Utilizing focused field as a probe for shape determination of subwavelength structures via coherent Fourier scatterometry

Nanopillars are widely used for various applications and require accurate shape characterization to enhance their performance and optimize fabrication processes. In this paper, we employ coherent Fourier scatterometry (CFS) combined with rigorous three-dimensional finite-difference time-domain simulations to accurately determine the shapes of nanopillars with various geometries, including cylindrical, triangular, square, and rectangular shapes. The nanopillars considered here have lateral dimensions (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>a</a:mi></a:math>) ranging from 100 to 1000 nm. Our methodology utilizes the preferential excitation of the nanostructures by a tightly focused beam and leverages their inherent symmetry to capture far-field signatures that vary periodically with rotation. This approach allows us to distinguish between different nanopillar shapes based on these rotational signatures. Our results demonstrate that the CFS method can reliably characterize nanopillars with lateral dimensions <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mi>a</d:mi><d:mo>≥</d:mo><d:mn>300</d:mn></d:math> nm, surpassing the conventional diffraction limit of 351 nm. However, the method reaches its fundamental limits for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><g:mi>a</g:mi><g:mo>≤</g:mo><g:mn>200</g:mn></g:math> nm, as also confirmed by simulations, where we approach the dipole approximation regime (<j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><j:mi>a</j:mi><j:mo>≪</j:mo><j:mi>λ</j:mi></j:math>). This constraint is not observed for rectangular nanopillars, owing to their constant breadth (<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><m:mi>b</m:mi><m:mo>=</m:mo><m:mn>1000</m:mn></m:math> nm), which prevents such a regime. Furthermore, our method successfully differentiates nanopillars transitioning from rectangular to square shapes. We also explored the method’s limitations concerning nanostructure height (<p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><p:mi>h</p:mi></p:math>), finding that triangular and square nanopillars could be characterized accurately for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><s:mi>h</s:mi><s:mo>≥</s:mo><s:mn>50</s:mn></s:math> nm and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><v:mi>h</v:mi><v:mo>≥</v:mo><v:mn>150</v:mn></v:math> nm, respectively. Furthermore, the method remains robust against shape distortions such as edge roundness. The method is primarily effective in determining the lateral (top-down) shape of nanopillars, it does not resolve longitudinal features. The ability to accurately characterize nanostructure shapes has significant implications in fields such as photonics and biosensing, where geometry critically influences device performance.