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22 February 2020 Transformational invariance in compact process modeling
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Background: Modern one-digit technological nodes demand strict reproduction of the optical proximity corrections for repeatable congruent patterns. To ensure this property, the optical and process simulations must be invariant to the geometrical transformations of the translation, rotation, and reflection. Simulators must support invariance both in theory, mathematically, and in practice, numerically. The invariance of compact modeling operators has never been scrutinized before.

Aim: We aim to examine manner and conditions under which optical simulations preserve or violate intrinsic invariances of exact imaging. We analyze invariances of Volterra operators, which are widely used in compact process modeling. Our goal is to determine necessary and sufficient conditions under which such operators become fully invariant

Approach: We use theoretical analysis to deduce full invariance conditions and numerical simulations to illustrate the results.

Results: The linear fully invariant operators are convolutions with rotationally symmetrical kernels. The fully invariant quadratic operators have special functional form with two radial and one polar argument and are not necessarily rotationally symmetrical. We deduced invariance conditions for the kernels of high-order Volterra operators.

Conclusions: We suggest to use fully invariant nonlinear Volterra operators as atomic construction blocks in machine learning and neural networks for compact process modeling.

© 2020 Society of Photo-Optical Instrumentation Engineers (SPIE) 1932-5150/2020/$28.00 © 2020 SPIE
Yuri Granik "Transformational invariance in compact process modeling," Journal of Micro/Nanolithography, MEMS, and MOEMS 19(1), 013502 (22 February 2020).
Received: 25 October 2019; Accepted: 5 February 2020; Published: 22 February 2020

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