3D profile measurement for stepped microstructures using region-based transport of intensity equation

Abstract

One of the major challenges in the semiconductor industry is to measure the three-dimensional (3D) profile of objects with large step height (>100 µm), as well as nanometer-level surface profiles. In this work, a novel technique called region-based transport of intensity equation (R-TIE) is explored to measure both large step heights as well as local surface profiles with nanometer resolution. The key factors of the R-TIE are the use of composite image segmentation, transport of intensity equation (TIE), and a smart imaging system. The imaging system incorporates an electrically tunable lens to record objects at different focus positions with large field of view, high speed, and no mechanical moving parts. The TIE part of the system allows for nanometer height measurement at areas of interest. We demonstrate the basic principle and feasibility of the proposed method by experimentally measuring different stepped specimens.

Comparative study of phase unwrapping algorithms based on solving the Poisson equation

“…As a result, the direct Poisson solvers can be regarded as a low pass filter. As a matter of fact, if we make the Fourier transform of the Poisson equation as shown in equation ( 2), we can get (10) where F represents the Fourier transform. If we consider the 1D case, the transfer function H( f ) = 1/f 2 , which is similar to a low pass filter as shown in figure 16.…”

“…Plenty of information that we are interested in is coded in the phase of light. To obtain the information we want, the phase needs to be decoded and different methods are proposed [1][2][3][4][5][6][7][8][9][10]. Generally, these methods can be clarified into two groups: the interferometric methods [1,6] and non-interferometric ones [2][3][4][5][7][8][9][10].…”

“…To obtain the information we want, the phase needs to be decoded and different methods are proposed [1][2][3][4][5][6][7][8][9][10]. Generally, these methods can be clarified into two groups: the interferometric methods [1,6] and non-interferometric ones [2][3][4][5][7][8][9][10]. Specifically, the non-interferometric methods can be divided into three types: the iterative ones [2], the deterministic ones [3,4,7,9,10] and the combination of the iterative and deterministic methods [5,8].…”

“…Generally, these methods can be clarified into two groups: the interferometric methods [1,6] and non-interferometric ones [2][3][4][5][7][8][9][10]. Specifically, the non-interferometric methods can be divided into three types: the iterative ones [2], the deterministic ones [3,4,7,9,10] and the combination of the iterative and deterministic methods [5,8]. Among these methods, the interferometric methods are the most representative ones due to its high accuracy.…”