Shapelet-based orientation and defect identification method for nanostructured surface imaging

Abstract

Structure-property relations are of fundamental importance for continued progress in materials research. Determining these relationships for nanomaterials introduces additional challenges, especially when nanostructure is present, either through self-assembly or nano-lithographic processes. Recent advances have been made for quantification of nanostructured surfaces, for which many robust experimental imaging methods exist. One promising approach is based on the use of shapelet functions for image analysis, which may be used as a reduced basis for surface pattern structure resulting from a broad range of phenomena (e.g. self-assembly). These shapelet-based methods enable automated quantification of nanostructured images, guided by the user/researcher, providing pixel-level information of local order without requiring detailed knowledge of order symmetries. In this work, enhancements to the existing shapelet-based response distance method are developed which enable further analysis of local order, including quantification of local orientation and identification of topological defects. The presented shapelet-based methods are applied to a representative set of images of self-assembled surfaces from experimental characterization techniques including scanning electron microscopy, atomic force microscopy and transmission electron microscopy. These methods are shown to be complementary in implementation and, importantly, provide researchers with a robust and generalized computational approach to comprehensively quantify nanostructure order, including local orientation and boundaries within well-aligned grains.

Shapelets: A Python package implementing shapelet functions and their applications

“…Shapelets are a class of complete localized orthogonal basis functions with a broad range of applications in image processing and reconstruction (Akdeniz et al, 2018;Massey & Refregier, 2005;Refregier, 2003;Suderman et al, 2015;Tino et al, 2024). Despite their increasingly widespread use, there is currently no single software package that is both broadly accessible (e.g.…”

“…Similarly, quantification of structure-property relationships for nanomaterials is critical for continued progress in materials research (Abukhdeir, 2016;Tino et al, 2024). This is especially true for nanomaterials with complex spatially-varying patterns, such as self-assembled materials (Abukhdeir, 2016).…”

“…Defect identification method for self-assembly microscopy imaging (Tino et al, 2024) via shapelets.self_assembly.defectid…”

“…Examples 1-3 demonstrate use of the shapelets.self_assembly submodule, with specific applications for the response distance method (Suderman et al, 2015), defect identification method (Tino et al, 2024), and local pattern orientation (Tino et al, 2024) (respectively).…”

“…The shapelets software package provides reference implementations and documentation for four different shapelet formulations: cartesian (Refregier, 2003), polar (Massey & Refregier, 2005), orthonormal polar with constant radial scale (Akdeniz et al, 2018), and exponential (Bergé et al, 2019). Additionally, the shapelets package provides reference implementations of several applications of shapelet functions in astronomy (galactic image decomposition and reconstruction (Massey & Refregier, 2005;Refregier, 2003)) and self-assembly (quantification of nanostructure order (Akdeniz et al, 2018;Suderman et al, 2015;Tino et al, 2024)). The coding style of shapelets is based on that of scipy.special (Virtanen et al, 2020).…”