Rapid optical metrology of critical dimensions in large-area nanopatterned structures

Modern high-throughput nanopatterning techniques, such as nanoimprint lithography, enable fabrication of Large-area Nanostructure Arrays (LNAs) on wafers and roll-to-roll substrates reaching scales as large as cm² or m². A significant challenge to scaling up manufacturing of nanopatterned surfaces is the fact that traditional metrology methods, such as microscopy or point-to-point scatterometry-based inspections, are not amenable to high manufacturing throughput. Recent research introduced significant increase in throughput of scatterometry metrology of nanopatterned surfaces by dramatically parallelizing the acquisition of reflectance spectra to enable significantly larger field of view, within which several million micrometer scale pixels act as receivers of scattered light spectra. Geometric characteristics, or so-called critical dimensions of nanofeatures associated with each pixel within that field of view, can then be inferred via the so-called inverse modeling process, which employs physics-based dependencies between geometric characteristics of the surfaces and reflectance spectra obtained from them. Inverse modeling-based inference of critical dimensions relies on an a priori generated library of reflectance spectra simulated for an exhaustive set of underlying critical dimensions. Inference of critical dimensions associated with a nanopatterned surface comes down locating in that library the spectrum that is nearest to the one obtained from the inspected nanopatterned surface and associating critical dimensions of that measured surface with geometric parameters of thus identified simulated spectrum from the library. When it comes to the advanced inspection devices such as hyperspectral imaging systems, the inverse modeling procedure implies that in each field of view, one needs to conduct several million nearest neighbor searches in the corresponding library of simulated spectra, which places tremendous importance on ensuring that such searches can be done fast and efficiently. Furthermore, depending on the number of parameters describing the nano-pattern, and the resolution with which simulations are conducted to generate the library of reflectance spectra, even the creation of a trustable library will be impossible and can take several decades, which further emphasizes the need for smart, efficient, and accurate library creation and library search methods. The objective of this dissertation is to address the aforementioned needs, and improve library creation and library search stages of the inverse modeling-based metrology procedure in order to enable metrology of large-area nanopatterned surfaces within relevant production cycle times and without interruptions of the production line. When it comes to the library search step, I proposed the use of distance-based tree-structured data organization to facilitate data searches with logarithmic speed gains compared to search speeds in databases organized as lists. Growing Self-Organizing Map (GSOM) based unsupervised clustering of the spectral metrology data is utilized to obtain clusters of databases and enable faster searches. Searching in such a database for entries that are nearest to some query item can be accomplished by first identifying the nearest SOM centroid to that query entry, after which nearest neighbors can be sought only in the corresponding cluster, rather than the entire database. Such “divide and conquer” database organization, enables dramatically faster retrieval of data that are near a given query data item. When it comes to the intelligent library creation, especially for nanostructures with complex patterns, brute force generation of an exhaustive library of spectra is not an option anymore and instead, inspection of critical dimensions of nanopatterned surfaces was pursued as an inverse problem in which optimization techniques were coupled with the efficient library searches. The process starts with an initial, incomplete library of simulated spectra, which was organized into a tree-based database structure. For each physically measured spectrum, the best matching simulated spectrum was efficiently sought in that library and was served as an initial guess for the optimization problem in which further refinement of simulated spectra was conducted to obtain estimates of the inspected nanopattern geometries with sufficient accuracy. However, even though utilizing aforementioned methods facilitated orders of magnitude faster measurements of LNA CDs, while at the same time maintaining the Gage R&R of SEM-based inspection , the time needed to fully measure a 300 mm wafer with hourglass nanostructures was still outside the unit process cycle times of such wafers (hours instead of minutes). Hence, significant improvements were still needed to further accelerate reflectance spectra-based inspection of LNAs, while at the same time minimally, or not at all jeopardizing its accuracy and Gage R&R. In order to further accelerate the optical metrology of CDs of LNAs, the following opportunities could be pursued. First off, even though utilizing optimization-based inverse problems resolved the need to generate an exhaustive library of reference reflectance spectra, it still required a considerable number of simulations in order to reach inverse problem convergence with sufficient accuracy. In addition, one needed to continuously perform millions of searches for best matches within the offline generated library of reflectance spectra in order to initiate the inverse-problem optimization and infer the underlying LNA CDs. I overcame both problems by employing advanced Machine Learning (ML)-based methods to realize inverse problem mappings between reflectance spectra and LNA CDs, rather than pursuing them using a more traditional, gradient-based optimization and nearest neighbor searches. The use of ML-models required only a one-time training to build the mappings between reflectance spectra and the underlying CDs based on the available simulated reflectance spectra. Once the training was accomplished, one could rapidly estimate CDs associated with a query reflectance spectrum, without any need to search through a reference library of reflectance spectra, or solve time-consuming optimization problems. Another element which strongly affected the speed of reflectance spectra-based CD metrology was the number of wavelengths one needed to consider during the inspection process. This choice affected the times needed to complete the experimental acquisition and simulations of reflectance spectra, as well as the process of matching of the physically acquired spectra with simulated ones, via which CDs were inferred. Utilizing a broader spectrum and a higher resolution of wavelengths generally improved the accuracy of the CD estimation by providing more optical information about the measured nanopatterned area. Nevertheless, it did adversely affect computational efforts and times associated with spectral simulations and matching. Thus, we pursued this opportunity for reduction of times needed to perform optical LNA metrology by employing ML-based strategic selection of spectral wavelengths which contained the greatest amount of optical information relevant to the measured nanopatterned surface area, while maintaining a sufficient accuracy of estimation of the underlying CDs. Capabilities of the aforementioned methods were evaluated through inspection of a semiconductor wafer sample with hourglass patterns, which were characterized by eight CDs. It was observed that the proposed method is capable of real-time CD metrology of large-area nanostructured surfaces with complex nanopatterns, with accuracy and repeatability comparable to that of Scanning Electron Microscopy.