JP2009302377A - Design method for control system, control method, device manufacturing method and control device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a design method of a control system for suppressing a time required for stabilizing state quantities. <P>SOLUTION: The design method of a control system including a first control unit for feedforward-controlling the state quantities of a control object includes: deriving a transfer function of the control object related with state quantities; setting a target response waveform of a whole system including the control object and the first control unit; deriving the differential waveform of the target response waveform differentiated only by the same number of times as the degrees of control object transfer function; and searching an input waveform to the control target by the first control unit in order to obtain an object response waveform by using the differential waveform. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a control system design method, control method, device manufacturing method, and control apparatus.

An exposure apparatus used in a photolithography process illuminates a mask on which a pattern is formed with exposure light, and exposes a photosensitive substrate with exposure light from the mask. For example, as disclosed in Patent Document 1, the exposure apparatus performs exposure by controlling the environment of a space through which exposure light passes by an environment control system called a chamber apparatus.
US Patent Application Publication No. 2003/0058426

  For example, if the time required to stabilize the state quantity such as the temperature in the chamber apparatus or the temperature of the optical element arranged in the optical path of the exposure light becomes long, the operation rate of the exposure apparatus may decrease. As a result, device productivity is reduced.

  A purpose of some aspects of the present invention is to provide a control system design method, control method, and control device capable of suppressing the time required to stabilize the state quantity. Moreover, the aspect of this invention aims at providing the device manufacturing method which can suppress the fall of productivity.

  According to the first aspect of the present invention, there is provided a design method for a control system including a first controller that feedforward-controls a state quantity of a controlled object, and a transfer function of the controlled object related to the state quantity is derived; Setting a target response waveform of the entire system including the control target and the first controller, deriving a differential waveform of the target response waveform differentiated by the same number of times as the order of the transfer function of the control target, And a method for designing a control system including obtaining an input waveform for a controlled object by a first controller so that a target response waveform is obtained.

  According to the second aspect of the present invention, there is provided a control method for controlling a state quantity of a controlled object, wherein the control system is designed using the design method of the first aspect, and the designed control system is used. And controlling a control object.

  According to a third aspect of the present invention, there is provided a device manufacturing method comprising: exposing a substrate using an exposure apparatus controlled by the control method of the second aspect; and developing the exposed substrate. Provided.

  According to a fourth aspect of the present invention, there is provided a control apparatus that controls a state quantity of a control target, and includes a control system designed using the design method of the first aspect.

  According to the present invention, the time required to stabilize the state quantity can be suppressed. Further, according to the present invention, it is possible to suppress a decrease in device productivity.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings, but the present invention is not limited thereto. FIG. 1 is a schematic block diagram that shows an example of an exposure apparatus EX according to the present embodiment.

  In FIG. 1, an exposure apparatus EX exposes a mask stage 1 that can move while holding a mask M, a substrate stage 2 that can move while holding a substrate P, and a mask M held by the mask stage 1 as exposure light. A chamber that forms an illumination system IL that illuminates with EL, a projection optical system PL that projects an image of the pattern of the mask M illuminated with exposure light EL onto the substrate P, and an internal space 3 in which at least the projection optical system PL is disposed. Device 4. The chamber device 4 includes an air conditioning unit 4U that can adjust the environment (including temperature, humidity, and cleanliness) of the internal space 3.

The illumination system IL illuminates a predetermined illumination area with exposure light EL having a uniform illuminance distribution. The illumination system IL illuminates at least a part of the mask M arranged in the illumination area with the exposure light EL having a uniform illuminance distribution. As the exposure light EL emitted from the illumination system IL, for example, far ultraviolet light (DUV light) such as bright lines (g-line, h-line, i-line) and KrF excimer laser light (wavelength 248 nm) emitted from a mercury lamp, ArF Excimer laser light (wavelength 193 nm), vacuum ultraviolet light (VUV light) such as F ₂ laser light (wavelength 157 nm), or the like is used. In the present embodiment, ArF excimer laser light, which is ultraviolet light (vacuum ultraviolet light), is used as the exposure light EL.

  The mask stage 1 is movable on the guide surface 5G of the base member 5 while holding the mask M. The mask stage 1 is movable in three directions, for example, an X axis, a Y axis, and a θZ direction by operation of a drive system including a linear motor or the like.

  The projection optical system PL irradiates a predetermined projection area with the exposure light EL. The projection optical system PL projects an image of the pattern of the mask M at a predetermined projection magnification onto at least a part of the substrate P arranged in the projection area. The projection optical system PL of the present embodiment is a reduction system whose projection magnification is, for example, 1/4, 1/5, or 1/8. Note that the projection optical system PL may be either an equal magnification system or an enlargement system. In the present embodiment, the optical axis of the projection optical system PL is parallel to the Z axis. The projection optical system PL may be any of a refractive system that does not include a reflective optical element, a reflective system that does not include a refractive optical element, and a catadioptric system that includes a reflective optical element and a refractive optical element. Further, the projection optical system PL may form either an inverted image or an erect image.

  Projection optical system PL has a plurality of optical elements, and these optical elements are held in lens barrel PK. In the present embodiment, the projection optical system PL includes a control system 5 that can adjust the temperature of the optical element held in the lens barrel PK. The control system 5 includes a supply system that supplies a temperature-adjusted gas (for example, nitrogen gas) into the lens barrel PK and a recovery system that recovers the gas in the lens barrel PK, and can adjust the temperature of the optical element. It is.

  The substrate stage 2 is movable on the guide surface 6G of the base member 6 while holding the substrate P. In the present embodiment, the substrate stage 2 is movable in six directions including the X-axis, Y-axis, Z-axis, θX, θY, and θZ directions by the operation of a drive system including, for example, a linear motor.

  In the present embodiment, the position information of the mask stage 1 and the substrate stage 2 is measured by an interferometer system (not shown) including a laser interferometer. When the substrate P is exposed with the exposure light EL or when a predetermined measurement process is executed, the position control of the mask stage 1 (mask M) and the substrate stage 2 (substrate P) is performed based on the measurement result of the interferometer system. Executed.

  Next, a design method for the control system 5 according to the present embodiment will be described. In the following description, a design method of the control system 5 including the first controller for feedforward control of the temperature of the optical element of the projection optical system PL arranged in the optical path of the exposure light EL will be described as an example. In this embodiment, the case where the control system 5 for adjusting an optical element to target temperature (23 degreeC) is designed is demonstrated.

  FIG. 2 is a flowchart showing an example of a design method of the control system 5 according to the present embodiment. As shown in FIG. 2, in this embodiment, step S1 for deriving a transfer function of the optical element related to temperature, step S2 for setting a target response waveform of the entire system including the optical element and the first controller, and optical Step S3 for deriving a differential waveform of the target response waveform differentiated by the same number of times as the order of the transfer function of the element, and an input waveform to the optical element by the first controller so as to obtain the target response waveform using the differential waveform Step S4 for obtaining.

  For example, after the temperature control of the optical element is stopped for some reason such as maintenance of the exposure apparatus EX, the time from the restart of the temperature control to the stabilization of the optical element to the target temperature (23 ° C.) is as long as possible. Shorter is preferable. For example, when an optical element at 22.216 ° C. is simply placed in a space at 23 ° C., the time until the optical element stabilizes at the target temperature (23 ° C.) (stabilization time) as shown by line L1 in FIG. ) Can take up to 10 hours. FIG. 3 is a diagram showing the relationship between the time since the start of temperature control and the temperature of the optical element, in which the horizontal axis represents time and the vertical axis represents temperature. Here, the line L1 is actual measurement data of the temperature of the optical element. In the present embodiment, the control system 5 is designed that can shorten the stabilization time until the optical element is stabilized at the target temperature (23 ° C.).

  In designing the control system 5, a numerical model (analysis model) of the optical element is required. Therefore, first, the optical element is modeled. In this embodiment, a cubic transfer function as shown in the following equation (1) is used as the transfer function of the numerical model.

As an example, in this embodiment, as a result of identification based on the transfer function of equation (1) and the measured data indicated by line L1 in FIG. 3, each parameter of equation (1) is
K = 0.99429,
Tp1 = 2551.2,
Tp2 = 304.18,
Tp3 = 0.001
Tz = 1252.8,
It became.

  Here, since the value of Tp3 is small, it is ignored. Also round off the numbers after the decimal point for each of the above parameters. Eventually, as the transfer function (numerical model) of the optical element, a second-order transfer function as shown by the following equation (2) is used (step S1).

  Here, for example, when an optical element at 22.216 ° C. is arranged in a space at 23 ° C., that is, when an optical element is arranged in a space having a temperature higher by 0.784 ° C. than the temperature of the optical element at 22.216 ° C. As described above, when heat is input stepwise to the optical element, the relationship between the input heat amount U (s), the output temperature Y (s) of the optical element, and the transfer function Gp (s) of the optical element is as follows. (3) of the formula.

  When designing the control system 5 including the first controller that executes the feedforward control for shortening the stabilization time, assuming that the transfer function of the first controller is FF (s), the following equation (4) A relationship is established.

  In the present embodiment, a target value (target response waveform) of the response waveform of the entire system including the optical element Gp (s) and the first controller FF (s) is set (step S2).

  FIG. 4 is a diagram illustrating an example of a target response waveform, in which the horizontal axis represents time and the vertical axis represents temperature. In the present embodiment, a case will be described in which the first controller FF (s) is designed so that the temperature of the optical element at 22.216 ° C. can be adjusted to 23 ° C. in about 30 minutes.

  In the present embodiment, when designing the first controller FF (s), a differential waveform of the target response waveform differentiated by the same number of times as the order of the transfer function Gp (s) of the optical element is derived (step S3). In this embodiment, since the transfer function Gp (s) is quadratic as shown by the equation (2), a differential waveform obtained by differentiating twice is derived. FIG. 5 shows a waveform obtained by differentiating the target response waveform once, and FIG. 6 shows a waveform obtained by differentiating the target response waveform twice.

When the one-time differential waveform in FIG. 5 is X and the two-time differential waveform in FIG. 6 is Y, the transfer function from X to Y is expressed using the following gain coefficients T ₁ and T ₂ ( 5) It becomes like a formula.

  When the numerator of the inverse function of the transfer function Gp (s) of the optical element is expanded, the equation (6) is obtained.

The coefficient of the numerator represented by the expression (6) is substituted into the gain coefficients T ₁ and T ₂ of the expression (5). As described above, the expression (5) is a transfer function from X to Y, and is the first for stabilizing the output temperature Y (s) of the optical element represented by the transfer function Gp (s) in a short time. The controller FF (s) is represented by the following equation (7).

  FIG. 7 is a diagram illustrating an example of an input waveform to the optical element by the first controller. As shown in FIG. 7, in order to shorten the stabilization time until the optical element is stabilized at the target temperature (23 ° C.), the first controller once increases the operation amount (input heat amount). Thereby, the target response waveform as shown in FIG. 4 can be obtained.

  As described above, the target response waveform of the entire system including the control target and the first controller is set, and the differential waveform of the target response waveform is derived, so that the desired output temperature ( It is possible to construct a first controller that can obtain a response waveform.

  Moreover, as shown in FIG. 8, based on the output temperature of an optical element, the 2nd controller which feedback-controls the input waveform with respect to an optical element is designed, and the 1st controller and the 2nd controller are used together, Temperature control of the optical element can be performed.

  In the present embodiment, the case where the control system for controlling the temperature of the optical element is designed has been described as an example. However, the present embodiment can be applied to the case where the control system for controlling the temperature of the internal space 3 is designed, for example. It is. Further, for example, the present invention can be applied to the design of a control system that controls state quantities other than temperature, such as humidity and pressure in the internal space 3.

  As the substrate P in each of the above embodiments, not only a semiconductor wafer for manufacturing a semiconductor device, but also a glass substrate for a display device, a ceramic wafer for a thin film magnetic head, or an original mask or reticle used in an exposure apparatus. (Synthetic quartz, silicon wafer) or the like is applied.

  As the exposure apparatus EX, in addition to the step-and-scan type scanning exposure apparatus (scanning stepper) that scans and exposes the pattern of the mask M by moving the mask M and the substrate P synchronously, the mask M and the substrate P Can be applied to a step-and-repeat type projection exposure apparatus (stepper) in which the pattern of the mask M is collectively exposed while the substrate P is stationary and the substrate P is sequentially moved stepwise.

  Further, in the step-and-repeat exposure, after the reduced image of the first pattern is transferred onto the substrate P using the projection optical system in a state where the first pattern and the substrate P are substantially stationary, the second pattern With the projection optical system, the reduced image of the second pattern may be partially overlapped with the first pattern and collectively exposed on the substrate P (stitch type batch exposure apparatus). ). Further, the stitch type exposure apparatus can be applied to a step-and-stitch type exposure apparatus in which at least two patterns are partially transferred on the substrate P, and the substrate P is sequentially moved.

  Further, as disclosed in, for example, US Pat. No. 6,611,316, two mask patterns are synthesized on a substrate via a projection optical system, and one shot area on the substrate is obtained by one scanning exposure. The present invention can also be applied to an exposure apparatus that performs double exposure almost simultaneously.

  Further, the present invention relates to US Pat. No. 6,341,007, US Pat. No. 6,400,441, US Pat. No. 6,549,269, US Pat. No. 6,590,634, US Pat. No. 6,208,407, US Pat. No. 6,262,796. The present invention can also be applied to a twin-stage type exposure apparatus having a plurality of substrate stages as disclosed in the specification and the like.

  Further, as disclosed in, for example, US Pat. No. 6,897,963 and European Patent Application Publication No. 1713113, a substrate stage for holding a substrate, a reference member on which a reference mark is formed, and / or various types The present invention can also be applied to an exposure apparatus that includes a measurement stage equipped with a photoelectric sensor. An exposure apparatus including a plurality of substrate stages and measurement stages can be employed.

  The type of exposure apparatus EX is not limited to an exposure apparatus for manufacturing a semiconductor element that exposes a semiconductor element pattern onto a substrate P, but an exposure apparatus for manufacturing a liquid crystal display element or a display, a thin film magnetic head, an image sensor (CCD). In addition, the present invention can be widely applied to an exposure apparatus for manufacturing a micromachine, MEMS, DNA chip, reticle, mask, or the like.

  As described above, the exposure apparatus EX according to the embodiment of the present application maintains various mechanical subsystems including the respective constituent elements recited in the claims of the present application so as to maintain predetermined mechanical accuracy, electrical accuracy, and optical accuracy. Manufactured by assembling. In order to ensure these various accuracies, before and after assembly, various optical systems are adjusted to achieve optical accuracy, various mechanical systems are adjusted to achieve mechanical accuracy, and various electrical systems are Adjustments are made to achieve electrical accuracy. The assembly process from the various subsystems to the exposure apparatus includes mechanical connection, electrical circuit wiring connection, pneumatic circuit piping connection and the like between the various subsystems. Needless to say, there is an assembly process for each subsystem before the assembly process from the various subsystems to the exposure apparatus. When the assembly process of the various subsystems to the exposure apparatus is completed, comprehensive adjustment is performed to ensure various accuracies as the entire exposure apparatus. The exposure apparatus is preferably manufactured in a clean room where the temperature, cleanliness, etc. are controlled.

  As shown in FIG. 9, a microdevice such as a semiconductor device includes a step 201 for designing a function / performance of the microdevice, a step 202 for producing a mask (reticle) based on the design step, and a substrate as a base material of the device. Manufacturing step 203, substrate processing step 204 including exposing the substrate with exposure light through a mask and developing the exposed substrate according to the above-described embodiment, device assembly step (dicing process, bonding process, (Including a processing process such as a packaging process) 205, an inspection step 206, and the like.

  Note that the requirements of the above-described embodiments can be combined as appropriate. Some components may not be used. In addition, as long as permitted by law, the disclosure of all published publications and US patents related to the exposure apparatus and the like cited in the above-described embodiments and modifications are incorporated herein by reference.

It is a schematic block diagram which shows an example of the exposure apparatus which concerns on this embodiment. It is a flowchart for demonstrating an example of the design method of the control system which concerns on this embodiment. It is a schematic diagram for demonstrating the characteristic of a control object. It is a figure for demonstrating an example of the design method of the control system which concerns on this embodiment. It is a figure for demonstrating an example of the design method of the control system which concerns on this embodiment. It is a figure for demonstrating an example of the design method of the control system which concerns on this embodiment. It is a figure for demonstrating an example of the design method of the control system which concerns on this embodiment. It is a figure for demonstrating an example of the design method of the control system which concerns on this embodiment. It is a flowchart figure which shows an example of the manufacturing process of a microdevice.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Mask stage, 2 ... Substrate stage, 5 ... Control system, PL ... Projection optical system, EL ... Exposure light, EX ... Exposure apparatus, P ... Substrate

Claims (9)

A control system design method including a first controller that feedforward-controls a state quantity to be controlled,
Deriving a transfer function of the controlled object related to the state quantity;
Setting a target response waveform of the entire system including the control object and the first controller;
Deriving a differentiated waveform of the target response waveform differentiated by the same number of times as the order of the transfer function to be controlled;
A control system design method comprising: obtaining an input waveform for the control object by the first controller so that the target response waveform is obtained using the differential waveform. Representing the transfer function for the differentiated waveform using a predetermined gain factor,
The control system design method according to claim 1, wherein a coefficient of a numerator of an inverse function of the transfer function to be controlled is substituted for the gain coefficient.   The control system design method according to claim 1, further comprising: designing a second controller that feedback-controls the input waveform based on the output of the control target related to the state quantity.   The control system design method according to claim 1, wherein the state quantity includes at least one of temperature, humidity, and pressure. A control method for controlling a state quantity of a controlled object,
Designing a control system using the design method according to claim 1;
Controlling the control object using the designed control system. An exposure apparatus control method for exposing a substrate with exposure light,
The exposure apparatus includes a portion where a state quantity changes,
A control method for controlling the state quantity of the part using the control method according to claim 5.   The control method according to claim 6, wherein the temperature of the optical element disposed in the optical path of the exposure light is controlled. Exposing the substrate using an exposure apparatus controlled by the control method according to claim 6 or 7,
Developing the exposed substrate; and a device manufacturing method. A control device for controlling a state quantity of a control target,
The control apparatus containing the control system designed using the design method as described in any one of Claims 1-4.

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