Edge diffraction by dielectric wedge of arbitrary angle

Sy, Kim; Woong, Jung; Shin, Sangho

doi:10.1049/el:19830579

Cited by 9 publications

(2 citation statements)

References 3 publications

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“…The first option is to provide undercuts beneath the chrome. [14][15][16][17][18] The objective of this work is to develop a useful formulation that can be applied on practical lithography problems. The second option is chrome biasing of the phase-shifted region.…”

Section: A Tempest Simulationmentioning

confidence: 99%

Edge effects characterization of phase shift mask

Chua

Tay

Quan

et al. 2005

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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The demand for steadily decreasing dimensions in semiconductor devices is driving the need for increased resolution in optical lithography. The use of phase shift masks ͑PSMs͒ is among such resolution enhancement techniques. PSM are well known to show prominent diffraction effects, which cannot be described by the assumption of an infinitely thin mask ͑Kirchhoff approach͒ that is used in many commercial photolithography simulators. A correct prediction of sidelobe printability, process window and linearity of an OPC mask requires a rigorous application of diffraction theory. Optical lithography simulation employing a time-domain finite-difference ͑TDFD͒ algorithm ͑TEMPEST͒ has been used effectively to study the problem of aerial image intensity imbalance through focus with alternating phase shift masks ͑altPSMs͒. Using Geometrical Theory of Diffraction ͑GTD͒, and the solutions to canonical problems, we obtained a relationship between mask edge and disturbance in an image space. The main objective to develop useful formulations that can be readily applied to diffraction in mask technology. Rigorous analysis of diffraction effect on altPSMs using the GTD approach is discussed and results show that the effect of shifter edge angle is equivalent to that of shifter width.

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Section: A Tempest Simulationmentioning

confidence: 99%

Edge effects characterization of phase shift mask

Chua

Tay

Quan

et al. 2005

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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“…The coupled difference equations (14), (17), and (18) on page 27 of the previous report [61] are solved by first eliminating the function C(v):…”

Section: Physical Impedance Boundary Conditionmentioning

confidence: 99%

Penetrable Wedge Analysis

Scarstein¹,

Davis²

1993

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(Maximum 200 words).The continuation of this wedge scattering research is proceeding as proposed, with several significant accomplishments and findings to date. The nature of this rigorous mathematical approach to scattering problems is such that original formulation is very important and usually very slow to evolve. For example, the previous work summarized in the report [61] had several abandoned and potentially useful starts, while the finished product is substantial. 94-03651

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Diffraction by an arbitrary-angled dielectric wedge. I. Physical optics approximation

Kim

Ra²,

Shin³

1991

IEEE Trans. Antennas Propagat.

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A complete form is presented of the physical optics Solution to the diffraction by an arbitrary-angled dielectric wedge with any relative dielectric constant in both cases of E-and H-polarized plane wave incidences upon one side of two dielecphysical optics approximation to the dual integral equation formulated in the spatial frequency domain, is constructed by the geometrical optics terms, including multiple reflection inside the wedge and the edge diffracted field. The diffraction coefficients of the edge diffracted field are represented in a quite simple form as two finite series of cotangent functions weighted by the Fresnel's reflection coefficients. Far-field patterns of the some authors [ll], [12] to apply perturbation schemes, but their solutions were valid only for the restricted dielectric constant or wedge angle. ~~~~~~l there have been polarized wave diffraction by dielectric wedges with right [13] and general angles [14]. In this paper, a complete form of the physical optics solution to diffraction by a dielectric wedge with arbitrary dielectric constant and wedge angle is presented. By applying the Fourier transformation to the well-known Fredholm inte-tric interfaces. The solution, which is obtained by performing in Obtaining asymptotic to the Ephysical optics solutions for wedge angle 45", relative dielectric constants 2, 10, and 100, and E-polarized incident angle 150" are plotted in figures, where abrupt discontinuities appear at dielectric interfaces. The error of the physical optics solution is also interpreted explicitly by nonzeroness of the edge diffracted field in the complementary plane where two media inside and outside the dielectric wedge are exchanged with each other.

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Edge diffraction by dielectric wedge of arbitrary angle

Cited by 9 publications

References 3 publications

Edge effects characterization of phase shift mask

Edge effects characterization of phase shift mask

Penetrable Wedge Analysis

Diffraction by an arbitrary-angled dielectric wedge. I. Physical optics approximation

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