Abstract:
A method and apparatus for controlling the leveling table of a wafer stage is described. More generally, the invention includes control circuitry for controlling motion of a stage, where the stage is adapted to support a workpiece. The control circuitry measures position in a vicinity of the workpiece. Based upon the measured position, the control circuitry drives the stage toward a target position while accounting for nonlinear dynamics of the stage. The nonlinear dynamics may include inertia, in which case the control circuitry adaptively estimates the inertia of the stage. The nonlinear dynamics may also include tilt due to acceleration or deceleration of the stage, in which case the circuitry adaptively estimates the tilt of the stage. The stage may generally travel in a plane, and the circuitry measures position in a direction orthogonal to the plane. The circuitry may measure the position of the workpiece itself, or the position of an upper surface of the stage. The workpiece may be a semiconductor wafer in an exposure system.

Description:
BACKGROUND 
     1. Field of the Invention 
     The present invention relates to semiconductor manufacturing, and more particularly to controlling the leveling (upper) table of a wafer stage in a wafer stepper. 
     2. Description of the Related Art 
     During the manufacture of integrated circuits, circuit patterns for multiple chips are made on a single semiconductor wafer using techniques such as e-beam or ultraviolet photolithography. The wafer rests on a wafer stage under the control of a feedback wafer controller. The wafer stage includes a lower XY stage and an upper leveling stage. To control the leveling stage, the feedback may be measured at the surface of the wafer, or alternatively at the actuators driving the leveling stage. The first configuration introduces inaccuracies into the system because of the delay between the measurement at the wafer surface and the actuation points below the leveling stage. By measuring position at the actuators themselves, the second technique eliminates this delay, but provides an inaccurate representation of the measurement at the wafer surface. 
     In particular, the leveling stage driving mechanism, including the actuators and the upper leveling stage itself, exhibits nonlinear dynamics. The nonlinear effects hamper the ability of the system to quickly and accurately position the wafer stage at a desired height and keep the wafer level as it moves. Improvements in positioning and leveling would result in a higher throughput and improved exposure image quality. 
     FIG. 1 is a simplified block diagram illustrating an example of a conventional wafer scanner-stepper, such as the Nikon Model NSR 201, used in the manufacture of semiconductor chips. A radiant energy source  100 , such as an ultraviolet light, is directed towards a reticle or mask  102 . The light passing through the mask falls on an exposure area of a wafer  104 . As a result, the area of the reticle illuminated by the light projects a corresponding pattern onto the exposure area of the wafer. The wafer  104  rests on a wafer stage  106 , which moves under the control of a feedback wafer controller  108 . The position of the wafer  104  is detected by a wafer position sensor  110 , which can be implemented with a laser interferometer for measuring position in the XY direction and an encoder for measuring position in the vertical direction, for example. 
     The reticle may be held by a two-part reticle stage structure which includes a fine motion stage  112  and a coarse motion stage  114 . The coarse stage motion is controlled by a coarse stage controller  116 , and the fine stage motion is controlled by a fine stage controller  118 . The XY position of the reticle is sensed by a reticle position sensor  120 , which can be implemented by a laser interferometer, for example. The present invention may be employed with this system or with many other scanner-steppers known in the art. 
     FIG. 2 illustrates the wafer stage  106  in more detail. The wafer stage  106  moves the wafer  104  in three dimensions. The wafer stage  106  includes a lower XY stage  200  and an upper leveling stage  202 . A wafer chuck  204  on the leveling stage  202  supports the wafer  104 . Interferometer mirrors  206  mounted on the leveling stage  202  reflect light back to the sensor circuitry  110  to determine the position of the leveling stage  202  in the XY direction. Interposed between the lower stage  200  and upper stage  202  are leveling drive mechanisms or actuators  208 . 
     As is well known in the art, the XY stage  200  carries the leveling stage  202 , and thus the wafer  104 , along a path in the XY plane. Typically, under control of the leveling stage  202  by three leveling mechanisms  208 , the wafer is positioned to a desired height and maintained in a level position as the wafer travels. As is known in the art, each leveling drive mechanism  208  may include a motor  210  that turns a lead screw  212 . The screw  212  is threaded into a wedge  214 , and also coupled to an encoder  216  of sensor  110 . Based upon rotation of the screw, the encoder  216  provides a measurement related to the height of a roller  218  supported by the wedge and thus related to the height of the leveling table  202 . 
     Rotation of the screw  212  translates rotational motion of the motor  210  into translational motion of the wedge  214 . The wedge  214  supports the roller  218 , which has a fixed axle. As the wedge  214  moves in the XY plane, that motion is translated into orthogonal vertical motion by the roller  218  moving up or down the wedge  214 . In this manner, three actuators  208  control the vertical position and leveling of the upper leveling stage  202 . 
     The scanner-stepper operates as follows. A control computer  122  generates commands specifying the position of the wafer. In response, the wafer controller  108  causes the wafer stage  106  to move toward the desired or target position. The actual position of the wafer  104  is detected by the wafer sensor  110  and is fed back to a first adder  124 . The difference between the commanded position and the sensed position is the following error of the wafer stage. The wafer controller  108  adjusts the position of the wafer stage  106  in response to this error. 
     Because of limitations on the resolving power of projection lenses used in the light source  100 , the wafer is typically exposed to only a small area of the reticle mask  102  to maintain a high resolution. The reticle motion is synchronized with the wafer motion to expose more of the reticle to the wafer. Typically, the coarse controller  116  first moves the coarse reticle stage  114  in a coarse adjustment. The reticle sensor  120  feeds the position of the reticle to a second adder  126 , which compares the sensed reticle position to the sensed wafer position. The difference is the synchronization error, which is used by the fine controller  118  to adjust the fine reticle stage  112  in order to minimize the synchronization error. 
     During exposure, the wafer  104  is scanned with the mask pattern at a constant velocity. Scanning is performed on a row of chip areas laid out in the Y direction. When the end of a row is reached, the control computer  122  inputs a command to step the wafer in the orthogonal X direction so that scanning may proceed on the next row. After stepping, motion in the X direction is halted and scanning continues in the reverse Y direction. As a result, the wafer is moved in a serpentine pattern. For more information on serpentine scanning, please refer to U.S. Pat. No. 4,818,885, issued to Davis, et al., which is incorporated by reference herein. 
     SUMMARY OF THE INVENTION 
     The present invention provides a method and apparatus for controlling the leveling table of a wafer stage. More generally, the invention includes control circuitry for controlling motion of a stage, where the stage is adapted to support a workpiece. The control circuitry measures position in a vicinity of the workpiece. Based upon the measured position, the control circuitry drives the stage toward a target position while accounting for nonlinear dynamics of the stage. The nonlinear dynamics may include inertia, in which case the control circuitry adaptively estimates the inertia of the stage. The nonlinear dynamics may also include tilt due to acceleration or deceleration of the stage, in which case the circuitry adaptively estimates the tilt of the stage. 
     The stage generally travels in a plane, and the circuitry measures position in a direction orthogonal to the plane. The circuitry may measure the position of the workpiece itself, or the position of an upper surface of the stage. The workpiece may be a semiconductor wafer in an exposure system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a simplified block diagram illustrating a wafer scanner-stepper. 
     FIG. 2 illustrates a wafer stage including a lower, XY stage and an upper, leveling stage. 
     FIG. 3 is a block diagram of the adaptive control system of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention provides a method and apparatus for controlling the leveling table of a wafer stage. In the following description, numerous details are set forth in order to enable a thorough understanding of the present invention. However, it will be understood by those of ordinary skill in the art that these specific details are not required in order to practice the invention. Further, well-known elements, devices, process steps and the like are not set forth in detail in order to avoid obscuring the present invention. 
     The dynamics of the leveling mechanism of the wafer table of FIG. 2 may be represented by the following simplified equation. 
     
       
           M ( q ) {umlaut over (q)}+C ( q,{dot over (q)} ) {dot over (q)}+Kq=T   (1) 
       
     
     where 
     q=[q 1 , q 2 , q 3  ] T  is a generalized coordinate measured by the encoders 
     T=[τ 1 , τ 2 , τ 3 ] T  is the torque force applied by the three actuator motors 
     M is a 3×3 matrix representing the inertia of the leveling assembly, including the leveling mechanism, the table itself, attachments such as interferometer mirrors, etc. 
     C is a 3×3 matrix representing centripetal and Coriolis forces of the leveling mechanism. 
     K represents the stiffness of the leveling mechanism, including stiffness corresponding to springs (not shown) interposed between the upper (leveling) table and the lower (XY) table. 
     Define the coordinate transformation matrix R as 
     
       
           Z=R ( q )  (2) 
       
     
     where Z=(z,θ x ,θ y ) T  represents the position at the wafer surface. Alternatively, Z may represent the upper surface of the leveling stage. Z may be measured by a standard AL/AF (auto-level/auto-focus) technique. For further reference, please see co-assigned U.S. Pat. No. 5,448,332, issued to Sakakibara et al, incorporation by reference herein. The R matrix transforms coordinates from q to Z, and may be calculated using well-known mathematical techniques. 
     With respect to differential motion, 
     
       
           ΔZ=J ( q ) Δq   (3) 
       
     
     where J is the Jacobian of R. 
     Now divide the control force T into what will be denoted a “feedback” force and a “feedforward” force. FIG. 3 is a block diagram of the adaptive control system  300  of the present invention that illustrates feedback and feedforward forces applied to the wafer stage. Note that the reticle mechanism and components relating to XY stage control have been omitted so as to not obscure the figure. The system comprises a feedback portion  302  and a feedforward portion  304 . The feedback portion  302  includes an encoder  216 , which is coupled to the actuator motor  210  and feeds back a signal q enc  representing the generalized coordinate at the actuator motor  210 . The generalized coordinate is subtracted from the input position q, and transformed by coordinate transform circuitry  305 , e.g., using J(q), to represent differential motion at or near the wafer. 
     Based on this transformed feedback measurement, a wafer controller  306  outputs a torque force T fb , which is added to feedforward forces (discussed below). The resulting sum is inversed transformed by inverse transform circuitry  307  back to the generalized coordinate domain, i.e., in coordinates corresponding to the leveling mechanism. This force is applied to the leveling assembly  308 , which supports wafer  104 . The leveling assembly  308  includes standard components such as the leveling mechanism  208  (e.g., motors, wedges, rollers ,etc.) and the leveling stage  202  of FIG.  2 . 
     The feedforward portion  304  includes a sensor  310 , such as an AL/AF sensor, which provides a signal ΔZ. The quantity ΔZ represents the change in height of the wafer  104  (or alternatively the upper surface of the stage) over one servo cycle. The servo cycle represents the time period between adjustments in the position of the wafer stage. The use of two sensors (e.g., encoder and AL/AF) for measuring position in the z direction distinguishes the invention from typical conventional systems. 
     The feedforward portion  304  also includes an adaptive inertial controller  312  that provides a torque output T ff , and an adaptive tilt controller  314  that provides a torque force T ffxy . All of the torque forces T fb , T ff  and T ffxy  are input to the wafer stage  308  (through inverse transformer  307 ) to control the actuator motors  210 . The feedback force T fb  is applied at all times. The feedforward force T ff  is applied when commands are input to move the leveling stage in the Z direction. The feedforward force T ffxy  is applied when commands are input to move the XY stage in the XY plane. 
     As is known in the art, feedback controllers such as the feedback wafer controller  306  correct relatively small errors. Conventional feedback controllers cannot completely correct large errors, such as those caused by inertia, and act on such errors only very slowly. 
     The feedforward control compensates for non-linear dynamics of the leveling assembly (e.g., stage, motors, wedges, rollers, etc.). Focusing first on the adaptive inertial controller  312 , the control force T can be rewritten as 
     
       
           T=T   ff    +T   fb   (4) 
       
     
     Referring back to Equation (1), the second and third terms are small quantities compared to the first term, and for the most part are corrected by the feedback force T fb . It is a good assumption that the feedforward force T ff  will compensate the larger first term in Equation (1), as follows. Define 
     
       
           M ( q ) {umlaut over (q)}≡T   ff   (5) 
       
     
     This equation illustrates that the feedforward force compensates for the inertia of the leveling assembly. This inertia includes all inertial errors between the encoders and the point where Z is measured, e.g., the upper surface of the wafer or the leveling stage. These inertial errors include, but are not limited to, the heavy mass of the leveling stage and nonlinear forces such as backlash, screw flexure, side force effects of the wedges, and nonlinear actuator effects. Traditional feedback action cannot effectively compensate for these errors. 
     In a real-time implementation, the acceleration {umlaut over (q)}is computed with difficulty. It may contain high-magnitude noise. The acceleration is calculated by taking the double derivative of the input position q. The acceleration is provided by the control computer of the system. The real inertia matrix M may also be unknown. To resolve this problem, a self-tuning or adaptive scheme is used. First, make the following approximation. 
     
       
           M ( q ) {umlaut over (q)}≡{circumflex over (M)}a   (6) 
       
     
     where 
     
       
           a=[a   z   ,a   θx   ,a   θy ] T   
       
     
     The acceleration a is defined as the acceleration in the Z direction. Through this definition, the force T ff  compensates for nonlinear dynamics when attempting to move the leveling stage in the Z direction. 
     Although the inertia is not time varying, the quantity {circumflex over (M)}is assumed to be a time-varying system in order to allow it to be adaptively updated. The matrix can be thought of as a virtual inertial mass. The acceleration a is an estimated desired acceleration input corresponding to {umlaut over (q)}. 
     By applying the well-known LMS (least mean square) method, {circumflex over (M)}can be updated by the following formula. 
       Δ{circumflex over (M)}=μ ( J   −1   ΔZ ) a   (7) 
     where μ is a symmetric positive definite matrix related to the correlation function of the input acceleration. A small μ requires a long convergence time, but typically indicates a stable system. Conversely, a large μ indicates a fast convergence, but is more likely to represent an unstable system. Calculation of μ is well known in the art. For further information, please refer to S. Haykin,  Adaptive Filter Theory , Prentice Hall, 2d edition, 1991, which is incorporated by reference herein. 
     To initialize the algorithm, {circumflex over (M)}can be initialized with each diagonal element representing the mass of the leveling stage. 
     During the servo cycle in which {circumflex over (M)}is updated, the next value of {circumflex over (M)}is calculated as follows. 
     
       
           {circumflex over (M)}   i+1   ={circumflex over (M)}   i+Δ   {circumflex over (M)}   (8) 
       
     
     where i is the servo cycle time index. (Generally, the index is included only where necessary for clarity, but otherwise is omitted for the sake of convenience.) 
     Based upon the updated value of the inertia, the inertial feedforward force may be calculated as follows. 
     
       
           T   ff   ≡{circumflex over (M)}a   (9) 
       
     
     The force is applied to the leveling mechanism to compensate for nonlinear dynamics, such as the effect of the inertia on control of the leveling stage. The known prior art ignores the effect of inertia. 
     Another effect ignored by the known prior art is tilt. When the lower (XY) stage accelerates or decelerates in the XY plane, a nonlinear coupling force will disturb the leveling upper stage in the z direction. 
     Using a technique similar to that employed to compensate for inertia, the system of the invention first assumes that there exists a virtual disturbance force D due to the effect of the lower stage. D is unknown and is a function of the X and Y acceleration on the lower stage: a x , a y . An additional feedforward force T ffxy  is added to compensate this disturbance. To adaptively calculate D, the following approximation is made. 
     
       
           D ( a   x   , a   y )≡ {circumflex over (D)}α   (10) 
       
     
     The matrix {circumflex over (D)}is assumed to be a time-varying system, and is initialized to zero. The matrix {circumflex over (D)}can be thought of as a virtual disturbance mass, and is associated with an acceleration: 
     
       
           α=[a   x   , a   y ] T   (11) 
       
     
     The XY table acceleration α is known from the control computer command given to the lower stage to move the lower stage along the scan and step path. Alternatively, α may be measured using standard techniques, such as laser interferometry. Through the definition of α, the force T ffxy  compensates for nonlinear dynamics when the control computer commands the XY stage to move in the XY plane. 
     {circumflex over (D)}may be updated as follows: 
     
       
           Δ{circumflex over (D)}=Γ ( J   −1   ΔZ )α  (12) 
       
     
     The matrix Γ is calculated using the same techniques used to calculate the matrix μ in Equation (7). 
     During each servo cycle {circumflex over (D)}is updated as follows: 
     
       
           {circumflex over (D)}   i+1   ={circumflex over (D)}   i   +Δ{circumflex over (D)}   (13) 
       
     
     The feedforward force T ffxy , applied by the adaptive tilt controller  314 , is calculated as follows: 
     
       
           T   ffxy   ≡{circumflex over (D)}α   (14) 
       
     
     This tilt compensation force is added to the inertial compensation force T ff , and the sum is applied to the leveling stage actuators. 
     The present invention provides for feedforward compensation of non-linear dynamic characteristics of the leveling stage, such as inertia and tilt. By doing so, the system of the present invention provides for more accurate positioning and leveling in the z direction, and a faster settling time than the prior art. In particular, by transforming the position measured by the encoders to position at the stage surface, the invention minimizes errors at the surface while reducing measurement delay. 
     Although the invention has been described in conjunction with particular embodiments, it will be appreciated that various modifications and alterations may be made by those skilled in the art without departing from the spirit and scope of the invention. For example, the control techniques of the invention do not apply only to a typical wafer stage. Therefore, the term “stage” as used herein means not only a stage used to support a semiconductor workpiece, but any object for which motion is controlled. Moreover, the invention may be incorporated into (and thereby include) a conventional semiconductor exposure system with appropriate modifications. Further, please note that the term “circuitry” as used herein includes any hardware, software or firmware that may be used to achieve the desired functionality. The invention is not to be limited by the foregoing illustrative details, but rather is to be defined by the appended claims.