Method for calibrating simulation process based on defect-based process window

Patent metadata

Field	Value
Publication number	US-12386268-B2
Application number	US-202117799019-A
Country	US
Kind code	B2
Filing date	Feb 18, 2021
Priority date	Feb 21, 2020
Publication date	Aug 12, 2025
Grant date	Aug 12, 2025

Abstract

Methods related to improving a simulation processes and solutions (e.g., retargeted patterns) associated with manufacturing of a chip. A method includes obtaining a plurality of dose-focus settings, and a reference distribution based on measured values of a characteristic of a printed pattern associated with each setting of the plurality of dose-focus settings. The method further includes, based on an adjustment model and the plurality of dose-focus settings, determining a probability density function (PDF) of the characteristic such that an error between the PDF and the reference distribution is reduced. The PDF can be a function of the adjustment model and variance associated with dose, the adjustment model being configured to change a proportion of non-linear dose sensitivity contribution to the PDF. A process window can be adjusted based on the determined PDF of the characteristic.

First claim

The invention claimed is:

1. A method for adjusting a process window, the method comprising:
obtaining: (i) a plurality of dose-focus settings, and (ii) a reference distribution based on measured values of a characteristic of a printed pattern associated with each setting of the plurality of dose-focus settings;
determining, by a hardware computer system and based on an adjustment model and the plurality of dose-focus settings, a probability density function (PDF) of the characteristic such that an error between the PDF and the reference distribution is reduced, the PDF being a function of the adjustment model and variance associated with dose, the adjustment model being configured to change a proportion of non-linear dose sensitivity contribution to the PDF; and
adjusting, based on the determined PDF of the characteristic, a process window associated with a patterning process.

2. The method of claim 1 , wherein the determining of the PDF is an iterative process, an iteration comprising:
determining, based on the adjustment model, an adjustment value for a given dose-focus setting of the plurality of dose-focus settings;
determining, based on the adjustment value, the PDF of the characteristic of a pattern;
determining an error between the PDF and the reference distribution; and
adjusting one or more parameters of the adjustment model for the given dose and focus setting of the plurality of dose-focus settings such that the error is minimized.

3. The method of claim 1 wherein the PDF is determined by a convolution of a first PDF and a second PDF, wherein the first PDF is a function of a first variation, the first variation being a product of the adjustment model and variation of dose, and the second PDF is a function of a second variation associated with factors other than dose contributing to variation in the characteristic of a pattern.

4. The method of claim 3 , wherein the determining of the PDF is an iterative process, an iteration comprising:
convoluting the first PDF and the second PDF to determine the PDF of the characteristic of a pattern;
determining an error between the PDF and the reference distribution; and
adjusting one or more parameters of the first variation and the second variation for a given dose and focus setting of the plurality of dose-focus settings such that the error is minimized.

5. The method of claim 2 , wherein the adjusting of the one or more parameters of the adjustment model is performed by an optimization algorithm selected from: adaptive moment estimation or a gradient decent method.

6. The method of claim 1 , wherein the adjustment model is a polynomial function of dose and focus.

7. The method of claim 4 , further comprising:
determining a plurality of adjustment values associated with the PDF having minimum error with respect to the reference distribution for each dose and each focus setting of the plurality of dose-focus settings; and
fitting, based on the plurality of adjustment values, a polynomial function of dose and focus to determine the adjustment model such that a difference between the fitted polynomial function and the plurality of adjustment model values is minimized.

8. The method of claim 1 , further comprising executing, using failure rate data associated with the pattern, the determined probability density function to determine a characteristic limit associated with a threshold failure rate.

9. A non-transitory computer-readable medium comprising instructions therein, the instructions, when executed by one or more processors, configured to cause the one or more processors to at least:
obtain: (i) a plurality of dose-focus settings, and (ii) a reference distribution based on measured values of a characteristic of a printed pattern associated with each setting of the plurality of dose-focus settings;
determine, based on an adjustment model and the plurality of dose-focus settings, a probability density function (PDF) of the characteristic such that an error between the PDF and the reference distribution is reduced, the PDF being a function of the adjustment model and variance associated with dose, the adjustment model being configured to change a proportion of non-linear dose sensitivity contribution to the PDF; and
adjust, based on the determined PDF of the characteristic, a process window associated with a patterning process.

10. The non-transitory computer-readable medium of claim 9 , wherein the determination of the PDF is an iterative process, an iteration comprising:
determination, based on the adjustment model, of an adjustment value for a given dose focus setting of the plurality of dose-focus settings;
determination, based on the adjustment value, of the PDF of the characteristic of a pattern;
determination of the error between the PDF and the reference distribution; and
adjustment of one or more parameters of the adjustment model for the given dose and focus setting of the plurality of dose-focus settings such that the error is minimized.

11. The non-transitory computer-readable medium of claim 9 , wherein the adjustment model is a polynomial function of dose and focus.

12. The non-transitory computer-readable medium of claim 9 , wherein the instructions are further configured to cause the one or more processors to execute comprising: executing, using failure rate data associated with the pattern, the determined probability density function to determine a characteristic limit associated with a threshold failure rate.

13. A method comprising:
obtaining: (i) a dose probability density function (dose PDF) to determine a probability of dose, the dose PDF being a function of (a) a characteristic of a feature and (b) a deviation of a mask characteristic, the mask characteristic being associated with a mask used to print the feature on a substrate, and (ii) a mask probability density function (mask PDF) to determine a probability in the deviation of the mask characteristic;
determining, by a hardware computer system, a probability density function associated with the characteristic by convoluting (i) the dose PDF and (ii) the mask PDF over a given range of mask characteristic values; and
adjusting, based on the determined probability density function associated with the characteristic, a process window associated with a patterning process.

14. The method of claim 13 , wherein the mask PDF incorporates dependency of a non-linear mask error enhancement factor (MEEF) that causes a skewness in the mask PDF, wherein the non-linear MEEF is computed using an inverse function of a relation between the mask characteristic and the characteristic of the printed on the substrate.

15. The method of claim 14 , wherein the mask PDF is computed by:

PDF
mask

(

δ
⁢

CD
mask

)

=

G
mask

(

g
mask

(

δ
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CD
mask

Assignees

• Asml Netherlands Bv

Inventors

• Van Ingen Schenau Koenraad
• Slachter Abraham
• Timoshkov Vadim Yourievich
• Kooiman Marleen
• Van Lare Marie-Claire
• Dillen Hermanus Adrianus
• Hunsche Stefan
• Colina Luis Alberto Colina Santamaría
• Jiang Aiqin
• Wang Fuming
• Raghunathan Sudharshanan

Classifications

• G03F7/70641

  Focus · CPC title

• G03F7/70633

  Overlay, i.e. relative alignment between patterns printed by separate exposures in different layers, or in the same layer in multiple exposures or stitching · CPC title

• G03F7/70625

  Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness · CPC title

• G03F7/70558 Primary

  Dose control, i.e. achievement of a desired dose · CPC title

• G03F7/705 Primary

  Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions · CPC title