Investigations on a robust profile model for the reconstruction of 2D periodic absorber lines in scatterometry

H Gross,A Rathsfeld,J Richter,M Bar

doi:10.2971/jeos.2010.10053

Abstract

Scatterometry as a non-imaging indirect optical method in wafer metrology is applicable to lithography masks designed for extreme ultraviolet (EUV) lithography , where light with wavelengths of about 13.5 nm is applied. The main goal is to reconstruct the critical dimensions (CD) of the mask, i.e., profile parameters such as line width, line height, and side-wall angle, from the measured diffracted light pattern and to estimate the associated uncertainties. The numerical simulation of the diffraction process for periodic 2D structures can be realized by the finite element solution of the two-dimensional Helmholtz equation. The inverse problem is expressed as a non-linear operator equation where the operator maps the sought mask parameters to the efficiencies of the diffracted plane wave modes. To solve this operator equation, the deviation of the measured efficiencies from the ones obtained computationally is minimized by a Gauss-Newton type iterative method. In the present paper, the admissibility of rectangular profile models for the evaluations of CD uniformity is studied. More precisely, several sets of typical measurement data are simulated for trapezoidal shaped EUV masks with different mask signatures characterized by various line widths, heights and side-wall angles slightly smaller than 90 degree. Using these sets, but assuming rectangular structures as the basic profiles of the numerical reconstruction algorithm, approximate line height and width parameters are determined as the critical dimensions of the mask. Finally, the model error due to the simplified shapes is analyzed by checking the deviations of the reconstructed parameters from their nominal values.

Highlights

As mask and wafer technologies proceed to ever smaller features sizes the demands for a tight control of critical dimensions (CD) on the photo lithographic mask becomes increasingly challenging [1]
In the present investigation we reduce the complexity of the above profile model by imposing a further constraint: All side-wall angles should be equal to 90◦
The objective of this study is to examine the mismatch of the reconstructed widths and heights in dependence on different mask signatures described by different line-to-space ratios, heights, and side-wall angles of the absorber line, respectively

Summary

INTRODUCTION

As mask and wafer technologies proceed to ever smaller features sizes the demands for a tight control of critical dimensions (CD) on the photo lithographic mask becomes increasingly challenging [1]. The cross section of the line-space structure is a symmetric polygonal domain composed of three trapezoidal layers of different materials (TaO, TaN, and SiO2). These trapezoids are defined by the heights pi, i = 1, 6, 11 and by the x-coordinates pi, i = 2, 3, 7, 8, 12, 13 of the corners. Measurement sets are simulated for trapezoidal shaped EUV masks with different mask signatures, i.e., with different side-wall angles, line heights and line-to-space ratios (cf Section 3) For these diffraction patterns, the deviations of the reconstructed profile parameters from the design or nominal values are evaluated applying a rectangle as the basic structure for the reconstruction.

MODEL OF SCATTEROMETRY

SIMPLIFIED PROFILE MODEL

Impact of different mask signatures

Impact of detector noise and multilayer perturbations

Findings

SUMMARY