Modeling of optical images in resists by vector potentials

Tanabe, Hiroyoshi

doi:10.1117/12.130360

Cited by 18 publications

(14 citation statements)

References 5 publications

(8 reference statements)

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“…Then the vector potential A is defined as H=VxA, (5) and we obtain from Equation (3) Vx(E-ikA) = 0, so that E can be defined in terms of a scalar potential E = ikA-V.…”

Section: Simulation Methodologymentioning

confidence: 99%

Metropole-3D: a rigorous 3D topography simulator

Lucas²,

Swecker

et al. 1998

SPIE Proceedings

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We have extended the capability of a vector 3D lithography simulator METROPOLE-3D from a photomask simulator to become a full 3D photolithography simulator. It is designed to run moderately fast on conventional engineering workstations. METROPOLE-3D solves Maxwell's equations rigorously in three dimensions to model how non-vertically incident light is scattered and transmitted in non-planar structures. METROPOLE-3D consists of several simulation modules: photomask simulator which models the aerial image of any mask pattern (including phase-shifting masks); exposure simulator which models light intensity distribution within the photoresist and arbitrary underlying non-planar substrate structures; postexposure baking module which models the photo-active compound diffusion, chemically amplified (CA) photoresist crosslinking and de-protection processes; and finally, 3D development module which models the photoresist development process using the level-set algorithm. This simulator has a wide range of applications in studying the pressing engineering problems encountered in state-of-the-art VLSI fabrication processes. The simulator has been applied to the layout printability! manufacturability analysis to study the dominant physical phenomena in lithography, deposition, CMP and etching processes that affect the transfer of mask patterns to the final etched structures on the wafers. Using this new 3D rigorous photolithography simulator, optical proximity effects have been studied. A reflective notching problem caused by the reflective substrate structure has been thoroughly studied, and an anti-reflective coating (ARC) solution to this notching problem has been optimized by the simulations. Finally, a 3D contamination to defect transformation study was successfully performed using our rigorous simulator.

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“…Then the vector potential A is defined as H=VxA, (5) and we obtain from Equation (3) Vx(E-ikA) = 0, so that E can be defined in terms of a scalar potential E = ikA-V.…”

Section: Simulation Methodologymentioning

confidence: 99%

Metropole-3D: a rigorous 3D topography simulator

Lucas²,

Swecker

et al. 1998

SPIE Proceedings

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“…The waveguide method was later extended to objects with arbitrary sidewall profiles [55] and applied to the modeling of alignment-target scattering, linewidth measurement and scattering from wafer topography [56]. Tanabe [57] extended the waveguide method to 3-D by formulating the problem in terms of the electromagnetic vector potential instead of the electric field. This approach was implemented in a complete 3-D photolithography simulator for modeling light scattering through mask apertures and from wafer topography during photoresist exposure [58].…”

Section: Full Solution Of Maxwell's Equations For Imaging Light mentioning

confidence: 99%

Using advanced simulation to aid microlithography development

Cole

Barouch²,

Conrad³

et al. 2001

Proc. IEEE

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“…Due to the periodic nature of the incident light (2) and the laterally periodic assumed simulation domain ( Fig. 3), the EM field inside the simulation domain can be expressed by a Fourier expansion 2 (8) Here, it is most important to emphasize that the above expressions are valid independently of which point source 2 For the sake of a compact notation we omit from now on the subscript k indicating the time step t k : Fig. 3.…”

Section: A Lateral Discretizationmentioning

confidence: 99%

Rigorous three-dimensional photoresist exposure and development simulation over nonplanar topography

Kirchauer

Selberherr

1997

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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A rigorous three-dimensional (3-D) simulation method for photoresist exposure and development is presented in which light scattering due to a nonplanar topography is calculated using the Maxwell equations. The method relies on a Fourier expansion of the electromagnetic field and extends the two-dimensional (2-D) differential method [1], [2] to the third dimension. The model accounts for partial coherent illumination and considers the nonlinear bleaching reaction of the photoresist. For the development process, the cellular-based topography simulator of [3] has been extended. A detailed description of the theory behind the simulation method is presented, the computational efficiency is discussed, and simulation results are given.

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Modeling of optical images in resists by vector potentials

Cited by 18 publications

References 5 publications

Metropole-3D: a rigorous 3D topography simulator

Metropole-3D: a rigorous 3D topography simulator

Using advanced simulation to aid microlithography development

Rigorous three-dimensional photoresist exposure and development simulation over nonplanar topography

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