Characterization and monitoring of photomask edge effects

Abstract

An experimental technique for quantitatively characterizing edge effect contributions in transmission through thick photomasks is described and evaluated through electromagnetic simulation. The technique consists of comparing the 0 th order transmission for various duty cycles to the expected experimental behavior from a thin mask model. The real electric field component from the edges is proportional to the shift in the position of the minimum energy in the 0 th order field away from the expected thin mask location. The square root of the minimum 0 th order diffraction energy normalized to a clear mask gives the imaginary edge contribution. The results indicate that Alternating Phase Shifting Masks (ALT-PSM) and Attenuating Phase Shifting Masks (ATT-PSM) technologies have significant edge effects on the order of 0.1λ to 0.2λ per edge respectively, as well as polarization dependence. For periods of 2 wavelengths and larger these edge contribution values are nearly independent of pitch. The existence of an imaginary (or quadrature) phase component is shown to result in an additive linear variation of line edge shortening through focus. This tilt can be interpreted as a focus shift of the normal parabolic behavior and is about 0.5 Rayleigh units (RU). This focus shift depends to some extent on the surrounding layout as well as the feature itself.

Analysis and modeling of photomask edge effects for 3D geometries and the effect on process window

“…11 When examining the intensity of the 0 th order transmission the 0 o and 180 o phase regions cancel each other out. Due to transmission imbalance in the two regions, by changing the duty cycle, we are able to find the maximum cancellation between the 0 o and 180 o areas.…”

“…11 Boundary layer (BL) modeling of edge effects is particularly appealing due to the natural extension for inclusion into OPC and pattern matching. 12 This paper presents an expansion of this method to off-axis illumination, alternate mask stacks, and 3D mask geometries.…”

Extensions of boundary layer modeling of photomask topography effects to fast-CAD using pattern matching

“…Intensity = |E| 2 , and with the math illustrated in Eqns. (4)(5)(6)(7)(8), we obtain a composite match factor compromised of the unaberrated airy function match and the spillover function. The composite match factor incorporates the influence of neighboring features, aberrations, and their complex interaction.…”

“…5,6 This paper focuses on the latter because BL modeling allows us to represent the errors as additional transmission regions on the mask layout, whereas DDM does not produce layout based corrections. This makes pattern matching, 7 a fast-CAD method for hot spot detection or design optimization, possible for EMF analysis.…”

If it moves, simulate it!

“…Mask edge effects are growing fourth challenge that spans both DUV and EUV. Electromagnetic studies of transmission through ATT-PSM by Marshal Miller [57] have found that the mask edges themselves produce imaginary or out of phase components on each edge as well as an effective bias toward the absorber. This is typically equivalent to a 0.1λ (20 nm) wide strip of quadrature phase electric field of the strength of the clear field at each mask edge.…”