The Level-Set Method for Multi-Material Wet Etching and Non-Planar Selective Epitaxy

Abstract

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.

Analysis of Etch Profiles on C-Plane Wafers in Wet Etching of Sapphire Based on Undercutting Rate Distributions in Mixture of H2SO4 and H3PO4 at 236 °C

“…Generally, for the wet etching of the cavity, characteristic planes with low undercutting rates dominate the temporal evolution, and characteristic planes with high undercutting rates are gradually replaced or even disappear. 21,[25][26][27][28] It can be seen from Fig. 7e that the order of undercutting rates of characteristic planes is {D}>{A}>{E}>{B}, which is consistent with the evolution law of etch profiles of square cavities shown in Figs.…”

“…The sapphire hemisphere can be regarded as an island without masks, and crystallographic planes with high etch rates dominate the temporal evolution. 21,[25][26][27][28] Therefore, planes {1 −1 0 11} gradually occupy the dominant position with the process of wet etching, which close to planes {1 −1 0 12} reported in the literatures. 11,29 Figures 1c and 1d show etch rate curves in the <1 1 −2 0 > and <−1 1 0 0 > crystallographic zones at two different concentrations (236 °C, H 2 SO 4 :H 3 PO 4 = 3:1 and 6:1), respectively.…”

Modeling and analysis of sulfur hexafluoride plasma etching for silicon microcavity resonators

“…These effects underscore the difference in reactant transport between low-voltage-bias plasma etching and isotropic wet etching processes which are also common in micromachining processing [45]. Wet etching processes in the reaction-limited regime are expected to have an equal supply of reactants to the exposed geometry [46], ultimately leading to a different surface.…”

Investigation on Chemical Etching Process of FPCB With 18 μm Line Pitch

“…In addition, finite element method [14], [15], [18], and finite volume method [16], [17] were widely applied to model for the study in the evolution of etching process, which could study the evolution of etching boundary, flow field, concentration field and velocity field on the macro scale, and provided guidance for the production process. There are various existing numerical approaches for model calculations, including the moving-grid approach [14], [18], the variational inequality approach [19], the level-set method [20]- [22], and total concentration fixed-grid method [23], [24]. Shin and Economou [14] used a moving-grid approach to simulate convection-driven wet chemical etching, and showed that the shape evolution of etching cavities was affected by the etchant flow field, but which had not been applied to high rate anisotropic etching and verified by experiment.…”