# US 9,519,231 B2 · Method for measuring and calibrating centroid of coarse stage of photolithography tool

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- Number: US 9,519,231 B2
- Document ID: US9519231B2
- Status: Granted
- Kind: B2
- Application number: 14/115,284
- Filed: 2012-04-28
- Published: 2014-03-13
- Granted: 2016-12-13
- Earliest claimed: 2011-05-03
- Assignees: Shanghai Micro Electronics Equipment Co., Ltd.
- Applicants: Liwei Wu; Junqing Dong
- Inventors: Liwei Wu; Junqing Dong
- Web page: https://patentgrep.com/patent/US9519231B2

## CPC

- G03F 7/70725: {control}
- G03F: PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR; (phototypographic composing devices B41B; photosensitive materials or processes for photographic purposes G03C; electrophotography, sensitive layers or processes therefor G03G)

## Abstract

A method for measuring and calibrating a centroid of a coarse stage of a photolithography tool by means of measuring an offset of the centroid relative to a midpoint of the coarse stage is disclosed. The method includes: individually performing closed-loop controls on parameters of the three degrees of freedom X, Y, and Rz of the coarse stage and converting the parameters into coordinates in a coordinate system of the coarse stage (601); for each of the X and Y directions, estimating a range for the centroid (604), equally dividing the range into N parts (605), and designating each dividing point as an eccentricity (605); obtaining N Rz direction positional deviations by conducting a compensation calibration and a calibration calculation based on each corresponding eccentricity (606-611); comparing a minimum of the N positional deviations with a preset Rz-direction positional deviation threshold (613), completing the measurement if the latter is greater (614), and otherwise designating a range between the eccentricities adjacently in front of and behind the eccentricity corresponding to the minimum positional deviation as a new range for the centroid (616-617) and repeating the measurement until the minimum is smaller than the preset threshold.

## Claims

### Claim 1

A method for measuring and calibrating a centroid of a coarse stage of a photolithography tool by means of measuring an offset of the centroid relative to a midpoint of the coarse stage, comprising the steps of:
step 1, individually performing closed-loop controls with a controller on parameters of three horizontal degrees of freedom (X, Y, Rz) of the coarse stage and converting the parameters into coordinates in a coordinate system of the coarse stage, wherein X and Y are two directions orthogonal to each other within a horizontal plane, and Rz is rotation about a vertical axis within the horizontal plane;
step 2, determining an initial X-direction range and an initial Y-direction range for the centroid in the coordinate system of the coarse stage and equally dividing each of the initial X-direction range and the initial Y-direction range into N parts, designating dividing points of the initial X-direction range as X-direction eccentricities Δx's, and designating dividing points of the initial Y-direction range as Y-direction eccentricities Δy's, wherein N is a natural number;
step 3, obtaining N Rz-direction positional deviations by conducting a calibration calculation with the controller based on the X-direction eccentricities Δx's, comparing a minimum Rz-direction positional deviation derived from the N Rz-direction positional deviations with a preset Rz-direction positional deviation threshold, if the minimum Rz-direction positional deviation is smaller than the preset Rz-direction positional deviation threshold, designating an X-direction eccentricity Δx corresponding to the minimum Rz-direction positional deviation as an actual X-direction eccentricity and proceeding to step 5, and otherwise designating an updated X-direction range whose limits are selected as X-direction eccentricities adjacently in front of and behind the X-direction eccentricity corresponding to the minimum Rz-direction positional deviation, respectively, equally dividing the updated X-direction range into N parts, designating dividing points of the updated X-direction range as updated X-direction eccentricities Δx's, and repeating step 3;
step 4, obtaining N Rz-direction positional deviations by conducting a calibration calculation with the controller based on the Y-direction eccentricities Δy's, comparing a minimum Rz-direction positional deviation derived from the N Rz-direction positional deviations with a preset Rz-direction positional deviation threshold, if the minimum Rz-direction positional deviation is smaller than the preset Rz-direction positional deviation threshold, designating a Y-direction eccentricity Δy corresponding to the minimum Rz-direction positional deviation as an actual Y-direction eccentricity and proceeding to step 5, and otherwise designating an updated Y-direction range whose limits are selected as Y-direction eccentricities adjacently in front of and behind the Y-direction eccentricity corresponding to the minimum Rz-direction positional deviation, respectively, equally dividing the updated Y-direction range into N parts, designating dividing points of the updated Y-direction range as updated Y-direction eccentricities Δy's, and repeating step 4; and
step 5, deriving the offset of the centroid according to results of steps 3 and 4,
wherein, step 3 is carried out prior to, subsequent to, or concurrently with step 4.

### Claim 2 (depends on 1)

The method of claim 1, further comprising: conducting a compensation calculation, based on the actual X-direction and Y-direction eccentricities and a midpoint coordinate of the coarse stage fed back in real time to the controller, to adjust the parameters of three horizontal degrees of freedom (X, Y, Rz) of the coarse stage.

### Claim 3 (depends on 2)

The method of claim 2, wherein the closed-loop control on the coarse stage in the X direction is performed by using an X-direction grating and the closed-loop controls on the coarse stage in the Y and Rz directions are performed by using two Y-direction gratings.

### Claim 4 (depends on 3)

The method of claim 3, wherein the coordinate system of the coarse stage is centered at a common zero position of the X-direction and Y-direction gratings and also at the midpoint of the coarse stage.

### Claim 5 (depends on 3)

The method of claim 3, wherein the coarse stage is driven by using an X-direction actuator, a first Y-direction actuator and a second Y-direction actuator, and wherein the compensation calculation includes: collecting readings of the respective gratings and obtaining midpoint coordinates of the coarse stage with respect to X, Y and Rz axes, respectively; receiving desired control forces from the controller for X, Y and Rz logic axes; and allocating output forces to physical axes of the respective actuators according to a compensation algorithm.

### Claim 6 (depends on 5)

The method of claim 5, wherein the compensation algorithm includes the following equation:
{
f
x
=
F
x
*
f
y
⁢
⁢
1
=
-
Δ
⁢
⁢
y
L
y
⁢
F
x
*
+
L
y
⁢
⁢
2
⁡
(
x
)
L
y
⁢
F
y
*
-
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
⁢
T
z
*
f
y
⁢
⁢
2
=
Δ
⁢
⁢
y
L
y
⁢
F
x
*
+
L
y
⁢
⁢
1
⁡
(
x
)
L
y
⁢
F
y
*
+
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
⁢
T
z
*
,
where, Δx represents an X-direction eccentricity of the coarse stage, Δy represents a Y-direction eccentricity of the coarse stage, Jz0 represents a rotational inertia of the coarse stage about the vertical axis of the centroid, x represents the reading of the X-direction grating, Fx*, Fy* and Tz* respectively represent the desired control forces for the X, Y and Rz logic axes, fx, fy1 and fy2 respectively represent desired output forces for the physical axes of the respective actuators Ly1(x) represents a distance from a force output point of the first Y-direction actuator to an X-direction centroid of the coarse stage, Ly2(x) represents a distance from a force output point of the second Y-direction actuator to the X-direction centroid of the coarse stage, Ly represents an interval between the first and second Y-direction actuators with respect to the X direction and,
J
z
⁡
(
x
)
=
J
z
⁢
⁢
0
+
m
x
m
y
⁢
(
m
y
-
m
x
)
·
x
2
+
m
y
·
Δ
⁢
⁢
x
2
,
wherein mx represents an X-direction mass and my represents a Y-direction mass.

### Claim 7 (depends on 6)

The method of claim 6, wherein the compensation algorithm further includes the following equations:
{
r
1
=
1
r
2
=
-
Δ
⁢
⁢
y
L
y
r
3
=
Δ
⁢
⁢
y
L
y
,
{
s
1
=
0
s
2
=
L
y
⁢
⁢
2
⁡
(
x
)
L
y
=
L
y
⁢
⁢
2
L
y
-
Δ
⁢
⁢
x
L
y
-
m
x
m
y
·
L
y
⁢
x
=
-
α
1
·
x
+
β
11
s
3
=
L
y
⁢
⁢
1
⁡
(
x
)
L
y
=
L
y
⁢
⁢
1
L
y
+
Δ
⁢
⁢
x
L
y
+
m
x
m
y
·
L
y
⁢
x
=
α
1
·
x
+
β
12
,
and
⁢
⁢
{
t
1
=
0
t
2
=
-
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
=
-
J
z
⁢
⁢
0
L
y
⁢
1
J
z
⁢
⁢
0
+
m
x
m
y
⁢
(
m
y
-
m
x
)
·
x
2
+
m
y
·
Δ
⁢
⁢
x
2
=
1
α
2
·
x
2
+
β
2
t
3
=
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
=
J
z
⁢
⁢
0
L
y
⁢
1
J
z
⁢
⁢
0
+
m
x
m
y
⁢
(
m
y
-
m
x
)
·
x
2
+
m
y
·
Δ
⁢
⁢
x
2
=
1
α
2
·
x
2
+
β
2
,
where, Δ1 represents a rate of change of a distance from a centroid of the X-direction mass mx to any of the fy1 and fy2 physical axes caused by a change in an X-direction displacement of a fine stage, β11 represents an allocation ratio of thrust command when the X-direction mass mx is at a zero position and a moment at a centroid of the Y-direction mass my is balanced in a direction of the fy1 physical axis, Δ2 represents a rate of change of an inertia moment about a Tz* axis at the centroid of the Y-direction mass my caused by the change in the X-direction displacement of the fine stage, β12 represents an allocation ratio of thrust command when the X-direction mass mx is at the zero position and a moment at the centroid of the Y-direction mass my is balanced in a direction of the fy2 physical axis, β2 represents a constant scaling factor of the inertia moment about the Tz* axis at the centroid of the Y-direction mass my caused by the change in the X-direction displacement of the fine stage, r1, r2, r3 respectively represent factors of transformation from physical axes fx, fy1, fy2 to logic axis Fy*, s1, s2, s3 respectively represent factors of transformation from physical axes fx, fy1, fy2 to logic axis Fy*, and t1, t2, t3 respectively represent factors of transformation from physical axes fx,fy1,fy2 to logic axis Tz*.

### Claim 8 (depends on 3)

The method of claim 3, wherein in step 3, during the calibration calculation based on the X-direction eccentricities Δx's, the coarse stage is kept at a zero position in both the X direction and the Rz direction by the closed-loop control, and the Y direction is provided with a motion trajectory.

### Claim 9 (depends on 8)

The method of claim 8, wherein the calibration calculation in step 3 includes the steps of:
S101, setting a value of Δx as a lower limit of the X-direction range;
S102, retrieving the coarse stage to a zero position of the X-direction grating and carrying out a closed-loop servo control;
S103, closed-loop controlling the coarse stage to keep at a zero position in the Rz direction, performing a closed-loop control in the Y direction and providing the Y direction with a one-pass forth-and-back trajectory, tracking and recording an Rz-direction positional deviation;
S104, treating each of the N equal parts of the X-direction range as a stroke and changing the value of Δx by one stroke, providing the Y direction with the same one-pass forth-and-back trajectory as in step S103, and recording a corresponding Rz-direction positional deviation;
S105, successively changing the value of Δx by one stroke and repeating step S104 until the upper limit of the X-direction range is reached; and
S106, fitting the Rz-direction positional deviations using a method of least squares to obtain a minimum Rz-direction positional deviation.

### Claim 10 (depends on 3)

The method of claim 3, wherein in step 4, during the calibration calculation based on the Y-direction eccentricities Δy, the coarse stage is kept at a zero position in both the Y direction and the Rz direction by the closed-loop control, and the X direction is provided with a motion trajectory.

### Claim 11 (depends on 10)

The method of claim 10, wherein the calibration calculation in step 4 includes the steps of:
S201, setting a value of Δy as a lower limit of the Y-direction range;
S202, retrieving the coarse stage to a zero position of the Y-direction grating and carrying out a closed-loop servo control;
S203, closed-loop controlling the coarse stage to keep at a zero position in the Rz direction, performing a closed-loop control in the X direction and providing the X direction with a one-pass forth-and-back trajectory, tracking and recording an Rz-direction positional deviation;
S204, treating each of the N equal parts of the Y-direction range as a stroke and changing the value of Δy by one stroke, providing the X direction with the same one-pass forth-and-back trajectory as in step S203, and recording a corresponding Rz-direction positional deviation;
S205, successively changing the value of Δy by one stroke and repeating step S204 until the upper limit of the Y-direction range is reached; and
S206, fitting the Rz-direction positional deviations using a method of least squares to obtain a minimum Rz-direction positional deviation.

### Claim 12 (depends on 1)

The method of claim 1, wherein the closed-loop control on the coarse stage in the X direction is performed by using an X-direction grating and the closed-loop controls on the coarse stage in the Y and Rz directions are performed by using two Y-direction gratings.

### Claim 13 (depends on 12)

The method of claim 12, wherein the coordinate system of the coarse stage is centered at a common zero position of the X-direction and Y-direction gratings and also at the midpoint of the coarse stage.

### Claim 14 (depends on 12)

The method of claim 12, wherein the coarse stage is driven by using an X-direction actuator, a first Y-direction actuator and a second Y-direction actuator, and wherein the compensation calculation includes: collecting readings of the respective gratings and obtaining midpoint coordinates of the coarse stage with respect to X, Y and Rz axes, respectively; receiving desired control forces from the controller for X, Y and Rz logic axes; and allocating output forces to physical axes of the respective actuators according to a compensation algorithm.

### Claim 15 (depends on 14)

The method of claim 14, wherein the compensation algorithm includes the following equation:
{
f
x
=
F
x
*
f
y
⁢
⁢
1
=
-
Δ
⁢
⁢
y
L
y
⁢
F
x
*
+
L
y
⁢
⁢
2
⁡
(
x
)
L
y
⁢
F
y
*
-
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
⁢
T
z
*
f
y
⁢
⁢
2
=
Δ
⁢
⁢
y
L
y
⁢
F
x
*
+
L
y
⁢
⁢
1
⁡
(
x
)
L
y
⁢
F
y
*
+
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
⁢
T
z
*
,
where, Δx represents an X-direction eccentricity of the coarse stage, Δy represents a Y-direction eccentricity of the coarse stage, Jz0 represents a rotational inertia of the coarse stage about the vertical axis of the centroid, x represents the reading of the X-direction grating, F x*, Fy*, and Tz* respectively represent the desired control forces for the X, Y and Rz logic axes, fx, fy1 and fy2 respectively represent desired output forces for the physical axes of the respective actuators Ly1(x) represents a distance from a force output point of the first Y-direction actuator to an X-direction centroid of the coarse stage, Ly2(x) represents a distance from a force output point of the second Y-direction actuator to the X-direction centroid of the coarse stage, Ly represents an interval between the first and second Y-direction actuators with respect to the X direction and Jz(x)=Jz0+mx/my(my−mx)·x2+my·Δx2, wherein mx represents an X-direction mass and my represents a Y-direction mass.

### Claim 16 (depends on 15)

The method of claim 15, wherein the compensation algorithm further includes the following equations:
{
r
1
=
1
r
2
=
-
Δ
⁢
⁢
y
L
y
r
3
=
Δ
⁢
⁢
y
L
y
,
{
s
1
=
0
s
2
=
L
y
⁢
⁢
2
⁡
(
x
)
L
y
=
L
y
⁢
⁢
2
L
y
-
Δ
⁢
⁢
x
L
y
-
m
x
m
y
·
L
y
⁢
x
=
-
α
1
·
x
+
β
11
s
3
=
L
y
⁢
⁢
1
⁡
(
x
)
L
y
=
L
y
⁢
⁢
1
L
y
+
Δ
⁢
⁢
x
L
y
+
m
x
m
y
·
L
y
⁢
x
=
α
1
·
x
+
β
12
,
and
⁢
⁢
{
t
1
=
0
t
2
=
-
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
=
-
J
z
⁢
⁢
0
L
y
⁢
1
J
z
⁢
⁢
0
+
m
x
m
y
⁢
(
m
y
-
m
x
)
·
x
2
+
m
y
·
Δ
⁢
⁢
x
2
=
1
α
2
·
x
2
+
β
2
t
3
=
J
z
⁢
⁢
0
L
y
·
J
z
⁡
(
x
)
=
J
z
⁢
⁢
0
L
y
⁢
1
J
z
⁢
⁢
0
+
m
x
m
y
⁢
(
m
y
-
m
x
)
·
x
2
+
m
y
·
Δ
⁢
⁢
x
2
=
1
α
2
·
x
2
+
β
2
,
where, α1 represents a rate of change of a distance from a centroid of the X-direction mass mx to any of the fy1 and fy2 physical axes caused by a change in an X-direction displacement of a fine stage, β11 represents an allocation ratio of thrust command when the X-direction mass mx is at a zero position and a moment at a centroid of the Y-direction mass my is balanced in a direction of the fy1 physical axis, α2 represents a rate of change of an inertia moment about a Tz* axis at the centroid of the Y-direction mass my caused by the change in the X-direction displacement of the fine stage, β12 represents an allocation ratio of thrust command when the X-direction mass mx is at the zero position and a moment at the centroid of the Y-direction mass my is balanced in a direction of the fy2 physical axis, β2 represents a constant scaling factor of the inertia moment about the Tz* axis at the centroid of the Y-direction mass my caused by the change in the X-direction displacement of the fine stage, r1, r2, r3 respectively represent factors of transformation from physical axes fx, fy1, fy2 to logic axis Fx*, s1, s2, s3 respectively represent factors of transformation from physical axes fx, fy1, fy2 to logic axis Fy*, and t1, t2, t3 respectively represent factors of transformation from physical axes fx,fy1,fy2 to logic axis Tz*.

### Claim 17 (depends on 12)

The method of claim 12, wherein in step 3, during the calibration calculation based on the X-direction eccentricities Δx's, the coarse stage is kept at a zero position in both the X direction and the Rz direction by the closed-loop control, and the Y direction is provided with a motion trajectory.

### Claim 18 (depends on 17)

The method of claim 17, wherein the calibration calculation in step 3 includes the steps of:
S101, setting a value of Δx as a lower limit of the X-direction range;
S102, retrieving the coarse stage to a zero position of the X-direction grating and carrying out a closed-loop servo control;
S103, closed-loop controlling the coarse stage to keep at a zero position in the Rz direction, performing a closed-loop control in the Y direction and providing the Y direction with a one-pass forth-and-back trajectory, tracking and recording an Rz-direction positional deviation;
S104, treating each of the N equal parts of the X-direction range as a stroke and changing the value of Δx by one stroke, providing the Y direction with the same one-pass forth-and-back trajectory as in step S103, and recording a corresponding Rz-direction positional deviation;
S105, successively changing the value of Δx by one stroke and repeating step S104 until the upper limit of the X-direction range is reached; and
S106, fitting the Rz-direction positional deviations using a method of least squares to obtain a minimum Rz-direction positional deviation.

### Claim 19 (depends on 12)

The method of claim 12, wherein in step 4, during the calibration calculation based on the Y-direction eccentricities Δy, the coarse stage is kept at a zero position in both the Y direction and the Rz direction by the closed-loop control, and the X direction is provided with a motion trajectory.

### Claim 20 (depends on 19)

The method of claim 19, wherein the calibration calculation in step 4 includes the steps of:
S201, setting a value of Δy as a lower limit of the Y-direction range;
S202, retrieving the coarse stage to a zero position of the Y-direction grating and carrying out a closed-loop servo control;
S203, closed-loop controlling the coarse stage to keep at a zero position in the Rz direction, performing a closed-loop control in the X direction and providing the X direction with a one-pass forth-and-back trajectory, tracking and recording an Rz-direction positional deviation;
S204, treating each of the N equal parts of the Y-direction range as a stroke and changing the value of Δy by one stroke, providing the X direction with the same one-pass forth-and-back trajectory as in step S203, and recording a corresponding Rz-direction positional deviation;
S205, successively changing the value of Δy by one stroke and repeating step S204 until the upper limit of the Y-direction range is reached; and
S206, fitting the Rz-direction positional deviations using a method of least squares to obtain a minimum Rz-direction positional deviation.

### Claim 21 (depends on 1)

The method of claim 1, wherein the initial X-direction and Y-direction ranges for the centroid in the coordinate system of the coarse stage are determined according to a mass and a design centroid of the coarse stage.