M. A. Gosálvez

An atomistic introduction to anisotropic etching

This review-oriented paper presents a simplified model of anisotropic etching of crystalline silicon for the three principal orientations (1 1 1), (1 1 0) and (1 0 0), including their vicinal surfaces. The model combines pit nucleation and step flow with micromasking and diffusion phenomena in order to explain the major morphologic features and their changes with concentration. It also qualitatively explains the orientation and concentration dependence of the etch rate. We conclude that the shallow round pits on (1 0 0) and the elongated zigzag structures on (1 1 0), each of which constitutes the basic morphology of the corresponding surface, are actually the result of the same physical phenomenon, diffusion, disguised by a different underlying symmetry. It is also shown that the formation of hillocks on the two surfaces at different concentrations is a related process. We also describe and support the idea that the rotation of the triangular pits on (1 1 1) is due to a selective blocking mechanism by the etchant cations and explain how the formation of polygonal steps and/or step bunches on miscut (1 1 1) surfaces can occur as a result of diffusion phenomena and not only due to micromasking. Finally, the particular features of Cu as a micromasking agent are explained.

Orientation- and concentration-dependent surfactant adsorption on silicon in aqueous alkaline solutions: explaining the changes in the etch rate, roughness and undercutting for MEMS applications

We combine spectroscopic ellipsometry (SE), Fourier transform infrared spectroscopy (FT-IR), kinetic Monte Carlo simulations (KMC) and convex corner undercutting analysis in order to characterize and explain the effect of the addition of small amounts of surfactant in alkaline aqueous solutions, such as Triton X-100 in tetra methyl ammonium hydroxide (TMAH). We propose that the surfactant is adsorbed at the silicon–etchant interface as a thin layer, acting as a filter that moderates the surface reactivity by reducing the amount of reactant molecules that reach the surface. According to the SE and FT-IR measurements, the thickness of the adsorbed layer is an orientation- and concentration-dependent quantity, mostly due to the orientation dependence of the surface density of H-terminations and the concentration dependence of the relative rates of the underlying oxidation and etching reactions, which have a direct impact on the number of OH terminations. For partial OH coverage of the surface, the hydration of the OH group effectively acts as an anchoring location for the hydration shell of a surfactant molecule, thus enabling the formation of hydration bridges that amplify the adsorption density of the surfactant. At high concentration, the model explains the large reduction in the etch rate of the exact and vicinal Si{1 1 0} surfaces, and the small changes in the etch rates for the exact and vicinal Si{1 0 0} surfaces. At low concentration, it explains how the etch rate for both families is significantly reduced. The orientation and concentration dependence of the surfactant adsorption explains the dramatic differences in the micron-scale wet-etched patterns obtained using TMAH and TMAH+Triton for microelectromechanical systems applications.

Surfactant Adsorption on Single-Crystal Silicon Surfaces in TMAH Solution: Orientation-Dependent Adsorption Detected by In Situ Infrared Spectroscopy

This paper focuses on two aspects, macroscopic and microscopic, of pure and surfactant-added tetramethylammonium hydroxide (TMAH) wet etching. The macroscopic aspects deal with the technological/engineering applications of pure and surfactant-added TMAH for the fabrication of microelectromechanical systems (MEMS). The microscopic view is focused on the in situ observation of the silicon surface during etching in pure and surfactant-added TMAH solutions using Fourier transform infrared (FT-IR) spectroscopy in the multiple internal reflection geometry. The latter is primarily aimed at investigating the causes behind the change in the orientation-dependent etching behavior of TMAH solution when the surfactant is added. Silicon prisms having two different orientations ({110} and {100}) were prepared for comparison of the amount of adsorbed surfactant using FT-IR. Stronger and weaker adsorptions were observed on {110} and {100}, respectively. Moreover, ellipsometric spectroscopy (ES) measurements of surfactant adsorption depending on the crystallographic orientation are also performed in order to gain further information about the differences in the silicon-surfactant interface for Si{100} and Si{110}. In this paper, we determine the differences in surfactant adsorption characteristics for Si{110} and Si{100} using FT-IR and ES measurements for the first time, focusing both on the mechanism and on the technological/engineering applications in MEMS.

Analytical Solution of the Continuous Cellular Automaton for Anisotropic Etching

The fabrication of micro- and nanoelectromechanical systems (MEMS/NEMS) is based on a wide variety of growth and etching technologies sequentially applied throughout process flows which may involve a dozen or more steps, their realistic simulation having become an essential part of the overall design. By focusing in the simulation of anisotropic etching as a complex example of microfabrication, in this paper, we show how to solve analytically the time evolution of the continuous cellular automaton method, thus providing a particularly suitable choice for the realization of realistic simulations for MEMS and NEMS applications. This paper presents a complete theoretical derivation of the analytical solution based on geometrical and kinetic aspects of step flow on any surface, including a new classification of the surface sites based on a mean-field treatment of the propagation of the steps. The results of the corresponding simulations are in good agreement with the experiments. The study can be seen as an example of a general procedure that is applicable to other interface propagation problems.

Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces

Abstract Presently, dynamic surface-based models are required to contain increasingly larger numbers of points and to propagate them over longer time periods. For large numbers of surface points, the octree data structure can be used as a balance between low memory occupation and relatively rapid access to the stored data. For evolution rules that depend on neighborhood states, extended simulation periods can be obtained by using simplified atomistic propagation models, such as the Cellular Automata (CA). This method, however, has an intrinsic parallel updating nature and the corresponding simulations are highly inefficient when performed on classical Central Processing Units (CPUs), which are designed for the sequential execution of tasks. In this paper, a series of guidelines is presented for the efficient adaptation of octree-based, CA simulations of complex, evolving surfaces into massively parallel computing hardware. A Graphics Processing Unit (GPU) is used as a cost-efficient example of the parallel architectures. For the actual simulations, we consider the surface propagation during anisotropic wet chemical etching of silicon as a computationally challenging process with a wide-spread use in microengineering applications. A continuous CA model that is intrinsically parallel in nature is used for the time evolution. Our study strongly indicates that parallel computations of dynamically evolving surfaces simulated using CA methods are significantly benefited by the incorporation of octrees as support data structures, substantially decreasing the overall computational time and memory usage.

Fabrication of novel microstructures based on orientation-dependent adsorption of surfactant molecules in a TMAH solution

In this work, the orientation-dependent adsorption of surfactant molecules on the silicon surface during etching in surfactant-added tetramethylammonium hydroxide (TMAH) is investigated. Triton X-100 (C14H22O(C2H4O)n, n = 9–10) and 25 wt% TMAH are used as surfactant and main etchant, respectively. The crystallographic planes affected by the surfactant molecules are determined by analyzing the etching behavior of different mask patterns on Si{1 0 0} wafers and silicon hemispheres in pure and surfactant-added TMAH. Taken together, the shapes of the etched profiles and the analysis of the hemispherical etch rates confirm that thick and dense adsorbed surfactant layers are typically formed on both the exact and vicinal Si{1 1 0} surfaces. In addition, the results indicate that the adsorbed surfactant layer behaves as a permeable mask, partially slowing down the etch rate of the affected surface orientation/s and thus enforcing their appearance on the etching front. The peculiar etching properties of surfactant-added and surfactant-free TMAH are then utilized for the fabrication of advanced micromechanical structures with new shapes on Si{1 0 0} wafers and polydimethylsiloxane based on complex Si{1 0 0} molds.

Complex chiral colloids and surfaces via high-index off-cut silicon

Silicon wafers are commonly etched in potassium hydroxide solutions to form highly symmetric surface structures. These arise when slow-etching {111} atomic planes are exposed on standard low-index surfaces. However, the ability of nonstandard high-index wafers to provide more complex structures by tilting the {111} planes has not been fully appreciated. We demonstrate the power of this approach by creating chiral surface structures and nanoparticles of a specific handedness from gold. When the nanoparticles are dispersed in liquids, gold colloids exhibiting record molar circular dichroism (>5 × 10(9) M(-1) cm(-1)) at red wavelengths are obtained. The nanoparticles also present chiral pockets for binding.

Experimental procurement of the complete 3D etch rate distribution of Si in anisotropic etchants based on vertically micromachined wagon wheel samples

This is part I of a series of two papers dedicated to the presentation of a novel, large throughput, experimental procedure to determine the three-dimensional distribution of the etch rate of silicon in a wide range of anisotropic etchants, including a total of 30 different etching conditions in KOH, KOH+IPA, TMAH and TMAH+Triton solutions at various concentrations and temperatures. The method is based on the use of previously reported, vertically micromachined wagon wheels (WWs) (Wind and Hines 2000 Surf. Sci. 460 21–38; Nguyen and Elwenspoek 2007 J. Electrochem. Soc. 154 D684–91), focusing on speeding up the etch rate extraction process for each WW by combining macrophotography and image processing procedures. The proposed procedure positions the WWs as a realistic alternative to the traditional hemispherical specimen. The obtained, extensive etch rate database is used to perform wet etching simulations of advanced systems, showing good agreement with the experimental counterparts. In part II of this series (Gosalvez et al J. Micromech. Microeng. 21 125008), we provide a theoretical analysis of the etched spoke shapes, a detailed comparison to the etch rates from previous studies and a self-consistency study of the measured etch rates against maximum theoretical values derived from the spoke shape analysis.

Evolutionary continuous cellular automaton for the simulation of wet etching of quartz

Anisotropic wet chemical etching of quartz is a bulk micromachining process for the fabrication of micro-electro-mechanical systems (MEMS), such as resonators and temperature sensors. Despite the success of the continuous cellular automaton for the simulation of wet etching of silicon, the simulation of the same process for quartz has received little attention—especially from an atomistic perspective—resulting in a lack of accurate modeling tools. This paper analyzes the crystallographic structure of the main surface orientations of quartz and proposes a novel classification of the surface atoms as well as an evolutionary algorithm to determine suitable values for the corresponding atomistic removal rates. Not only does the presented evolutionary continuous cellular automaton reproduce the correct macroscopic etch rate distribution for quartz hemispheres, but it is also capable of performing fast and accurate 3D simulations of MEMS structures. This is shown by several comparisons between simulated and experimental results and, in particular, by a detailed, quantitative comparison for an extensive collection of trench profiles.

Simulating anisotropic etching of silicon in any etchant: evolutionary algorithm for the calibration of the continuous cellular automaton

An evolutionary algorithm is presented for the automated calibration of the continuous cellular automaton for the simulation of isotropic and anisotropic wet chemical etching of silicon in as many as 31 widely different and technologically relevant etchants, including KOH, KOH+IPA, TMAH and TMAH+Triton, in various concentrations and temperatures. Based on state-of-the-art evolutionary operators, we implement a robust algorithm for the simultaneous optimization of roughly 150 microscopic removal rates based on the minimization of a cost function with four quantitative error measures, including (i) the error between simulated and experimental macroscopic etch rates for numerous surface orientations all over the unit sphere, (ii) the error due to underetching asymmetries and floor corrugation features observed in simulated silicon samples masked using a circular pattern, (iii) the error associated with departures from a step-flow-based hierarchy in the values of the microscopic removal rates, and (iv) the error associated with deviations from a step-flow-based clustering of the microscopic removal rates. For the first time, we present the calibration and successful simulation of two technologically relevant CMOS compatible etchants, namely TMAH and, especially, TMAH+Triton, providing several comparisons between simulated and experimental MEMS structures based on multi-step etching in these etchants.