Semiconductor device dimensions have been decreasing steadily over the past several decades, generating the need to overcome fundamental limitations of both the materials they are made of and the fabrication techniques used to build them. Modern metal gates are no longer a simple polysilicon layer, but rather consist of a stack of several different materials, often requiring multiple processing steps each, to obtain the characteristics needed for stable operation. In order to better understand the underlying mechanics and predict the potential of new methods and materials, technology computer aided design has become increasingly important. This review will discuss the fundamental methods, used to describe expected topology changes, and their respective benefits and limitations. In particular, common techniques used for effective modeling of the transport of molecular entities using numerical particle ray tracing in the feature scale region will be reviewed, taking into account the limitations they impose on chemical modeling. The modeling of surface chemistries and recent advances therein, which have enabled the identification of dominant etch mechanisms and the development of sophisticated chemical models, is further presented. Finally, recent advances in the modeling of gate stack pattering using advanced geometries in the feature scale are discussed, taking note of the underlying methods and their limitations, which still need to be overcome and are actively investigated.

We present numerical methods to enable accurate and robust level-set based simulation of anisotropic wet etching and non-planar epitaxy for semiconductor fabrication. These fabrication techniques are characterized by highly crystal orientation-dependent etch/growth rates, which lead to non-convex Hamiltonians in their description by the level-set equation. As a consequence, instable surface propagation may emerge, leading to unphysical results. We propose a calibration-free Stencil Lax-Friedrichs scheme and an advanced adaptive time-stepping approach, tailored to the level-set speed functions associated with anisotropic etching and epitaxy. The scheme calculates the numerical dissipation based on information about the local geometry and the nature of the etch rates/growth function, which enables an optimized tradeoff between overly rounding of sharp geometric features and stable surface propagation. Furthermore, we introduce the deposition top layer method, which allows for robust handling of multiple material regions in non-planar epitaxy simulations. Both methods are demonstrated in a prototypical implementation, which is used to validate the capability and accuracy of our approaches. In particular, two-dimensional wet etching and three-dimensional epitaxy simulations are performed and characteristic geometry parameters are compared to the ideally expected values, showing robustness and high accuracy.

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