JP6737346B2 - Stage assembly, exposure apparatus, and process - Google Patents

Description

This application claims priority to US Provisional Application No. 62/344,262, filed June 1, 2016, entitled "Control System for Controlling Fluid Actuators". To the extent permitted, the content of US Provisional Application No. 62/344,262 is hereby incorporated by reference.

Exposure devices are commonly used to transfer an image from a mask onto a workpiece such as an LCD flat panel display or semiconductor wafer. A general exposure apparatus monitors the position or movement of an illumination source, a mask stage assembly that holds and precisely positions a mask, a lens assembly, a work stage assembly that holds and precisely positions a work, and the position and movement of the mask and work. Measuring system. There is an endless need to accurately position masks and/or workpieces while reducing the cost of actuators used to position these components.

The present invention relates to a stage assembly for positioning a work along a movement axis. In one embodiment, the stage assembly includes a stage, a base, a fluid actuator assembly, and a control system. The stage is configured to bond to and hold a work piece. The fluid actuator assembly is coupled to the stage and moves the stage relative to the base along a movement axis. A fluid actuator assembly includes a piston housing defining a piston chamber, a piston disposed within the piston chamber and moving relative to the piston chamber along a piston axis, and a valve assembly controlling flow of piston fluid to the piston chamber. Can be included. The valve assembly includes a first inlet valve having a first inlet valve characteristic. The control system controls the valve assembly to control the flow of piston fluid into the piston chamber. In particular embodiments, the control system utilizes an inverse function of the first inlet valve characteristic to control the valve assembly.

In one embodiment, the piston fluid is a gas and the invention is described as a pneumatic control application. Alternatively, the piston fluid may be a liquid such as oil and different equations may be utilized.

As described herein, the control system precisely controls the fluid pressure against the sides of the piston to generate the desired force for the purpose of precisely driving and positioning the stage. In certain embodiments, the valve assembly is evaluated to identify non-linearities inherent in the system. These non-linearities include the valve characteristics of each valve. Non-exclusive examples of valve characteristics relate to (i) fluid pressure variation as a function of chamber volume, (ii) proportional valve backlash and differential pressure dependency, and (iii) upstream and downstream pressures. The non-linearity of the flow rate may be mentioned. Non-linearities can be identified by testing, modeling, or simulation. The valve characteristics are then inverted and used in the control loop of the control system to linearize the system and precisely control the fluid actuator assembly.

Therefore, the problem of system non-linearity of fluid cylinder pressure and valve dynamics associated with applying the fluid cylinder to the orbital motion of the stage is solved by incorporating the identified system dynamics model into the control design.

In a particular embodiment, the piston divides the piston chamber into a first chamber and a second chamber on opposite sides of the piston. Additionally, the valve assembly controls the flow of piston fluid to/from the first chamber and the second chamber.

In one embodiment, a valve assembly includes (i) a first inlet valve that controls the flow of piston fluid into the first chamber and (ii) a first inlet valve that controls the flow of piston fluid from the first chamber. Outlet valve, (iii) a second inlet valve controlling the flow of piston fluid to the second chamber, and (iv) a second outlet valve controlling the flow of piston fluid from the second chamber. including. Further, the first outlet valve has a first outlet valve characteristic, the second inlet valve has a second inlet valve characteristic, and the second outlet valve has a second outlet valve characteristic. Have. In this embodiment, the control system also utilizes an inverse function of the first outlet valve characteristic, an inverse function of the second inlet valve characteristic, and an inverse function of the second outlet valve characteristic to control the valve assembly.

As a non-exclusive example, the first inlet valve characteristic can be measured using empirical testing of the first inlet valve and the first outlet valve characteristic can be empirically measured for the first outlet valve. The second inlet valve characteristic can be measured using a test, the second inlet valve characteristic can be measured using an empirical test of the second inlet valve, and the second outlet valve characteristic can be measured using a second outlet valve characteristic. It can be measured using empirical testing of valves.

As described herein, for example, each valve characteristic may include (i) current command and effective orifice area relationship for the valve, (ii) current command and valve position relationship for the valve, and (Iii) It may be the relationship between the effective orifice area and the valve position regarding the valve.

The present invention also relates to an exposure apparatus and a process for manufacturing a device that includes the steps of providing a substrate and imaging the substrate with the exposure apparatus.

The invention also relates to a method for positioning a workpiece along a movement axis. In one embodiment, the method comprises the steps of (i) providing a base, (ii) coupling a workpiece to a stage, and (iii) moving the stage along a movement axis using a fluid actuator assembly. Wherein a fluid actuator assembly controls a piston housing defining a piston chamber, a piston disposed within the piston chamber and moving relative to the piston chamber along a piston axis, and a piston fluid flow to the piston chamber. A valve assembly having a first inlet valve having a first inlet valve characteristic, and (iv) using a control system to control the flow of piston fluid into the piston chamber. Controlling the valve assembly, the control system utilizing an inverse function of the first inlet valve characteristic to control the valve assembly.

The novel features of the invention and the invention itself, both as to its structure and its operation, are best understood from the accompanying drawings in conjunction with the accompanying description. Note that the same reference numerals indicate the same parts.

FIG. 6 is a simplified side view of a stage assembly having features of the present invention.

6 is a control block diagram illustrating a method for controlling a fluid actuator assembly.

It is a control block diagram of a chamber controller.

FIG. 3 is a simplified diagram of one of the piston chambers and one of the valve subassemblies having features of the invention.

FIG. 6 is a simplified diagram of a pipe including an orifice.

FIG. 6 is a simplified cross-sectional view of a non-exclusive example of a valve. FIG. 6 is a simplified cross-sectional view of a non-exclusive example of a valve. FIG. 6 is a simplified cross-sectional view of a non-exclusive example of a valve.

6 is a graph showing valve characteristics of the valves of FIGS. 5A to 5C.

6 is a graph showing a reversing valve characteristic of the valves of FIGS. 5A to 5C.

FIG. 6 is a simplified diagram of another type of valve in one valve position. FIG. 6 is a simplified diagram of another type of valve in another valve position. FIG. 6 is a simplified diagram of another type of valve in yet another valve position. FIG. 6 is a simplified diagram of another type of valve in yet another valve position.

FIG. 7 is a simplified view of the outlet and valve body in a partially open position.

7A-7D are graphs showing calculated and normalized effective orifice area versus normalized spool position for the valve shown in FIGS. 7A-7D.

6 is a graph plotting spool position versus normalized effective orifice area.

It is a graph which shows the test result of a spool valve.

It is a graph which shows the simulation result of a spool valve.

Two valve characteristics of the spool valve are shown.

Two reversal valve characteristics are shown.

It is a schematic diagram of an exposure apparatus having the features of the present invention.

3 is a flow chart outlining a process for manufacturing a device in accordance with the present invention.

Embodiments of the present invention are described herein with respect to a stage assembly that includes a stage and a control system that controls a fluid actuator assembly that moves the stage. Those skilled in the art will appreciate that the following detailed description of the present invention is illustrative only and not in any way limiting. Other embodiments of the invention will be readily apparent to those of ordinary skill in the art having the benefit of this disclosure. Reference will now be made in detail to the embodiments of the invention, as illustrated in the accompanying drawings. The same or similar reference numbers are used throughout the drawings and the following detailed description to refer to the same or like parts.

In the interest of clarity, not all of the routine features of the embodiments described herein are shown and described. It goes without saying that in the development of such an actual implementation, a number of implementation-specific decisions must be made to achieve the developer's specific goals, such as compliance with application-related and business-related constraints. , As well as those particular goals, will vary from implementation to implementation and from developer to developer. Further, it will be appreciated that such a development effort, despite being complex and time consuming, is an engineering trivial task for one of ordinary skill in the art having the benefit of this disclosure.

FIG. 1 is a simplified diagram of a stage assembly 10 including a base 12, a stage 14, a stage mover assembly 16, a measurement system 18, and a control system 20 (shown as a square frame). The design of each of these components can be modified to suit the design requirements of the stage assembly 10. The stage assembly 10 is particularly useful for precisely positioning a work piece 22 (sometimes also referred to as a device) during the manufacturing and/or inspection process.

As an overview, in certain embodiments, the stage mover assembly 16 includes a fluid actuator assembly 24 that is relatively inexpensive to manufacture. Moreover, after the unique calibration and identification process described herein, the control system 20 can control the fluid actuator assembly 24 to accurately position the work piece 22. As a result, the stage assembly 10 is less expensive to manufacture and the workpiece 22 is still positioned with the desired level of accuracy.

The type of workpiece 22 that is positioned and moved by the stage assembly 10 can vary. For example, the work 22 can be an LCD flat panel display, a semiconductor wafer, or a mask, and the stage assembly 10 can be used as part of an exposure apparatus. Alternatively, for example, the stage assembly 10 may be used to move other types of devices during manufacturing and/or inspection, to move the device under an electron microscope (not shown), or to perform precision metrology operations. It can be used to move the device into (not shown).

Some of the figures described herein include coordinate systems that specify the X, Y, and Z axes. It should be appreciated that the coordinate system is for reference only and can be changed. For example, the X and Y axes can be interchanged and/or the stage assembly 10 can be rotated. Further, these axes may alternatively be referred to as the first axis, the second axis, or the third axis.

The base 12 supports the stage 14. In the non-exclusive embodiment shown in FIG. 1, the base 12 is rigid and generally rectangular in plate shape. Further, the base 12 can be firmly fixed to the base mount 26. Alternatively, the base 12 can be fixed to another structure.

The stage 14 holds the work 22. In one embodiment, the stage is precisely moved relative to the base 12 by the stage mover assembly 16 to precisely position the stage 14 and the work piece 22. In FIG. 1, the stage 14 has a substantially rectangular shape and includes a device holder (not shown) for holding the work 22. The device holder can be a vacuum chuck, an electrostatic chuck, or some other type of clamp that couples the work piece 22 directly to the stage 14. In the embodiments shown herein, the stage assembly 10 includes a single stage 14 that holds a work piece 22. Alternatively, for example, the stage assembly 10 can be designed to include multiple stages that are individually moved and positioned. As an example, the stage assembly 10 is moved with respect to the coarse movement stage using a coarse movement stage (not shown) moved by the stage mover assembly 16 and a fine movement stage mover assembly (not shown). And a fine movement stage (not shown) for holding.

Further, in FIG. 1, the stage 14 can be supported with respect to the base 12 using a bearing assembly 28 that allows movement of the stage 14 with respect to the base 12. For example, the bearing assembly 28 can be a roller bearing, a fluid bearing, a linear bearing, or another type of bearing.

The measurement system 18 monitors the movement and/or position of the stage 14 relative to a reference, such as an optical assembly (not shown in FIG. 1) or the base 12, and provides measurement information to the control system 20. This information can be used to control the stage mover assembly 16 by the control system 20 to precisely position the stage 14. The design of the measurement system 18 can be changed according to the movement requirement of the stage 14. In one embodiment, the measurement system 18 can include a linear encoder that monitors movement of the stage 14 along the Y-axis. Alternatively, the measurement system 18 can include an interferometer or another type of movement or position sensor.

The stage mover assembly 16 is controlled by the control system 20 to move the stage 14 relative to the base 12. In FIG. 1, the stage mover assembly 16 includes a fluid actuator assembly 24 that moves the stage 14 along a single axis of movement 30 (eg, the Y axis).

The design of the fluid actuator assembly 24 can be modified according to the teachings described herein. In one non-exclusive embodiment, a fluid actuator assembly 24 includes (i) a piston assembly 31 including a piston housing 32 defining a piston chamber 34 and a piston 36 disposed within the piston chamber 34; and (ii) a piston chamber. Valve assembly 38 for controlling the flow of piston fluid 40 (shown as a small circle) to/from 34. For example, the piston fluid 40 can be air or another type of fluid. The design of these components can be modified according to the teachings described herein.

In one embodiment, the piston housing 32 is rigid and defines a generally rectangular cylindrical piston chamber 34. In this embodiment, the piston housing 32 includes a tubular side wall 32A, a disc-shaped first end wall 32B, and a disc-shaped second end wall 32C spaced from the first end wall 32B. One or both of the end walls 32B, 32C can include a wall opening 32D for receiving a portion of the piston 36.

The piston housing 32 can be firmly fixed to the piston mount 42. Alternatively, the piston housing 32 can be secured to another structure such as the base 12. Still alternatively, the piston housing 32 receives the reaction forces generated by the stage mover assembly 16, so that the piston housing 32 offsets, reduces, and reduces the effects of reaction forces from the stage mover assembly 16 at other structural locations. Can be coupled to a minimizing reaction assembly. For example, the piston housing 32 may be maintained on a large countermass (not shown) using reaction bearings (not shown) that allow movement of the piston housing 32 along the axis of movement 30. (Not shown).

The piston 36 is disposed within the piston chamber 34 and moves relative to the piston chamber 34 along the piston axis 36A. In a particular embodiment, the piston shaft 36A is coaxial with the movement shaft 30. In the non-exclusive embodiment shown in FIG. 1, the piston 36 seals (i) a rigid disc-shaped piston body 36B and (ii) a region between the piston body 36B and the piston housing 32. A piston seal 36C and (iii) a rigid first beam 36D attached to the piston body 36B and protruding from the piston body 36B like a cantilever, passing through the wall opening 32D of the first end wall 32B. A first beam 36D extending in a vertical direction, and (iv) a rigid second beam 36E attached to the piston body 36B and protruding from the piston body 36B like a cantilever, which is a wall of the second end wall 32C. A second beam 36E extending through the opening 32D; (iv) a first beam seal (not shown) that seals the area between the first beam 36D and the first end wall 32B; ) A second beam seal (not shown) that seals the area between the second beam 36E and the second end wall 32C.

In this embodiment, the second beam 36E is also fixedly secured to the stage 14. In other words, the second beam 36E extends between the piston body 36B and the stage 14 so that when the piston body 36B moves, the stage 14 also moves. Further, in this embodiment, the first beam 36D is provided such that the effective areas of both sides of the piston body 36B are the same for ease of calculation. Alternatively, for example, the fluid actuator assembly 24 can be designed without the first beam 36D. In such an alternative design, the effective area of the left side surface of piston body 36B is greater than the effective area of the right side surface of piston body 36B.

The piston body 36B divides the piston chamber 34 into a first chamber 34A (also called "chamber 1") and a second chamber 34B (also called "chamber 2") on either side of the piston body 36B. In FIG. 1, the first chamber 34A is on the left side of the piston body 36B and the second chamber 34B is on the right side of the piston body 36B. Further, the first chamber 34A has the effective piston area (A ₁ ) of chamber 1, is filled with piston fluid 40 at a _first pressure (P ₁ ) and is at a first temperature (T ₁ ). , Having a _first volume (V ₁ ). Similarly, the second chamber 34B has the effective piston area (A ₂ ) of the chamber 2 and is filled with the piston fluid 40 at the second pressure (P ₂ ) and at the second temperature (T ₂ ). And has a second volume (V ₂ ). In this non-exclusive example shown in FIG. 1, fluid actuator assembly 24 is designed so that the effective piston area (A ₁ ) of chamber ₁ is approximately equal to the effective piston area (A ₂ ) of chamber 2.

The first pressure (P ₁ ) of the piston fluid 40 in the first chamber 34A produces a first force (F ₁ ) on the piston body 36B, which causes a second pressure of the piston fluid 40 in the second chamber 34B. Pressure (P ₂ ) of generates a _second force (F ₂ ) on the piston body 36B. The resultant force (F) 44 (indicated by the arrow) generated by the fluid actuator assembly 24 is equal to the _first force (F ₁ ) minus the _second force (F ₂ ) (F=F ₁ −F _{2 ).} ).

In the non-exclusive design shown in FIG. 1, when the first pressure (P ₁ ) is greater than the second pressure (P ₂ ), the first force (F ₁ ) is the second force (F ₂ ). And the resultant force (F) is positive and biases the piston body 36B and the stage 14 from left to right. On the contrary, when the first pressure (P ₁ ) is smaller than the second pressure (P ₂ ), the first force (F ₁ ) is smaller than the second force (F ₂ ), and the resultant force (F) Is negative and biases the piston body 36B and the stage 14 from right to left.

In one embodiment, the valve assembly 38 is controlled by the control system 20 to precisely and individually control the pressure within each of the chambers 34A, 34B. As one non-exclusive embodiment, the valve assembly 38 controls (i) the flow of piston fluid 40 to/from the first chamber 34A to precisely control the _first pressure (P ₁ ). The first valve subassembly 38A to be controlled to (ii) flow the piston fluid 40 to/from the second chamber 34B in order to precisely control the _second pressure (P ₂ ). A second valve subassembly 38B that is controlled to control. In this embodiment, the first valve subassembly 38A includes a first inlet valve 38C that is controlled to control the flow of piston fluid 40 to the first chamber 34A, and a piston from the first chamber 34A. A first outlet valve 38D that is controlled to control the flow of fluid 40. Similarly, the second valve subassembly 38B includes a second inlet valve 38E that is controlled to control the flow of piston fluid 40 into the second chamber 34B and a piston fluid 40 from the second chamber 34B. A second outlet valve 38F that is controlled to control the flow of

In this embodiment, the fluid actuator assembly 24 may include one or more fluid pressure sources 46 (two are shown) that supply pressurized piston fluid 40 to the inlet valves 38C, 38E. Further, each of the fluid pressure sources 46 controls the pressure of the fluid tank 46A, the compressor 46B for generating the pressurized piston fluid 40 in the tank 46A, and the pressure of the piston fluid 40 supplied to the inlet valves 38C, 38E. And a regulator 46C. In addition, outlet valves 38D, 38F allow venting to atmosphere or low pressure areas such as vacuum chambers.

In particular embodiments, each of valves 38C, 38D, 38E, 38F includes one or more valve characteristics that affect control of those valves 38C, 38D, 38E, 38F. For example, (i) first inlet valve 38C has one or more first inlet valve characteristics and (ii) first outlet valve 38D has one or more first outlet valve characteristics. Where (iii) the second inlet valve 38E has one or more second inlet valve characteristics, and/or (iv) the second outlet valve 38F has one or more second outlet valves. Has characteristics. In one embodiment, each of the valves 38C, 38D, 38E, 38F is individually tested to measure the individual valve characteristics of the respective valve 38C, 38D, 38E, 38F. In this design, the individual valve characteristics of each valve 38C, 38D, 38E, 38F are used to control each of the valves 38C, 38D, 38E, 38F. Alternatively, if each of the valves 38C, 38D, 38E, 38F is similar and has similar valve characteristics, one of the valves 38C, 38D, 38E, 38F can be tested and the valve 38C can be tested. , 38D, 38E, 38F, the valve characteristics of that valve can be used to control all of them.

The type of valves 38C, 38D, 38E, 38F used can vary. As a non-exclusive example, each of the valves 38C, 38D, 38E, 38F may be a proportional valve such as a poppet (“mushroom”) type valve or a spool type valve.

The type of valve characteristic will vary depending on the type of valve 38C, 38D, 38E, 38F used. Some non-exclusive types of valves 38C, 38D, 38E, 38F and non-exclusive examples of valve characteristics are described in detail below. It should be noted that the valves 38C, 38D, 38E, 38F may differ from the examples described herein and the valve characteristics may differ from the examples described herein.

As described herein, for each of the valves 38C, 38D, 38E, 38F, their corresponding valve characteristics can be measured by empirical testing, simulation, or a combination of both.

The control system 20 controls the valve assembly 38 to control the flow of piston fluid 40 to/from each of the chambers 34A, 34B. A controllable force on piston body 36B that causes valve assembly 38 to accurately move piston body 36B and stage 14 by selectively controlling the flow rate of piston fluid 40 to/from each of chambers 34A, 34B. 44 (“F”) can be controlled.

The control system 20 is electrically connected to the valve assembly 38 and controls the current applied to the valve assembly 38 to precisely position the stage 14 and workpiece 22. In one embodiment, the control system 20 measures (i) to constantly measure the position (“x”) of the stage 14 and (ii) to pass current through the valve assembly 38 for the purpose of positioning the stage 14. Use information from system 18. The control system 20 may include one or more processors 20A and electronic data storage 20B. Control system 20 uses one or more algorithms to perform the steps described herein.

In a particular embodiment, the control system 20 controls the first valve (P ₁ ) to control the _first pressure (P ₁ ) in the first chamber 34A for the purpose of producing the desired first force (F ₁ ). Each of 38C and 38D is controlled individually. Similarly, the control system 20 controls the second valves 38E, 38F to control the _second pressure (P ₂ ) in the second chamber 34B for the purpose of producing the desired second force (F ₂ ). Control each of the. Therefore, by controlling valves 38C, 38D, 38E, 38F, control system 20 can control fluid actuator assembly 24 to generate a desired resultant force (F) 44 on stage 14.

In certain embodiments, when the control system 20 determines that the piston fluid 40 needs to be added to the first chamber 34A, the control system 20 controls the first outlet valve 38D to close and the piston fluid 40D. The first inlet valve 38C is controlled to add 40 to open the appropriate amount. Further, when the control system 20 determines that the piston fluid 40 needs to be removed from the first chamber 34A, the control system 20 controls and closes the first inlet valve 38C to expel the piston fluid 40. For this purpose, the first outlet valve 38D is controlled to open by an appropriate amount. In this example, one of the first valves 38C and 38D is always controlled to be closed. Alternatively, control system 20 may controllably open both first valves 38C, 38D during the addition and/or removal of piston fluid 40 to/from first chamber 34A.

Similarly, when the control system 20 determines that the piston fluid 40 needs to be added to the second chamber 34B, the control system 20 controls and closes the second outlet valve 38F to add the piston fluid 40. In order to do so, the second inlet valve 38E is controlled to open an appropriate amount. Further, when the control system 20 determines that the piston fluid 40 needs to be removed from the second chamber 34B, the control system 20 controls and closes the second inlet valve 38E, releasing the piston fluid 40. In order to do so, the second outlet valve 38F is controlled to open an appropriate amount. In this example, one of the second valves 38E and 38F is always controlled to be closed. Alternatively, control system 20 may controllably open both second valves 38E, 38F during the addition and/or removal of piston fluid 40 to/from second chamber 34B.

Precise fluid pressure control of the two chambers 34A, 34B is performed to generate the desired force 44 and drive the stage 14. To accurately control the fluid actuator assembly 24, (i) variation of fluid pressure as a function of chamber volume, (ii) backlash and differential pressure dependence of proportional valves 38C, 38D, 38E, 38F, and (iii) 3.) It is important to measure the non-linearities inherent in the system, such as the non-linearities of the upstream and downstream pressure related flow rates. Through empirical testing and/or modeling, these non-linearities can be identified and compensated by the control system 20.

For example, the control system 20 may include (i) an inverse function of the first inlet valve characteristic to control the first inlet valve 38C, and (ii) a first outlet valve to control the first outlet valve 38D. An inverse function of the valve characteristic, (iii) an inverse function of the second inlet valve characteristic for controlling the second inlet valve 38E, and (iv) a second function of controlling the second outlet valve 38F. An inverse function of the outlet valve characteristic can be utilized. Since the control system 20 utilizes the inverse function of each valve characteristic, each of the valves 38C, 38D, 38E, 38F can be controlled with improved accuracy.

FIG. 2A is a control block diagram 220 illustrating a non-exclusive example of a method for controlling the fluid actuator assembly 24 to accurately position the stage 14. More specifically, control block diagram 220 illustrates one non-exclusive method for passing current through valve assembly 38 to control piston assembly 31 for the purpose of precisely positioning stage 14. In the control block diagram 220, the stage 14 is measured at an instantaneous stage position (“x”) as measured by the measurement system 18 (shown in FIG. 1) (eg, the measurement axis 30 (FIG. 1)). ) Along)).

」）、所望の加速度（「

」）、及びステージジャーク基準（「

」）を与えるステージ基準ブロック２６０と、（ｉｉ）ステージフィードバック（「ＦＢ」）コントローラ２６２と、（ｉｉｉ）ステージフィードフォワード（「ＦＦ」）コントローラ２６４と、（ｉｖ）フィードバック力コマンドをフィードバック圧力コマンドに変換するフィードバックコンバータ２６６と、（ｖ）フィードフォワード力コマンドをフィードフォワード圧力コマンドに変換するフィードフォワードコンバータ２６８と、（ｖｉ）第１のチャンバコントローラ２７０と、（ｖｉｉ）第２のチャンバコントローラ２７２と、（ｖｉｉｉ）ステージ１４の測定された位置（「ｘ」）に基づいて第１のチャンバの現在の第１のチャンバ容積（「Ｖ_１」）及び第１の容積変化率（「

」）を推定し、ステージ１４の測定された位置に基づいて第２のチャンバの現在の第２のチャンバ容積（「Ｖ_２」）及び第２の容積変化率（「

」）を推定するチャンバ容積推定器２７８とを含む。 In this embodiment, the control block diagram 220 includes (i) a desired stage reference position or trajectory (“x _d ”) of the stage 14 (eg, along the axis of travel 30 (shown in FIG. 1)), desired. Speed of ("

)), the desired acceleration (“

)) and stage jerk criteria (“

)), (ii) stage feedback (“FB”) controller 262, (iii) stage feedforward (“FF”) controller 264, and (iv) feedback force command to feedback pressure command. A feedback converter 266 for converting, (v) a feedforward converter 268 for converting a feedforward force command into a feedforward pressure command, (vi) a first chamber controller 270, (vii) a second chamber controller 272, (Viii) The current first chamber volume (“V ₁ ”) of the first chamber and the first rate of change of volume (““ based on the measured position (“x”) of stage 14).

)) and based on the measured position of the stage 14, the current second chamber volume (“V ₂ ”) of the second chamber and the second rate of volume change (“

)) for estimating the chamber volume.

Note that some of the blocks of control block diagram 220 of FIG. 2A are optional, and/or control block diagram 220 may include additional control blocks. For example, the control block diagram 220 can be designed without the loop of the stage feedforward controller 264. Additionally or alternatively, the control block diagram 220 can be designed to include an iterative learning loop (not shown).

」）、ステージ加速度基準（「

」）、及びステージジャーク基準（

）が、システム時間遅延及び軌道などを補償するために必要な力コマンドを表すステージフィードフォワード力コマンド（「Ｆ_ｆｆ」）を生成するステージフィードフォワードコントローラ２６４に供給される。 In the control block diagram 220 traveling from left to right, the position or trajectory (“x _d ”) of the stage desired reference 260 represents the error between the desired position of the stage 14 and the measured position, the stage tracking error ( "E") is compared to the stage measurement position ("x"). The stage tracking error (“e”) then produces a stage feedback force command (“F _fb ”) that represents the force command required to move the stage 14 from the measured position to the reference position. 262. At the same time, the desired reference position (“x _d ”), stage velocity reference (““

)), stage acceleration reference (“

)) and stage jerk criteria (

) Is supplied to a stage feedforward controller 264 that produces a stage feedforward force command (“F _ff ”) that represents the force command required to compensate for system time delays, trajectories, and the like.

」）及び第２のチャンバのための第２のフィードフォワード圧力変化率コマンド（「

」）に変換する。 Then, in this embodiment, the stage feedback force command (“F _fb ”) and the feedforward force command (“F _ff ”) are combined force commands (“F _cmd ”) supplied to the feedback converter 266. Combined to produce a combined force command, the feedback converter 266 produces a combined feedback command of the first feedback pressure command for the first chamber (“P1 _fb ”or “P _{1, cmd} ”) and the second chamber. To a second feedback pressure command (“P2 _fb ”or “P _{2, cmd} ”). Similarly, the stage feedforward force command (“F _ff ”) is provided to the feedforward converter 268, which feedforward force command 168 to feed the first feedforward pressure change for the first chamber. Rate command ("

)) and a second feedforward pressure change rate command for the second chamber ("

)).

」）、第１の測定された圧力（「Ｐ_１」）、第１のチャンバ容積（「Ｖ_１」）、及び第１の容積変化率（「

」）を使用する。同様に、第２のチャンバコントローラ２７２は、第２のバルブサブアセンブリに送られる第２のバルブサブアセンブリ電流コマンド（「ｕ_２」）を決定するために、第２のフィードバック圧力コマンド（「Ｐ_{２，ｃｍｄ}」）、第２のフィードフォワード圧力コマンド（「

」）、第２の測定された圧力（「Ｐ_２」）、第２のチャンバ容積（「Ｖ_２」）、及び第２の容積変化率（「

」）を使用する。バルブアセンブリ３８への電流により、ピストンアセンブリ３１へのピストン流体が制御され、ステージ１４に対する力（「Ｆ」）が生成される。 Thereafter, the first chamber controller 270 determines a first feedback pressure command (“P _1, ” to determine a _first valve subassembly current command (“u ₁ ”) sent to the first valve subassembly _{. cmd} "), the first feedforward pressure command ("

)), a first measured pressure ("P ₁ "), a first chamber volume ("V ₁ "), and a first rate of change of volume ("

)) is used. Similarly, the second chamber controller 272 determines a second feedback sub-command current command (“u ₂ ”) to be sent to the second valve sub-assembly to determine a second feedback pressure command (“P ₂ ”). _{, Cmd} "), the second feedforward pressure command ("

″), a second measured pressure (“P ₂ ”), a second chamber volume (“V ₂ ”), and a second rate of volume change (“

)) is used. The current to the valve assembly 38 controls the piston fluid to the piston assembly 31 and produces a force (“F”) on the stage 14.

As described herein, the chamber controllers 270, 272 perform an inverse function of the valve characteristics to accurately determine the respective current commands required to accurately control the pressure in the two chambers. To use. This process is described in more detail below with reference to FIG. 2B.

Note that in embodiments where one of the valves in each valve subassembly is always closed, only a single current command is required for each valve subassembly. Alternatively, if both valve subassemblies can be open at all times, the chamber controllers 270, 272 need to be designed to provide separate current commands for each valve.

上記のように、Ｆは、合力であり、Ｆ_１は、第１のチャンバによって発生する力であり、Ｆ_２は、第２のチャンバによって発生する力である。 Many equations are useful for understanding the forces generated by the stage mover assembly 16 and for understanding the control of the stage mover assembly 16 by the control system 20. As described above, the resultant force generated by the stage mover assembly 16 is defined as follows.

As mentioned above, F is the resultant force, F ₁ is the force generated by the first chamber, and F ₂ is the force generated by the second chamber.

上記のように、Ｐ_１は、第１のチャンバ内の第１のチャンバ圧力であり、Ａ_１は、第１のチャンバの有効ピストン面積であり、Ｐ_２は、第２のチャンバ３４Ｂ内の第２のチャンバ圧力であり、Ａ_２は、第２のチャンバ３４Ｂの有効ピストン面積である。 Equation 1 can be rewritten as:

As mentioned above, P ₁ is the first chamber pressure in the first chamber, A ₁ is the effective piston area of the first chamber, and P ₂ is the first chamber pressure in the second chamber 34B. 2 is the chamber pressure and A ₂ is the effective piston area of the second chamber 34B.

式３及び他の箇所において、Ｍは、ステージ（ワークを含む）の質量であり、Ｃは、減衰係数であり、

は、ステージの質量の加速度であり、

は、ステージの速度である。 Further, the force on the stage can be expressed as:

In Equation 3 and elsewhere, M is the mass of the stage (including the work piece), C is the damping coefficient,

Is the acceleration of the stage mass,

Is the speed of the stage.

式４及び他の箇所において、ｉは、それぞれのチャンバ（第１のチャンバ（「１」）又は第２のチャンバ（「２」）のいずれか）であり、Ｐ_ｉは、それぞれのチャンバ内の圧力であり、Ｖ_ｉは、それぞれのチャンバの容積であり、Ｒは、気体定数であり、ｍ_ｉは、それぞれのチャンバ内の気体質量であり、Ｔ_ｉは、それぞれのチャンバ内の温度である。 The equation of state of gas can be expressed as follows.

In Equation 4 and elsewhere, i is the respective chamber (either the first chamber (“1”) or the second chamber (“2”)) and P _i is the a pressure, V _i is the volume of the respective chambers, R represents the gas constant, m _i is the gas mass in the respective chambers, T _i is the temperature in each chamber ..

式５及び他の箇所において、

は、それぞれのチャンバの圧力変化率であり、

は、それぞれのチャンバの容積変化率であり、

は、それぞれのチャンバの質量流量である。 Equation 4 can be rewritten as:

In Equation 5 and elsewhere,

Is the pressure change rate of each chamber,

Is the volume change rate of each chamber,

Is the mass flow rate of each chamber.

Equation 5 can be rewritten as chamber pressure modeling as follows:

Further, Equation 5 can be rewritten as chamber mass flow control as follows:

同様に、第２のチャンバ３４Ｂの第２の容積Ｖ_２は、以下のようにステージ位置の関数として書くことができる。

式８及び９並びに他の箇所において、Ａ_１は、第１のチャンバの有効ピストン面積であり、Ａ_２は、第２のチャンバの有効ピストン面積であり、ｘは、ステージの現在の位置であり、ｘ_１，ｏは、第１のチャンバの無効長（ｄｅａｄ ｌｅｎｇｔｈ）であり、ｘ_２，ｏは、第２のチャンバの無効長である。 The first volume V ₁ of the first chamber 34A can be written as a function of stage position as follows:

Similarly, the second volume V ₂ of the second chamber 34B can be written as a function of stage position as follows:

In equations 8 and 9 and elsewhere, A ₁ is the effective piston area of the first chamber, A ₂ is the effective piston area of the second chamber, and x is the current position of the stage. , X _1,o is the dead length of the first chamber and x _2,o is the dead length of the second chamber.

同様に、式９は、以下のように書き直すことができる。

これらの式及び他の箇所において、

は、第１のチャンバの容積変化率であり、

は、第２のチャンバの容積変化率である。 Equation 8 can be rewritten as:

Similarly, Equation 9 can be rewritten as:

In these equations and elsewhere,

Is the volume change rate of the first chamber,

Is the rate of change in volume of the second chamber.

式１２及び１３並びに他の箇所において、Ｆ_ｃｍｄは、力コマンドであり、Ｆ_feedforwardは、フィードフォワード力コマンドであり、Ｆ_feedbackは、フィードバック力コマンドであり、

は、ステージ加速度基準であり、

は、ステージ速度基準であり、

は、ステージジャーク基準であり、ｘ_ｄは、基準位置であり、Ｃは、ステージとアクチュエータシステムの減衰比であり、Ｃ_ｆｂ（ｓ）は、ステージフィードバック制御フィルタであり、ｘは、ステージの現在の測定された位置であり、Ｐ_{１，ｃｍｄ}は、第１のチャンバへの圧力コマンドであり、Ｐ_{２，ｃｍｄ}は、第２のチャンバへの圧力コマンドである。 The chamber pressure control for each of the chambers 34A, 34B can be expressed as:

In equations 12 and 13 and elsewhere, F _cmd is the force command, F _feedforward is the feedforward force command, F _feedback is the feedback force command,

Is the stage acceleration reference,

Is the stage speed reference,

Is the stage jerk reference, x _d is the reference position, C is the damping ratio of the stage and actuator system, C _fb (s) is the stage feedback control filter, and x is the current of the stage. , P _{1, cmd} is the pressure command to the first chamber and P _{2, cmd} is the pressure command to the second chamber.

式１４及び１５並びに他の箇所において、Ｆ_ｏは、オフセット力コマンドであり、ｒは、第１のチャンバと第２のチャンバの配分比である。特定の実施形態において、ｒの値は、０よりも大きく、１よりも小さい（０＜ｒ＜１）が、公称値はｒ＝０．５である。 Equations 12 and 13 can be rewritten as follows:

In equations 14 and 15 and elsewhere, F _o is the offset force command and r is the distribution ratio of the first chamber to the second chamber. In a particular embodiment, the value of r is greater than 0 and less than 1 (0<r<1), but the nominal value is r=0.5.

Equations 14 and 15 can be rewritten as follows:

さらに、式１８は、以下のように表すことができる。

The chamber pressure control can be expressed as:

Further, Equation 18 can be expressed as:

式２１及び他の箇所において、

は、第１のチャンバ及び第２のチャンバの一方に対する質量流量コマンドである。 Similar to Equation 7, the mass flow control of the chamber can be expressed as:

In Equation 21 and elsewhere,

Is the mass flow command for one of the first chamber and the second chamber.

」）を生成する。圧力−質量流量コンバータ２９２は、圧力変化率コマンド（「

」）、チャンバ圧力（「Ｐ_ｉ」）、現在のチャンバ容積（「Ｖ_ｉ」）、及び容積変化率（「

」）を受け取り、入口バルブのための質量流量コマンド（「

」）及び出口バルブのための質量流量コマンド（「

」）を生成する。圧力−質量流量コンバータ２９２は、本明細書に記載されている式２１及び２２を使用することができる。 FIG. 2B is a control block diagram showing how one of the chamber controllers 270, 272 (shown in FIG. 2A) can be configured. In this embodiment, the chamber controller comprises (i) a pressure feedback controller 290, (ii) a pressure to mass flow converter 292, (iii) an inlet mass flow to orifice area converter 294, and (iv) an outlet mass flow to orifice. Area converter 296, (v) inlet orifice area-current converter 297, and (vi) outlet orifice area-current converter 298. In this embodiment, the pressure feedback controller 290 receives the pressure error P _i,err for each chamber _{and returns} the pressure change rate feedback (“

)) is generated. The pressure-mass flow rate converter 292 uses the pressure change rate command (“

)), chamber pressure (“P _i ”), current chamber volume (“V _i ”), and volume change rate (“

)) and a mass flow command for the inlet valve ("

)) and the mass flow command for the outlet valve ("

)) is generated. The pressure-to-mass flow converter 292 can use equations 21 and 22 described herein.

」）及びチャンバ圧力（「Ｐ_ｉ」）を受け取り、入口バルブのための入口オリフィス面積コマンド（「ａ_{ｉ，ｃｍｄ＋}」）を生成する。入口質量流量−オリフィス面積コンバータ２９４は、本明細書に記載されている式２４を使用することができる。ある程度同様に、出口質量流量−オリフィス面積コンバータ２９６は、質量流量コマンド（「

」）及びチャンバ圧力（「Ｐ_ｉ」）を受け取り、出口バルブのための出口オリフィス面積コマンド（「ａ_{ｉ，ｃｍｄ−}」）を生成する。出口質量流量−オリフィス面積コンバータ２９６は、本明細書に記載されている式２５を使用することができる。 The inlet mass flow rate-orifice area converter 294 uses the mass flow rate command ("

)) and chamber pressure ("P _i ") and produces an inlet orifice area command ("a _{i, cmd+} ") for the inlet valve. Inlet mass flow to orifice area converter 294 may use Equation 24 described herein. To some extent, the outlet mass flow-to-orifice area converter 296 uses the mass flow command ("

)) and chamber pressure ("P _i ") and produces an exit orifice area command ("a _{i, cmd-} ") for the exit valve. The outlet mass flow rate-orifice area converter 296 can use Equation 25 described herein.

The inlet orifice area-to-current converter 297 then uses the inlet orifice area command ("a _{i, cmd+} ") to generate the inlet current command ("u _{i, cmd+} ") for the inlet valve. The inlet orifice area-to-current converter 297 can use Equation 27 described herein. Similarly, the outlet orifice area - current converter 298 uses the outlet current command for the outlet valve ( _{"u i, cmd-")} exit orifice area command to generate a ( _{"a i, cmd-")} .. The outlet orifice area-to-current converter 298 can use Equation 28 described herein.

式２２及び他の箇所において、

は、選択されたチャンバ３３４ｉに対する入口バルブ３３８ｉｉのための質量流量コマンドであり、

は、選択されたチャンバ３３４ｉに対する出口バルブ３３８ｉｏのための質量流量コマンドである。本明細書に記載されているように、特定の実施形態において、チャンバ３３４ｉへの質量流量を増加させる（

）ことが望ましい場合、出口バルブ３３８ｉｏは閉鎖され（

）、入口バルブ３３８ｉｉの質量流量コマンドと等しくなるように設定される質量流量コマンドが、質量流量コマンドに設定される（

）。同様に、特定の実施形態において、チャンバ３３４ｉからの質量流量を増加させる（

）ことが望ましい場合、入口バルブ３３８ｉｉは閉鎖され（

）、出口バルブ３３８ｉｏの質量流量コマンドと等しくなるように設定される質量流量コマンドが、質量流量コマンドに設定される（

）。 FIG. 3 is a simplified diagram of one of the piston chambers 334i and one of the valve subassemblies 338i. As shown in FIG. 3, in this embodiment, the chamber mass flow to/from the chamber 334i is controlled by an inlet valve 338ii and an outlet valve 338io. In this embodiment, pressure source 346 supplies pressurized piston fluid 340 to the inlet of inlet valve 338ii at a pressure called P _source . Further, the pressure at the outlet of the outlet valve 338io is P _drain . The chamber mass flow control of Equation 21 can be rewritten as:

In Equation 22 and elsewhere,

Is the mass flow command for the inlet valve 338ii for the selected chamber 334i,

Is the mass flow command for the outlet valve 338io for the selected chamber 334i. In certain embodiments, increasing the mass flow rate to chamber 334i (as described herein).

) Is desired, the outlet valve 338io is closed (

), the mass flow command set to be equal to the mass flow command of the inlet valve 338ii is set to the mass flow command (

). Similarly, in certain embodiments, increasing the mass flow rate from chamber 334i (

) Is desired, the inlet valve 338ii is closed (

), a mass flow command that is set equal to the mass flow command of the outlet valve 338io is set to the mass flow command (

).

式２３及び他の箇所において、ａは、開放されているバルブオリフィスの面積であり、数学的関数であり、Ｐ_upstreamは、バルブオリフィスの上流の圧力であり、Ｐ_downstreamは、バルブオリフィスの下流の圧力である。したがって、質量流量は、開放されているバルブオリフィスの面積に、上流圧力及び下流圧力の関数を掛けたものと等しい。 The valve flow formula can be written as:

In Equation 23 and elsewhere, a is the area of the open and has a valve orifice, a mathematical function, P _upstream is the pressure upstream of the valve orifice, P _downstream is the downstream of the valve orifice It is pressure. Thus, the mass flow rate is equal to the open valve orifice area times a function of upstream and downstream pressure.

これらの式及び他の箇所において、ａ_{ｉ，ｃｍｄ＋}は、選択されたチャンバ３３４ｉの入口バルブ３３８ｉｉのためのバルブオリフィスコマンドであり、ａ_{ｉ，ｃｍｄ−}は、選択されたチャンバ３３４ｉに対する出口バルブ３３８ｉｏのためのバルブオリフィスコマンドである。 FIG. 4 is a simplified diagram of a pipe 400 that includes an orifice 402 similar to the valve orifice of a valve when opened. In this example, the upstream pressure and the downstream pressure are labeled and the orifice 402 has an orifice area. Referring to FIGS. 3 and 4, Equation 23 can be rewritten as the valve orifice area command below.

In these equations and elsewhere, a _i,cmd+ is the valve orifice command for the inlet valve 338ii of the selected chamber 334i, and a _i,cmd− is the outlet valve 338io of the selected chamber 334i. Valve orifice command for.

式２６において、ａは、バルブオリフィス面積であり、Ａは、バルブ面積式であり、ｕは、バルブ電流である。バルブ面積式については、以下でより詳細に説明する。 The valve area formula can be written as:

In Equation 26, a is the valve orifice area, A is the valve area expression, and u is the valve current. The valve area formula will be described in more detail below.

式２７及び２８並びに他の箇所において、ｕ_{ｉ，ｃｍｄ＋}は、入口バルブへのバルブ電流コマンドであり、

は、入口バルブのバルブ面積式の逆数であり、ａ_{ｉ，ｃｍｄ＋}は、入口バルブのバルブオリフィス面積であり、ｕ_{ｉ，ｃｍｄ−}は_、出口バルブへのバルブ電流コマンドであり、

は、出口バルブのバルブ面積式の逆数であり、ａ_{ｉ，ｃｍｄ−}は、出口バルブのバルブオリフィス面積である。 Equation 26 can be rewritten as a valve current command as follows:

In equations 27 and 28 and elsewhere, u _i,cmd+ is the valve current command to the inlet valve,

Is the inverse of the valve area type inlet _{valve, a i, cmd +} is a valve orifice area of the inlet _{valve, u i, cmd- is} valve current command to the outlet valve,

Is the reciprocal of the valve area formula of the outlet valve, and a _i,cmd− is the valve orifice area of the outlet valve.

亜音速流の場合、下流圧力で割った上流圧力は、シータ（「θ」）以下であり（

）、したがって、

（式３０）である。
超音速流の場合、下流圧力で割った上流圧力は、シータ（「θ」）よりも大きく（

）、したがって、以下である。

これらの式において、

、

、及び

であるが、ただし、ｃは、排出係数であり、Ｍ_ｍは、気体の分子質量であり、Ｚは、気体圧縮率因子であり、ｋは、比熱比であり、Ｒは、普遍的な気体法則定数であり、Ｔは、温度である。 Equations 24 and 25 can be written more generally as:

For subsonic flow, the upstream pressure divided by the downstream pressure is less than theta (“θ”) (

), therefore

(Equation 30)
For supersonic flow, the upstream pressure divided by the downstream pressure is greater than theta (“θ”) (

), therefore:

In these equations,

,

,as well as

Where c is the emission coefficient, M _m is the molecular mass of the gas, Z is the gas compressibility factor, k is the specific heat ratio, and R is the universal gas. Is a law constant and T is temperature.

5A is a simplified cross-sectional view of a non-exclusive example of valve 538 that may be used as one of valves 38C, 38D, 38E, 38F of FIG. In this embodiment, the valve 538 includes a valve housing 539A, a movable valve body 539B, an inlet conduit 539C, an outlet conduit 539D, and an elastic member 539E (eg, a spring) that biases the valve body 539B toward the inlet conduit 539C. , A solenoid 539F, and a poppet type valve.

In this simple example, the valve housing 538A is somewhat cylindrical, the valve body 539B is disk-shaped, and the conduits 539C, 539D are tubular. Further, in FIG. 5A, valve 538 is shown in the closed position when the control system (not shown in FIG. 5A) is not energizing solenoid 539F. As a result, elastic member 539E biases valve body 539B toward the top of inlet conduit 539C to close valve 538.

Note that when the solenoid 539F is not energized, the valve remains closed as long as the spring preload force is greater than the force generated by the pressure differential between the upstream pressure and the downstream pressure.

5B is a simplified cross-sectional view of valve 538 of FIG. 5A with valve 538 in the open position. At this time, the control system (not shown in FIG. 5B) is supplying current to the solenoid 539F. When a current is applied to the solenoid, this produces a solenoid force F _solenoid that biases (pulls) the valve body 539B upward from the top of the inlet conduit 539C. Generally, the magnitude of the solenoid force is proportional to the current. When sufficient current is applied to the solenoid 539F, the spring preload force of the elastic member 539F is overcome, the valve body 539B is separated from the top of the inlet conduit 539C and the valve 538 is opened. Further, the amount of current determines how much valve 538 is opened. Generally, the magnitude of the valve opening increases as the current increases.

As shown in FIG. 5B, the amount by which the valve body 539B has moved from the closed position to the open position is referred to as “y”.

FIG. 5C is a simplified cross-sectional view of valve 538 of FIG. 5A with inlet conduit 539C removed and solenoid 539F not activated and pressure in conduit 539D . At this time, the elastic member 539E is biased downwardly the valve body 539B by preload distance _{y o.} The valve body 539B in the closed position is shown in dashed lines for reference. When inlet conduit 539C (as shown in FIG. 5A) in place, the elastic member 539E is added equal spring preload force and multiplied by the preload distance _{y o} in the spring constant _{k s} of the elastic member 539E.

式３２及び他の箇所において、Ｍ_ｖは、バルブ本体５３９Ｂの質量であり、

は、バルブ本体５３９Ｂの加速度であり、Ｃ_ｖは、ばね摩擦によって発生する減衰であり、

は、バルブ本体５３９Ｂの速度であり、ｋ_ｓは、弾性部材５３９Ｅのばね定数であり、ｙ_ｏは、予荷重距離であり、ｋ_ｆは、ソレノイド力定数であり、ｕは、ソレノイドに送られる電流コマンドであり、ｒは、入口導管５３９Ｃの頂部の半径であり、デルタ圧力は、上流圧力と下流圧力の差である（ΔＰ＝Ｐ_ｕ−Ｐ_ｄ）。 The control of valve 538 can be expressed as:

In Equation 32 and elsewhere, M _v is the mass of the valve body 539B,

Is the acceleration of the valve body 539B, C _v is the damping caused by spring friction,

Is the velocity of the valve body 539B, _{k s} is the spring constant of the elastic member 539E, _{y o} is the preload distance, _{k f} is a solenoid force constant, u is sent to the solenoid Is the current command, r is the radius of the top of the inlet conduit 539C, and Delta pressure is the difference between the upstream pressure and the downstream pressure (ΔP=P _u −P _d ).

式３３及び３４並びに他の箇所において、Ａは、バルブ面積式であり、Ａ^−１は、バルブ面積式の逆数である。 The effective orifice area “a” of the valve 538 shown in FIGS. 5A-5C can be expressed as:

In equations 33 and 34 and elsewhere, A is the valve area equation and A ⁻¹ is the reciprocal of the valve area equation.

The dead-zone current u _o required to overcome the spring preload force can be expressed as:

For valve 538 shown in FIGS. 5A-5C, the maximum leak-free allowable pressure difference ΔP _max can be expressed as:

For the valve 538 shown in FIGS. 5A-5C, the static control current can be expressed as:

As mentioned above, in order to accurately control the fluid actuator assembly 24, it is important to measure the non-linearity inherent in each of the valves 38C, 38D, 38E, 38F. In certain embodiments, each of the valves 38C, 38D, 38E, 38F is not disassembled to identify the valve characteristics of each of the valves 38C, 38D, 38E, 38F. Instead, each of the physical valves 38C, 38D, 38E, 38F of valve assembly 24 are tested to measure their respective valve characteristics. For example, for each of the valves 38C, 38D, 38E, 38F, the flow rate is measured using different valve current commands with different inlet/outlet pressure differentials. Then, for each of the valves 38C, 38D, 38E, 38F, the effective orifice area can be calculated from the flow rate information using a flow rate equation (see Equations 24-31).

FIG. 6A is a graph showing valve effective orifice area versus current command for various delta pressures (“ΔP”). This graph was created by experimentally testing poppet valves at various delta pressures. For example, the flow rate was measured with several different current commands to the solenoid while maintaining a delta pressure of 350 kPa. The effective orifice area was then calculated for each measured flow rate and plotted in Figure 6A as a small square frame. The curve fit of these data points then produced line 600A. Line 600A represents the valve orifice area versus current command for a delta pressure of 350 kPa.

The flow rate was then measured with multiple different current commands to the solenoid while maintaining a delta pressure of 300 kPa. The effective orifice area was then calculated for each measured flow rate and plotted as a small circle in Figure 6A. Curve fit of these data points then produced line 602A. Line 602A represents valve orifice area versus current command for a delta pressure of 300 kPa.

Similarly, the flow rate was measured with different current commands to the solenoid while maintaining a delta pressure of 250 kPa. The effective orifice area was then calculated for each measured flow rate and plotted in Figure 6A as a small "x". Curve fit of these data points then produced line 604A. Line 604A represents the valve orifice area versus current command for a delta pressure of 250 kPa.

In addition, the flow rate was measured with several different current commands to the solenoid while maintaining a delta pressure of 200 kPa. The effective orifice area was then calculated for each measured flow rate and plotted in Figure 6A as a small "z". Curve fit of these data points then produced line 606A. Line 606A represents the valve orifice area versus current command for a delta pressure of 200 kPa.

In addition, the flow rate was measured with multiple different current commands to the solenoid while maintaining a delta pressure of 150 kPa. The effective orifice area was then calculated for each measured flow rate and plotted in Figure 6A as a small triangle. The curve fit of these data points then produced line 608A. Line 608A represents the valve orifice area versus current command for a delta pressure of 150 kPa.

Additionally, the flow rate was measured with several different current commands to the solenoid while maintaining a delta pressure of 100 kPa. The effective orifice area was then calculated for each measured flow rate and plotted in Figure 6A as a small "+". A curve fit of these data points then produced line 610A. Line 610A represents the valve orifice area versus current command for a delta pressure of 100 kPa.

Finally, the flow rate was measured with several different current commands to the solenoid while maintaining a delta pressure of 50 kPa. The effective orifice area was then calculated for each measured flow rate and plotted in FIG. 6A as “D”. Then generate the line 612 A by the curve fit of these data points. Line 612 A represents the valve orifice area versus current command for a delta pressure of 50 kPa.

In this example, the valve characteristic 614 of this valve represents the effective valve orifice area versus current command relationship for many different delta pressures. Alternatively, for example, valve characteristic 614 may include (i) effective valve orifice area versus voltage relationship for many different delta pressures, (ii) flow rate versus current command relationship for many different delta pressures, and/or (Iii) There may be a flow-to-voltage relationship for many different delta pressures.

As noted above, in certain embodiments, the valve characteristic 614 is inverted to produce the reversing valve characteristic 616, which is then used to control that valve. For example, the data of FIG. 6A can be inverted (the X and Y axes of the graph can be swapped) to produce the reversal valve characteristic 616 shown in FIG. 6B.

More specifically, FIG. 6B is a graph showing valve current command versus effective orifice area, which is an inversion of the graph of FIG. 6A. In this example, the data of Figure 6A is inverted to produce the data of Figure 6B. Curve fitting is then used to generate the curve of FIG. 6B.

For example, a delta pressure of 350 kPa represents the data as a small square frame. Thereafter, curve fit of these data points produced line 600B. Line 600B represents the valve current command versus valve orifice area for a delta pressure of 350 kPa.

Then, for a delta pressure of 300 kPa, the data are represented as small circles. Thereafter, a curve fit of these data points generated line 602B. Line 602B represents the valve current command versus valve orifice area for a delta pressure of 300 kPa.

Similarly, for a delta pressure of 250 kPa, the data is represented as a small "x". The curve fit of these data points then produced line 604B. Line 604B represents the valve current command versus valve orifice area for a delta pressure of 250 kPa.

Furthermore, at a delta pressure of 200 kPa, the data is represented as a small "z". The curve fit of these data points then produced line 606B. Line 606B represents the valve current command versus valve orifice area for a delta pressure of 200 kPa.

Moreover, at a delta pressure of 150 kPa, the data are represented as small triangles. The curve fit of these data points then generated line 608B. Line 608B represents the valve current command versus valve orifice area for a delta pressure of 150 kPa.

Additionally, at 100 kPa delta pressure, the data is represented as a small "+". The curve fit of these data points then produced line 610B. Line 610B represents the valve current command versus valve orifice area for a delta pressure of 100 kPa.

Finally, at 50 kPa delta pressure, the data is represented as a small "D". A curve fit of these data points then produced line 612B. Line 612B represents the valve current command versus valve orifice area for a delta pressure of 50 kPa.

Note that the reversal valve characteristic 616 data in the graph of FIG. 6B can be used by the control system to precisely control the valve. It should also be noted that the control system may utilize interpolation to generate data for other delta pressures to precisely control the valve at other delta pressures.

7A-7D are simplified cross-sectional views of another type of valve 738 in various valve positions that may be used as one of the valves 38C, 38D, 38E, 38F of FIG. More specifically, FIG. 7A is a simplified side view of the spool type valve 738 in the fully closed position, and FIG. 7B is a simplified side view of the spool type valve 738 in the reference closed (preparing to open) position. Yes, FIG. 7C is a simplified side view of the spool type valve 738 in the partially open position, and FIG. 7D is a simplified side view of the spool type valve 738 in the fully open position.

In this embodiment, the valve 738 includes a valve housing 739A, a movable valve body 739B (sometimes referred to as a "spool"), an inlet opening (not shown), an outlet opening 739D, and a valve body 739B from the right. It is a spool type valve including an elastic member 739E (for example, a spring) that urges to the left and a solenoid 739F that moves the valve body 739B from the left to the right.

In this simple example, the valve housing 739A has a somewhat hollow cylindrical shape, the valve body 739B has a disk shape, and the openings 739D have a circular shape, and are arranged on opposite side surfaces of the valve housing 739A . The valve body 739B is arranged between them.

Note that the delta pressure does not affect the opening and closing of the valve 738 because the upstream pressure and the downstream pressure are orthogonal to the valve body 739B.

Further, in FIG. 7A, valve 738 is shown in a fully closed position when a control system (not shown in FIG. 7A) is not energizing solenoid 739F. At this time, the valve body 739B covers both the inlet and the outlet 739D and closes the valve 738.

7B is a simplified cross-sectional view of the valve 738 of FIG. 7A with the valve 738 in the reference position just prior to opening. At this time, the control system (not shown in FIG. 7B) is supplying current to the solenoid 739F. When a current is applied to the solenoid, this produces a solenoid force F _solenoid that biases the valve body 739B by y _{b to a} reference position where the valve 738 is ready to open.

7C is a simplified cross-sectional view of valve 738 of FIG. 7A with valve 738 in a partially open position. At this time, the control system (not shown in FIG. 7C) is supplying current to the solenoid 739F. When a current is applied to the solenoid, this produces a solenoid force F _solenoid that biases the valve body 739B by y to a position where the valve 738 is partially open.

Generally, the magnitude of the solenoid force is proportional to the current. When a sufficient current is applied to the solenoid 739F, the spring preload force of the elastic member 739F is overcome and the valve body 739B is moved. Moreover, the amount of current determines how much the valve 738 is opened. Generally, the magnitude of the valve opening increases as the current increases.

7D is a simplified cross-sectional view of the valve 738 of FIG. 7A with the valve 738 in the fully open position.

式３８及び他の箇所において、Ｍ_ｖは、バルブ本体７３９Ｂの質量であり、

は、バルブ本体７３９Ｂの加速度であり、Ｃ_ｖは、ばね摩擦によって発生する減衰であり、

は、バルブ本体７３９Ｂの速度であり、ｋ_ｓは、弾性部材７３９Ｅのばね定数であり、ｙ_ｏは、予荷重距離であり、ｋ_ｆは、ソレノイド力定数であり、ｕは、ソレノイドに送られる電流コマンドであり、ｆ_preloadは、弾性部材７３９Ｅの予荷重力である。 In this embodiment, the valve mechanics of the valve 738 shown in FIGS. 7A-7D can be expressed as:

In Equation 38 and elsewhere, M _v is the mass of the valve body 739B,

Is the acceleration of the valve body 739B, C _v is the damping caused by spring friction,

Is the velocity of the valve body 739B, _{k s} is the spring constant of the elastic member 739E, _{y o} is the preload distance, _{k f} is a solenoid force constant, u is sent to the solenoid Is a current command and f _preload is the preload force of the elastic member 739E.

FIG. 7E is a simplified diagram of outlet 739D and valve body 739B in a partially open position to help explain effective orifice area. In this example, x= _yo +y. Further, the effective orifice area A _{eff for} this type of valve 738 can be calculated as:

FIG. 8A is a graph showing normalized effective orifice area vs. normalized spool position calculated using the above equation for the valve shown in FIGS. 7A-7D. In this example, the valve characteristic 814 of this valve represents the normalized effective orifice area versus normalized spool position relationship.

As noted above, in certain embodiments, the valve characteristic 814 is inverted to produce the reversing valve characteristic 816 shown in FIG. 8B, which reversal valve characteristic 816 is then used to control that valve. For example, the data of FIG. 8A can be inverted (the X and Y axes of the graph to produce the reversal valve characteristic 816 shown in FIG. 8B, which plots spool position versus normalized effective orifice area. Can be replaced).

Certain valves (eg, spool valves) have backlash-like hysteresis. In these valves, the spool position may be different depending on the previous command history even for the same current command.

FIG. 9A is a graph showing the test results of the spool valve. In FIG. 9A, the graph shows spool position versus voltage. Further, FIG. 9B is a graph showing the simulation result of the spool valve. In FIG. 9B, the graph shows spool position versus current. These figures show that even for the same current command (or voltage command), the spool position may be different depending on the previous command history. For example, referring to FIG. 9A, the spool position will be different depending on the previous command even for the same command (eg, 5 volts). Similarly, referring to FIG. 9B, the spool position will be different depending on the previous command even for the same command (eg, 0.5 amps).

As described herein, referring to FIG. 9A, another valve characteristic 914 of this valve is represented by the spool position versus voltage relationship. Yet another valve characteristic 915 of this valve is represented by the spool position vs. current relationship with reference to FIG. 9B. Therefore, spool valve nonlinearities (backlash and effective orifice geometry) can be calibrated and modeled as described herein. The inverse functions can then be applied to the control software to linearize the spool valve.

The method used to calculate the valve backlash can vary. In one embodiment, the calibration can be done by gradually increasing the current (or voltage) command from zero to a maximum and then gradually decreasing it to zero while monitoring the position of the valve body. The current (or voltage) command versus spool position data is then used as a compensation map.

In certain embodiments, the reference position y _o of the valve can be determined with calibrated backlash. The reference position can be determined by checking the outlet flow rate of the valve while slightly increasing the current command to measure when the orifice begins to open.

FIG. 10A shows two valve characteristics of a spool valve. More specifically, FIG. 10A illustrates (i) a first valve characteristic 1014, eg, a graph showing normalized effective orifice area versus normalized spool position, and (ii) a second valve characteristic 1015. , For example, a graph showing spool position versus current. The data of the graphs 1014 and 1015 can be acquired experimentally or can be calculated.

As described above, in certain embodiments, the valve characteristics 1014, 1015 are inverted to produce the reversal valve characteristics 1016, 1017 shown in FIG. 10B, and the reversal valve characteristics 1016, 1017 then control the valve. Used for. For example, the data in graph 1014 is inverted (the X and Y axes of the graph are swapped) to produce graph 1016 that plots normalized spool position versus normalized effective orifice area. In addition, the data in graph 1015 is inverted (the X and Y axes of the graph are swapped) to produce graph 1017 that plots current versus spool position. As described herein, the reversing valve characteristics 1016, 1017 help to accurately control the effective orifice area of the valve despite the non-linearity of the valve.

Note that the reversal valve characteristics 1016, 1017 may be in the form of look-up tables, maps, graphs, charts, or analytical or fitted models.

FIG. 11 is a schematic diagram showing an exposure apparatus 1170 useful in the present invention. The exposure apparatus 1170 includes an apparatus frame 1172, an illumination system 1182 (irradiation apparatus), a mask stage assembly 1184, an optical assembly 1186 (lens assembly), a plate stage assembly 1110, a mask stage assembly 1184 and a plate stage assembly 1110. Control system 1120 for controlling.

The exposure apparatus 1170 is particularly useful as a lithographic device that transfers a pattern (not shown) of a liquid crystal display device from the mask 1188 to the work 1122.

The device frame 1172 is rigid and supports the components of the exposure device 1170. The design of the apparatus frame 1172 can be modified to meet the remaining design requirements of the exposure apparatus 1170.

Illumination system 1182 includes an illumination source 1192 and an illumination optics assembly 1194. Illumination source 1192 emits a beam (illumination) of light energy. Illumination optics assembly 1194 directs a beam of light energy from illumination source 1192 to mask 1188. The beam selectively illuminates different portions of mask 1188 to expose work 1122.

The optical assembly 1186 projects and/or focuses the light that has passed through the mask 1188 onto the work 1122. Depending on the design of exposure apparatus 1170, optical assembly 1186 can magnify or reduce the illuminated image of mask 1188.

The mask stage assembly 1184 holds and positions the mask 1188 with respect to the optical assembly 1186 and the work 1122. Similarly, the plate stage assembly 1110 holds and positions the work 1122 with respect to the projected image of the illuminated portion of the mask 1188.

There are many different types of lithographic devices. For example, the exposure apparatus 1170 can be used as a scanning photolithography system that exposes a pattern from the mask 1188 to the glass work 1122 while moving the mask 1188 and the work 1122 in synchronization. Alternatively, the exposure apparatus 1170 can be a step-and-repeat type photolithography system that exposes the mask 1188 while the mask 1188 and the work 1122 are fixed.

However, use of the exposure apparatus 1170 and stage assembly described herein is not limited to photolithography systems for the manufacture of liquid crystal display devices. The exposure apparatus 1170 can be used as, for example, a semiconductor photolithography system for exposing an integrated circuit pattern onto a wafer or a photolithography system for manufacturing a thin film magnetic head. Furthermore, the present invention can be applied to a proximity photolithography system that exposes a mask pattern by placing the mask and substrate in proximity without the use of a lens assembly. Additionally, the invention described herein can be used in other devices including flat panel display processing equipment, elevators, machine tools, metal cutting machines, inspection machines, and disk drives. ..

According to the above-described embodiment, by assembling various subsystems including the elements described in the appended claims so that a predetermined mechanical accuracy, electrical accuracy, and optical accuracy are maintained. A photolithography system can be built. In order to maintain varying accuracies, before and after assembly, all optics are adjusted to achieve their optical accuracies. Similarly, all mechanical systems and all electrical systems are adjusted to achieve their respective mechanical and electrical accuracies. The process of assembling each subsystem into a photolithography system includes mechanical connections between each subsystem, electrical circuit wiring connections, and pneumatic tubing connections. Of course, there are also processes to assemble each subsystem before assembling the photolithography system from the various subsystems. Once the photolithography system has been assembled using the various subsystems, global adjustments are made to ensure accuracy in the complete photolithography system. Additionally, it is desirable to manufacture the exposure system in a clean room with controlled temperature and cleanliness.

Further, the device can be manufactured using the system described above by the process schematically shown in FIG. In step 1201, the device functional and performance characteristics are designed. Next, in step 1202, a mask (reticle) having a pattern is designed according to the previous design step, and in parallel step 1203, a glass plate is manufactured. In step 1204, the mask pattern designed in step 1202 is exposed on the glass plate of step 1203 by the photolithography system described above in accordance with the present invention. In step 1205, the flat panel display device is assembled (including dicing process, bonding process, and packaging process), and finally, in step 1206 the device is inspected.

Although many different embodiments of stage assembly 10 are shown and described herein, one or more features of any one embodiment may be one or more of the other provided that they meet the spirit of the invention. Can be combined with one or more features of the above embodiments.

Although many exemplary aspects and embodiments of stage assembly 10 are shown and disclosed herein above, those of ordinary skill in the art will appreciate these specific modifications, substitutions, additions, and subcombinations. Will. Accordingly, the following appended claims and the claims below are to be construed to include all modifications, substitutions, additions, and subcombinations that fall within their true spirit and scope. It is intended and is not intended to limit the details of construction or design shown herein.

Claims (7)

A stage assembly for positioning a workpiece along a movement axis,
A stage configured to couple to the workpiece,
A piston housing defining a piston chamber; a piston disposed within the piston chamber and moving relative to the piston chamber along a piston axis; and a valve assembly controlling flow of piston fluid to the piston chamber. A fluid actuator assembly coupled to the stage for moving the stage along the axis of movement ;
And a control system for controlling the valve assembly for controlling the flow of said piston fluid to the piston chamber,
The valve assembly includes a housing, a first inlet valve formed in the housing to cover an outlet opening for allowing the piston fluid in the housing to flow into the piston chamber, and the first inlet valve. An elastic member for controlling the opening/closing amount of the outlet opening by
The control system includes an inverse function of a first inlet valve characteristic, which is a relationship between a current command sent to the elastic member and a valve position to control the opening/closing amount , and the outlet opening by the first inlet valve. A control system that controls the valve assembly by utilizing a characteristic that calibrates a difference in the characteristic of the first inlet valve between an opened state and a closed state . The piston divides the piston chamber into a first chamber and a second chamber on opposite sides of the piston, and the valve assembly allows the piston fluid to flow into the first chamber and the second chamber. The stage assembly of claim 1, wherein the stage assembly controls flow. The valve assembly controls the flow of the piston fluid from the first chamber and the second chamber, the stage assembly according to claim 2. The valve assembly includes (i) the first inlet valve controlling the flow of the piston fluid to the first chamber; and (ii) the first inlet valve controlling the flow of the piston fluid from the first chamber. A first outlet valve, (iii) a second inlet valve controlling the flow of the piston fluid to the second chamber, and (iv) a second inlet valve controlling the flow of the piston fluid from the second chamber. The stage assembly of claim 3, including two outlet valves. The first outlet valve has a first outlet valve characteristic, the second inlet valve has a second inlet valve characteristic, and the second outlet valve has a second outlet valve characteristic. The control system has an inverse function of the first outlet valve characteristic, an inverse function of the second inlet valve characteristic, and an inverse function of the second outlet valve characteristic for controlling the valve assembly. The stage assembly of claim 4, which also utilizes: An illumination source,
Exposure apparatus comprising a stage assembly according to any one of claims 1-5 for moving the stage with respect to the illumination source. A step of preparing a substrate,
Using an exposure apparatus according to claim 6 and forming an image on the substrate, a process for manufacturing a device.

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