Level Set Approach to Anisotropic Wet Etching of Silicon

Miodrag Mitrić,Marija Radmilović-Radjenović,Branislav Radjenović

doi:10.3390/s100504950

Miodrag Mitrić, Marija Radmilović-Radjenović + Show 1 more

Open Access

https://doi.org/10.3390/s100504950

Copy DOI

Journal: Sensors	Publication Date: May 17, 2010
Citations: 46	License type: CC BY 4.0

Affiliation: Institute of Economic Sciences

Abstract

In this paper a methodology for the three dimensional (3D) modeling and simulation of the profile evolution during anisotropic wet etching of silicon based on the level set method is presented. Etching rate anisotropy in silicon is modeled taking into account full silicon symmetry properties, by means of the interpolation technique using experimentally obtained values for the etching rates along thirteen principal and high index directions in KOH solutions. The resulting level set equations are solved using an open source implementation of the sparse field method (ITK library, developed in medical image processing community), extended for the case of non-convex Hamiltonians. Simulation results for some interesting initial 3D shapes, as well as some more practical examples illustrating anisotropic etching simulation in the presence of masks (simple square aperture mask, convex corner undercutting and convex corner compensation, formation of suspended structures) are shown also. The obtained results show that level set method can be used as an effective tool for wet etching process modeling, and that is a viable alternative to the Cellular Automata method which now prevails in the simulations of the wet etching process.

Highlights

Micro- and Nano Electro Mechanical Systems (MEMS and NEMS) represent a rapidly expanding field of semiconductor fabrication technologies for producing micro and nano scale mechanical, Sensors 2010, 10 electric, optical, fluidic, and other devices [1]
In this paper we have shown that the profile evolution during anisotropic wet etching of silicon can be described by the non-convex Hamiltonian arising in the Hamilton-Jacobi equation for the level set function
Angular dependence of the etching rate is calculated on the base of full silicon symmetry properties, by means of the interpolation technique using experimentally obtained values of the etching rates for principal and some of high order planes in KOH solutions

Summary

Introduction

Micro- and Nano Electro Mechanical Systems (MEMS and NEMS) represent a rapidly expanding field of semiconductor fabrication technologies for producing micro and nano scale mechanical, Sensors 2010, 10 electric, optical, fluidic, and other devices [1]. In an ideal M(N)EMS design environment, it would be of great importance first to simulate the fabrication process steps in order to generate three dimensional (3D) geometrical models, including fabrication-dependent material properties and initial conditions. Refined control of etched profiles is one of the most important tasks of M(N)EMS manufacturing process. In spite of its wide use, the simulation of etching for M(N)EMS applications has been so far a partial success only, a great number of commercial and academic research tools dedicated to this problem are developed. Two types of simulations exist [2]: the first category includes simulators describing etching process on the atomistic level, usually including the description of etched surface morphologies. The second type deals with the prediction of the etching profile evolution in engineering applications, typically including the combination of etching with other MEMS manufacturing techniques. The so called atomistic simulators based on cellular automata and Monte Carlo methods [2,3,4,5,6,7]

Objectives

Results

Conclusion