Improved modeling performance with an adapted vectorial formulation of the Hopkins imaging equation

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Ability to predict process behavior under defocus has until now relied on explicit calculations, which while accurate, cannot be realistically used in full-chip optical and process correction strategies due to the long run times. In this work, we have applied a vector model for the optics, and a compact model for the resist development process. Simulations with these models are fast enough to be the basis of full-chip OPC. We verify this strategy with an independent set of measurements, and compare it to current lithographic process fitting strategies. The results indicate that by describing optical processes as accurately as possible, the model accuracy improves over a wider range of defocus conditions when compared to the traditional calibration method.As long as the calibration process successfully decouples optical and resist effects, relatively simple resist models deliver excellent accuracy within the noise level of the metrology measurements. Our data are based on onedimensional and two-dimensional results using a 193nm system using 0.75 NA and off axis illumination with 6% attenuated phase shift mask. In all cases, a wide variety of sub-resolution assist feature rules were used in order to further test the ability of the models to predict various optical and resist environments.

Section: Methodsmentioning

confidence: 99%

Calibration of OPC models for multiple focus conditions

Schacht¹,

Herold²,

Zimmermann³

et al. 2004

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“…(8) and (9) by evaluating the derivatives given in Eqs. (1) and (2). The field intensity is given by the z-component of the Poynting vector, or…”

Section: Resultsmentioning

confidence: 99%

“…Recently vector diffraction theory has been used in a wide variety of scientific and engineering fields including focusing of light by micro-lenses [1], lithography [2], tight laser beam focusing [3], etc. For a plane wave incident upon an aperture of arbitrary shape, the Hertz vector method provides a convenient way to describe the distribution of all the components of the electromagnetic field beyond the aperture [4,5].…”

Section: Introductionmentioning

confidence: 99%

Vector diffraction theory of light propagation through nanostructures

Gillen

Guha

2005

It is well known that "vector" diffraction theory needs to be invoked to describe the propagation of light through apertures having dimensions on the order of the wavelength of light. For regions close to the aperture, use of Kirchhoff boundary conditions in the aperture plane is invalid. The Hertz vector formalism provides a way to describe the diffraction of light beams through apertures having sizes ranging from half the wavelength of light to larger values. Here we will present a summary of the method used to calculate the distribution of all of the electromagnetic field components and a Poynting vector component at and near the plane of a single elliptical aperture.

“…In a similar vein, state-of-the-art OPC tools now use vector imaging models which incorporate vector effects, film stack, source map, pupil map, polarization, and a non-air ambient medium [2], [3]. This reflects a modern trend in OPC modeling methodology: move away from the "black box" modeling, to develop physically-based models, able to reliably predict CD variability under changing process conditions.…”

Section: Model Accuracymentioning

confidence: 97%

New concepts in OPC

Cobb

Granik

2004

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In this paper, we will discuss two new concepts to be used in model-based OPC: model-based fragmentation, and model tagging to account for long-range proximity effects. In model-based fragmentation we create an initial fragmentation consisting of small fragmentation across the design. Then, specific fragments are removed according to image criteria in order to keep only those fragmentation points which affect the aerial image the most. Optical flare and long-range etch effects are challenging because they have long interaction ranges. We describe here an edge tagging technique that binds different models to different regions on the layout enabling aberration-or density-sensitive corrections. We show application of this technique on a layout section. We discuss how to implement these techniques in practice and what impact they have on OPC speed and accuracy.