Optimizing hybrid metrology: rigorous implementation of Bayesian and combined regression

Abstract

Hybrid metrology, e.g., the combination of several measurement techniques to determine critical dimensions, is an increasingly important approach to meet the needs of the semiconductor industry. A proper use of hybrid metrology may yield not only more reliable estimates for the quantitative characterization of 3-D structures but also a more realistic estimation of the corresponding uncertainties. Recent developments at the National Institute of Standards and Technology (NIST) feature the combination of optical critical dimension (OCD) measurements and scanning electron microscope (SEM) results. The hybrid methodology offers the potential to make measurements of essential 3-D attributes that may not be otherwise feasible. However, combining techniques gives rise to essential challenges in error analysis and comparing results from different instrument models, especially the effect of systematic and highly correlated errors in the measurement on the χ2 function that is minimized. Both hypothetical examples and measurement data are used to illustrate solutions to these challenges.

Appraising the Extensibility of Optics-Based Metrology for Emerging Materials

“…Imaging these targets permits spatial localization of a region of interest (ROI) smaller than the scatterometric spot size, and several targets can be imaged within the field of view of the microscope without degrading the dimensional measurements (27). Our group has also yielded imagebased measurements of overlay using finite sets of arrayed lines (3) and has also concentrated on the measurement of line width, often referred to in nanoelectronics as the "critical dimension" (CD) (28).…”

Metrology and inspection required for next generation lithography

“…For 1x nm and beyond, however, TMU should be more improved. Hybrid metrology [33][34][35] and= or X-ray metrology [36][37][38] will be candidate in addition to optical scatterometry.…”

“…This combined use of different metrology tools is known as hybrid metrology. [33][34][35] The scatterometry results were validated by scanning transmission electron microscopy (STEM). As a reference, we also tried conventional scatterometry in which spectra were acquired only after development to simultaneously analyze both guide and DSA pattern.…”

Optimizing hybrid metrology: rigorous implementation of Bayesian and combined regression

“…The regression problem then amounts to minimizing the difference between the modeled and the measured data. We therefore solve for the parameter vector that minimizes the so-called χ 2 function, measuring the goodness of fit of the simulation to the measurement data given by the weighted norm (3) In this formulation we implicitly assume that the measurement data y is a noisy realization of the model, and that we have an additive error model where (4) Note that the the errors that are added to each of the model values can also be arranged as an m-dimensional vector. We assume the errors to be normally distributed with zero mean and m × m covariance matrix Σ ϵ .…”

“…This paper can be seen as a continuation of that work and Ref. [4], with an emphasis on the proper treatment of the measurement errors, including highly correlated and systematic errors and their influence on hybrid metrology. Tool-induced errors for OCD and scale errors for SEM are investigated, and it is shown how the parametric uncertainties can be decreased if those issues are addressed accurately in the hybridization.…”