Mathematical Statistical methods for ML algorithms for EUVL

The primary goal of this research topic is to develop a new paradigm of innovative mathematics for statistical analysis to characterize state-of-the-art EUV patterning at resolution limits, where imaging optics, resist physical and chemical properties, resist chemistry and etch stochastic effects, interact and mix generating new-found performance-limiting mechanisms, i.e., “mechanistic-stochastic defectivity”, that could only be detected from statistics-math analysis of very large data sets; a “very large” data set usually means an average of larger than 10¹⁰ data points, or in some process instances, even larger. Furthermore, the project seeks to take the mathematical statistics analysis results to create innovative machine learning algorithms with unique models to examine, compare and correlate multi-parameter data sets describing the complex EUV patterning processes that play a key role in CMOS device scaling at and beyond A14 technology node.

These novel ML models, seek to correlate X-Y-Z dimensions i.e., feature linear CD, height, profile shape asymmetry induced by high exposure angles of the EUV image, surface and left-right lateral roughness of a EUV patterned structure.

An additional goal is to develop innovative mathematical-statistical methods, followed by ML modelling of data sets with different structures, linear distributions of the typical critical dimensions, “CD’s”, 2D dimensional spatially distributed (vectors) maps, and, data with complex XYZ volume-space distribution within photoresist thickness,

In this pathfinding project, approaches for correlating the statistical data analysis from wafer metrology will be developed by correlating it with geometrical design of CMOS device structures, EUV imaging characteristics, EUV photoresist chemical attributes, scanner sensor metrology and correction knobs that can be used to compensate data variability and enhance patterning performance at resolution limit,