Snell or Fresnel: the influence of material index on hyper-NA lithography

Bruce Smith; Jianming Zhou

doi:10.1117/12.713203

26 March 2007 Snell or Fresnel: the influence of material index on hyper-NA lithography

Bruce Smith, Jianming Zhou

Proceedings Volume 6520, Optical Microlithography XX; 65200A (2007) https://doi.org/10.1117/12.713203
Event: SPIE Advanced Lithography, 2007, San Jose, California, United States

Abstract

As immersion lithography is extended to ever increasing resolution, the resulting propagation angles in the materials involved become closer to grazing than to normal incidence. Classical laws of refraction and reflection cannot be used with either assumption however, as a collection of angles may exist across the entire range. Fresnel reflection at these angles becomes large enough that small disparities in refractive indices at material interfaces may lead to adverse effects. As an example, when water is used at numerical apertures approaching its refractive index, reflection effects are greater than the constraints imposed by refraction or absorption. This will limit the maximum NA value allowed by any given material to values sufficiently lower than its refractive index. Additionally, we have grown accustom to expanding the application of the Snell-Descartes Law to materials with low absorption, assuming that the contribution of the imaginary component of the refractive index is negligible. This is not the case for photoresists, fluids, or glasses, which can not strictly be considered as non-absorbing media. We have expanded the Snell-Descartes Law for absorbing media, with some interesting consequences. We will show that there is no real limit on the numerical aperture into a material, so long as its extinction coefficient is not zero. The relationship that lithographers have been using recently where NA< min[n_glass, n_fluid, n_resist] will be shown to be inadequate and imaging at numerical apertures up to 1.85 will be demonstrated using materials with significantly lower (real) refractive index values.

Citation Download Citation

Bruce Smith and Jianming Zhou "Snell or Fresnel: the influence of material index on hyper-NA lithography", Proc. SPIE 6520, Optical Microlithography XX, 65200A (26 March 2007); https://doi.org/10.1117/12.713203

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