range 460 is determined by the location of the middle arms 448F, 448S of the electromagnets 436F, 436S because the electromagnetic force that attracts the target 440F, 440S toward the electromagnet 436F, 436S substantially emanates from the middle arm 448F, 448S and the conductor 438F, 438S of each electromagnet 436F, 436S.
The force functional range 460 has a first functional range end 460F, a second functional range end 460S and a functional range midpoint 460M which is located at the center of the force functional range 460. The functional range midpoint 460M varies depending upon the extent of any lack of parallelism between the electromagnets 436F, 436S and the corresponding target surfaces 442F, 442S of the E/I core actuator pair 426. The distance between the functional range midpoint 460M and the centerline 456 of the stage 408 is referred to herein as {overscore (x)}. In
{overscore (x)}=x−Δx. (3)
Further, the gap distance between the first target surface 442F and the middle end region 450F of the first middle arm 448F is referred to herein as a first functional gap {overscore (g)}1. Somewhat similarly, the gap distance between the second target surface 442S and the middle end region 450S of the second middle arm 448S is referred to herein as a second functional gap {overscore (g)}2. Alternatively, the first functional gap {overscore (g)}1 and/or the second functional gap {overscore (g)}2 can be defined by the distance between another portion of the electromagnets 436F, 436S and the corresponding targets 440F, 440S.
The force functional range 460 can be determined by measurement. For example, one or more sensors 223 (illustrated in
The difference between the first functional gap {overscore (g)}1 and the first physical gap g1 is referred to as the first gap error Δg1. The difference between the second functional gap {overscore (g)}2 and the second physical gap g2 is referred to as the second gap error Δg2.
Thus, g1={overscore (g)}1−Δg1, (4)
and g2={overscore (g)}2−Δg2. (5)
Ideally, the force functional range 460 is the same as the stage physical range 458, which would be indicative of precise manufacturing and exact parallelism of the electromagnets 436F, 436S relative to the corresponding target surfaces 442F, 442S. However, any deviation during manufacturing or a lack of parallelism of the electromagnets 436F, 436S relative to the target surfaces 442F, 442S during operation can exist. Any such ill-parallelism of the E/I core actuator pair 426 which occurs during manufacturing or operation of the precision assembly 10 results in a disparity between the force functional range 460 and the stage physical range 458. More specifically, the force functional range 460 is greater than the stage physical range 458 and/or the force functional range 460 is somewhat offset, e.g., slightly toward or away from the first electromagnet 436F, from the stage physical range 458. Consequently, any ill-parallelism between one or more of the electromagnets 436F, 436S and one or more of the target surfaces 442F, 442S can cause a disparity between a desired net force ΔFD and an actual net force ΔFA. Stated another way, from the perspective of the control system 424, current is being directed to the conductors 438F, 438S as though the range of movement of the targets 440F, 440S and the stage 408 were within the force functional range 460. However, in actuality, the range of movement of the targets 440F, 440S and the stage 408 is physically limited to the stage physical range 458. The control system 424 provided herein takes this disparity into account before and/or during movement of the stage 408.
For example, if the stage 408 is positioned at the physical range midpoint 458M, and equal current is directed to the first conductor 438F and the second conductor 438S, equal forces should be imparted on the stage 408 by the actuators 428F, 428S because g1={overscore (g)}1=g2={overscore (g)}2. Assuming precise parallelism between the electromagnets 436F, 436S and the corresponding target surfaces 442F, 442S, the stage 408 should remain stationary. However, any lack of precise parallelism can result in {overscore (g)}1 being greater or less than {overscore (g)}2, which can indicate that the stage physical range 458 differs from the force functional range 460. The extent of this disparity can vary from one E/I core actuator pair 426 to another, and can vary over time.
Because the force functional range 460 can be larger than the stage physical range 458, if the stage assembly 420 did not take into account the lack of parallelism of each electromagnet 436F, 436S relative to the corresponding target surface 442F, 442S, the control system 424 could impose electromagnetic forces on the stage 408 resulting in an increased following error xerr of the stage 408 (explained in greater detail below) and/or a collision between one of the targets 440F, 440S and the corresponding electromagnet 436F, 436S. Stated another way, absent the calibration capabilities of the present invention as described herein, the control system 424 may not recognize that the stage physical range 458 can be smaller than the force functional range 460, which could cause damage to the stage assembly 420 and/or manufacturing of semiconductor wafers of a decreased quality.
As illustrated in
The first angle θ1 can be measured from a line formed by any two measurement points on the first electromagnet 436F, in relation to the first target surface 442F. Somewhat similarly, the second angle θ2 can be measured from a line formed by any two measurement points on the second electromagnet 436S, in relation to the second target surface 442S. For example, with respect to the first angle θ1, a first measurement point can be located on the first lower end region 454F, and the second measurement point can be located on the first middle end region 450F. Alternatively, the first measurement point can be located on the first lower end region 454F and the second measurement point can be located on the first upper end region 446F. Still alternatively, the measurement points can be located elsewhere on the first electromagnet 436F or the first conductor 438F, provided the line formed by the measurement points forms a theoretical first angle θ1 with the first target surface 440F.
The second angle θ2 can utilize similar measurement points located on the second electromagnet 436S, which define a line that forms the second angle θ2 with the second target surface 442S.
In the example illustrated in
In the embodiment illustrated in
The first angle θ1 and the second angle θ2 for each E/I core actuator pair 426 can vary during operation of the precision assembly 10. Moreover, at a given time, the first angle θ1 can differ from the second angle θ2 or the angles θ1, θ2 can be the same. The control system 424 as provided herein can accurately calibrate and/or account for these angles θ1, θ2 at various times by varying the current that is directed to the conductors 438F, 438S. With this design, the control system 424 inhibits potential collisions between one or more of the electromagnets 436F, 436S and one or more of the targets 440F, 440S which could otherwise damage the stage assembly 420 and/or produce semiconductor wafers of a decreased quality.
Theoretically, as provided herein, the desired force output F1 for the first actuator 428F can be expressed as follows:
F1=k(I12)/(g1+a)(g1+b) (6)
Similarly, the desired output force F2 generated by the second actuator 428S can be expressed as follows:
F2=k(I22)/(g2+a)(g2+b) (7)
In one embodiment, k is an E/I force constant wherein k=½N2μowd; where N=the number of coil turns in the conductor; μo=a physical constant of about 1.26×10−6 H/m; w=the half width of the center of the E core, in meters; and d=the depth of the center of the E core, in meters. For example, in one embodiment, k=7.73×10−6 kg m3/s2A2; the terms a and b for each actuator are determined by experimental testing of the assembled actuator pair and are related to the shape and alignment of the electromagnets 436F, 436S and the targets 440F, 440S; and where either the measured physical gaps g1, g2 or equivalently the parameters (a and b) are modified to match the force output F1, F2.
The commutation formula which transforms the desired forces F1, F2 to the required currents I1, I2 to be directed to each conductor is therefore:
where go is the nominal operating E/I gap which is equal to (i) the initial gap distance between the first target surface 442F and the first physical range end 458F, and (ii) the initial gap distance between the second target surface 442S and the second physical range end 458S, when the stage 408 is at the initial position.
g1=g0−x, (9)
and g2=g0+x. (10)
In a first embodiment of the present invention, the control system 424 calibrates the functional range midpoint 460M according to a first calibration algorithm, which is based on the physical range midpoint 458M. Stated another way, the control system 424 calibrates the physical gaps g1 and g2 relative to the force functional range 460 of the stage 408. In this embodiment, (g1,2=go∓x) can be calibrated by replacing the distance between the physical range midpoint 458M and the centerline 456 of the stage 408, x, with the distance between the functional range midpoint 460M and the centerline 456 of the stage 408, {overscore (x)}, so that
g1,2=go∓{overscore (x)}. (11)
Further, because {overscore (x)}=x−Δx, (12)
g1,2=go∓(x−Δx) (13)
By adding the same force profile simultaneously to both actuators 428F, 428S of the E/I core actuator pair 426, the fine adjustment term Δx is adapted to reduce the position following error xerr as follows.
Δx(t)=Δx(t−1)+λxerr(t) (14)
where λ is the adaptation gain. Alternatively, the fine adjustment term Δx is adapted to reduce the feedback control force F as follows:
Δx(t)=Δx(t−1)+λF(t). (15)
where λ is the adaptation gain.
In contrast,
By comparison, without using the first calibration algorithm, the following error xerr can be approximately 50˜100 times greater than when using the first calibration algorithm. For example, the following error xerr can be on the order of ±1.0 to 7.0 μm or more when not using one or more of the calibration algorithms provided herein. Moreover, without using the first calibration algorithm, the following error xerr tends to increase as a greater force is applied, e.g. 54N, or decrease as a lesser force is applied.
In contrast, without calibrating the force functional range 460 with the stage physical range 458, a substantial difference in control forces would occur, resulting in a relatively large following error xerr. In fact, without utilizing the control system which uses the first calibration algorithm described herein, a disparity of up to or greater than 8N can occur under similar testing circumstances. Further, the disparity increases or decreases depending upon the extent of the force applied to the stage 408. In this example, without taking into account the positioning, including the angle, of each electromagnet 436F, 436S relative to each corresponding target surface 442F, 442S, a different control force can occur for each actuator 428F, 428S in the E/I core actuator pair 426, leading to greater following errors xerr.
In a second embodiment of the present invention, the control system 424 calibrates and corrects gap errors Δg1, Δg2 due to a lack of parallelism according to a second calibration algorithm. In this embodiment, the gaps (g1,2=go∓x) can be calibrated by adding individual gap error Δg1, Δg2 adjustment terms such that:
g1,2=go∓x−Δg1,2 (16)
to account for any lack of parallelism of the actuators 428F, 428S. The position following error xerr can be maintained at a very small magnitude by an initial, a periodic or a continuous adaptation, e.g. by calculation of the gap errors Δg1, Δg2 in the E/I core commutation. Consequently, the resulting calculated gap errors Δg1,2 will be very close to the actual gap errors of Δg1, Δg2. In one embodiment, a gradient method can be used for this type of adaptive control, as provided in the following gap error calibration algorithm:
where λ is the adaptation gain.
The following error is expressed as:
xerr(s)=Gplant(s)(F2−F1) (18)
and is proportional to the force difference of both actuators 428F, 428S, i.e. xerr(t) ∞F2−F1. Accordingly,
Without loss of generality, the term
can merge into the adaptation parameter λ. With the partial differentiations of force with respect to gap,
Because the gap errors Δg1, Δg2 can change during operation of the precision assembly 10 due to the forces imposed upon the actuators 428F, 428S, each gap error Δg1, Δg2 can be periodically or continually monitored and/or calibrated during operation. For example, the gap error calibration algorithm at equation (17) can be further described in the following form which can be used to determine each gap error Δg1, Δg2 at time t during operation of the precision assembly:
In one embodiment, equation (21) is utilized to continually calculate Δg1 and Δg2 with the initial condition of Δg1,2(0)=0.
In a third embodiment of the present invention, calibration of the functional range midpoint 460M relative to the physical range midpoint 458M during operation can occur using a lookup table. In this embodiment, once the desired force is determined by the control system, a lookup table is used to adjust the current that is directed to one or more of the actuators 428F, 428S (illustrated in
The controller s806 determines the amount of required net force ΔF s810, and determines the force s814 of each actuator to exert at a particular time to maintain the desired position of the stage. In the embodiment illustrated in
Stated another way, the commutation formula s816A receives the force profile, uses one or more of the calibration formulae s818, and calculates the first current I1 needed at the first actuator and the second current I2 needed at the second actuator to attempt to produce the required net force ΔF to be exerted on the stage and maintain the stage at the desired position. The currents I1, I2 are directed to the respective actuators, and the actuators impart an actual force on the stage, and the stage responds to the input. The measurement system 22 monitors the movement of the stage s822, the sensor signal vector S changes, and the cycle is repeated.
Semiconductor devices can be fabricated using the above described systems, by the process shown generally in
At each stage of wafer processing, when the above-mentioned preprocessing steps have been completed, the following post-processing steps are implemented. During post-processing, first, in step 915 (photoresist formation step), photoresist is applied to a wafer. Next, in step 916 (exposure step), the above-mentioned exposure device is used to transfer the circuit pattern of a mask (reticle) to a wafer. Then in step 917 (developing step), the exposed wafer is developed, and in step 918 (etching step), parts other than residual photoresist (exposed material surface) are removed by etching. In step 919 (photoresist removal step), unnecessary photoresist remaining after etching is removed. Multiple circuit patterns are formed by repetition of these preprocessing and post-processing steps.
While the particular stage assembly and commutation formula as shown and disclosed herein is fully capable of obtaining the objects and providing the advantages herein before stated, it is to be understood that it is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.
