Patent Publication Number: US-2011069291-A1

Title: Physical sensor for autofocus system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present invention claims priority of U.S. Provisional Patent Application No. 61/241,493, filed Sep. 11, 2009, which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to equipment used in photolithography systems. More particularly, the present invention relates to a system which efficiently measures the height of a wafer surface. 
     2. Description of the Related Art 
     In many photolithography systems, the accuracy with which various measurements are made is crucial. For example, when the height of a photoresist-coated wafer surface is not accurately measured, then processes which depend on the height measurement may be compromised. Additionally, a wafer may be exposed to an image transmitted from a mask through a projection lens while not in the focal plane of the projection lens, which may lead to blurred exposure on the wafer. 
     Optical measurement systems may be used to measure heights of photoresist-coated wafer surfaces. An optical measurement system, e.g., an autofocus system, that measures a height of a wafer surface may utilize a vibrating mirror to deflect light beams at glancing angles over the wafer surface. The deflected light beams are sensitive to patterns on the wafer surface, as well as to thin film effects, e.g., Goos-Hanchen effects. 
     Thin film effects typically have an adverse effect on the measurement of heights of wafer surfaces. Unless there is some compensation for the thin film effects, the measurement of heights using optical technology is generally subject to inaccuracies. Significant measurement errors may occur. As there are effectively no practical solutions for Goos-Hanchen effects, the use of optical technologies to measure heights of photoresist-coated surfaces may be undesirable. 
     SUMMARY OF THE INVENTION 
     The present invention pertains to a measurement system which utilizes an air gauge arrangement and a vacuum preload to effectively measure the height of a photoresist-coated surface of a wafer. 
     According to one aspect of the present invention, a method for measuring a height associated with a wafer includes utilizing a measurement of an air flow through an air gauge or air bearing to estimate the height, determining a first magnitude of a bearing load exerted on the wafer from the air flow measurement, and compensating for the bearing load. The bearing load is exerted in a first direction. Compensating for the bearing load includes applying an opposing force to the wafer that includes at least a vacuum preload force. The vacuum preload force is applied in a second direction that is opposite from the first direction. The opposing force is calculated to have a second magnitude that is approximately equal to the first magnitude. 
     In one embodiment, the opposing force includes an electromagnetic force that is also applied in the second direction. In such an embodiment, the opposing force includes the electromagnetic force when the height is not approximately equal to a nominal height. 
     According to another aspect of the present invention, an apparatus includes a stage arrangement, an air bearing arrangement, and a vacuum supply arrangement. The stage arrangement supports a wafer which has a first height. The air bearing arrangement includes an air gauge configured to measure the first height, and provides a bearing pressure signal. The air bearing arrangement exerts a bearing force, which has a first magnitude, in a first direction. The vacuum supply arrangement applies a vacuum preload force that opposes the bearing force. The vacuum preload force is applied on a second region of the wafer that is substantially adjacent to the first region of the wafer. The vacuum preload force is dynamically adjusted based on the bearing pressure signal. 
     Other aspects of the present invention will become apparent from the following detailed description taken in conjunction with the accompanying drawings which illustrate, by way of example, the principles of some embodiments of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be readily understood by the following detailed description in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a diagrammatic representation of a system in which an air gauge is configured to function as a relatively low stiffness air bearing and in which forces applied by the air gauge may be dynamically cancelled in accordance with an embodiment of the present invention. 
         FIG. 2  is a process flow diagram which illustrates a process of operating a system which utilizes an air gauge arrangement to measure the height of a photoresist-coated wafer surface, and a vacuum preload to compensate for forces applied by the air gauge arrangement, in accordance with an embodiment of the present invention. 
         FIG. 3  is a block diagram representation of an overall system which utilizes an air gauge arrangement and a vacuum preload arrangement, as well as a controller, to efficiently measure the height of a photoresist-coated wafer surface in accordance with an embodiment of the present invention. 
         FIG. 4  is a block diagram representation of an overall system which utilizes an air gauge arrangement, a vacuum preload arrangement, and electromagnetic forces to efficiently measure the height of a photoresist-coated wafer surface in accordance with an embodiment of the present invention. 
         FIG. 5  is a process flow diagram which illustrates a process of operating a system which utilizes an air gauge to measure the height of a photoresist-coated wafer surface, and both a vacuum preload force and an electromagnetic force to compensate for forces applied by the air gauge arrangement, in accordance with an embodiment of the present invention. 
         FIG. 6A  is a diagrammatic representation of an air bearing arrangement with a vacuum preload from a side view in accordance with an embodiment of the present invention. 
         FIG. 6B  is a diagrammatic representation of an air bearing arrangement with a vacuum preload from a bottom perspective in accordance with an embodiment of the present invention. 
         FIG. 7A  is a diagrammatic representation of an air bearing arrangement with a vacuum preload and an electromagnet arrangement in accordance with an embodiment of the present invention. 
         FIG. 7B  is a diagrammatic representation of an air bearing arrangement with a vacuum preload and an electromagnet arrangement, e.g., air bearing arrangement  704  of  FIG. 7A , as shown with a control system in accordance with an embodiment of the present invention. 
         FIG. 8  is a diagrammatic bottom-view representation of an air bearing arrangement which includes electromagnets in accordance with an embodiment of the present invention. 
         FIG. 9  is a diagrammatic representation of a photolithography apparatus in accordance with an embodiment of the present invention. 
         FIG. 10  is a process flow diagram which illustrates the steps associated with fabricating a semiconductor device in accordance with an embodiment of the present invention. 
         FIG. 11  is a process flow diagram which illustrates the steps associated with processing a wafer, i.e., step  1004  of  FIG. 10 , in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Example embodiments of the present invention are discussed below with reference to the various figures. However, those skilled in the art will readily appreciate that the detailed description given herein with respect to these figures is for explanatory purposes, as the invention extends beyond these embodiments. 
     Optical methods used to measure the height of a photoresist-coated wafer surface are typically sensitive to patterns on the wafer, and to thin film effects. Thus, optical methods may be subject to error and, hence, undesirable. 
     In one embodiment, a non-optical method that utilizes an air gauge and a vacuum preload accurately measures the height of a photoresist-coated wafer surface, substantially without sensitivity to patterns on the wafer and susceptibility to thin film effects. An air gauge arrangement may be used to measure the height of a photoresist-coated wafer surface when in proximity to the wafer surface. Such an air gauge arrangement and a wafer may be configured to function as a relatively low stiffness air bearing, and may therefore have a relatively large sensitivity to the height of a photoresist-coated wafer surface. An air bearing supplies a flow of air or other gas between two proximate surfaces, thereby maintaining a desired separation between the surfaces, despite external forces which would operate to substantially bring the surfaces together in the absence of the flow. The stiffness of the bearing is defined, in one embodiment, as the amount of external force required to change the separation by a specified amount. A low stiffness air bearing may utilize a relatively small amount of additional external force to reduce the separation by the specified amount. 
     Because an air gauge arrangement or, more specifically, the flow of air associated with the air gauge arrangement, applies a load or force to a wafer, dynamic compensation may be provided to substantially counteract the load. The dynamic compensation may take on a variety of different forms including, but not limited to include, applying a vacuum preload to the air gauge arrangement and/or utilizing an electromagnetic arrangement to provide attractive forces. It should be appreciated that the vacuum preload is typically applied in an opposite direction from the load applied by the air gauge arrangement, i.e., the bearing load or force, such that compensation for the bearing load may be substantially provided. 
     As mentioned above, the flow of air associated with the air gauge arrangement applies a load or force to a wafer. This force is compensated for because the wafer is mounted to a mechanical structure which has a finite stiffness. A vertical force imposed on the structure will, in general, cause a vertical displacement of the wafer which degrades the accuracy of the wafer height measurement. The vertical force may also degrade the positioning accuracy of the mechanical assembly to which the wafer is attached, such as a wafer stage. For example, a mechanical structure with a stiffness of approximately 100 N/micron is typically considered to be a fairly stiff structure. Nevertheless, a force of approximately 1 N may create a displacement of approximately 10 nm, which may be a potentially significant error. If the wafer is mounted to a fine stage whose vertical height is maintained by a control system, limitations of frequency response and the stage mass may limit the effective stiffness of the stage to approximately 10 N/micron or less. In this case, the force induced height error may be approximately 100 nm or more. 
     An air gauge arrangement, in addition to a vacuum preload arrangement and/or an electromagnetic arrangement, may generally be provided as a part of an autofocus system of a photolithography system. It should be understood, however, that the air gauge arrangement, vacuum preload arrangement, and electromagnetic arrangement are not limited to being included in an autofocus system, and may be incorporated into any suitable system or apparatus. Examples of autofocus systems are described, for example, in U.S. Pat. No. 5,191,200 and U.S. Pat. No. 5,602,399, which are each incorporated herein by reference in their entireties. 
     Referring initially to  FIG. 1 , a system in which an air gauge is configured to function as a relatively low stiffness air bearing and in which forces applied by the air gauge may be dynamically cancelled will be described in accordance with an embodiment of the present invention. A system  100  includes a wafer  108  and an air gauge  104  which are separated by a gap  114  with a height ‘h’. Wafer  108  may generally be held by a wafer stage arrangement (not shown) such that wafer  108  remains beneath air gauge  104 . 
     Air gauge  104  is arranged to allow air  112  to flow therethrough, and is arranged to effectively measure the height of a photoresist-coated top surface  110  of wafer  108 . Air gauge  104  is designed to function as an air bearing with a relatively large wafer height sensitivity. Thus, air gauge  104  is sensitive to changes in the height of photoresist-coated top surface  110  of wafer  108 . Although any suitable air gauge  104  may be used to identify changes in the height of photoresist-coated top surface  110  of wafer  108 , one suitable air gauge  104  may include a hot wire mass flow sensor which uses a sensor bridge to measure air flow within air gauge  104 , and thereby determine height ‘h’ from a model or previous calibration. 
     As gap  114  and, hence, height ‘h’ varies, the flow of air  112  through air gauge  104  and over wafer  108  varies. Further, as air flow changes, pressure in air gauge  104  changes. Increasing air flow, i.e., increasing the flow rate of air  112 , increases the pressure or force exerted by air  112  on photoresist-coated top surface  110  of wafer  108 . By measuring the flow of air  112  on wafer  108 , changes in height ‘h’ may be determined. Changes in the force exerted by the air gauge on the wafer may be inferred from the air flow changes. 
       FIG. 2  is a process flow diagram which illustrates a process of operating a height measurement system which utilizes an air gauge arrangement to measure the height of a photoresist-coated wafer surface, and a vacuum preload to compensate for forces applied by the air gauge arrangement, in accordance with an embodiment of the present invention. A process  201  of operating a height measurement system begins at step  205  in which the air flow in an air bearing, e.g., an air gauge which substantially functions as a relatively low stiffness air bearing with a relatively high sensitivity to wafer height, is determined. The force on the wafer that is due to the air bearing is effectively inferred from, or otherwise calculated using, the measured air flow, either from a model or by calibration. 
     Once the air flow through the air gauge is determined, a wafer height signal is obtained from an air bearing controller in step  209 . The wafer height signal is used in step  213  to dynamically adjust the vacuum preload force in order to compensate for the force on the wafer provided by the air bearing. As such, at least some degree of bearing force cancellation may be achieved in the presence of fluctuations in the height of a photoresist-coated wafer surface. In one embodiment, a vacuum preload force may be applied at a magnitude, and in a direction, that substantially opposes the bearing force applied on the wafer stage. That is, the vacuum preload force may be adjusted such that the vacuum preload force is substantially equal to and applied in a direction that counteracts the bearing force. Once the vacuum preload force is dynamically adjusted as appropriate to compensate for a bearing force, a final wafer height is established and the process of operating a height measurement system is completed. 
     To compensate for bearing forces exerted on a wafer, a vacuum preload is applied. A vacuum preload may be provided by any suitable arrangement which may apply vacuum forces that substantially opposes bearing forces.  FIG. 3  is a block diagram representation of an overall system which utilizes an air gauge arrangement, a controller, and a vacuum preload arrangement to efficiently measure the height of a photoresist-coated wafer surface in accordance with an embodiment of the present invention. An overall system  300  includes a wafer  308 , an air gauge arrangement  304 , a controller  306 , and a vacuum preload arrangement  316 . A measurement of air flow in air gauge arrangement  304  is monitored by controller  306  which sends a controlling signal to vacuum preload arrangement  316 . Vacuum preload arrangement  316  is configured to apply a vacuum force to wafer  308 . Hence, while air gauge arrangement  304  applies a bearing force to wafer  308 , vacuum preload arrangement  316  applies a vacuum preload force on wafer  308  that opposes the bearing force, and effectively compensates for the bearing force. Generally, air gauge arrangement  304  may apply the bearing force to wafer  308  in one direction along a z-axis  318 , and vacuum preload arrangement  316  may apply a vacuum preload force in an opposite direction along z-axis  318 . As will be appreciated by those skilled in the art, a bearing force or load may be caused by an airflow associated with air gauge arrangement  304 . 
     The amount of vacuum preload force that is provided by vacuum preload arrangement  316  may be dynamically adjusted. In one embodiment, the amount of vacuum preload force is dynamically adjusted based on a signal derived from a wafer height measurement. Hence, the vacuum preload force may substantially cancel the bearing force even in the presence of wafer height fluctuations. 
     A vacuum preload force may be capable of compensating for a bearing force in some systems. In other systems, a vacuum preload force alone may not be sufficient to effectively compensate for the bearing force. For example, in addition to providing a vacuum preload force, a system may also utilize electromagnetic forces to maintain bearing force cancellation With reference to  FIG. 4 , an overall system which utilizes an air gauge arrangement, a vacuum preload arrangement, and electromagnetic forces to efficiently measure the height of a photoresist-coated wafer surface will be described in accordance with an embodiment of the present invention. An overall system,  400  includes a wafer  408  that is situated on a stage arrangement  420 , in addition to an air gauge arrangement  404 , a controller  406 , and a vacuum preload arrangement  416 . Air gauge arrangement  404  is effectively an air bearing arrangement. Vacuum preload arrangement  416  is arranged to generate a vacuum preload force that at least partially compensates for a bearing force or load exerted on wafer  408  by air gauge arrangement  404 . 
     Air gauge arrangement  404  includes electromagnets  428  that are substantially mounted on a body associated with air gauge arrangement  404 . Electromagnets  428  are configured to attract a ferromagnetic plate  424  installed on stage arrangement  420  to provide bearing force cancellation. A measurement of air flow in air gauge arrangement  404  is monitored by controller  406 , which sends controlling signals to vacuum preload arrangement  416  and to electromagnets  428 . Attractive forces between electromagnets  428  and ferromagnetic plate  424  and a vacuum preload force generated by vacuum preload arrangement  416  oppose a bearing force caused by air gauge arrangement  428 . For example, attractive forces and a vacuum preload force may act in an opposite direction along a z-axis  418  than a bearing force. 
     As the height of a photoresist-coated surface of wafer  408  changes, currents in electromagnets  428  may be dynamically adjusted, as for example by controller  406 , as necessary to maintain the cancellation of bearing forces exerted on wafer  408 . Adjusting the currents provided to electromagnets  428  causes electromagnetic forces to be substantially adjusted. By adjusting currents provided to electromagnets  428 , electromagnetic forces may be adjusted. In addition to adjusting electromagnetic forces to compensate for bearing forces, electromagnetic forces may be adjusted to compensate for substantially any moments about the center of air gauge arrangement  404 . It should be appreciated that the amount of vacuum preload force may generally also be dynamically adjusted to maintain the cancellation of bearing forces. 
       FIG. 5  is a process flow diagram which illustrates a process of operating a system which utilizes an air gauge to measure the height of a photoresist-coated wafer surface, and both a vacuum preload force and an electromagnetic force to compensate for forces applied by the air gauge arrangement, in accordance with an embodiment of the present invention. A process  501  of operating a system, which may be part of an autofocus system used in an overall photolithography apparatus, that measures the height of a photoresist-coated wafer surface begins at step  505  in which a bearing force, or a force or load exerted by an air bearing arrangement, on a wafer stage is determined. After the bearing force is determined, a wafer height signal is obtained from an air gauge in step  509 . A determination is then made in step  511  as to whether the wafer height or, more specifically, a photoresist-coated surface of the wafer, is substantially fixed. In one embodiment, the wafer height may be considered to be substantially fixed when the wafer height is near a nominal height. 
     If the determination in step  511  is that the wafer height is substantially fixed, the compensation for the bearing force may be provided, in one embodiment, using substantially only a vacuum preload. In other words, when the wafer height deviates little from a nominal height, the vacuum preload force may be sufficient to compensate for, e.g., oppose, the bearing force or load. As such, in step  513 , the vacuum preload force is dynamically adjusted, based on the wafer height signal, to compensate for the bearing force. Once the vacuum preload force is dynamically adjusted, the process of operating a system that measures the height of a photoresist-coated wafer surface is completed. 
     Alternatively, if the determination in step  511  is that the wafer height is not substantially fixed, the indication is that both a vacuum preload force and an electromagnetic force are to be used to compensate for a bearing force. In the described embodiment, the implication is that the wafer height is not substantially fixed. Accordingly, process flow moves from step  511  to step  517  in which the vacuum preload force is dynamically adjusted, based on the wafer height signal, to partially compensate for a bearing force. After the vacuum preload force is dynamically adjusted, the current provided to electromagnets is dynamically adjusted in step  521 . The currents are dynamically adjusted to enable electromagnetic forces to compensate for a bearing force, and to compensate for moments about a center of an air bearing arrangement. Upon dynamically adjusting currents provided to electromagnets, the process of operating a system that measures the height of a photoresist-coated wafer surface is completed. 
     With reference to  FIG. 6A and 6B , an air gauge or air bearing arrangement with a vacuum preload will be described in more detail in accordance with an embodiment of the present invention.  FIG. 6A  is a diagrammatic cross-sectional side-view representation of one embodiment of an air gauge arrangement. An overall air gauge arrangement  604  is arranged to be positioned over a top surface of a wafer  608 , and has a surface  642  that is configured to interface with a metrology frame (not shown). Air gauge arrangement  604  includes a pressure supply groove  632  which is arranged to be coupled to an air supply (not shown) that provides pressurized air to air gauge arrangement  604 . 
     As shown, flow restrictors  633  are arranged to restrict the flow of air via pressure supply passage  632 . Flow restrictors  633  may isolate pressure measurements associated with a bearing differential pressure signal  648  from variations in an air supply pressure. The presence of flow restrictors  633  increases stiffness in air gauge arrangement  604 . Flow restrictors  633  may be, but are not limited to being, orifices, capillary tubes, and/or porous plugs. As will be appreciated by those skilled in the art, capillary tubes and porous plugs are generally laminar flow restrictors. 
     An exhaust passage  636  is configured to exhaust air to an ambient environment. As shown, exhaust passage  636  may be positioned substantially between pressure supply passage  632  and vacuum supply passage  640 . 
     A vacuum supply passage  640  is coupled to a vacuum supply (not shown) that supplies a vacuum through vacuum supply passage  640 . The vacuum provides a vacuum preload force that opposes forces provided by pressurized air supplied through pressure supply passage  632 . 
     Previous embodiments of the invention employ a measurement of the air flow through the air bearing to estimate the wafer height and the bearing load on the wafer. Such embodiments suffer from inaccuracies which occur when the supply pressure or the ambient pressure change by small relatively amounts. For example, changes in the supply pressure or the ambient pressure of approximately 1 Pa can affect the air flow through the air bearing and cause significant errors in the wafer height if not corrected. These errors can be limited to some extent by configuring the air gauge arrangement such that a wafer height change causes large changes in the air flow which exceed those caused by nominal changes in supply pressure or ambient pressure. 
     To avoid these types of errors, the embodiment shown in  FIGS. 6A and 6B  combines two air gauge arrangements  604   a  and  604   b.  Air gauge arrangement  604   a  forms an air bearing with wafer  608 . The resulting air flow in the bearing creates an internal pressure  648   a  for a gap  646   a  separating the air gauge from the wafer. Air gauge arrangement  604   b  forms an air bearing with a plate  645  which is securely positioned at a fixed gap  646   b  from the air gauge arrangement  604   b.  The resulting air flow in the bearing creates an internal pressure  648   b.  Since the fixed gap  646   b  doesn&#39;t change, the pressure  648   b  does not change, except when system conditions change, such as caused by changes to the supply pressure or the ambient pressure. Since both supply pressure and ambient pressure are common to the two air gauge arrangements, it follows that the difference of the two pressure signals  648   a,    648   b,  or a differential pressure  648 , is typically not sensitive to such perturbations. Therefore, the differential pressure signal  648  represents a more stable and accurate signal for obtaining the wafer height than the signal  648   a  alone. Air gauge arrangement  604   a  is sometimes referred to as the measurement gauge, and air gauge arrangement  604   b  is sometimes referred to as the reference gauge. For maximum cancellation of common mode perturbations, the structures of air gauge arrangement  604   a  and air gauge arrangement  604   b  should be similar. 
       FIG. 6B  shows a bottom view of the embodiment. A description is given for air gauge arrangement  604   a . Pressurized air from air gauge emerges through exhaust  634   a  into bearing surface  664   a . Bearing surface  664   a  is surrounded by exhaust groove  638   a  which conveys air from bearing surface  664   a  to exhaust passage  636   a  where it escapes to ambient. Surrounding exhaust groove  638   a  is a flat surface coplanar with the bearing surface  664   a . The flat surface may extend to the outer surface of air arrangement  604   a  or it may end at a perimeter  637   a , where the gap between the wafer surface and the air gauge surface is increased. A vacuum groove  642   a  surrounds the exhaust groove  638   a  and enables vacuum supply passage  640  and  640   a  to establish a relatively uniform partial vacuum region between approximately the perimeter  637   a  and the outer edge of air arrangement  604   a . Such a geometry enables a vacuum preload to counter the bearing load without creating torques which could tend to tilt the wafer and/or air gauge assembly. 
     The bottom of air arrangement  604  is generally similar to the bottom of air gauge arrangement  604   a  for maximum cancellation of common mode perturbations. However, if the plate  645  which provides the gap  646   b  is sufficiently rigid, the bearing load of air gauge arrangement  604   b  may not significantly change the gap  646   b.  In that case a vacuum preload may not be necessary, and the related structures  637   b,    640   b,    642   b  and  644   b  may not be needed. 
     As previously mentioned, a bearing force or load exerted by an air gauge or air bearing arrangement may be compensated for by both a vacuum preload force and an electromagnetic force.  FIG. 7A  is a diagrammatic cross-sectional side-view representation of an air bearing arrangement with a vacuum preload and an electromagnet arrangement in accordance with an embodiment of the present invention. An overall air gauge arrangement  704  is arranged to be positioned over a top surface of a wafer  708 , and has a surface  742  that is configured to interface with a metrology frame (not shown). Wafer  708  is positioned substantially on a wafer stage arrangement  720 . Air gauge arrangement  704  includes a pressure supply passage  732 , a vacuum supply passage  740 , and an exhaust passage  736 . 
     Optional flow restrictors  733  are arranged to restrict the flow of air via pressure supply passage  732 . Flow restrictors  733 , when present, are configured to substantially isolate pressure measurements associated with a bearing differential pressure signal DP  748  from variations in an air supply pressure. 
     Bearing differential pressure signal DP  748  may be used to adjust the amount of vacuum provided through vacuum supply passage  740 . In addition, bearing differential pressure signal DP  748  may also be used to adjust electromagnetic forces provided by an electromagnet arrangement  728 . As will be appreciated by those skilled in the art, attractive forces may exist between electromagnet arrangement  728  and a ferromagnetic plate  724  installed in stage arrangement  720 . Such attractive forces, i.e., electromagnetic forces, may be dynamically altered by altering the amount of current provided to electromagnet arrangement  728 . 
     Ferromagnetic plate  724  will add weight to stage arrangement  720  and, thus, ferromagnetic plate  724  is preferably as thin as possible. However, as the magnetic flux flowing through ferromagnetic plate  724  is to be substantially prevented from changing the properties of a magnetic circuit formed between electromagnet arrangement  728  and ferromagnetic plate  724 , the thickness of ferromagnetic plate  724  is chosen to prevent the magnetic flux from essentially saturating ferromagnetic plate  724  In general, the thickness of ferromagnetic plate  724  may vary widely based on a variety of different factors including, but not limited to including, the maximum magnetic field in a gap between air gauge arrangement  704  and wafer  708 , a saturation point associated with ferromagnetic plate  724 , and/or a maximum force from electromagnet arrangement  728 . For example, for a maximum magnetic field in the gap between air gauge arrangement  704  and wafer  708  is approximately 0.1 Tesla (T), and ferromagnetic plate  724  saturates at approximately 1 T, then the thickness of ferromagnetic plate  724  may be approximately 0.5 millimeters (mm). If ferromagnetic plate  724  is approximately 0.5 mm thick, and wafer  708  has a diameter of approximately 450 mm, then the mass of ferromagnetic plate  724  may be approximately 0.6 kilograms if ferromagnetic plate  724  is formed from steel. It should be understood that ferromagnetic plate  724  may be formed from materials other than steel. Other materials may include, but are not limited to including, invar. 
     As the height of a photoresist-coated surface of wafer  708  changes, the amount of current provided to electromagnet arrangement  728  may be adjusted by bearing differential pressure signal DP  748  to maintain force cancellation. More specifically, the amount of current provided to electromagnet arrangement  728  as well as the amount of vacuum preload force provided through vacuum supply passage  740  may be dynamically adjusted as necessary based on bearing differential pressure signal DP  748  such that the bearing force exerted by air gauge arrangement  704  on wafer  708  may be substantially cancelled. The amount of current provided to electromagnet arrangement  728  may also be adjusted to substantially cancel moments about a center of air gauge arrangement  704 . 
     In general, air gauge arrangement  704  may be coupled to at least one controller that provides circuitry and/or logic which allows vacuum preload forces and electromagnetic forces to be substantially adjusted based on the height of a photoresist-coated surface of wafer  708 .  FIG. 7B  is a diagrammatic representation of an air bearing arrangement with a vacuum preload and an electromagnet arrangement, e.g., air gauge or bearing arrangement  704  of  FIG. 7A , as shown with a control system in accordance with an embodiment of the present invention. An air gauge arrangement  704 ′ includes a controller  750  which obtains bearing differential pressure signal DP  748 , and processes bearing differential pressure signal DP  728  such that an amount of vacuum provided from a vacuum supply  758 , or a partial vacuum supply, to vacuum supply passage  740  may be controlled through a valve  754 . Controller  750  also processes bearing differential pressure signal DP  728  such that a current provided to electromagnet arrangement  728  may be controlled by amplifier current supply  762 . 
       FIG. 8  is a diagrammatic bottom-view representation of an air bearing arrangement which includes electromagnets in accordance with an embodiment of the present invention. An air gauge or bearing arrangement  804  generally includes a bearing surface  864 , an exhaust pressure supply passage  832 , an exhaust passage  836  and an exhaust groove  838 , and a vacuum supply passage  840  and a vacuum groove  842  which assists the distribution of vacuum to a region  844 . A plurality of electromagnet arrangements  828 , which may each include one or more electromagnets (not shown), are positioned substantially on an exterior surface of air gauge arrangement  804 . As shown, vacuum supply passage  840 , which supplies a vacuum preload region  844 , substantially surrounds the perimeter of bearing surface  864 . Hence, a bearing force or load is applied by bearing surface  864  in a first region on a wafer (not shown), and a vacuum preload force is applied by vacuum supply passage  840  in a second region of the wafer that substantially surrounds the perimeter of the first region. With reference to  FIG. 9 , a photolithography apparatus which may include an air gauge configured to be sensitive to a wafer height will be described in accordance with an embodiment of the present invention. A photolithography apparatus (exposure apparatus)  40  includes a wafer positioning stage  52  that may be driven by a planar motor (not shown), as well as a wafer table  51  that is magnetically coupled to wafer positioning stage  52  by utilizing an ELI-core actuator. The planar motor which drives wafer positioning stage  52  generally uses an electromagnetic force generated by magnets and corresponding armature coils arranged in two dimensions. 
     A wafer  64  is held in place on a wafer holder or chuck  74  which is coupled to wafer table  51 . Wafer positioning stage  52  is arranged to move in multiple degrees of freedom, e.g., in up to six degrees of freedom, under the control of a control unit  60  and a system controller  62 . In one embodiment, wafer positioning stage  52  may include a plurality of actuators and have a configuration as described above. The movement of wafer positioning stage  52  allows wafer  64  to be positioned at a desired position and orientation relative to a projection optical system  46 . 
     Wafer table  51  may be levitated in a z-direction lob by any number of voice coil motors (not shown), e.g., three voice coil motors. In one described embodiment, at least three magnetic bearings (not shown) couple and move wafer table  51  along a y-axis lea. The motor array of wafer positioning stage  52  is typically supported by a base  70 . Base  70  is supported to a ground via isolators  54 . Reaction forces generated by motion of wafer stage  52  may be mechanically released to a ground surface through a frame  66 . One suitable frame  66  is described in JP Heir 8-166475 and U.S. Pat. No. 5,528,118, which are each herein incorporated by reference in their entireties. 
     An illumination system  42  is supported by a frame  72 . Frame  72  is supported to the ground via isolators  54 . Illumination system  42  includes an illumination source, which may provide a beam of light that may be reflected off of a reticule. In one embodiment, illumination system  42  may be arranged to project a radiant energy, e.g., light, through a mask pattern on a reticule  68  that is supported by and scanned using a reticule stage  44  which may include a coarse stage and a fine stage, or which may be a single, monolithic stage. The radiant energy is focused through projection optical system  46 , which is supported on a projection optics frame  50  and may be supported the ground through isolators  54 . Suitable isolators  54  include those described in JP Hei 8-330224 and U.S. Pat. No. 5,874,820, which are each incorporated herein by reference in their entireties. 
     A first interferometer  56  is supported on projection optics frame  50 , and functions to detect the position of wafer table  51 . Interferometer  56  outputs information on the position of wafer table  51  to system controller  62 . In one embodiment, wafer table  51  has a force damper which reduces vibrations associated with wafer table  51  such that interferometer  56  may accurately detect the position of wafer table  51 . A second interferometer  58  is supported on projection optical system  46 , and detects the position of reticle stage  44  which supports a reticle  68 . Interferometer  58  also outputs position information to system controller  62 . 
     It should be appreciated that there are a number of different types of photolithographic apparatuses or devices. For example, photolithography apparatus  40 , or an exposure apparatus, may be used as a scanning type photolithography system which exposes the pattern from reticle  68  onto wafer  64  with reticle  68  and wafer  64  moving substantially synchronously. In a scanning type lithographic device, reticle  68  is moved perpendicularly with respect to an optical axis of a lens assembly (projection optical system  46 ) or illumination system  42  by reticle stage  44 . Wafer  64  is moved perpendicularly to the optical axis of projection optical system  46  by a wafer stage  52 . Scanning of reticle  68  and wafer  64  generally occurs while reticle  68  and wafer  64  are moving substantially synchronously. 
     Alternatively, photolithography apparatus or exposure apparatus  40  may be a step-and-repeat type photolithography system that exposes reticle  68  while reticle  68  and wafer  64  are stationary, i.e., at a substantially constant velocity of approximately zero meters per second. In one step and repeat process, wafer  64  is in a substantially constant position relative to reticle  68  and projection optical system  46  during the exposure of an individual field. Subsequently, between consecutive exposure steps, wafer  64  is consecutively moved by wafer positioning stage  52  perpendicularly to the optical axis of projection optical system  46  and reticle  68  for exposure. Following this process, the images on reticle  68  may be sequentially exposed onto the fields of wafer  64  so that the next field of semiconductor wafer  64  is brought into position relative to illumination system  42 , reticle  68 , and projection optical system  46 . 
     It should be understood that the use of photolithography apparatus or exposure apparatus  40 , as described above, is not limited to being used in a photolithography system for semiconductor manufacturing. For example, photolithography apparatus  40  may be used as a part of a liquid crystal display (LCD) photolithography system that exposes an LCD device pattern onto a rectangular glass plate or a photolithography system for manufacturing a thin film magnetic head. 
     The illumination source of illumination system  42  may be g-line (436 nanometers (nm)), i-line (365 nm), a KrF excimer laser (248 nm), an ArF excimer laser (193 nm), and an F2-type laser (157 nm). Alternatively, illumination system  42  may also use charged particle beams such as x-ray and electron beams. For instance, in the case where an electron beam is used, thermionic emission type lanthanum hexaboride (LaB6) or tantalum (Ta) may be used as an electron gun. Furthermore, in the case where an electron beam is used, the structure may be such that either a mask is used or a pattern may be directly formed on a substrate without the use of a mask. 
     With respect to projection optical system  46 , when far ultra-violet rays such as an excimer laser are used, glass materials such as quartz and fluorite that transmit far ultra-violet rays is preferably used. When either an F2-type laser or an x-ray is used, projection optical system  46  may be either catadioptric or refractive (a reticle may be of a corresponding reflective type), and when an electron beam is used, electron optics may comprise electron lenses and deflectors. As will be appreciated by those skilled in the art, the optical path for the electron beams is generally in a vacuum. 
     In addition, with an exposure device that employs vacuum ultra-violet (VUV) radiation of a wavelength that is approximately 200 nm or lower, use of a catadioptric type optical system may be considered. Examples of a catadioptric type of optical system include, but are not limited to, those described in Japan Patent Application Disclosure No. 8-171054 published in the Official gazette for Laid-Open Patent Applications and its counterpart U.S. Pat. No. 5,668,672, as well as in Japan Patent Application Disclosure No. 10-20195 and its counterpart U.S. Pat. No. 5,835,275, which are all incorporated herein by reference in their entireties. In these examples, the reflecting optical device may be a catadioptric optical system incorporating a beam splitter and a concave mirror. Japan Patent Application Disclosure (Hei) No. 8-334695 published in the Official gazette for Laid-Open Patent Applications and its counterpart U.S. Pat. No. 5,689,377, as well as Japan Patent Application Disclosure No. 10-3039 and its counterpart U.S. Pat. No. 5,892,117, which are all incorporated herein by reference in their entireties. These examples describe a reflecting-refracting type of optical system that incorporates a concave mirror, but without a beam splitter, and may also be suitable for use with the present invention. 
     The present invention may be utilized, in one embodiment, in an immersion type exposure apparatus if suitable measures are taken to accommodate a fluid. For example, PCT patent application WO 99/49504, which is incorporated herein by reference in its entirety, describes an exposure apparatus in which a liquid is supplied to a space between a substrate (wafer) and a projection lens system during an exposure process. Aspects of PCT patent application WO 99/49504 may be used to accommodate fluid relative to the present invention. 
     Further, semiconductor devices may be fabricated using systems described above, as will be discussed with reference to  FIG. 10 .  FIG. 10  is a process flow diagram which illustrates the steps associated with fabricating a semiconductor device in accordance with an embodiment of the present invention. A process  1001  of fabricating a semiconductor device begins at step  1003  in which the function and performance characteristics of a semiconductor device are designed or otherwise determined. Next, in step  1005 , a reticle or mask in which has a pattern is designed based upon the design of the semiconductor device. It should be appreciated that in a substantially parallel step  1009 , a wafer is typically made from a silicon material. In step  1013 , the mask pattern designed in step  1005  is exposed onto the wafer fabricated in step  1009 . One process of exposing a mask pattern onto a wafer will be described below with respect to  FIG. 11 . In step  1017 , the semiconductor device is assembled. The assembly of the semiconductor device generally includes, but is not limited to including, wafer dicing processes, bonding processes, and packaging processes. Finally, the completed device is inspected in step  1021 . Upon successful completion of the inspection in step  1021 , the completed device may be considered to be ready for delivery. 
       FIG. 11  is a process flow diagram which illustrates the steps associated with wafer processing in the case of fabricating semiconductor devices in accordance with an embodiment of the present invention. In step  1101 , the surface of a wafer is oxidized. Then, in step  1105  which is a chemical vapor deposition (CVD) step in one embodiment, an insulation film may be formed on the wafer surface. Once the insulation film is formed, then in step  1109 , electrodes are formed on the wafer by vapor deposition. Then, ions may be implanted in the wafer using substantially any suitable method in step  1113 . As will be appreciated by those skilled in the art, steps  1101 - 1113  are generally considered to be preprocessing steps for wafers during wafer processing. Further, it should be understood that selections made in each step, e.g., the concentration of various chemicals to use in forming an insulation film in step  1105 , may be made based upon processing requirements. 
     At each stage of wafer processing, when preprocessing steps have been completed, post-processing steps may be implemented. During post-processing, initially, in step  1117 , photoresist is applied to a wafer. Then, in step  1121 , an exposure device may be used to transfer the circuit pattern of a reticle to a wafer. Transferring the circuit pattern of the reticle of the wafer generally includes scanning a reticle scanning stage which may, in one embodiment, include a force damper to dampen vibrations. 
     After the circuit pattern on a reticle is transferred to a wafer, the exposed wafer is developed in step  1125 . Once the exposed wafer is developed, parts other than residual photoresist, e.g., the exposed material surface, may be removed by etching in step  1129 . Finally, in step  1133 , any unnecessary photoresist that remains after etching may be removed. As will be appreciated by those skilled in the art, multiple circuit patterns may be formed through the repetition of the preprocessing and post-processing steps. 
     Although only a few embodiments of the present invention have been described, it should be understood that the present invention may be embodied in many other specific forms without departing from the spirit or the scope of the present invention. By way of example, although electromagnets have been described as being used in conjunction with a vacuum preload to compensate for a bearing force, electromagnets may be used without a vacuum preload to compensate for a bearing force. In other words, electromagnetic forces alone may be used to compensate for a bearing force exerted on a wafer. 
     An air gauge arrangement has been described as being suitable for measuring a height of a photoresist-coated top surface of a wafer. However, an air gauge arrangement is not limited to measuring a height of a photoresist-coated top surface of a wafer. An air gauge arrangement which includes a vacuum preload as described above may be used to measure substantially any height. 
     In one embodiment, when electromagnets are used, shielding may be included within an overall system. Shielding may, for example, prevent the electromagnets from having an adverse effect on components which are sensitive to, and may interact with, the electromagnets. 
     A wafer may move upwards and downwards in some systems. In such systems, a servo motor may be used to move a wafer stage on which the wafer is positioned, or to move an air gauge or bearing arrangement, such that the distance between the wafer stage and the air gauge arrangement may remain substantially unchanged. When a servo motor is used, either an open-loop or closed-loop servo controller may be used to control the servo motor. In one embodiment, a signal from the air gauge arrangement may be provided to the servo controller. 
     The amount of bearing forces or load exerted on a wafer may vary widely. For example, the supply pressure of air supplied to an air gauge or bearing arrangement may be reduced such that bearing forces may be kept below approximately ten milliNewtons (mN). In the event that there are higher bearing forces, an increased vacuum preload which substantially surrounds the perimeter of the bearing, e.g., as shown in  FIG. 8 , may substantially cancel out the higher bearing forces. 
     The embodiments of the present invention may be implemented as hardware and/or software logic embodied in a tangible medium that, when executed, is operable to perform the various methods and processes described above. That is, the logic may be embodied as physical arrangements or components, or as software logic. For example, derivative controllers that derive or otherwise construct velocities and accelerations based on position measurements may be implemented as include hardware logic, software logic, or a combination of both hardware and software logic. The tangible medium may be substantially any computer-readable medium that is capable of storing logic which may be executed, e.g., by a computing system, to perform methods and functions associated with the embodiments of the present invention. 
     The operations associated with the various methods of the present invention may vary widely. By way of example, steps may be added, removed, altered, combined, and reordered without departing from the spirit or the scope of the present invention. 
     The many features of the present invention are apparent from the written description. Further, since numerous modifications and changes will readily occur to those skilled in the art, the invention should not be limited to the exact construction and operation as illustrated and described. Hence, all suitable modifications and equivalents may be resorted to as falling within the scope of the invention.