CN116819902B - Six-degree-of-freedom distributed composite control system and control method for ultra-precise lithography equipment - Google Patents
Six-degree-of-freedom distributed composite control system and control method for ultra-precise lithography equipment Download PDFInfo
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Abstract
A six-degree-of-freedom distributed composite control system and a control method for ultra-precise lithography equipment relate to the ultra-precise lithography equipment control system and the method. The control system comprises a motion track generation part, a feedback control part, a feedforward control part, a decoupling control part, a six-degree-of-freedom motion table and a position measurement part, wherein the decoupling control part comprises a static decoupling part and a dynamic decoupling part, the static decoupling part consists of a gain planning matrix, a gain balance matrix and a Coriolis force compensation vector, and the dynamic decoupling part consists of a dynamic decoupling matrix. The feedback and feedforward controllers are simple in design, crosstalk influence among various degrees of freedom is reduced in a static and dynamic combination mode, and control accuracy is improved.
Description
Technical Field
The invention relates to an ultra-precise lithography equipment control system and method, in particular to a six-degree-of-freedom distributed composite control system and method for ultra-precise lithography equipment, and belongs to the technical field of ultra-precise equipment manufacturing.
Background
Ultra-precise photoetching equipment such as wafer detection equipment, exposure machines, photoetching machines and the like commonly adopts a six-degree-of-freedom motion platform as a wafer carrying platform, for example, a workpiece platform in a scanning photoetching system is a six-degree-of-freedom motion platform, wherein the x direction of the workpiece platform is mainly responsible for switching different exposure fields on a silicon wafer, and the z direction and three rotation directions theta x 、θ y 、θ z The scanning exposure process is performed in the y direction, and is used for maintaining the wafer surface to be always in the focal plane of the objective lens.
How to realize the ultra-precise motion with six degrees of freedom has an important influence on the exposure quality of the chip, and the key is how to decouple the motion with six degrees of freedom to reduce the crosstalk influence of each degree of freedom and how to break through the limitation of a mechanical flexible mode on the single-degree-of-freedom closed-loop control bandwidth to realize the nano-precision motion.
However, the conventional single feedback control method is limited by a mechanical flexible mode, so that the adjustment time and the control precision are difficult to achieve, the design process of the controller of the conventional multivariable control method is very complex, and engineering application is inconvenient.
Disclosure of Invention
In order to solve the problems that the traditional multi-degree-of-freedom control method cannot effectively reduce the crosstalk influence of each degree and is difficult to realize the accurate control of the exposure field position under the objective lens coordinate system, the invention provides the six-degree-of-freedom distributed composite control system and the control method for the ultra-precise photoetching equipment, which realize the conversion from the control quantity under the objective lens coordinate system to the control quantity under the centroid coordinate system of the moving table in a mode of combining static decoupling and dynamic decoupling, reduce the crosstalk influence between the respective degrees and improve the control precision.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the six-degree-of-freedom distributed composite control system of the ultra-precise lithography equipment comprises a motion trail generation part S r Feedback control section S fb Feedforward control section S ff Decoupling control section S dc Six-degree-of-freedom motion stage P and position measuring section S ms ；
The motion trail generation part S r Generating a desired motion trail r= [ r ] x r y r θz r z r θx r θy ] T ；
The position measuring part S ms Generating an actual motion trail y ms ＝[x y θ z z θ x θ y ] T ；
The expected motion trail r and the actual motion trail y ms Motion error e= [ e ] is generated by the difference of the motion error e= [ e ] x e y e θz e z e θx e θy ] T The motion error e passes through the feedback control section S fb Generating a feedback control quantity f fb ＝[f fb,x f fb,y f fb,θz f fb,z f fb,θx f fb,θy ] T And the desired motion trajectory r passes through the feedforward control section S ff Generating a feedforward control quantity f ff ＝[f ff,x f ff,y f ff,θz f ff,z f ff,θx f ff,θy ] T The feedback control amount f fb And the feedforward control quantity f ff And generating a control quantity f in the objective lens coordinate system len ；
Control quantity f in the objective lens coordinate system len Through the decoupling control part S dc Generating an actuator control quantity f act The actuator control amount f act Generating a motion stage output y by inputting the motion stage output y to the six-degree-of-freedom motion stage P p The motion stage outputs y p Through the position measuring section S ms Generating an actual motion trail y ms ；
Wherein the decoupling control section S dc Comprising a static decoupling portion S dc,s And a dynamic decoupling portion S dc,d The static decoupling part S dc,s From gain planning matrix C GS Gain balance matrix C GB And coriolis force compensation vector f cor Composition of the dynamic decoupling portion S dc,d From a dynamic decoupling matrix C D Constructing;
control quantity f in objective lens coordinate system len Through the gain planning matrix C GS Generates its output f gs At the same time, the control quantity f under the objective lens coordinate system len Through the dynamic decoupling matrix C D Generates its output f d The output f gs Said output f d With the coriolis force compensation vector f cor Is used for generating a control quantity f under a centroid coordinate system of a moving platform cog Control quantity f under mass center coordinate system of the moving table cog Through the gain balance matrix C GB Generating an actuator control quantity f act 。
The six-degree-of-freedom distributed composite control method for the ultra-precise photoetching equipment comprises the following steps:
feedforward control section S ff From a diagonal matrix C ff The constitution is that:
feedback control section S fb From a diagonal matrix C fb The constitution is that:
wherein s is Laplacian, C ff,k (s)＝Ω k s 2 ，k＝x,y,θ z ,z,θ x ,θ y Representing different degrees of freedom, Ω x ＝Ω y ＝Ω z ＝m，Ω θx ＝J x ，Ω θy ＝J y ，Ω θz ＝J z M represents the mass, J, of the six-degree-of-freedom motion stage P x 、J y 、J z Respectively express theta x 、θ y 、θ z The moment of inertia of the degree of freedom.
Further, C fb,k (s)，k＝x,y,θ z ,z,θ x ,θ y The design can be performed as follows:
wherein, xi lp,k The value range is 0.5-1, K P,k 、w i,k 、w d,k And w lp,k Determined as follows:
wherein alpha is k ＞1，w b,k Representing the desired open loop cut-off frequency for the kth degree of freedom.
Further, C fb,k (s)，k＝x,y,θ z ,z,θ x ,θ y The design can also be performed as follows:
wherein the method comprises the steps of，K P,k 、w i,k 、w 1,k And w 2,k Determined as follows:
wherein w is b,k Representing the desired open loop cut-off frequency for the kth degree of freedom,γ(w b,k ) Indicating the desired phase margin, delta, for the kth degree of freedom k ＝2°～10°。
Further, a static decoupling portion S dc,s Gain planning matrix C GS The design is carried out as follows:
wherein H is len Representing the distance from the origin of the centroid coordinate system of the motion platform to the centroid of the upper surface of the motion platform;
static decoupling portion S dc,s Coriolis force compensation vector f cor Determined by the following formula:
static decoupling portion S dc,s Gain balance matrix C GB According to the physical layout design of the actuator;
dynamic decoupling portion S dc,d Dynamic decoupling matrix C of (a) D The design is carried out as follows:
wherein z is a time advance operator, and->Is a finite impulse response filter.
Compared with the prior art, the invention has the beneficial effects that: the traditional multi-degree-of-freedom control method based on the multivariable control is more in controller number, difficult in control parameter setting and serious in crosstalk influence of each degree of freedom, accurate control of the exposure field position under the objective lens coordinate system cannot be achieved.
Drawings
FIG. 1 is a topology of a control system of the present invention;
fig. 2 is a desired motion trajectory in embodiment 1;
FIG. 3 is a diagram showing the simulation comparison of the motion error of the present invention with the conventional single feedback control in example 1;
FIG. 4 is a gain balance matrix C in example 1 GB A contrast graph is influenced on each degree of freedom crosstalk error;
FIG. 5 is a gain planning matrix C in embodiment 1 GS A contrast graph is influenced on each degree of freedom crosstalk error;
FIG. 6 is a gain-free programming matrix C of example 1 GS A frequency characteristic diagram at the time (000000) position;
FIG. 7 is a gain planning matrix C in embodiment 1 GS A frequency characteristic diagram at the time (000000) position;
FIG. 8 is a gain-free programming matrix C of example 1 GS Amplitude frequency at time (0.100000) positionA characteristic diagram;
FIG. 9 is a gain planning matrix C in example 1 GS A graph of amplitude versus frequency characteristics at the time (0.100000) location;
FIG. 10 is a Coriolis force compensation vector f of example 1 cor A contrast graph is influenced on each degree of freedom crosstalk error;
fig. 11 is a desired motion trajectory in embodiment 2;
FIG. 12 is a Coriolis force compensation vector f of example 2 cor The contrast graph is affected by the crosstalk error of each degree.
Detailed Description
The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the invention, but not all embodiments, and all other embodiments obtained by those skilled in the art without making creative efforts based on the embodiments of the present invention are all within the protection scope of the present invention.
As shown in FIG. 1, the six-degree-of-freedom distributed composite control system of the ultra-precise lithography equipment comprises a motion track generation part S r Feedback control section S fb Feedforward control section S ff Decoupling control section S dc Six-degree-of-freedom motion stage P and position measuring section S ms ；
The motion trail generation part S r Generating a desired motion trail r= [ r ] x r y r θz r z r θx r θy ] T ；
The position measuring part S ms Generating an actual motion trail y ms ＝[x y θ z z θ x θ y ] T ；
The expected motion trail r and the actual motion trail y ms Motion error e= [ e ] is generated by the difference of the motion error e= [ e ] x e y e θz e z e θx e θy ] T The motion error e passes through the feedback control section S fb Generating a feedback control quantity f fb ＝[f fb,x f fb,y f fb,θz f fb,z f fb,θx f fb,θy ] T And the desired motion trajectory r passes through the feedforward control section S ff Generating a feedforward control quantity f ff ＝[f ff,x f ff,y f ff,θz f ff,z f ff,θx f ff,θy ] T The feedback control amount f fb And the feedforward control quantity f ff And generating a control quantity f in the objective lens coordinate system len ；
Control quantity f in the objective lens coordinate system len Through the decoupling control part S dc Generating an actuator control quantity f act The actuator control amount f act Generating a motion stage output y by inputting the motion stage output y to the six-degree-of-freedom motion stage P p The motion stage outputs y p Through the position measuring section S ms Generating an actual motion trail y ms ；
Wherein the decoupling control section S dc Comprising a static decoupling portion S dc,s And a dynamic decoupling portion S dc,d The static decoupling part S dc,s From gain planning matrix C GS Gain balance matrix C GB And coriolis force compensation vector f cor Composition of the dynamic decoupling portion S dc,d From a dynamic decoupling matrix C D Constructing;
control quantity f in objective lens coordinate system len Through the gain planning matrix C GS Generates its output f gs At the same time, the control quantity f under the objective lens coordinate system len Through the dynamic decoupling matrix C D Generates its output f d The output f gs Said output f d With the coriolis force compensation vector f cor Is used for generating a control quantity f under a centroid coordinate system of a moving platform cog Control quantity f under mass center coordinate system of the moving table cog Through the gain balance matrix C GB Generating an actuator control quantity f act 。
As shown in fig. 1, the six-degree-of-freedom distributed composite control method for ultra-precise lithography equipment comprises the following steps:
feedforward control sectionS ff From a diagonal matrix C ff The constitution is that:
feedback control section S fb From a diagonal matrix C fb The constitution is that:
wherein s is Laplacian, C ff,k (s)＝Ω k s 2 ，k＝x,y,θ z ,z,θ x ,θ y Representing different degrees of freedom, Ω x ＝Ω y ＝Ω z ＝m，Ω θx ＝J x ，Ω θy ＝J y ，Ω θz ＝J z M represents the mass, J, of the six-degree-of-freedom motion stage P x 、J y 、J z Respectively express theta x 、θ y 、θ z The moment of inertia of the degree of freedom.
C fb,k (s)，k＝x,y,θ z ,z,θ x ,θ y The design can be performed as follows:
wherein, xi lp,k The value range is 0.5-1, K P,k 、w i,k 、w d,k And w lp,k Determined as follows:
wherein alpha is k ＞1，w b,k Representing the desired open loop cut-off frequency for the kth degree of freedom.
C fb,k (s)，k＝x,y,θ z ,z,θ x ,θ y Can alsoThe design is carried out as follows:
wherein K is P,k 、w i,k 、w 1,k And w 2,k Determined as follows:
wherein w is b,k Representing the desired open loop cut-off frequency for the kth degree of freedom,γ(w b,k ) Indicating the desired phase margin, delta, for the kth degree of freedom k ＝2°～10°。
Static decoupling portion S dc,s Gain planning matrix C GS The design is carried out as follows:
wherein H is len Representing the distance from the origin of the centroid coordinate system of the motion platform to the centroid of the upper surface of the motion platform;
static decoupling portion S dc,s Coriolis force compensation vector f cor Determined by the following formula:
static decoupling portion S dc,s Gain balance matrix C GB According to the physical layout design of the actuator;
dynamic decoupling portion S dc,d Dynamic decoupling matrix C of (a) D The design is carried out as follows:
wherein z is a time advance operator, and->Is a finite impulse response filter.
Example 1
In the present embodiment, the mass m=11.5 of the six-degree-of-freedom motion stage P, and the moment of inertia of the three rotation axes are J respectively x ＝0.098、J y ＝0.119、J z ＝0.209。
Motion trail generation section S r The generated expected motion trail r= [ r ] x r y r θz r z r θx r θy ] T As shown in connection with fig. 2. For the feedforward control part S ff Diagonal matrix C of (2) ff ，C ff,k (s)＝Ω k s 2 ，k＝x,y,θ z ,z,θ x ,θ y Theoretically omega k The value of (2) should be omega x ＝Ω y ＝Ω z ＝m，Ω θx ＝J x ，Ω θy ＝J y ，Ω θz ＝J z However, in practice, the mass and moment of inertia of the six-degree-of-freedom motion stage are difficult to be known precisely, Ω is taken in the present embodiment x ＝Ω y ＝Ω z ＝0.9m，Ω θx ＝0.9J x ，Ω θy ＝0.9J y ，Ω θz ＝0.9J z . For the feedback control part S fb Diagonal matrix C of (2) fb C in the present embodiment fb,k (s)，k＝x,y,θ z ,z,θ x ,θ y In the first way, wherein alpha k Take the value of 3, xi lp,k The value is 0.707, w b,x The value is 2 pi multiplied by 80, w b,y The value is 2 pi multiplied by 80, w b,θz The value is 2 pi multiplied by 30, w b,z The value is 2pi×40, w b,θx The value is 2 pi multiplied by 30, w b,θy The value is 2pi×30. For static decoupling portion S dc,s Gain planning matrix C GS In the present embodiment H len Gain balance matrix c=0.05 GB According to the physical layout design of the actuator, the values in this embodiment are as follows:
for the dynamic decoupling portion S dc,d Dynamic decoupling matrix C of (a) D The order of the finite impulse response filter in this embodiment is taken to be 12.
In order to illustrate the effectiveness of the feedforward and feedback composite control of the present invention, the six-degree-of-freedom motion error comparison of the method of the present invention with the conventional single feedback control method is shown in conjunction with fig. 3, and it can be seen that the present invention can effectively reduce the motion error of the acceleration and deceleration section, thereby reducing the adjustment time for entering the constant speed section; the gain balance matrix C is shown in conjunction with FIG. 4 GB The influence of the precision of (2) on the six-degree-of-freedom motion error can be seen as an inaccurate gain balance matrix C GB Can cause crosstalk between various degrees of freedom, and the accurate gain balance matrix C GB Crosstalk effects can be eliminated; the gain planning matrix C is shown in conjunction with FIG. 5 GS It can be seen that the gain planning matrix C is not conventionally introduced GS The rotation motion will affect the translation, and the gain planning matrix C provided by the invention GS The crosstalk influence of the motion of the rotation degree of freedom on the translation degree of freedom can be effectively eliminated.
Referring to FIGS. 6-9, the gain planning matrix C according to the present invention is shown from the standpoint of amplitude-frequency characteristics GS Is given by the function of the gain planning matrix C GS The influence on the amplitude-frequency characteristics of different positions can be seen that the gain planning matrix C is not present GS In the case of (a), the non-zero elements exist in the non-diagonal terms of the six-degree-of-freedom amplitude-frequency characteristic diagram, which represent the crosstalk effect between different degrees of freedom, while the invention proposesThe gain planning matrix C GS Off-diagonal elements may be eliminated, thereby eliminating cross-talk between the respective degrees of freedom.
The coriolis force compensation vector f is shown in conjunction with fig. 10 cor Because the six degrees of freedom in the embodiment move in sequence, there is no simultaneous movement, according to f cor The expression shows that f at this time cor And does not function, this result is confirmed in fig. 10.
To further illustrate the coriolis force compensation vector f cor Designed example 2 was as follows:
example 2
Unlike embodiment 1, the motion trajectory generation part S of the present embodiment r The generated expected motion trail r= [ r ] x r y r θz r z r θx r θy ] T It can be seen from the combination of FIG. 11 that there are y degrees of freedom and θ in this embodiment x The degree of freedom moves simultaneously. The coriolis force compensation vector f is shown in conjunction with fig. 12 cor It can be seen that the conventional method without introducing the coriolis force compensation vector is that y and θ are x When the degrees of freedom move simultaneously, the z degree of freedom is influenced, so that crosstalk errors are caused; the coriolis force compensation vector f provided by the invention cor The design method effectively eliminates the crosstalk influence on other degrees of freedom when the translational degree of freedom and the rotational degree of freedom move simultaneously.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (5)
1. The six-degree-of-freedom distributed composite control system for the ultra-precise lithography equipment is characterized in that: comprises a motion trail generating part S r Feedback control section S fb Feedforward control section S ff Decoupling control section S dc Six-degree-of-freedom motion stage P and position measuring section S ms ；
The motion trail generation part S r Generating a desired motion profile
The position measuring part S ms Generating an actual motion trail y ms ＝[x yθ z zθ x θ y ] T ；
The expected motion trail r and the actual motion trail y ms Generates motion error by difference of (a)The motion error e passes through the feedback control section S fb Generating feedback control quantityAnd the desired motion trajectory r passes through the feedforward control section S ff Generating feedforward control amount->The feedback control amount f fb And the feedforward control quantity f ff And generating a control quantity f in the objective lens coordinate system len ；
Control quantity f in the objective lens coordinate system len Through the decoupling control part S dc Generating an actuator control quantity f act The actuator control amount f act Generating a motion stage output y by inputting the motion stage output y to the six-degree-of-freedom motion stage P p The motion stage outputs y p Through the position measuring section S ms Generating an actual motion trail y ms ；
Wherein the decoupling control section S dc Comprising a static decoupling portion S dc,s And a dynamic decoupling portion S dc,d The static decoupling part S dc,s From gain planning matrix C GS Gain balance matrix C GB And coriolis force compensation vector f cor Composition of the dynamic decoupling portion S dc,d From a dynamic decoupling matrix C D Constructing;
control quantity f in objective lens coordinate system len Through the gain planning matrix C GS Generates its output f gs At the same time, the control quantity f under the objective lens coordinate system len Through the dynamic decoupling matrix C D Generates its output f d The output f gs Said output f d With the coriolis force compensation vector f cor Is used for generating a control quantity f under a centroid coordinate system of a moving platform cog Control quantity f under mass center coordinate system of the moving table cog Through the gain balance matrix C GB Generating an actuator control quantity f act 。
2. The six-degree-of-freedom distributed composite control method for the ultra-precise photoetching equipment is characterized by comprising the following steps of: the control system according to claim 1, wherein the control method comprises the following:
feedforward control section S ff From a diagonal matrix C ff The constitution is that:
feedback control section S fb From a diagonal matrix C fb The constitution, i.e：
Wherein s is Laplacian, C ff,k (s)＝Ω k s 2 ，k＝x,y,θ z ,z,θ x ,θ y Representing different degrees of freedom, Ω x ＝Ω y ＝Ω z ＝m，Ω θx ＝J x ，Ω θy ＝J y ，Ω θz ＝J z M represents the mass, J, of the six-degree-of-freedom motion stage P x 、J y 、J z Respectively express theta x 、θ y 、θ z The moment of inertia of the degree of freedom.
3. The control method according to claim 2, characterized in that: c (C) fb,k (s)，k＝x,y,θ z ,z,θ x ,θ y The design is carried out as follows:
wherein, xi lp,k The value range is 0.5-1, K P,k 、w i,k 、w d,k And w lp,k Determined as follows:
wherein alpha is k ＞1，w b,k Representing the desired open loop cut-off frequency for the kth degree of freedom.
4. The control method according to claim 2, characterized in that: c (C) fb,k (s)，k＝x,y,θ z ,z,θ x ,θ y The design is carried out as follows:
wherein K is P,k 、w i,k 、w 1,k And w 2,k Determined as follows:
wherein w is b,k Representing the desired open loop cut-off frequency for the kth degree of freedom,γ(w b,k ) Indicating the desired phase margin, delta, for the kth degree of freedom k ＝2°～10°。
5. The control method according to claim 2, characterized in that:
static decoupling portion S dc,s Gain planning matrix C GS The design is carried out as follows:
wherein H is len Representing the distance from the origin of the centroid coordinate system of the motion platform to the centroid of the upper surface of the motion platform;
static decoupling portion S dc,s Coriolis force compensation vector f cor Determined by the following formula:
static decoupling portion S dc,s Gain balance matrix C GB According to the physical layout design of the actuator;
dynamic decoupling portion S dc,d Dynamic decoupling matrix C of (a) D The design is carried out as follows:
wherein z is a time advance operator, and->Is a finite impulse response filter.
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