Numerical Simulation Of Plasma Etching Based On Level Set Method

This paper introduces a level set method to simulate the profile evolution in the plasma etching process. We describe the initial profile with level set function and obtain the velocity from distribution of plasma energy and angle, then simulate the evolution process of etching profile by solving the equation of Hamilton-Jacob i. We have established a level set algorithm of two-dimensional to simulate isotropic etching, bowl etching, anisotropic etching and micro groove etching which often occur in the etching process. These computation verifies that the level set method is able to simulate profile evolution in plasma etching. In order to meet the requirements of semiconductor industry, we extend the two dimensional level set algorithm to three dimensions, considering the case of the square etching grooves and cylinder etching grooves. In the square situation, we contrast level set method with string algorithm and demonstrate that the level set method is more efficient and accurate. In the case of cylinder groove, we consider about completely anisotropic etching and non-fully anisotropic etching, considering the combined effect of physical sputtering and chemical reaction. These computation proves the applicability of the level set method to simulate complex situation of etching process.In order to make level set method include the physical process in plasma etching, we combine the superiority of cellular method and level set method, and proposed an integrated cellular-level set method. In order to describe the interaction of ions in the groove and the material surface, we obtain electric field distribution in the etching groove by solving the Poisson equation, and trace ion trajectory through the electric field distribution, then obtain the profile evolution through etching yield and cellular model. After that we obtain velocity from the result of cellular model, and call level set method to trace the profile. Then combine level set method and cellular method to form a new method. This method is more efficient and accurate comparing with the pure cellular method, etching interlace of this method is more smooth, and the interface geometric can be obtained more easily. We test the applicability of integrated method with two examples, one is the profile with steady changes, the other one is profile with dramatically changes. When profile changes steady, the integrated method is much more efficient, and the result of integrated method is similar to the result of cellular method. When profile changes dramatically, the balance between the efficiency and the accuracy of the simulation can be guaranteed by adjusting the step of cellular method and level set method.This study shows that the level set method is an efficient algorithm for plasma etching profile evolution. It can describe profile shape that may appear in plasma etching process easily, and can be easily extended to three dimension to meet the requirement of simulating the complex profile in practical etching process. In the same time, we propose an integrated method of cellular method and level set method, introducing the micro-physical processes of plasma etching to level set method, providing a new idea to solve the problem of huge computation in three dimension plasma etching.