Analytic theory of symmetric two-beam interference in high-NA optical lithography

Shinn-Sheng Yu; Burn J. Lin

doi:10.1117/12.601564

12 May 2005 Analytic theory of symmetric two-beam interference in high-NA optical lithography

Shinn-Sheng Yu, Burn J. Lin

Proceedings Volume 5754, Optical Microlithography XVIII; (2005) https://doi.org/10.1117/12.601564
Event: Microlithography 2005, 2005, San Jose, California, United States

Abstract

It is well known that TM-waves are not as effective as TE-waves in forming interference fringes in oblique incidence. In lithography, this corresponds to contrast loss when imaging with the high-NA exposure tool that employs strong off-axis illumination. One usually explains that there is an angle between electric fields of TM-waves in the resist. However, when the resist is absorptive, the calculation of reduction of contrast for TM-waves becomes rather complicated. In this paper, we show that the analytic formula for symmetric two-beam interference can be derived by straightforward full-vector approach. With the help of the Poynting vector and Poynting's theorem, aerial image in the resist can be calculated. The contrast-reduction factor for TM-waves is thus be found to be [formula] where k₀⁺ is the wave vector in the resist and N₀ is the complex index of refraction of the resist. When the resist is non-absorptive, the contrast loss factor for TM-waves reduces to the well-known form ε, = cos2θ₀, where θ₀ is the angle of refraction in the resist. It can also be shown that for TE-waves aerial image in the resist is separable in its transverse and longitudinal coordinate dependence, as is also true for TM-waves under reasonable approximations. That is, the thin-film effect can be regarded as independent of aerial image formation. This conclusion makes possible the development of an efficient methodology for optimizing the thin-film stack used in optical lithography.

Citation Download Citation

Shinn-Sheng Yu and Burn J. Lin "Analytic theory of symmetric two-beam interference in high-NA optical lithography", Proc. SPIE 5754, Optical Microlithography XVIII, (12 May 2005); https://doi.org/10.1117/12.601564

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

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