Removal probability function for Kinetic Monte Carlo simulations of anisotropic etching of silicon in alkaline etchants containing additives

• Published in: Sensors and actuators. A. Physical. 2015-09, Vol.233, p.451-459
• Main Authors: Zhang, Hui, Xing, Yan, Gosálvez, Miguel A., Pal, Prem, Sato, Kazuo
• Format: Article
• Language: English
• Subjects: Additives; Alcohol; Anisotropy; Computer simulation; Etchants; Etching; Evolutionary algorithm; Kinetic Monte Carlo; KOH; Mathematical models; Monte Carlo methods; Silicon; Simulation; Surfactant; TMAH; Wet etching
• ISSN: 0924-4247; 1873-3069
• DOI: 10.1016/j.sna.2015.07.031

•A S-RPF Function is proposed for evolutionary KMC to simulate conformal wet etching.•A novel transformation matrix is introduced to fast determine the model parameters.•Much better accuracy in simulating conformal etching solutions than reported methods. A new Surfactant-based Removal Probability Function (S-RPF) is proposed to perform Kinetic Monte Carlo simulations of anisotropic etching of silicon in alkaline solutions containing additives, such as tetramethyl ammonium hydroxide (TMAH) or potassium hydroxide (KOH) with small amounts of surfactants (e.g., Triton) and/or alcohols (e.g., Isopropanol=IPA). The S-RPF is built as the product of (i) a modified removal probability function (M-RPF), for pure etchants, and (ii) an additive inhibition term (I-RPF), which describes the orientation-dependent reduction in certain etch rates due to the selective adsorption of the additive on particular silicon surfaces. By construction these functions depend only on a few parameters, whose values are determined by an evolutionary algorithm (EA), which minimizes the differences between the experimental and simulated etch rates for a small set of silicon surfaces. In this respect, the paper introduces a transformation matrix to constrain the evolutionary search space, thus accelerating the convergence for both the M-RPF and I-RPF parameters. The simulated etch rates for numerous silicon orientations in TMAH+trion at different temperatures as well as KOH+IPA show good agreement with the experimental data. Compared to previous studies, the new S-RPF model describes the anisotropy at local etch rate maxima and minima around Si(100) and Si(110) with much better accuracy. The simulation of three-dimensional microstructures confirms the validity of the new S-RPF model for MEMS fabrication in alkaline etchants containing additives.