CN103345197B

CN103345197B - Six-freedom-degree decoupling modeling method of workpiece platform micro-motion part

Info

Publication number: CN103345197B
Application number: CN201310296004.4A
Authority: CN
Inventors: 陈兴林; 王一光; 李晓杰
Original assignee: Harbin Institute of Technology
Current assignee: Hit Robot Group Co ltd
Priority date: 2013-07-15
Filing date: 2013-07-15
Publication date: 2015-07-22
Anticipated expiration: 2033-07-15
Also published as: CN103345197A

Abstract

The invention discloses a six-freedom-degree decoupling modeling method of a workpiece platform micro-motion part, and mainly relates to a six-freedom-degree decoupling modeling method of a photo-etching machine workpiece platform micro-motion part. The six-freedom-degree decoupling modeling method aims to solve the coupling problem of a vertical direction three-freedom-degree motion model of the photo-etching machine workpiece platform micro-motion part and a horizontal direction three-freedom-degree motion model of the photo-etching machine workpiece platform micro-motion part. The six-freedom-degree decoupling modeling method comprises the steps of 1 establishing the conversion relationships between centroid driving force of the workpiece platform micro-motion part and torque of the workpiece platform micro-motion part and driving force of a voice coil motor; 2 establishing the position relationship between an exposure center and the workpiece platform micro-motion part centroid; 3 conducting secondary derivation on the position relationship obtained in the step 2 and ignoring primary derivative items; 4 obtaining the relation between the driving force exerted on the workpiece platform micro-motion part centroid and the torque exerted on the workpiece platform micro-motion part centroid and the acceleration of the exposure area center according to the Newton second law; 5 listing equations about the centroid driving force and torque through the results obtained in the step 1and the step 4, and obtaining the relation between the exposure center position and the driving force of the voice coil motor. The invention belongs to the field of super precision manufacturing.

Description

A kind of workpiece platform micro-motion part six degree of freedom decoupling zero modeling method

Technical field

The invention belongs to super hot investment casting field, what relate generally to is a kind of photo-etching machine work-piece platform fine motion part six degree of freedom decoupling zero modeling method.

Background technology

Litho machine is the key equipment manufacturing large scale integrated circuit, is mainly used in the research and production of integrated circuit, semiconductor components and devices, optoelectronic device, optical device.Workpiece table system is the key components of litho machine, mainly realizes the multifreedom motion function of litho machine.The precision of its motion and speed directly have influence on resolution and the production efficiency of litho machine.Work stage nanoscale superhigh precision is dynamically followed the tracks of and located is the gordian technique that litho machine is researched and developed.Because Long travel linear electric motors cannot ensure nano level kinematic accuracy, then need voice coil motor as actuator, but voice coil motor stroke very limited (normally millimeter magnitude).So at field of nanofabrication, traditional single kind method of actuator control cannot solve the contradiction between high precision and Long Distances.In view of above consideration, in Optical Coatings for Photolithography, usually adopt grand microstructure.Grand dynamic part mainly completes high speed and large stroke motion, and fine motion part main task realizes nano level dynamic tracking and location.Photo-etching machine work-piece platform fine motion part is the ultraprecise spatial movement body of multivariate, six degree of freedom, and its kinetic characteristic is carried out co-controlling by six voice coil motors and realized.Wherein the voice coil motor of three horizontal directions drives its translation carrying out horizontal direction and rotation, and the voice coil motor of other three vertical directions drives it to carry out vertical direction motion.Motion due to it is by multiple motor-driven, so there is very strong non-linear and coupling.Traditional modeling method is that six voice coil motors are divided into two groups, three of horizontal direction voice coil motors are set up photo-etching machine work-piece platform fine motion part of horizontal direction Three Degree Of Freedom model as research object, and this model is mainly photo-etching machine work-piece platform scanning, step motion service; Three of vertical direction voice coil motors are set up the Three Degree Of Freedom model in photo-etching machine work-piece platform fine motion straightened portion direction as research object, this model is mainly photo-etching machine work-piece platform leveling, focusing movements service.Due to the out-of-flatness of silicon chip surface and the out of focus of projection objective focal plane or the exposure quality tilting all can have a strong impact on silicon chip, along with improving constantly of litho machine precision and resolution requirement, traditional silicon chip one-time leveling focusing can not meet accuracy requirement, so carry out the leveling of exposure area one by one and focusing is inevitable choice while scan exposure motion.But due to the coupled relation between voice coil motor, utilize the model realization leveling of vertical direction Three Degree Of Freedom and focusing movements can produce a very large impact utilizing the exposure scanning motion of horizontal direction Three Degree Of Freedom model realization, and then the exposure quality of silicon chip is had an immense impact on.So traditional two Three Degree Of Freedom modeling methods can not meet the needs of current ultra-precision table system motion control.

Summary of the invention

The present invention is the coupled problem that will solve photo-etching machine work-piece platform fine motion straightened portion direction three-degree-of-freedom motion model and horizontal direction three-degree-of-freedom motion model, and provides a kind of workpiece platform micro-motion part six degree of freedom decoupling zero modeling method.

Workpiece platform micro-motion part six degree of freedom decoupling zero modeling method realizes according to the following steps:

One, workpiece platform micro-motion part centroids driving force and the transformational relation between barycenter torque and voice coil motor driving force is set up according to the installation site of voice coil motor and angle;

Two, the position relationship between exposure center and workpiece platform micro-motion part centroids is set up;

Three, position relationship secondary differentiate step 2 obtained also ignores once differentiation item, obtains the acceleration of workpiece platform micro-motion part centroids and the acceleration relation of exposure center;

Four, the relational expression acting on workpiece platform micro-motion part centroids driving force and barycenter torque and exposure center acceleration is drawn according to Newton second law

F_{cog} = M_{cog} \cdot Q \cdot [\begin{matrix} \overset{\cdot \cdot}{x} \\ \overset{\cdot \cdot}{y} \\ {\overset{\cdot \cdot}{r}}_{z} \\ \overset{\cdot \cdot}{z} \\ {\overset{\cdot \cdot}{r}}_{x} \\ {\overset{\cdot \cdot}{r}}_{y} \end{matrix}]

Wherein

M_{cog} = [\begin{matrix} m & 0 & 0 & 0 & 0 & 0 \\ 0 & m & 0 & 0 & 0 & 0 \\ 0 & 0 & J_{z} & 0 & 0 & 0 \\ 0 & 0 & 0 & m & 0 & 0 \\ 0 & 0 & 0 & 0 & J_{x} & 0 \\ 0 & 0 & 0 & 0 & 0 & J_{y} \end{matrix}]

M is workpiece platform micro-motion part mass, J _x, J _y, J _zfor workpiece platform micro-motion part is relative to x, y, the moment of inertia of z-axis;

Five, utilize step one and step 4 acquired results to arrange the equation write about barycenter driving force and barycenter torque, obtain the relational expression between exposure center position and voice coil motor driving force.

Invention effect:

Due to the coupled problem of traditional two Three Degree Of Freedom model modeling modes, the leveling and focusing of vertical direction is moved and brings very large impact to the exposure scanning motion of horizontal direction.Workpiece platform micro-motion part six degree of freedom decoupling zero modeling method proposed by the invention can well solve the problem.The six degree of freedom Decoupled Model utilizing method provided by the invention to set up can ensure the kinematic accuracy of photo-etching machine work-piece platform fine motion part when vertical direction and horizontal direction move simultaneously, thus significantly improves the exposure quality of silicon chip.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is in step one, the installation site of voice coil motor, force direction and workpiece platform micro-motion part centroids position relative relation schematic diagram;

Fig. 3 is in step 2, the relativeness schematic diagram of the motion of workpiece platform micro-motion part centroids and exposure area central motion.

Embodiment

Embodiment one: the workpiece platform micro-motion part six degree of freedom decoupling zero modeling method of present embodiment realizes according to the following steps:

F_{cog} = M_{cog} \cdot Q \cdot [\begin{matrix} \overset{\cdot \cdot}{x} \\ \overset{\cdot \cdot}{y} \\ {\overset{\cdot \cdot}{r}}_{z} \\ \overset{\cdot \cdot}{z} \\ {\overset{\cdot \cdot}{r}}_{x} \\ {\overset{\cdot \cdot}{r}}_{y} \end{matrix}]

Wherein

M_{cog} = [\begin{matrix} m & 0 & 0 & 0 & 0 & 0 \\ 0 & m & 0 & 0 & 0 & 0 \\ 0 & 0 & J_{z} & 0 & 0 & 0 \\ 0 & 0 & 0 & m & 0 & 0 \\ 0 & 0 & 0 & 0 & J_{x} & 0 \\ 0 & 0 & 0 & 0 & 0 & J_{y} \end{matrix}]

Present embodiment effect:

Due to the coupled problem of traditional two Three Degree Of Freedom model modeling modes, the leveling and focusing of vertical direction is moved and brings very large impact to the exposure scanning motion of horizontal direction.The workpiece platform micro-motion part six degree of freedom decoupling zero modeling method that present embodiment proposes can well solve the problem.The six degree of freedom Decoupled Model that the method utilizing present embodiment to provide is set up can ensure the kinematic accuracy of photo-etching machine work-piece platform fine motion part when vertical direction and horizontal direction move simultaneously, thus significantly improves the exposure quality of silicon chip.

Embodiment two: present embodiment and embodiment one unlike: set up workpiece platform micro-motion part centroids driving force in step one and the transformational relation between barycenter torque and voice coil motor driving force is specially: F _cog=Lf

Wherein matrix F _cog=[F _xcogf _ycogt _zcogf _zcogt _xcogt _ycog] ^t,

f＝[f ₁f ₂f ₃f ₄f ₅f ₆] ^T，

L = [\begin{matrix} - \cos θ_{1} & - \cos θ_{2} & \cos θ_{3} & 0 & 0 & 0 \\ \sin θ_{1} & - \sin θ_{2} & \sin θ_{3} & 0 & 0 & 0 \\ L_{1} & L_{2} & L_{3} & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 \\ - L_{4} \sin θ_{1} & L_{4} \sin θ_{2} & L_{4} \sin θ_{3} & - L_{5} & L_{6} & L_{6} \\ - L_{7} \cos θ_{1} & - L_{7} \cos θ_{2} & L_{7} \cos θ_{3} & - L_{8} & - L_{9} & L_{10} \end{matrix}]

F ₁, f ₂, f ₃for the acting force of horizontal direction three voice coil motors; f ₄, f ₅, f ₆for the acting force of vertical direction three voice coil motors; L ₁, L ₂, L ₃for barycenter is to f ₁, f ₂, f ₃distance on direction; L ₄, L ₇for barycenter is to f ₁, f ₂, f ₃the vertical distance of place plane; L ₅, L ₆for barycenter is to f ₄, f ₅y on direction is to distance; L ₈, L ₉, L ₁₀for barycenter is to f ₄, f ₅, f ₆x on direction is to distance; θ ₁, θ ₂, θ ₃for f ₁, f ₂, f ₃relative to the angle of x-axis; F _xcog, F _ycog, F _zcog, T _xcog, T _ycog, T _zcogfor acting on along the barycenter driving force in x, y, z direction and torque on workpiece platform micro-motion part centroids, T is matrix transpose symbol.Other step and parameter identical with embodiment one.

Embodiment three: present embodiment and embodiment one or two unlike: the position relationship set up in step 2 between exposure center and workpiece platform micro-motion part centroids is specially;

\{\begin{matrix} x_{cog} = x - (y + y_{0}) r_{z} + (z + z_{0}) r_{y} \\ y_{cog} = y + (x + x_{0}) r_{z} - (z + z_{0}) r_{x} \\ r_{zcog} = r_{z} \\ z_{cog} = z + (y + y_{0}) r_{x} - (x + x_{0}) r_{y} \\ r_{xcog} = r_{x} \\ r_{ycog} = r_{y} \end{matrix}

Wherein, Cog, O are respectively barycenter and surving coordinate initial point; x ₀, y ₀, z ₀for the skew of workpiece platform micro-motion part centroids and surving coordinate initial point; X, y, z are the translation displacements of exposure center; r _x, r _y, r _zfor the rotational angle of exposure area; x _cog, y _cog, z _cogfor the translation displacements of workpiece platform micro-motion part centroids; r _xcog, r _ycog, r _zcogfor the rotational angle of workpiece platform micro-motion part.Other step and parameter identical with embodiment one or two.

Embodiment four: one of present embodiment and embodiment one to three are unlike: position relationship secondary differentiate step 2 obtained in step 3 and ignore once differentiation item and be specially:

[\begin{matrix} {\overset{\cdot \cdot}{x}}_{cog} \\ {\overset{\cdot \cdot}{y}}_{cog} \\ {\overset{\cdot \cdot}{r}}_{zcog} \\ {\overset{\cdot \cdot}{z}}_{cog} \\ {\overset{\cdot \cdot}{r}}_{xcog} \\ {\overset{\cdot \cdot}{r}}_{ycog} \end{matrix}] = Q \cdot [\begin{matrix} \overset{\cdot \cdot}{x} \\ \overset{\cdot \cdot}{y} \\ {\overset{\cdot \cdot}{r}}_{z} \\ \overset{\cdot \cdot}{z} \\ {\overset{\cdot \cdot}{r}}_{x} \\ {\overset{\cdot \cdot}{r}}_{y} \end{matrix}]

Wherein

Q = [\begin{matrix} 1 & 0 & - (y + y_{0}) & 0 & 0 & z + z_{0} \\ 0 & 1 & x + x_{0} & 0 & - (z + z_{0}) & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & y + y_{0} & - (x + x_{0}) \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}]

for the acceleration of motion of workpiece platform micro-motion part centroids; for the acceleration of motion at workpiece platform micro-motion Partial exposure center.Other step and parameter identical with one of embodiment one to three.

Embodiment five: one of present embodiment and embodiment one to four unlike: utilize step one and step 4 acquired results to arrange the equation write about barycenter driving force and torque in step 5, the relational expression obtained between exposure center position and voice coil motor driving force is specially:

S = D \cdot [\begin{matrix} f_{1} \\ f_{2} \\ f_{3} \\ f_{4} \\ f_{5} \\ f_{6} \end{matrix}]

Wherein

D = \frac{1}{s^{2}} \cdot Q^{- 1} \cdot {M_{cog}}^{- 1} \cdot L = Q^{- 1} \cdot \begin{matrix} [\begin{matrix} \frac{1}{m s^{2}} & 0 & 0 & 0 & 0 & 0 \\ 0 & \frac{1}{m s^{2}} & 0 & 0 & 0 & 0 \\ 0 & 0 & \frac{1}{J_{z} s^{2}} & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{m s^{2}} & 0 & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{J_{x} s^{2}} & 0 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{J_{y} s^{2}} \end{matrix}] \end{matrix} \cdot L

S is differentiating operator, and S is that the six degree of freedom of workpiece platform micro-motion part exports.Other step and parameter identical with one of embodiment one to four.

Claims

1. a workpiece platform micro-motion part six degree of freedom decoupling zero modeling method, is characterized in that workpiece platform micro-motion part six degree of freedom decoupling zero modeling method realizes according to the following steps:

F_{cog} = M_{cog} \cdot Q \cdot [\begin{matrix} \overset{\cdot \cdot}{x} \\ \overset{\cdot \cdot}{y} \\ {\overset{\cdot \cdot}{r}}_{z} \\ \overset{\cdot \cdot}{z} \\ {\overset{\cdot \cdot}{r}}_{x} \\ {\overset{\cdot \cdot}{r}}_{y} \end{matrix}]

Wherein

M_{cog} = [\begin{matrix} m & 0 & 0 & 0 & 0 & 0 \\ 0 & m & 0 & 0 & 0 & 0 \\ 0 & 0 & J_{z} & 0 & 0 & 0 \\ 0 & 0 & 0 & m & 0 & 0 \\ 0 & 0 & 0 & 0 & J_{x} & 0 \\ 0 & 0 & 0 & 0 & 0 & J_{y} \end{matrix}]

Q = [\begin{matrix} 1 & 0 & - (y + y_{0}) & 0 & 0 & z + z_{0} \\ 0 & 1 & x + x_{0} & 0 & - (z + z_{0}) & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & y + y_{0} & - (x + x_{0}) \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}]

X ₀, y ₀, z ₀for the skew of workpiece platform micro-motion part centroids and surving coordinate initial point; X, y, z are the translation displacements of exposure center, and m is workpiece platform micro-motion part mass, J _x, J _y, J _zfor workpiece platform micro-motion part is relative to x, y, the moment of inertia of z-axis, F _cogrepresent the driving force on workpiece platform micro-motion part centroids, Q is acceleration relational matrix, M _cogfor inertial matrix, for the acceleration of motion at workpiece platform micro-motion Partial exposure center;

2. a kind of workpiece platform micro-motion part six degree of freedom decoupling zero modeling method according to claim 1, is characterized in that setting up workpiece platform micro-motion part centroids driving force in step one and the transformational relation between barycenter torque and voice coil motor driving force is specially: F _cog=Lf

Wherein matrix F _cog=[F _xcogf _ycogt _zcogf _zcogt _xcogt _ycog] ^t,

f＝[f ₁f ₂f ₃f ₄f ₅f ₆] ^T，

L = [\begin{matrix} - \cos θ_{1} & - \cos θ_{2} & \cos θ_{3} & 0 & 0 & 0 \\ \sin θ_{1} & - \sin θ_{2} & \sin θ_{3} & 0 & 0 & 0 \\ L_{1} & L_{2} & L_{3} & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 \\ - L_{4} \sin θ_{1} & L_{4} \sin θ_{2} & L_{4} \sin θ_{3} & - L_{5} & L_{6} & L_{6} \\ - L_{7} \cos θ_{1} & - L_{7} \cos θ_{2} & L_{7} \cos θ_{3} & - L_{8} & - L_{9} & L_{10} \end{matrix}]

F ₁, f ₂, f ₃for the acting force of horizontal direction three voice coil motors; f ₄, f ₅, f ₆for the acting force of vertical direction three voice coil motors; L ₁, L ₂, L ₃for barycenter is to f ₁, f ₂, f ₃distance on direction; L ₄, L ₇for barycenter is to f ₁, f ₂, f ₃the vertical distance of place plane; L ₅, L ₆for barycenter is to f ₄, f ₅y on direction is to distance; L ₈, L ₉, L ₁₀for barycenter is to f ₄, f ₅, f ₆x on direction is to distance; θ ₁, θ ₂, θ ₃for f ₁, f ₂, f ₃relative to the angle of x-axis; F _xcog, F _ycog, F _zcog, T _xcog, T _ycog, T _zcogfor acting on along the barycenter driving force in x, y, z direction and torque on workpiece platform micro-motion part centroids, T is matrix transpose symbol, and L represents power relational matrix, and f represents voice coil motor driving force.

3. a kind of workpiece platform micro-motion part six degree of freedom decoupling zero modeling method according to claim 1, is characterized in that the position relationship set up in step 2 between exposure center and workpiece platform micro-motion part centroids is specially;

\{\begin{matrix} x_{cog} = x - (y + y_{0}) r_{z} + (z + z_{0}) r_{y} \\ y_{cog} = y + (x + x_{0}) r_{z} - (z + z_{0}) r_{x} \\ r_{zcog} = r_{z} \\ z_{cog} = z + (y + y_{0}) r_{x} - (x + x_{0}) r_{y} \\ r_{xcog} = r_{x} \\ r_{ycog} = r_{y} \end{matrix}

Wherein, Cog, O are respectively barycenter and surving coordinate initial point; x ₀, y ₀, z ₀for the skew of workpiece platform micro-motion part centroids and surving coordinate initial point; X, y, z are the translation displacements of exposure center; r _x, r _y, r _zfor the rotational angle of exposure area; x _cog, y _cog, z _cogfor the translation displacements of workpiece platform micro-motion part centroids; r _xcog, r _ycog, r _zcogfor the rotational angle of workpiece platform micro-motion part.

4. a kind of workpiece platform micro-motion part six degree of freedom decoupling zero modeling method according to claim 1, is characterized in that the position relationship secondary differentiate that step 2 obtained in step 3 and ignores once differentiation item being specially:

[\begin{matrix} {\overset{\cdot \cdot}{x}}_{cog} \\ {\overset{\cdot \cdot}{y}}_{cog} \\ {\overset{\cdot \cdot}{r}}_{zcog} \\ {\overset{\cdot \cdot}{z}}_{cog} \\ {\overset{\cdot \cdot}{r}}_{xcog} \\ {\overset{\cdot \cdot}{r}}_{yocg} \end{matrix}] = Q \cdot [\begin{matrix} \overset{\cdot \cdot}{x} \\ \overset{\cdot \cdot}{y} \\ {\overset{\cdot \cdot}{r}}_{z} \\ \overset{\cdot \cdot}{z} \\ {\overset{\cdot \cdot}{r}}_{x} \\ {\overset{\cdot \cdot}{r}}_{y} \end{matrix}]

Wherein

Q = [\begin{matrix} 1 & 0 & - (y + y_{0}) & 0 & 0 & z + z_{0} \\ 0 & 1 & x + x_{0} & 0 & - (z + z_{0}) & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & y + y_{0} & - (x + x_{0}) \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}]

for the acceleration of motion of workpiece platform micro-motion part centroids; for the acceleration of motion at workpiece platform micro-motion Partial exposure center, x ₀, y ₀, z ₀for the skew of workpiece platform micro-motion part centroids and surving coordinate initial point; X, y, z are the translation displacements of exposure center.

5. a kind of workpiece platform micro-motion part six degree of freedom decoupling zero modeling method according to claim 1, it is characterized in that utilizing step one and step 4 acquired results to arrange the equation write about barycenter driving force and torque in step 5, the relational expression obtained between exposure center position and voice coil motor driving force is specially:

S = D \cdot [\begin{matrix} f_{1} \\ f_{2} \\ f_{3} \\ f_{4} \\ f_{5} \\ f_{6} \end{matrix}]

Wherein

D = \frac{1}{s^{2}} \cdot Q^{- 1} \cdot {M_{cog}}^{- 1} \cdot L = Q^{- 1} \cdot [\begin{matrix} \frac{1}{{ms}^{2}} & 0 & 0 & 0 & 0 & 0 \\ 0 & \frac{1}{{ms}^{2}} & 0 & 0 & 0 & 0 \\ 0 & 0 & \frac{1}{J_{z} s^{2}} & 0 & 0 & 0 \\ 0 & 0 & 0 & \frac{1}{{ms}^{2}} & 0 & 0 \\ 0 & 0 & 0 & 0 & \frac{1}{J_{x} s^{2}} & 0 \\ 0 & 0 & 0 & 0 & 0 & \frac{1}{J_{y} s^{2}} \end{matrix}] \cdot L

S is differentiating operator, and S is that the six degree of freedom of workpiece platform micro-motion part exports, f ₁, f ₂, f ₃for the acting force of horizontal direction three voice coil motors; f ₄, f ₅, f ₆for the acting force of vertical direction three voice coil motors, L represents power relational matrix.