Fast pixel-based mask optimization for inverse lithography

Yuri Granik

doi:10.1117/1.2399537

Abstract

The direct problem of optical microlithography is to simulate printing features on the wafer under the given mask, imaging system, and process characteristics. The goal of inverse problems is to find the best mask, imaging system, or process to print the given wafer features. In this study, we proposed the strict formalization and fast solution methods of inverse mask problems. We stated inverse mask problems (or "layout inversion" problems) as nonlinear, constrained minimization problems over a domain of mask pixels. We considered linear, quadratic, and nonlinear formulations of the objective function. The linear problem is solved by an enhanced version of the Nashold projections. The quadratic problem is addressed by eigenvalue decompositions and quadratic programming methods. The general nonlinear formulation is solved by the local variations and gradient descent methods. We showed that the gradient of the objective function can be calculated analytically through convolutions. This is an important practical result because it enables layout inversion on a large scale in order of M log M operations for M pixels.

Citation Download Citation

Yuri Granik, "Fast pixel-based mask optimization for inverse lithography," Journal of Micro/Nanolithography, MEMS, and MOEMS 5(4), 043002 (1 October 2006). https://doi.org/10.1117/1.2399537

ACCESS THE FULL ARTICLE

PERSONAL SIGN IN
Full access may be available with your subscription

Email or Username Forgot your username?

Password Forgot your password?

Show

Remember Email/Username on this computer

Remember Password

No SPIE account? Create an account
or Institutional Sign In via Shibboleth

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $20.00

Non-members: $25.00 ADD TO CART

Show All Keywords

Keywords/Phrases

Search In:

Publication Years