Method, system and medium for controlling manufacture process having multivariate input parameters

• US 7,272,459 B2
• Filed: 11/14/2003
• Issued: 09/18/2007
• Est. Priority Date: 11/15/2002
• Status: Expired due to Fees

• Current Assignee: Applied Materials Incorporated
• Original Assignee: Applied Materials Incorporated
• Inventors: Schwarm, Alexander T., Kokotov, Yuri, Fisher, Yossi, Sarel, Shalomo, Shanmugasundram, Arulkumar P., Paik, Young Jeen, Entin, Efim, Seror, Jacques
• Primary Examiner(s): Bahta; Kidest
• Application Number:
  US10/712,273
• Publication Number:
  US 20040225377A1
• Time in Patent Office: 1,404 Days
• Field of Search: 700/42, 700/28, 700/37, 700/46, 700/52, 700/121, 700/97, 708/539, 708/523, 438/14, 438/404, 257/E21.324
• US Class Current: 700/97
• CPC Class Codes: G05B 11/32 with inputs from more than one sensing element; with outputs to more than one correcting element
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 13/048 using a predictor
• CPC Class Codes: Y02P 90/02 Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

A method, system, and medium of modeling and/or for controlling a manufacturing process is disclosed. In particular, a method according to embodiments of the present invention includes the step of identifying one or more input parameters. Each input parameter causes a change in at least two outputs. The method also includes the step of storing values of the identified inputs and corresponding empirical output values along with predicted output values. The predicted output values are calculated based on, in part, the values of the identified inputs. The method also includes the step of calculating a set of transform coefficients by minimizing a score equation that is a function of differences between one or more of the empirical output values and their corresponding predicted output values. The method further includes the steps of receiving a new set of values for the identified inputs, transforming the new set of values for the identified input using the set of coefficients, and calculating a set of predicted output values using the transformed input values.

Claims

1. A computer implemented method for controlling a manufacturing apparatus, the method comprising:

(a) identifying at least one input, the at least one input causing a change in at least two of a plurality of outputs;

(b) storing values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;

(c) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values, wherein the score equation is;

$S_p=\underset{i,k}{\sum <br><br>}<br><br>{W_{i,k}<br><br>\left(y_{\mathrm{actual}}^{i<br><br><br><br>k}-y_{\mathrm{predicted}}^{i<br><br><br><br>k}<br><br>\left({\stackrel{\to <br><br>}{X}}^{{i<br><br>}^{\mathrm{\prime <br><br>}}}<br><br>\left({\stackrel{\to <br><br>}{X}}^i,\stackrel{\to <br><br>}{P}\right)\right)\right)}^2$

where;

i—

number of wafer;

k—

number of output;

y_actual—

an empirical output value;

y_predicted—

a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}^i′

)

{right arrow over (X)}^i′

=(X₁^i′

,X₂^i′

,X₃^i′

) is transformed input values in a vector format;

({right arrow over (X)}^i′

)=(X₁^i′

,X₂^i′

,X₃^i′

) for wafer i together with the transformation parameters ({right arrow over (P)}), to thereby calculate an optimal value of P;

(d) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients; and

(e) communicating the transformed input values of (d) to a manufacturing apparatus.

2. The method of claim 1, further comprising;

collecting additional empirical data and corresponding input values;

calculating a new set of coefficients {right arrow over (P)}_new ; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.

3. The method of claim 1 further comprising;

collecting additional empirical data and corresponding input values;

calculating a new set of coefficients as

{right arrow over (P)}_new≡

{right arrow over (P)}_previous+K({right arrow over (P)}_optimum−

{right arrow over (P)}_previous),

wherein K<

1 and {right arrow over (P)}_previous is a previously calculated optimal value of {right arrow over (P)}; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.

4. A computer implemented system for controlling a manufacturing apparatus, the system comprising:

(a) means for identifying at least one input, the at least one input causing a change in at least two of a plurality of outputs;

(b) a memory device configured to store values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;

(c) means for calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values, wherein the score equation is;

$S_p=\underset{i,k}{\sum <br><br>}<br><br>{W_{i,k}<br><br>\left(y_{\mathrm{actual}}^{i<br><br><br><br>k}-y_{\mathrm{predicted}}^{i<br><br><br><br>k}<br><br>\left({\stackrel{\to <br><br>}{X}}^{{i<br><br>}^{\mathrm{\prime <br><br>}}}<br><br>\left({\stackrel{\to <br><br>}{X}}^i,\stackrel{\to <br><br>}{P}\right)\right)\right)}^2$

where;

i—

number of wafer;

k—

number of output;

y_actual—

an empirical output value;

y_predicted—

a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}^i′

)

{right arrow over (X)}^i′

=(X₁^i′

,X₂^i′

,X₃^i′

) is transformed input values in a vector format;

{right arrow over (X)}ⁱ=(X₁ⁱ,X₂ⁱ,X₃ⁱ) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)};

(d) means for calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients; and

(e) means for communicating the transformed input values of (d) to a manufacturing apparatus.

5. The system of claim 4, further comprising:

means for collecting additional empirical data and corresponding input values; and

means for calculating a new set of coefficients {right arrow over (P)}_new, wherein the new set of coefficients is defined as the optimal value of {right arrow over (P)}.

6. The system of claim 4, further comprising:

means for collecting additional empirical data and corresponding input values; and

means for calculating a new set of coefficients as

{right arrow over (P)}_new≡

{right arrow over (P)}_previous+K({right arrow over (P)}_optimum−

{right arrow over (P)}_previous),

wherein K<

1 and {right arrow over (P)}_previous is a previously calculated optimal value of {right arrow over (P)}, wherein the new set of coefficients is defined as the optimal value of {right arrow over (P)}.

7. A computer readable medium for storing instructions being executed by one or more computers, the instructions directing the one or more computers to perform a method for predicting output characteristics of a device produced by a manufacturing apparatus, the method comprising:

(a) identifying at least one input, the at least one input causing a change in at least two of a plurality of outputs;

(b) storing values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;

(c) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values, wherein the score equation is;

$S_p=\underset{i,k}{\sum <br><br>}<br><br>{W_{i,k}<br><br>\left(y_{\mathrm{actual}}^{i<br><br><br><br>k}-y_{\mathrm{predicted}}^{i<br><br><br><br>k}<br><br>\left({\stackrel{\to <br><br>}{X}}^{{i<br><br>}^{\mathrm{\prime <br><br>}}}<br><br>\left({\stackrel{\to <br><br>}{X}}^i,\stackrel{\to <br><br>}{P}\right)\right)\right)}^2$

where;

i—

number of wafer;

k—

number of output;

y_actual—

an empirical output value;

y_predicted—

a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}^i′

)

{right arrow over (X)}^i′

=(X₁^i′

,X₂^i′

,X₃^i′

) is transformed input values in a vector format;

{right arrow over (X)}ⁱ=(X₁ⁱ,X₂ⁱ,X₃ⁱ) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)};

(d) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients; and

(e) communicating the transformed input values of (d) to a manufacturing apparatus.

8. The medium of claim 7, wherein the method further comprises:

collecting additional empirical data and corresponding input values;

calculating a new set of coefficients {right arrow over (P)}_new; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.

9. The medium of claim 7, wherein the method further comprises:

collecting additional empirical data and corresponding input values;

calculating a new set of coefficients as

{right arrow over (P)}_new≡

{right arrow over (P)}_previous+K({right arrow over (P)}_optimum−

{right arrow over (P)}_previous),

wherein K<

1 and {right arrow over (P)}_previous is a previously calculated optimal value of {right arrow over (P)}; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.

10. A computer implemented method for controlling a manufacturing apparatus, the method comprising:

(a) identifying at least one input that causes a change in at least two of a plurality of outputs;

(b) storing values of the identified inputs and corresponding empirical output values;

(c) calculating and storing predicted output values, based on, in part, the values of the identified inputs;

(d) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values;

(e) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients; and

(f) providing the transformed input values of (e) to a manufacturing apparatus.

11. The method of claim 10, wherein the score function is:

$S_p=\underset{i,k}{\sum <br><br>}<br><br>{W_{i,k}<br><br>\left(y_{\mathrm{actual}}^{i<br><br><br><br>k}-y_{\mathrm{predicted}}^{i<br><br><br><br>k}<br><br>\left({\stackrel{\to <br><br>}{X}}^{{i<br><br>}^{\mathrm{\prime <br><br>}}}<br><br>\left({\stackrel{\to <br><br>}{X}}^i,\stackrel{\to <br><br>}{P}\right)\right)\right)}^2$

where;

i—

number of wafer;

k—

number of output;

y_actual—

an empirical output value;

y_predicted—

a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}^i′

)

{right arrow over (X)}^i′

=(X₁^i′

,X₂^i′

,X₃^i′

) is transformed input values in a vector format;

{right arrow over (X)}ⁱ=(X₁ⁱ,X₂ⁱ,X₃ⁱ) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)}.

12. The method of claim 10, further comprising:

collecting additional empirical data and corresponding input values;

calculating a new set of coefficients {right arrow over (P)}_new; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.

13. The method of claim 10 further comprising:

collecting additional empirical data and corresponding input values; and

calculating a new set of coefficients based on the additional empirical data.

14. The method of claim 13, further comprising

calculating the new set of coefficients using:

{right arrow over (P)}_new≡

{right arrow over (P)}_previous+K({right arrow over (P)}_optimum−

{right arrow over (P)}_previous),

wherein K<

1 and {right arrow over (P)}_previous is a previously calculated optimal value of {right arrow over (P)}; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.

15. A computer implemented system for controlling a manufacturing apparatus, the system comprising:

(a) means for identifying at least one input that causes a change in at least two of a plurality of outputs;

(b) a memory device configured to store values of the identified inputs and corresponding empirical output values along with predicted output values, wherein the predicted output values are calculated based on, in part, the values of the identified inputs;

(c) means for calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values;

(d) means for calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients; and

(e) means for communicating the transformed input values of (d) to a manufactoring apparatus.

16. The system of claim 15, wherein the score equation is:

$S_p=\underset{i,k}{\sum <br><br>}<br><br>{W_{i,k}<br><br>\left(y_{\mathrm{actual}}^{i<br><br><br><br>k}-y_{\mathrm{predicted}}^{i<br><br><br><br>k}<br><br>\left({\stackrel{\to <br><br>}{X}}^{{i<br><br>}^{\mathrm{\prime <br><br>}}}<br><br>\left({\stackrel{\to <br><br>}{X}}^i,\stackrel{\to <br><br>}{P}\right)\right)\right)}^2$

where;

i—

number of wafer;

k—

number of output;

y_actual—

an empirical output value;

y_predicted—

a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}^i′

)

{right arrow over (X)}^i′

=(X₁^i′

,X₂^i′

,X₃^i′

) is transformed input values in a vector format;

{right arrow over (X)}ⁱ=(X₁ⁱ,X₂ⁱ,X₃ⁱ) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)}.

17. The system of claim 15, further comprising:

means for collecting additional empirical data and corresponding input values; and

means for calculating a new set of coefficients {right arrow over (P)}_new, wherein the new set of coefficients is defined as the optimal value of {right arrow over (P)}.

18. The system of claim 15, further comprising:

means for collecting additional empirical data and corresponding input values; and

means for calculating a new set of coefficients based on the additional empirical data.

19. The system of claim 18, wherein the means for calculating is further configured to use the following equation in calculating the new of coefficients:

{right arrow over (P)}_new≡

{right arrow over (P)}_previous+K({right arrow over (P)}_optimum−

{right arrow over (P)}_previous),

wherein K<

1 and {right arrow over (P)}_previous is a previously calculated optimal value of {right arrow over (P)}, wherein the new set of coefficients is defined as the optimal value of {right arrow over (P)}.

20. A computer readable medium for storing instructions being executed by one or more computers, the instructions directing the one or more computers to perform a method for predicting output characteristics of a device produced by a manufacturing apparatus, the method comprising:

(a) identifying at least one input that causes a change in at least two of a plurality of outputs;

(b) storing values of the identified inputs and corresponding empirical output values;

(c) calculating and storing predicted output values, based on, in part, the values of the identified inputs;

(d) calculating a set of transform coefficients by minimizing a score equation that is a function of, in part, differences between one or more of the empirical output values and their corresponding predicted output values;

(e) calculating one or more input values for one or more desired output values based on, in part, the calculated set of transform coefficients; and

(f) communicating the transformed input values of (d) to a manufacturing apparatus.

21. The medium of claim 20, wherein the score function is:

$S_p=\underset{i,k}{\sum <br><br>}<br><br>{W_{i,k}<br><br>\left(y_{\mathrm{actual}}^{i<br><br><br><br>k}-y_{\mathrm{predicted}}^{i<br><br><br><br>k}<br><br>\left({\stackrel{\to <br><br>}{X}}^{{i<br><br>}^{\mathrm{\prime <br><br>}}}<br><br>\left({\stackrel{\to <br><br>}{X}}^i,\stackrel{\to <br><br>}{P}\right)\right)\right)}^2$

where;

i—

number of wafer;

k—

number of output;

y_actual—

an empirical output value;

y_predicted—

a predicted output value, as calculated based on transformed inputs for a particular wafer i ({right arrow over (X)}^i′

)

{right arrow over (X)}^i′

=(X₁^i′

,X₂^i′

,X₃^i′

) is transformed input values in a vector format;

{right arrow over (X)}ⁱ=(X₁ⁱ,X₂ⁱ,X₃ⁱ) for wafer i together with the transformation parameters {right arrow over (P)}, to thereby calculate an optimal value of {right arrow over (P)}.

22. The medium of claim 20, wherein the method further comprises:

collecting additional empirical data and corresponding input values;

calculating a new set of coefficients {right arrow over (P)}_new; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.

23. The medium of claim 20, wherein the method further comprises:

collecting additional empirical data and corresponding input values;

calculating a new set of coefficients as

{right arrow over (P)}_new≡

{right arrow over (P)}_previous+K({right arrow over (P)}_optimum−

{right arrow over (P)}_previous),

wherein K<

1 and {right arrow over (P)}_previous is a previously calculated optimal value of {right arrow over (P)}; and

using the new set of coefficients as the optimal value of {right arrow over (P)}.