Method of determining a performance parameter distribution
AssigneeASML Netherlands B.V.
InventorsVahid BASTANI, Raoul Maarten Simon KNOPS, Thomas THEEUWES, Adam Jan URBANCZYK, Jochem Sebastiaan WILDENBERG, Robert Jan VAN WIJK
Life of this patent
Estimating the term…
Abstract
A method of determining a performance parameter distribution and/or associated quantile function. The method includes obtaining a quantile function prediction model operable to predict a quantile value for a substrate position and given quantile probability such that the predicted quantile values vary monotonically as a function of quantile probability and using the trained quantile 5 function prediction model to predict quantile values for a plurality of different quantile probabilities for one or more locations on the substrate.
Claims20
A method of determining a performance parameter distribution and/or associated quantile function, the performance parameter being associated with a semiconductor manufacturing process for forming one or more structures on a substrate, the method comprising:
- obtaining a quantile function prediction computer model configured to predict a quantile value for a location on the substrate and given quantile probability such that the predicted quantile values vary monotonically as a function of quantile probability;
- and
- using, by a hardware computer system, the model to predict quantile values for one or more quantile probabilities relating to one or more locations on the substrate.
A method of representing parameter distribution data describing a variation of the parameter over a range of values as a Bernstein coefficient representation, the method comprising:
- determining an empirical cumulative distribution function from the parameter distribution data;
- transforming cumulative distribution function values from the empirical cumulative distribution function using an inverse cumulative distribution function of a normal distribution to obtain quantiles;
- mapping the quantiles to an interval [0,1], based on a chosen range for a fitting;
- and
- fitting, by a hardware computer, a Bernstein computer model using Bernstein basis polynomials to the quantiles to obtain a set of Bernstein coefficients, the fit being subject to at least one constraint to impose monotonicity.
Dependencies are inferred from the claim text.