Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Defocus based phase imaging for quantifying electromagnetic edge effects in photomasks

Aamod Shanker

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2014-105
May 16, 2014

http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-105.pdf

The edges of absorbing regions used to define features on photomasks have inherent electromagnetic diffraction effects that limit the focus tolerance during projection printing. In this work it is shown that the thin mask boundary layers used to characterize these effects can be directly measured by capturing through-focus aerial images, a routine procedure for local quality inspection during mask fabrication. The Transport of Intensity phase imaging method is used to recover quantitative phase from a stack of intensity images, the phase near feature edges directly corresponding to edge effects at the mask. We discover that the Transport of Intensity solver produces errors in the solved phase near sharp corners due to strong curl effects in the power flow, and an iterative solver is developed to remedy the artifacts. Using the improved algorithm, polarization-dependent edge effects are observed experimentally in the quantitative phase images for both OMOG and ATT-PSM masks. The measured edge effects correspond to 20nm wide imaginary valued boundary layers for ATT-PSM, and half that for OMOG masks, values which agree with those predicted by full-wave simulations in literature. Finally, the TIE is extended for the case of general illumination, and it is shown that the phase can be recovered from intensity measurements at a single focal plane by illumination patterning.

Advisor: Laura Waller


BibTeX citation:

@mastersthesis{Shanker:EECS-2014-105,
    Author = {Shanker, Aamod},
    Editor = {Waller, Laura and Neureuther, Andrew R.},
    Title = {Defocus based phase imaging for quantifying electromagnetic edge effects in photomasks},
    School = {EECS Department, University of California, Berkeley},
    Year = {2014},
    Month = {May},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-105.html},
    Number = {UCB/EECS-2014-105},
    Abstract = {The edges of absorbing regions used to define features on photomasks have inherent electromagnetic diffraction effects that limit the focus tolerance during projection printing. In this work it is shown that the thin mask boundary layers used to characterize these effects can be directly measured by capturing through-focus aerial images, a routine procedure for local quality inspection during mask fabrication. The Transport of Intensity phase imaging method is used to recover quantitative phase from a stack of intensity images, the phase near feature edges directly corresponding to edge effects at the mask. We discover that the Transport of Intensity solver produces errors in the solved phase near sharp corners due to strong curl effects in the power flow, and an iterative solver is developed to remedy the artifacts. Using the improved algorithm, polarization-dependent edge effects are observed experimentally in the quantitative phase images for both OMOG and ATT-PSM masks. The measured edge effects correspond to 20nm wide imaginary valued boundary layers for ATT-PSM, and half that for OMOG masks, values which agree with those predicted by full-wave simulations in literature. Finally, the TIE is extended for the case of general illumination, and it is shown that the phase can be recovered from intensity measurements at a single focal plane by illumination patterning.}
}

EndNote citation:

%0 Thesis
%A Shanker, Aamod
%E Waller, Laura
%E Neureuther, Andrew R.
%T Defocus based phase imaging for quantifying electromagnetic edge effects in photomasks
%I EECS Department, University of California, Berkeley
%D 2014
%8 May 16
%@ UCB/EECS-2014-105
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-105.html
%F Shanker:EECS-2014-105