Abstract:
An exemplary interferometer system includes an interferometer producing data from at least one interferometer beam. A source of gently flowing gas or gas mixture (atmosphere) produces a gas flow substantially normal to the beam pathway. A perturbation source (e.g., resistance heater) upstream of the beam pathway produces, in a repetitively pulsed manner, perturbed loci in the flowing atmosphere in selected locations upstream of the beam pathway. The perturbed loci flow to the interferometer beam(s). Data from the interferometer are received by a processor programmed with an algorithm that calculates, based on the data obtained during a perturbation pulse, the effect of the perturbed loci on the at least one interferometer beam as the loci pass through the interferometer beam. The processor also updates the algorithm based on data obtained from the interferometer during a subsequent perturbation pulse, compared to a previous perturbation pulse.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to, and the benefit of, U.S. Provisional Application No. 61/081,631, filed on Jul. 17, 2008, which is incorporated herein by reference in its entirety. 
     
    
     FIELD 
       [0002]    This disclosure pertains to, inter alia, interferometric position-measuring devices and methods for determining position of a first object relative to a second object or relative to a location, such as, for example, position of a stage relative to an optical system or to an axis of the optical system in a microlithographic exposure system. 
       BACKGROUND 
       [0003]    The proper functioning of various systems and apparatus relies upon an ability to position an object, such as a workpiece, accurately and precisely, such as relative to a machining tool, processing tool, or imaging device. Object placement is perhaps most critical in lithographic exposure systems used in the fabrication of microelectronic devices, displays, and the like. These systems, called microlithography systems, must satisfy extremely demanding criteria of image-placement, image-resolution, and image-registration on the lithographic substrate. For example, to achieve feature sizes, in projected images, of 100 nm or less on the substrate, placement of the substrate for exposure must be accurate at least to within a few nanometers or less. Such criteria place enormous technical demands on stages and analogous devices used for holding and moving the substrate and for, in some systems, holding and moving a pattern-defining body such as a reticle or mask. 
         [0004]    The current need for stages capable of providing extremely accurate placement and movement of reticles, substrates, and the like has been met in part by using laser interferometers for determining stage position. Microlithography systems typically use at least two perpendicular sets of laser interferometer beams to measure the horizontal (x-y) two-dimensional position of a stage movable in the x and y directions. The stage and interferometer system are enclosed in an environmental chamber containing a flow of highly filtered and temperature-controlled air, in part to prevent deposition of particulate matter on the lithographic substrate or on the reticle. The environmental chamber thus assists in maintaining the index of refraction of the air at a substantially constant value by maintaining constancy of the air temperature. 
         [0005]    In many types of microlithography systems, a projection-optical system (“projection lens”) is situated between a reticle stage and a substrate (wafer) stage. The projection lens is rigidly mounted on a rigid, vibration-isolation support to suppress motion of the projection lens. The projection lens must remain very still during the making of lithographic exposures from the reticle to the substrate. 
         [0006]    In view of the importance of aligning the stages very accurately with the projection lens, the projection lens (or stable structure to which the projection lens is mounted) is often used as a reference body for determining the position of the stages. In other words, the respective position of each stage is determined relative to the projection lens. For such a purpose, reference mirrors for reflecting reference interferometer beams are mounted to the column containing the projection lens. Usually, for each stage two reference mirrors (at right angles to each other) are provided on the projection lens, one for reflecting x-direction reference interferometer beams and the other for reflecting y-direction reference interferometer beams. 
         [0007]    This scheme is illustrated in  FIGS. 1(A)-1(C) , showing a projection lens  202 , a stage  204  (e.g., wafer stage), one x-direction “fixed” reference beam  206  produced by an x-direction reference interferometer  208 , and two y-direction reference beams  210 ,  212 . The x-direction reference beam  206  is incident on the mirror  214 , and the y-direction reference beams  210 ,  212  are incident on the mirror  216 . The mirrors  214 ,  216  are at right angles to each other and are mounted on or at least associated with the projection lens  202 . Associated with the x-direction reference beam  206  is an x-direction measurement beam  218 , produced by an x-direction measurement interferometer  220 , incident on a mirror  222  on the stage  204 . Similarly, associated with each y-direction reference beam  210 ,  212  is a respective y-direction measurement beam (not shown) incident on the stage  204 . These two y-direction measurement beams are used for detecting yaw of the stage  204  (i.e., motions of the stage about the axis Ax extending in the z-direction). Additional interferometer beams may be present to provide corrections to the stage position from other motions of the stage, such as pitch, roll, or height. 
         [0008]    Stage position in the x-direction, for example, can then be corrected for small motions of the lens, by subtracting the lens x-position, determined from the x-direction reference beam  206 , from the stage x-position. If the stage is traveling only in the x-direction, the length of the x-direction reference beam  206  can be subtracted directly from the x-direction measurement beam  218 . If the stage motion is not purely in the x-direction, the length of the x-direction reference beam  206  is subtracted from the x-displacement component, which is calculated from measurement information obtained from the stage-measurement interferometers. This correction method assumes any changes in the path-length of the x-direction reference beam  206  are caused by motion of the projection lens  202 . However, if the optical path-length of the x-direction reference beam  206  changes because the optical properties of the ambient atmosphere change, an erroneous correction to the position of the projection lens  202  will be produced. 
         [0009]    Fluctuations in the optical path-length of the x-direction measurement beam  218 , caused by changes in the optical properties of the ambient atmosphere through which the beam propagates, will cause further errors in the stage position. For example, air experiencing local variations in temperature exhibits corresponding variations in density and refractive index. If air turbulence is occurring in the propagation pathway of an interferometer beam, the turbulence can form regions, or cells, of air of different refractive indices. The cells change the optical path length of the beam, and thus degrade the accuracy and precision of positional measurements determined by the interferometer. Various approaches have been adopted to address this problem, notably by enclosing the stages and interferometers in an environmental chamber, as noted above, and by producing and maintaining improved (gentle laminar flow and constant temperature) air circulation in the vicinity of the interferometers and stages. Exemplary approaches are discussed in, for example, U.S. Pat. No. 4,814,625 to Yabu, U.S. Pat. No. 5,141,318 to Miyazaki, and U.S. Pat. No. 5,870,197 to Sogard et al., all incorporated herein by reference. In general, referring again to  FIGS. 1(A)-1(C) , the corresponding reference and measurement beams  206 ,  218  are situated as close as possible to each other and have similar respective lengths. The beams  206 ,  218  are situated in a stream of air (arrows  224 ) flowing from the reference beam(s) to the measurement beam(s). The air flow  224  is at a right angle to the beams  206 ,  218 . 
         [0010]    It has been proposed to use air-temperature fluctuations in the pathway of a wafer-stage reference interferometer beam, which propagates to a fixed mirror on the projection lens, to correct for air fluctuations in a wafer-stage measurement interferometer beam that is close to the reference beam but downstream from and parallel to it. The general concept is that air fluctuations contained in the down-flow of air perturb the reference beam, and that these air fluctuations propagate substantially unchanged from the reference beam to the measurement beam where the fluctuations contribute similar perturbations. However, the fluctuations at the measurement beam are actually not identical to the fluctuations at the reference beam. Also, there is a time delay in air flow from the reference beam to the measurement beam that depends upon the air-flow velocity, and the air-flow velocity in this region fluctuates in time. Consequently, a simple static predictive algorithm does not provide sufficiently accurate predictions. In this regard, reference is made to U.S. Patent Publication No. US-2008/0291464-A1, incorporated herein by reference. 
         [0011]    The conventional algorithm operates “open loop,” without feedback from the measurement signal to check the algorithm during operation. In  FIG. 2  the reference interferometer beam  206  reflects from a mirror  214  on the projection lens  202 , and the measurement interferometer beam  218  reflects from a mirror  222  on the stage  204 . Air flow is indicated by the arrows  224 . A stage controller  230  is connected to the stage  204 . The stage controller  230  controls execution of an algorithm  232  according to data  234  from the reference interferometer  208 . The algorithm  232  determines reference data  236  (not shown in  FIG. 2 ) that includes the effects of detected fluctuations in the reference interferometer beam  206 . Measurement data  238  obtained by the measurement interferometer  220  are compared with the reference data  236  to produce “fluctuation-corrected” measurement-interferometer data  240 . 
         [0012]    Operating open loop, the data obtained from the conventional algorithm concerning measurement-beam fluctuations are not checked in real time. Rather, only an initial calibration is performed, based on a difference measurement. Thus, especially over time, there is also no way to check that the measurement-beam fluctuations have been corrected accurately by the algorithm  232 . The calibration is performed using, for example, field image alignment (FIA) measurements of alignment marks. 
         [0013]    Air fluctuations are associated with turbulence in the air flow, and turbulence is a non-stationary process that cannot be entirely addressed by operation of a fixed (unchanging or non-adaptable) algorithm. For example, in an air stream, air-flow velocity tends to fluctuate somewhat in time and space.  FIG. 3  shows a plot, obtained in an analysis of air flow in an interferometer test fixture, of the time-delay of correlated cells of air traveling between two parallel interferometer beams. The unit of time delay on the ordinate is given as “lags.” One “lag” is equal to a time delay of 1.536 millisecond. Ideally,  FIG. 3  is a straight line, but that is not actually the case. If the time-delay varies as shown, then predicted corrections may be applied out of phase with actual fluctuations in the measurement, leading to error. (In this regard, “phase” is related to the delay time of a perturbation between the reference and measurement beams.) Similarly, the cells of air of varying index of refraction may change shape or size as they travel from the first beam to the second beam, also leading to error. 
         [0014]    As described in the &#39;464 application mentioned above, it is possible to improve performance over the conventional algorithm by introducing an adaptive algorithm, or adaptive filter, that changes its properties with changes to the air-flow properties, such as changes in time delay or large-scale properties of the air flow. The &#39;464 application describes an adaptive filter that predicts fluctuations in a measurement interferometer beam from fluctuations in a reference interferometer beam located in the same air flow from the measurement beam. Obtaining real-time fluctuation information from the measurement beam, in order to update the parameters of the adaptive filter, is however very difficult because the fluctuations have to be separated from the much larger changes to the measurement interferometer signal from stage motion. 
         [0015]    A better application of adaptive filters is to provide a second, redundant reference interferometer beam that is parallel to and upstream from the first reference interferometer beam. As described in the &#39;464 application an adaptive filter can be constructed that predicts fluctuations in both the measurement-interferometer beam and the first reference-interferometer beam. The adaptive filter parameters are updated based on the measured fluctuations in the first reference-interferometer beam. It must be assumed that the changes to the air-flow properties, recorded between the two reference interferometer beams, must apply as well to the measurement-interferometer beam and the first reference-interferometer beam. This algorithm is believed to be superior to the simple open-loop algorithm. 
         [0016]    However, adding a second reference interferometer beam may be difficult and/or expensive, since space is typically very limited near the projection lens, and a very high degree of mechanical stability is required in order to make the addition worthwhile. 
         [0017]    In view of the above, an algorithm is needed that is not fixed, but rather is updated sufficiently frequently, and which is compact, easy to install, and relatively inexpensive. 
       SUMMARY 
       [0018]    The deficiencies of the prior art summarized above are resolved using interferometer systems and methods according to various aspects of the invention, as summarized below. According to one aspect, an interferometer system is provided that comprises an interferometer that produces data from at least one interferometer beam. The system also includes a source of a gently flowing gas or gas mixture (atmosphere) that flows substantially normal to the beam pathway. A perturbation source (such as, but not limited to, a resistance heater) is situated upstream of the beam pathway. The perturbation source produces, in a repetitively pulsed manner, perturbed loci in the flowing atmosphere in selected locations upstream of the beam pathway, such that the perturbed loci flow to the at least one interferometer beam. Data from the interferometer are received by a processor. The processor is programmed with an algorithm that calculates, based on the data obtained during a perturbation pulse, the effect of the perturbed loci on the at least one interferometer beam as the loci pass through the interferometer beam. The processor also updates the algorithm based on data obtained from the interferometer during a subsequent perturbation pulse, compared to a previous perturbation pulse. 
         [0019]    The perturbations in the interferometer beam typically produce respective peaks or analogous features in the interferometer signal. Passing the interferometer data through, for example, a low-pass filter or band pass filter isolates the peaks reasonably well by removing high-frequency components of the signal. In other words, the signal fluctuations arising from operation of the perturbation source are separable from other fluctuations, especially if the fluctuations from the perturbation source occur at an approximately fixed repetition rate and amplitude. Although the fluctuations tend to increase the total interferometer fluctuations to be removed, the algorithm corrects for the fluctuations. 
         [0020]    The interferometer system desirably includes at least a reference interferometer that produces at least one reference interferometer beam. The interferometer system also can comprise a measurement interferometer that produces data from at least one measurement interferometer beam. These data are compared by the processor with data obtained from the reference interferometer beam. The measurement-interferometer beam desirably propagates parallel to the reference-interferometer beam and is situated such that the flowing atmosphere, with perturbed loci, reaches the measurement-interferometer beam after passing across the reference-interferometer beam pathway. 
         [0021]    In some embodiments an exemplary perturbation source is a resistance heater or other heat source situated in the flowing atmosphere upstream of the interferometer beam. A repetitively pulsed power source is connected to the heater and operated to produce loci (“cells”) of heated air. These cells are carried along by the flowing atmosphere to the interferometer beam(s) where the cells cause corresponding fluctuations in the beams. A particularly effective configuration of resistance heater comprises at least one wire extending parallel to the interferometer-beam pathway, normal to the flow direction of the atmosphere and upstream of the interferometer beams. 
         [0022]    In embodiments including at least one reference interferometer and at least one measurement interferometer, the respective interferometer beams are located in the flowing atmosphere and propagate parallel to each other in a direction normal to the direction of flow of the atmosphere. For example, the measurement interferometer beam is located downstream of the reference interferometer beam. A processor connected to the reference and measurement interferometers is programmed with an algorithm that, based on received data (including the fluctuations) from the interferometers, calculates corrections to the measurement-beam data based on detected time delays of the fluctuations in the reference and measurement beams. The processor can be further configured to detect changes in amplitude of the interferometer signals caused by the perturbation source and to determine amplitude corrections based on the detected changes. 
         [0023]    The system can further comprise a filter connected to the reference interferometer to isolate perturbations of data from the reference interferometer caused by the perturbation source heating the atmosphere flowing past the reference and measurement beams. For improved detection of perturbation peaks in the interferometer signals, the system can further comprise a low-pass filter connected between the reference interferometer and the filter. 
         [0024]    According to another aspect, methods are provided determining the position of an object using interferometry. An embodiment of the method comprises directing an interferometer beam along a beam pathway to the object so as to reflect from the object. The interferometer beam thus produces data from the interferometer beam regarding position of the object. Meanwhile, flow of an atmosphere is directed substantially normal to the beam pathway. In a repetitively pulsed manner, a pulses of perturbed loci are produced in selected locations in the flowing atmosphere upstream of the beam pathway such that the perturbed loci flow to and across the beam pathway. Using an algorithm, data are produced from the interferometer beam as the perturbed loci pass across the beam pathway(s) during the perturbation pulse. During a subsequent perturbation pulse, data from the interferometer beam reflect the perturbation as the respective perturbed loci pass across the beam pathway. The algorithm is updated based on changes in the data obtained during the subsequent pulse compared to data obtained during the first pulse. 
         [0025]    The various aspects of the invention summarized below provide greater accuracy in determinations of position and movement performed by interferometry. Obtaining this greater accuracy is especially important in precision systems including one or more interferometers. An example precision system is, but is not limited to, a microlithography system used for exposing patterns of extremely small features onto the exposure-sensitive surface of a lithographic substrate such as a semiconductor wafer. 
         [0026]    The foregoing and additional features and advantages of the subject invention will be more apparent from the following detailed description, which proceeds with reference to the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0027]      FIGS. 1(A)-1(C)  are respective orthogonal views of a conventional manner of interferometrically determining position of a stage relative to a projection lens. 
           [0028]      FIG. 2  is a control diagram of a conventional open-loop manner of controlling position and movement of a substrate stage. 
           [0029]      FIG. 3  is a plot, obtained in an analysis of air flow in a conventional interferometer test fixture, of the time-delay of correlated cells of air traveling between two parallel interferometer beams. 
           [0030]      FIGS. 4(A)-4(B)  are orthogonal views of an embodiment including a heating element located in an air stream upstream of the reference interferometer beam. The heating element in this embodiment is energized periodically by a pulse train of electrical power from a power source. 
           [0031]      FIG. 5(A)  is a time plot of electrical power pulses delivered to the heating element in the embodiment shown in  FIG. 4(A) . 
           [0032]      FIG. 5(B)  is a time plot of signals produced by the reference interferometer in  FIG. 4(A)  as heated air from the heating element passes across the interferometer beam. 
           [0033]      FIG. 5(C)  is a time plot of signals produced by the reference interferometer in  FIG. 4(A)  in the absence of units of heated air from the heating element passing across the interferometer beam. 
           [0034]      FIG. 5(D)  is a time plot of signals summed from  FIGS. 5(B) and 5(C) . 
           [0035]      FIG. 6(A)  is a plot of wire temperature versus time as the heating element is energized in a repetitively pulsed manner; data are presented for three different time constants at a pulse rate of 10 Hz. 
           [0036]      FIG. 6(B)  is a plot of wire temperature versus time as the heating element is energized in a repetitively pulsed manner; data are presented for three different time constants at a pulse rate of 5 Hz. 
           [0037]      FIG. 7  is a plot of wire time-constants as a function of wire diameter for four different wire materials considered for use as a heating element. Air velocity=0.3 m/sec. 
           [0038]      FIG. 8  is a control diagram of an embodiment of a fluctuation-corrected interferometer system. 
           [0039]      FIG. 9(A)  is a schematic diagram of an example embodiment of a microlithography system comprising at least one fluctuation-corrected interferometer system. 
           [0040]      FIG. 9(B)  is a schematic isometric view of a substrate stage, such as used in the system embodiment of  FIG. 9(A) , including at least one fluctuation-corrected interferometer system. 
           [0041]      FIG. 9(C)  is a schematic plan view of the substrate stage shown in  FIG. 9(B) . 
           [0042]      FIG. 10  is a block diagram of a micro-device fabrication process including a wafer-processing step comprising a microlithography step performed using a microlithography system such as shown in  FIG. 9(A) , for example. The depicted process includes design of the function and performance characteristics of the micro-device. 
           [0043]      FIG. 11  is a block diagram of representative details of a wafer-processing process including a microlithography step performed using a microlithography system such as shown n  FIG. 9(A) , for example. 
       
    
    
     DETAILED DESCRIPTION 
       [0044]    This disclosure is set forth in the context of representative embodiments that are not intended to be limiting in any way. 
         [0045]    As used in this application and in the claims, the singular forms “a,” “an,” and “the” include the plural forms unless the context clearly dictates otherwise. Additionally, the term “includes” means “comprises.” Further, the term “coupled” encompasses mechanical as well as other practical ways of coupling or linking items together, and does not exclude the presence of intermediate elements between the coupled items. 
         [0046]    The described things and methods described herein should not be construed as being limiting in any way. Instead, this disclosure is directed toward all novel and non-obvious features and aspects of the various disclosed embodiments, alone and in various combinations and sub-combinations with one another. The disclosed things and methods are not limited to any specific aspect or feature or combinations thereof, nor do the disclosed things and methods require that any one or more specific advantages be present or problems be solved. 
         [0047]    Although the operations of some of the disclosed methods are described in a particular, sequential order for convenient presentation, it should be understood that this manner of description encompasses rearrangement, unless a particular ordering is required by specific language set forth below. For example, operations described sequentially may in some cases be rearranged or performed concurrently. Moreover, for the sake of simplicity, the attached figures may not show the various ways in which the disclosed things and methods can be used in conjunction with other things and method. Additionally, the description sometimes uses terms like “produce” and “provide” to describe the disclosed methods. These terms are high-level abstractions of the actual operations that are performed. The actual operations that correspond to these terms will vary depending on the particular implementation and are readily discernible by one of ordinary skill in the art. 
         [0048]    In the following description, certain terms may be used such as “up,” “down,” “upper,” “lower,” “horizontal,” “vertical,” “left,” “right,” and the like. These terms are used, where applicable, to provide some clarity of description when dealing with relative relationships. But, these terms are not intended to imply absolute relationships, positions, and/or orientations. For example, with respect to an object, an “upper” surface can become a “lower” surface simply by turning the object over. Nevertheless, it is still the same object. 
         [0049]    As discussed above, the fluctuations from air turbulence in air flowing from a reference interferometer beam to a measurement interferometer beam are not constant; they fluctuate in time. This fluctuation adversely affects the phase of the correction that is applied by a conventional fixed algorithm to the measurement beam. 
         [0050]    In various embodiments as disclosed herein, substantially real-time corrections are made to the predictive algorithm used for correcting measurement-interferometer data based on deliberate air-current perturbations detected by a corresponding reference interferometer. In other words, a known perturbation in time is introduced to the reference-interferometer signal, wherein the perturbation is related to the properties of air flow across the reference-interferometer beam. An embodiment  400  is shown in  FIGS. 4(A)-4(B) , in which a known perturbation over time is introduced to the reference-interferometer signal. The perturbation is related to the properties of the air flow past the reference beam. Shown are a projection-lens system  402  and a wafer stage  404  situated downstream of the projection-lens system  402  relative to the optical axis Ax. A mirror  406  is mounted to the projection-lens system  402  (or to an optical frame, not shown, to which the projection-lens system  402  is mounted). A mirror  408  is mounted to the wafer stage  404 . A reference interferometer  410  directs a reference beam  412  to the mirror  406 , and a measurement interferometer  414  directs an interferometer measurement beam  416  to the mirror  408 . Situated above the reference beam  412  is an air source  423  (not shown) that releases a gentle flow of air (arrows  422 ) toward the reference beam  412 . Situated between the reference beam  412  and the air source  424  is a resistive heater  418  that extends parallel to the reference beam. The distance between the resistive heater  418  and the reference beam  412  is denoted “h”. This distance is a key variable used in calculations involving air-flow velocity. The resistive heater  418  desirably is configured as a longitudinally extended wire or the like that is connected to a power supply  420  configured to generate a pulse train of electrical current. The resistive heater  418 , reference beam  412 , and measurement beam  416  are situated within a duct  422  or analogous enclosure. 
         [0051]    The pulse train produced by the source  420  generally has a pre-set fixed frequency. As a pulse of electrical current is delivered to the resistive heater  418 , the resistive heater produces a corresponding pulse of heat that is imparted to the air  422  passing by the resistive heater. An example temperature increase of the air is 50° C. above ambient, but this magnitude is not limiting. The heat pulses create small cells of heated air that flow (indicated by the arrows  422 ) to the reference interferometer beam  412 , causing fluctuations in the reference beam. The air cells then proceed to the measurement interferometer beam  416 . Based upon the pulse waveform, these deliberate perturbations imparted by the air cells in the environment of the reference beam can be separated (e.g., by use of a filter) from the data obtained by the reference interferometer. This separation is facilitated by the fact that the perturbations occur at a substantially fixed rate and have substantially equal magnitude, which produces accurate data regarding changing properties of the flowing air. Since the power spectrum of air-temperature fluctuations falls rapidly with increasing frequency, in many embodiments a repetition rat of 5-10 Hz generally allows a clean separation of the deliberate fluctuations from normal, non-deliberate, fluctuations, especially if filtering is used to perform the separation. 
         [0052]    Plots of representative signals are provided in FIGS. ( 5 A)- 5 (D).  FIG. 5(A)  is a plot of the pulse train delivered by the source  420  to the resistance heater  418 . In this example, the pulse frequency is 5 Hz, in which a pulse is produced every 0.2 second. Note that the pulses are reproducible and at fixed intervals. Although the ordinate is in pulse units, it alternatively could be in units of electrical power, such as watts.  FIG. 5(B)  is a plot of corresponding signals as sensed at the reference beam  412 . Although somewhat similar, the pulses exhibit some variation in shape, such as differences in amplitude for example. The pulses also have slightly variable arrival time. These differences reflect that, with each successive (and identical) pulse delivered to the resistance heater  418 , the resulting effect on the air  422  is not identical. In addition, the pulse shape is asymmetric, reflecting the finite temperature-decay rate of the heater material.  FIG. 5(C)  is a plot of the reference-beam signal in the absence of pulses being delivered to the resistance heater  418 ; i.e., the power source  420  is off during the time the data of  FIG. 5(C)  were obtained.  FIG. 5(D)  is a plot of the reference-beam signal with pulses being delivered to the resistance heater  418 . In the plot the peaks (corresponding to the peaks shown in  FIG. 5(B) ) are superimposed on the reference-beam signal of  FIG. 5(C) . 
         [0053]    Passing the signal in  FIG. 5(D)  through a low-pass filter isolates the peaks reasonably well by removing high-frequency components of the signal. In other words, the signal fluctuations arising from operation of the resistance heater  418  ( FIG. 5(B) ) are separable from the original fluctuations ( FIG. 5(C)  because the fluctuations arising from the resistance heater occur at an approximately fixed repetition rate and amplitude. Although the fluctuations tend to increase the total interferometer fluctuations to be removed, the algorithm serves to correct for the fluctuations. 
         [0054]    If the resistance heater  418  being turned on disturbs other portions of the lithography system, production and delivery of the pulses to the resistance heater can be limited, for example, to times in which exposures are not being made or otherwise when the added fluctuations do not disturb exposure. For example, the pulses can be produced during periods in which the stage  404  is turning around or while a substrate is being loaded or unloaded from the stage, during which the fluctuations normally do not cause a problem. 
         [0055]    The resistance heater  418  in this embodiment comprises a wire as shown in  FIG. 4 . The power source  420  delivers sufficient power to the wire to raise the wire&#39;s temperature only slightly (e.g., 50° C.), which prevents significant thermal deformation of the wire. The wire material can be a suitable metal that has long life under the conditions of use, that is chemically inert in its usage environment and conditions, and that has a coefficient of thermal expansion suitable for preventing significant thermal distortion of the wire during use. 
         [0056]    Alternatively to using a wire, the resistance heater  418  can comprise a resistance ribbon, which would provide more surface area than a wire. More surface area may provide more efficient heat transfer from the resistance heater  118  to the air  22 . Another alternative configuration is of a helical wire coil, which may offer the same benefits as a resistance ribbon. 
         [0057]    The air perturbations imparted by pulsing the resistance heater  418 , made in the manner described above, are repetitive and have a substantially constant magnitude. These characteristics facilitate correction for their effects almost entirely. Also, even though a fairly large amplitude perturbation was used to obtain the data of  FIGS. 5(A)-5(D) , use of a low-pass filter to isolate the pulse train can allow a much smaller-amplitude signal. 
         [0058]    The advantage of using a filter, such as a low-pass filter, to isolate further the interferometer response to the pulsed thermal perturbation must be weighed against the possible disadvantage of the unavoidable time delay associated with such filters. The time delay may make establishing real-time corrections to the correction algorithm more difficult. 
         [0059]    The output of the filter provides an update to the algorithm. Multiple outputs over time provide an ongoing update (calibration) of the algorithm. This ongoing update can be in real time. 
         [0060]    One can obtain further information about the change in fluctuation with height by adding additional resistive-heater wires at different heights above the measurement beam and pulsing them out of phase with each other or at incommensurate frequencies. A second reference beam would allow adaptation to be added to the algorithm, which can allow, for example, a check for motion of the optical system  402 . 
         [0061]    The wire of the resistance heater  418  desirably produces a sufficiently rapid temperature response to support stable heat-pulse trains. Also, the wire should be as thick as possible for safety. Regarding temperature response, after the wire receives a first power pulse, it is desirable that the temperature of the wire return to its initial (pre-pulse) value before commencing the next pulse. Reference is made to  FIG. 6(A) , which is a plot of wire temperature as a function of time, for three different representative time constants: 0.05, 0.025, and 0.01 second at a pulse frequency of 10 Hz. (These time constants assume exponential decay of wire temperature, with time after a pulse, to 0.37 of initial value.) The plot indicates that a time constant of 0.01 sec provides good separation of the temperature pulse peaks from each other.  FIG. 6(B)  is a similar plot for 5-Hz pulses. This plot indicates that time constants of 0.01 and 0.025 sec provide good separation of the temperature peaks. 
         [0062]      FIG. 7  is a plot of wire time constants as functions of wire diameter in air flowing at 0.3 m/sec. Copper and molybdenum wires of diameters ranging from 50 to 200 μm provide time constants in the range of about 0.007 second to 0.08 second. From these data, it is concluded that copper or molybdenum wire approximately 100 micrometers thick can be used for the wire in the resistance heater  418 . 
         [0063]      FIG. 8  is a block diagram of an embodiment of an interferometric position-measurement system  500 . The system  500  comprises an optical system  502  having an optical axis Ax, a stage  504  that is movable relative to the optical system, and a controller  506 . The optical system includes a stationary mirror  508 , and the stage  504  includes a moving mirror  510 . A reference interferometer  512  produces a reference beam  516 , and a measurement interferometer  514  produces a measurement beam  518 . The reference beam  516  reflects from the stationary mirror  508 , and the measurement beam  518  reflects from the moving mirror  510 . The interferometers  512 ,  514  and their respective beams  516 ,  518  are enclosed in a housing  520  into which air is introduced by an air source  522 . The air flows in a downward direction (arrows  524 ) past the reference and measurement beams  516 ,  518 . The housing  520  also includes a resistive heater  526  extending upstream of and parallel to the reference beam  516 . The resistive heater  526  is powered in a repetitively pulsed manner by a power supply  528 . The controller  506  is connected to the power supply  528  and to the stage  504 . Position data obtained by the reference interferometer  512  is routed to a filter  530 , desirably via a low-pass filter  532 . In some embodiments there is no filter. In other embodiments the filter  532  is a band pass filter. If present, the filter  530  is connected to the algorithm processor  534 , which also receives operational commands from the controller  506 . Position data obtained by the reference interferometer  512  is also routed to a calibration processor  536 . The calibration processor  536 , also operating according to commands from the controller  506 , generates calibrated data that are routed via a low-pass filter  538  to the filter  530 . The output of the filter, comprising correction data, is routed to the algorithm processor  534  to update the algorithm therein. The algorithm processor  534  thus produces a fluctuation-corrected command  540 , based upon what is occurring with actual air fluctuations in the air through which the reference beam  516  propagates. The corrected command  540  is subtracted from the measurement-interferometer signal  542 , and the result can be fed back to the controller  506  and/or fed back to the filter  530 . This embodiment can provide substantially real-time correction data that yield a more accurate control of stage position relative to the optical system  502 , compared to conventional control systems. 
       Microlithography System 
       [0064]    The aspects of the invention described above are especially applicable to precision systems, of which an exemplar is a microlithography system. 
         [0065]      FIGS. 9(A)-9(C)  schematically depict an example embodiment of a microlithography system EX comprising features as described above. In  FIG. 9(A)  the microlithography system EX comprises a reticle stage  301  that is movable while holding a patterned reticle M, a substrate stage  302  that is movable while holding a substrate P, a first driving system  318  that controllably moves the reticle stage  301 , a second driving system  321  that controllably moves the substrate stage  302 , a measurement system  303  that includes laser interferometers for measuring and obtaining position data for the reticle stage  301  and substrate stage  302 , an illumination-optical system IL that illuminates the reticle M with an energy beam EL, a projection-optical system PL that projects the image of the pattern on the reticle M illuminated by the energy beam EL onto the substrate P, and a controller  304  that controls the operation of the entire microlithography system EX. 
         [0066]    The substrate P referred to herein is a substrate used for fabricating micro-devices. The substrate P is a semiconductor wafer, e.g., a silicon wafer, or other suitable substrate on which a photosensitive film has been formed. The photosensitive film is of photosensitive material (“photoresist”). Alternatively, the substrate P may have different types of films formed thereon such as a protective film (top-coat film) aside from a photosensitive film. The reticle M (also called a “mask”) defines a device pattern to be projected onto the substrate P. An example of a reticle is a transparent plate member, such as a glass plate, on which a given pattern has been formed using a light-shielding film such as chrome. This transmissive reticle is not limited to a binary reticle onto which a pattern is formed with a light-shielding film, but also includes a phase-shift mask such as a half-tone phase-shift mask or a spatial frequency-modulated phase-shift mask. Alternatively, a reflective reticle can be used, especially if the exposure wavelength requires a reflective reticle. 
         [0067]    In the present embodiment, descriptions will be given using an example where the microlithography system EX is an immersion-exposure system that exposes the substrate P with an energy beam EL through a liquid LQ. In this embodiment, a liquid immersion space LS is formed such that the liquid LQ fills the space of the optical path of the energy beam EL on the image-plane side of an endmost optical element  305 , closest to the image plane of the projection-optical system PL among a plurality of optical elements of the projection-optical system PL. The space of the optical path of the energy beam EL is a space that includes the optical path through which the energy beam EL passes. The liquid immersion space LS is a space filled with the liquid LQ. In this embodiment, water (purified water) is used as the liquid LQ. 
         [0068]    The microlithography system EX comprises a liquid-immersion member  306  used for forming the liquid space LS. The liquid-immersion member  306  is located near the endmost optical element  305 . The liquid-immersion member  306  can be as disclosed in International Published Patent Application No. 2006/106907, for example. The liquid-immersion space LS is formed between the endmost optical element  305  and the liquid-immersion member  306  and the object arranged in a position facing the endmost optical element  305  and the liquid-immersion member  306 . In this embodiment, objects that can be placed in the position facing the endmost optical element  305  and the liquid-immersion member  306  include the substrate stage  302  and the substrate P held by the substrate stage  302 . 
         [0069]    In this embodiment, the microlithography system EX utilizes a local liquid-immersion method in which the liquid-immersion space LS is formed such that a region on the substrate P that includes a projection region PR of the projection-optical system PL is partially covered by the liquid LQ. 
         [0070]    The microlithography system EX in this embodiment is a scanning-type exposure system (what is called “scanning stepper”) that projects the image of the pattern on the reticle M onto the substrate P while synchronously moving the reticle M and the substrate P in a given scan direction. When the substrate P is exposed, the reticle M and the substrate P are moved in a given scan direction in the XY plane that intersects with an optical axis AX 1  (optical path of the energy beam EL), of the projection-optical system PL, which is nearly parallel to the Z axis. In this embodiment, the scan direction (direction of the synchronous motion) of the substrate P is the Y-axis direction, and the scan direction (direction of the synchronous motion) of the reticle M is also the Y-axis direction. The microlithography system EX irradiates the energy beam EL onto the substrate P through the projection-optical system PL and the liquid LQ in the liquid-immersion space LS over the substrate P. Meanwhile, the system moves the substrate P in the Y-axis direction relative to the projection region PR of the projection-optical system PL, and also moves the reticle M in the Y-axis direction relative to an illumination region IR of the illumination-optical system IL in synchrony with the motion of the substrate P in the Y-axis direction. Thus, the image of the pattern on the reticle M is projected onto the substrate P, and the substrate P is exposed with the energy beam EL. 
         [0071]    The microlithography system EX comprises a body  309  that includes a first column  307  provided on a floor FL and a second column  308  provided on the first column  307 . The first column  307  comprises a plurality of first pillars  310  provided on the floor FL and a first surface plate  312  supported by the first pillars  310  via first anti-vibration devices  311 . The second column  308  comprises a plurality of second pillars  313  provided on the first surface plate  312  and a second surface plate  315  supported by the second pillars  313  via second anti-vibration devices  314 . The exposure system EX also comprises a third surface plate  317  supported by the floor FL via third anti-vibration devices  316 . Each of the first anti-vibration devices  311 , second anti-vibration devices  314 , and third anti-vibration devices  316  includes an active anti-vibration device comprising respective actuators and damper mechanisms. 
         [0072]    The illumination-optical system IL illuminates the given illumination region IR on the reticle M with the energy beam EL having a uniform illumination-intensity distribution. As the energy beam EL emitted from the illumination-optical system IL, emission lines (g-line, h-line, i-line) emitted from a mercury lamp, deep ultraviolet lights (DUV light) such as a KrF excimer laser light (with a wavelength of 248 nm), vacuum ultraviolet (VUV) light such as an ArF excimer laser light (with a wavelength of 193 nm) or an F 2  laser light (with a wavelength of 157 nm) can be used, for example. In this embodiment, an ArF excimer laser light, which is a VUV light, is used as the energy beam EL. 
         [0073]    The reticle stage  301  is made movable by the first driving system  318  that includes an actuator such as a linear motor while holding the reticle M. The reticle stage  301  moves on the second surface plate  315 . The second surface plate  315  has a guide surface  315 G that movably supports the reticle stage  301 . The guide surface  315 G is nearly parallel to the XY plane. The reticle stage  301  is movable in the XY plane that includes the location at which the energy beam EL from the illumination-optical system IL is irradiated. In this embodiment, the location at which the energy beam EL from the illumination-optical system IL is irradiated includes the location that intersects the optical axis AX 1  of the projection-optical system PL. Furthermore, the reticle M held by the reticle stage  301  is also movable in the XY plane that includes the location at which the energy beam EL from the illumination-optical system IL is irradiated. In this embodiment, the reticle stage  301  is movable in the X-axis, Y-axis, and θ Z  directions. 
         [0074]    The projection-optical system PL projects the image of the pattern, defined on the reticle M, onto the substrate P at a certain projection magnification. Multiple optical elements of the projection-optical system PL are mounted in a “barrel.” The barrel  319  has a flange  320 , and the projection-optical system PL is supported by the first surface plate  312  via the flange  320 . An anti-vibration device can be arranged between the first surface plate  312  and the flange  320  (barrel  319 ). 
         [0075]    The projection-optical system PL in this embodiment is a reduction system, with a projection magnification such as ¼, ⅕, or ⅛. The projection-optical system PL can also be either a 1× system or a magnification system. In this embodiment, the optical axis AX 1  of the projection-optical system PL is parallel to the Z axis. Furthermore, the projection-optical system PL can be any of a dioptric system that does not include catoptrical elements, a catoptrical system that does not include dioptric elements, or a catadioptric system that includes dioptric elements and catoptrical elements. In addition, the projection-optical system PL may form either an inverted image or an erected image. 
         [0076]    The substrate stage  302  is made movable by the second driving system  321 , including an actuator such as a linear motor, while holding the substrate P. The substrate stage  302  moves on the third surface plate  317 . The third surface plate  317  has a guide surface  173 G that movably supports substrate stage  302 . The guide surface  317 G is nearly parallel to the XY plane. The substrate stage  302  is movable in the XY plane that includes the location where the energy beam EL from the endmost optical element  305  (projection-optical system PL) is irradiated. In this embodiment, the location where the energy beam EL from the endmost optical element  305  is irradiated includes the location facing an exit plane  305 K of the endmost optical element  305  and the location that intersects with the optical axis of the endmost optical element  305  (optical axis AX 1  of the projection-optical system PL). In addition, the substrate P held by the substrate stage  302  is also movable in the XY plane that includes the location where the energy beam EL from the endmost optical element  305  (projection-optical system PL) is irradiated. In this embodiment, the substrate stage  302  is movable in six directions: X axis, Y axis, Z axis, θ X , θ Y , and θ Z . 
         [0077]    The substrate stage  302  has a substrate chuck  302 H that holds the substrate P, and has an upper surface  302 T arranged around the substrate chuck  302 H. The upper surface  302 T of the substrate stage  302  is a flat surface that is nearly parallel to the XY plane. The substrate chuck  302 H is located in a concave area  302 C arranged on the substrate stage  302 . The substrate chuck  2 H holds the substrate P such that the surface of the substrate P is nearly parallel to the XY plane. The surface of the substrate P held by the substrate chuck  302 H and the upper surface  302 T of the substrate stage  302  are placed in nearly the same plane and thus are nearly coplanar. 
         [0078]    Further with respect to  FIG. 9(A) , the microlithography system EX in this embodiment comprises a first detection device  323  for acquiring position data concerning the shot region on the substrate P. The first detection device  323  includes an off-axis-type alignment system arranged near the projection-optical system PL. At least some part of the first detection device  323  is located near the projection-optical system PL. The first detection device  323  is able to detect alignment marks AM on the substrate P and first fiducial marks FM 1  placed on the substrate stage  302  (reference plate  322 ; see  FIG. 9(C) ). The first detection device  323  in this embodiment adopts the FIA (Field Image Alignment) method, such as the one disclosed in the Japan Laid-Open Patent Application No. 4-65603 (corresponding to U.S. Pat. No. 5,493,403), where a broadband detection light flux that does not expose the photosensitive material on the substrate P is irradiated on target marks (such as the alignment marks AM formed on the substrate P and the first fiducial marks FM 1 ). An image of the target mark imaged on the light-receiving surface by the reflected light from the target mark and an index (index mark placed on an index plate placed inside the first detection device  323 ) is taken using an imaging device (such as a CCD). The imaging signals are image-processed to measure the position of the marks. 
         [0079]    In this embodiment, the first detection device  323  is located adjacent to the −Y side of the projection-optical system PL (endmost optical element  305 ). In this embodiment, the first detection device  323  is supported by the first surface plate  312 . 
         [0080]    The microlithography system EX in this embodiment also comprises a second detection device  324  for acquiring position information of the image of the pattern on the reticle M projected onto the image-plane side of the projection-optical system PL. The second detection device  324  includes a TTR (Through The Reticle) alignment system that uses a light having the wavelength of the exposure beam. At least some part of second detection device  324  is located near the reticle stage  301 . The second detection device  324  is able to observe simultaneously a pair of alignment marks on the reticle M and a conjugate image through the projection-optical system PL of second fiducial marks FM 2  placed on the substrate stage  302  (reference plate  322 ; see  FIG. 9(C) ) corresponding to the alignment marks. The second detection device  324  in this embodiment adopts the VRA (Visual Reticle Alignment) method, such as the one disclosed in Japan Laid-Open Patent Application No. 7-176468 (corresponding to U.S. Pat. No. 6,498,352), in which a light is irradiated on a mark, and image data of the mark imaged by an imaging device such as a CCD camera are image-processed to detect the position of the mark. 
         [0081]      FIG. 9(B)  is a schematic isometric view of an interferometer system  303 P for the substrate stage. The interferometer system  303 P has a first interferometer system  331 , a second interferometer system  332 , and a third interferometer system  333 . The first interferometer system  331  is arranged on the −X side relative to the projection-optical system PL. The second interferometer system  332  is arranged on the −X side relative to the first detection device  323 . The third interferometer system  333  is arranged on the −Y side relative to the first detection device  323 . The first detection device  323  is arranged on the −Y side of the projection-optical system PL. 
         [0082]    The first interferometer system  331  comprises a first interferometer  351  having a first beam-exit part  351 S from which a first beam B 1  is emitted and a second interferometer  352  having a second beam-exit part  352 S from which a second beam B 2  is emitted. The first and second interferometers  351  and  352  are laser interferometers, and the first and second beams B 1  and B 2  are laser beams. The first interferometer  351  obtains interferometric information based on the first beam B 1  by irradiating the first beam B 1  onto a first reflective surface  341  and receiving the reflected light of the first beam B 1  irradiated on first reflective surface  341 . The second interferometer  352  obtains interferometric information based on the second beam B 2  by irradiating the second beam B 2  onto a second reflective surface  342  and receiving the reflected light of the second beam irradiated on second reflective surface  42 . 
         [0083]    The first reflective surface  341  is a surface perpendicular to the X axis. That is, the first reflective surface  341  is a surface parallel to the YZ plane. For the first interferometer  351 , the X axis is the measurement axis. The first beam B 1  from the first interferometer  351  travels in the X-axis direction and is incident on the first reflective surface  341 . The first interferometer  351  receives the first beam B 1  reflected from the first reflective surface  341  and measures the position information of the first reflective surface  341  with respect to the X-axis direction. 
         [0084]    The second reflective surface  342  is a surface perpendicular to the X axis. That is, the second reflective surface  342  is a surface parallel to the YZ plane. For the second interferometer  352 , the X axis is the measurement axis. The second beam B 2  from the second interferometer  352  travels in the X-axis direction and is incident on the second reflective surface  342 . The second interferometer  352  receives the second beam B 2  reflected from the second reflective surface  342  and measures the position information of the second reflective surface  342  with respect to the X-axis direction. 
         [0085]    The first reflective surface  341  is arranged so as to be nearly stationary. In this embodiment, the first reflective surface  341  is arranged on a fixed member  341 B that is fixed such that it is nearly stationary. The second reflective surface  342  is arranged on the substrate stage  302 . The first interferometer system  331  measures the position information of the substrate stage  302  with respect to the X-axis direction based on the measurement results of the first interferometer  351  and the measurement results of the second interferometer  352 . 
         [0086]    The second interferometer system  332  comprises a third interferometer  353  having a third beam-exit part  353 S from which a third beam B 3  is emitted and a fourth interferometer  354  having a fourth beam-exit part  354 S from which a fourth beam B 4  is emitted. The third and fourth interferometers  353  and  354  are laser interferometers, and the third and fourth beams B 3  and B 4  are laser beams. The third interferometer  353  obtains interferometric data based on the third beam B 3  by irradiating the third beam B 3  onto a third reflective surface  343  and receiving the reflected light of the third beam B 3  irradiated on the third reflective surface  343 . The fourth interferometer  354  obtains interferometric data based on the fourth beam B 4  by irradiating the fourth beam B 4  onto the second reflective surface  342  and receiving the reflected light of the fourth beam B 4  irradiated on the second reflective surface  342 . 
         [0087]    The third reflective surface  343  is a surface perpendicular to the X axis. That is, the third reflective surface  343  is a surface parallel to the YZ plane. For the third interferometer  353 , the X axis is the measurement axis. The third beam B 3  from the third interferometer  353  travels in the X-axis direction and enters the third reflective surface  343 . The third interferometer  353  receives the light of the third beam B 3  reflected from the third reflective surface  343  and measures the position information of the third reflective surface  343  with respect to the X-axis direction. 
         [0088]    For the fourth interferometer  354 , the X axis is the measurement axis. The fourth beam B 4  from the fourth interferometer  354  travels in the X-axis direction and is incident on the second reflective surface  342 . The fourth interferometer  354  receives the light of the fourth beam B 4  reflected from the second reflective surface  342  and measures the position information of the second reflective surface  342  with respect to the X-axis direction. 
         [0089]    The third reflective surface  343  is arranged to be nearly stationary. In this embodiment, the third reflective surface  343  is arranged on a fixed member  343 B that is fixed such that it is nearly stationary. The second interferometer system  332  measures the position information of the substrate stage  302  with respect to the X-axis direction based on the measurement results of the third interferometer  353  and the measurement results of the fourth interferometer  354 . 
         [0090]    The third interferometer system  333  comprises a fifth interferometer  355  having a fifth beam-exit part  355 S, from which a fifth beam B 5  is emitted, and a sixth interferometer  356  having a sixth beam-exit part  356 S from which a sixth beam B 6  is emitted. The fifth and sixth interferometers  355  and  356  are laser interferometers, and the fifth and sixth beams B 5  and B 6  are laser beams. The fifth interferometer  355  obtains interferometric data based on the fifth beam B 5  by irradiating the fifth beam B 5  onto a fifth reflective surface  345  and receiving the reflected light of the fifth beam B 5  irradiated on the fifth reflective surface  345 . The sixth interferometer  356  obtains interferometric data based on the sixth beam B 6  by irradiating the sixth beam B 6  onto a sixth reflective surface  346  and receiving the reflected light of the sixth beam B 6  irradiated on the sixth reflective surface  346 . 
         [0091]    The fifth reflective surface  345  is a surface perpendicular to the X axis. That is, the fifth reflective surface  345  is a surface parallel to the XZ plane. For the fifth interferometer  355 , the Y axis is the measurement axis. The fifth beam B 5  from the fifth interferometer  355  travels in the Y-axis direction and is incident on the fifth reflective surface  345 . The fifth interferometer  355  receives the light of the fifth beam B 5  reflected from the fifth reflective surface  345  and measures the position information of the fifth reflective surface  345  with respect to the Y-axis direction. 
         [0092]    The sixth reflective surface  346  is a surface perpendicular to the Y axis. That is, the sixth reflective surface  346  is a surface parallel to the XZ plane. For the sixth interferometer  356 , the Y axis is the measurement axis. The sixth beam B 6  from the sixth interferometer  356  travels in the Y-axis direction and is incident on the sixth reflective surface  346 . The sixth interferometer  356  receives the light of the sixth beam B 6  reflected from the sixth reflective surface  346  and obtains position data regarding the sixth reflective surface  346  with respect to the Y-axis direction. 
         [0093]    The fifth reflective surface  345  is arranged to be substantially stationary. In this embodiment, the fifth reflective surface  345  is arranged on a fixed member  345 B that is fixed such that it is nearly stationary. The sixth reflective surface  346  is arranged on the substrate stage  302 . The third interferometer system  333  obtains position data of the substrate stage  302  with respect to the Y-axis direction based on the measurement results of the fifth interferometer  355  and the measurement results of the sixth interferometer  356 . 
         [0094]    The first beam B 1  and second beam B 2  from the first interferometer system  331  travel in the X-axis direction towards the optical axis AX 1  of the projection-optical system PL. The third beam B 3  and the fourth beam B 4  from the second interferometer system  332  travel in the X-axis direction toward the optical axis AX 2  of first detection device  323 . The optical axis AX 1  of the projection-optical system PL and the optical axis AX 2  of the first detection device  323  are arranged along a given axis parallel to the Y axis. The fifth beam B 5  and the sixth beam B 6  from the third interferometer system  333  travel in the Y-axis direction toward the optical axis AX 1  of the projection-optical system PL and the optical axis AX 2  of the first detection device  323 . 
         [0095]    Furthermore, the fixed member  41 B having the first reflective surface  341  is located on the −X side relative to the projection-optical system PL and is fixed onto the first surface plate  312 . The first reflective surface  341  is located on the −X side relative to the projection-optical system PL and is facing the −X direction. The fixed member  43 B having the third reflective surface  343  is located on the −X side relative to the first detection device  323  and is fixed onto the first surface plate  312 . The third reflective surface  343  is located on the −X side relative to the first detection device  323  is facing the −X direction. The fixed member  345 B having the fifth reflective surface  345  is located on the −Y side relative to first detection device  323  and is fixed onto the first surface plate  312 . The fifth reflective surface  345  is located on the −Y side relative to the first detection device  323  is facing the −Y direction. 
         [0096]    The first reflective surface  341  of the fixed member  341 B supported by the first surface plate  312  may be placed near the second reflective surface  342 . Similarly, the third reflective surface  343  of the fixed member  343 B supported by the first surface plate  312  may be placed near the second reflective surface  342 . Similarly, the fifth reflective surface  345  of the fixed member  345 B supported by the first surface plate  312  may be placed near the sixth reflective surface  346 . Furthermore, by mounting the first, third, and fifth reflective surfaces  341 ,  343 ,  345  of the fixed members  341 B,  343 B,  345 B, respectively, on the first surface plate  312 , effects on the first, third, and fifth reflective surfaces  341 ,  343 ,  345  by the motion of the projection-optical system PL (barrel  319 ) are suppressed. 
         [0097]    The second reflective surface  342  is located on the −X side relative to the substrate stage  302  and is facing the −X direction. The second reflective surface  342  has an outer shape that is long in the Y-axis direction. The sixth reflective surface  346  is located on the −Y side of the substrate stage  302  and is facing the −Y direction. The sixth reflective surface  346  has an outer shape that is long in the Y-axis direction. 
         [0098]      FIG. 9(C)  is a plan view from the +Z side. As shown in  FIG. 9(C) , in this embodiment, when the center position of the substrate P being held by the substrate stage  302  is in a position facing the beam-exit plane  305 K of the endmost optical element  305  (position at which the center position of the substrate P corresponds to the optical axis AX 1 ), the distance between the first beam-exit part  351 S of the first interferometer system  331  and the first reflective surface  341 , and the distance between the second beam-exit part  352 S and the second reflective surface  342  almost coincide. 
         [0099]    Meanwhile, the center position of the substrate P is the center position of the surface of the substrate P; that is, the center position of the substrate P in the XY plane. 
         [0100]    The first interferometer system  331  measures and obtains, by using the first reflective surface  341  and the second reflective surface  342 , position data regarding the substrate stage  302  with respect to the X-axis direction, at least whenever the center position of the substrate P held by the substrate stage  302  is in a position facing the beam-exit plane  305 K of the endmost optical element  305 . 
         [0101]    Furthermore, as shown in  FIG. 9(C) , in this embodiment, whenever the center position of the substrate P held by the substrate stage  302  is in a position facing the beam-exit plane  305 K of the endmost optical element  305  (position at which the center position of the substrate P corresponds to the optical axis AX 1 ), the distance between the fifth beam-exit part  355 S of the third interferometer system  333  and the fifth reflective surface  345 , and the distance between the sixth beam-exit part  356 S and the sixth reflective surface  346  almost coincide. 
         [0102]    The third interferometer system  333  measures, by using the fifth reflective surface  345  and the sixth reflective surface  346 , the position information of the substrate stage  302  with respect to the Y-axis direction at least when the center position of the substrate P held by the substrate stage  302  is in a position facing the beam-exit plane  305 K of the endmost optical element  305 . 
         [0103]    The principles set forth in the foregoing disclosure further alternatively can be used with any of various other apparatus, including (but not limited to) other microelectronic-processing apparatus, machine tools, metal-cutting equipment, and inspection apparatus. 
       Semiconductor-Device Fabrication 
       [0104]    Semiconductor devices can be fabricated by processes including microlithography steps performed using a microlithography system as described above. Referring to  FIG. 10 , in step  701  the function and performance characteristics of the semiconductor device are designed. In step  702  a reticle defining the desired pattern is designed according to the previous design step. Meanwhile, in step  703 , a substrate (wafer) is made and coated with a suitable resist. In step  704  the reticle pattern designed in step  702  is exposed onto the surface of the substrate using the microlithography system. In step  705  the semiconductor device is assembled (including “dicing” by which individual devices or “chips” are cut from the wafer, “bonding” by which wires are bonded to the particular locations on the chips, and “packaging” by which the devices are enclosed in appropriate packages for use). In step  706  the assembled devices are tested and inspected. 
         [0105]    Representative details of a wafer-processing process including a microlithography step are shown in  FIG. 11 . In step  711  (oxidation) the wafer surface is oxidized. In step  712  (CVD) an insulative layer is formed on the wafer surface. In step  713  (electrode formation) electrodes are formed on the wafer surface by vapor deposition for example. In step  714  (ion implantation) ions are implanted in the wafer surface. These steps  711 - 714  constitute representative “pre-processing” steps for wafers, and selections are made at each step according to processing requirements. 
         [0106]    At each stage of wafer processing, when the pre-processing steps have been completed, the following “post-processing” steps are implemented. A first post-process step is step  715  (photoresist formation) in which a suitable resist is applied to the surface of the wafer. Next, in step  716  (exposure), the microlithography system described above is used for lithographically transferring a pattern from the reticle to the resist layer on the wafer. In step  717  (development) the exposed resist on the wafer is developed to form a usable reticle pattern, corresponding to the resist pattern, in the resist on the wafer. In step  718  (etching), regions not covered by developed resist (i.e., exposed material surfaces) are etched away to a controlled depth. In step  719  (photoresist removal), residual developed resist is removed (“stripped”) from the wafer. 
         [0107]    Formation of multiple interconnected layers of circuit patterns on the wafer is achieved by repeating the pre-processing and post-processing steps as required. Generally, a set of pre-processing and post-processing steps are conducted to form each layer. 
         [0108]    Whereas the disclosure has been set forth in the context of multiple representative embodiments, it will be understood that the disclosure is not limited to those embodiments. On the contrary, the disclosure is intended to encompass all modifications, alternatives, and equivalents as may be included within the spirit and scope of the invention, as defined by the appended claims.