A multiscale systems approach to microelectronic processes

Abstract This paper describes applications of molecular simulation to microelectronics processes and the subsequent development of techniques for multiscale simulation and multiscale systems engineering. The progression of the applications of simulation in the semiconductor industry from macroscopic to molecular to multiscale is reviewed. Multiscale systems are presented as an approach that incorporates molecular and multiscale simulation to design processes that control events at the molecular scale while simultaneously optimizing all length scales from the molecular to the macroscopic. It is discussed how design and control problems in microelectronics and nanotechnology, including the targeted design of processes and products at the molecular scale, can be addressed using the multiscale systems tools. This provides a framework for addressing the "grand challenge" of nanotechnology: how to move nanoscale science and technology from art to an engineering discipline

Simulation and characterisation of electroplated micro-copper columns for electronic interconnection

Growth mechanism of electroplated copper columns has been systematically studied by simulations and characterizations. A two-dimensional cross-sectional kinetic Monte Carlo (2DCS-KMC) model has been developed to simulate the electrodeposition of single crystal copper. The evolution of the microstructure has been visualized. The cluster density, average cluster size, variance of the cluster size and average aspect ratio were obtained from the simulations. The growth history of the deposition from the first atom to an equivalent of 100 monolayers was reconstructed. Following the single-lattice 2DCS-KMC model for a single crystal, a two-dimensional cross-sectional poly-lattice kinetic Monte Carlo (2DCSP-KMC) model has been developed for simulation of the electrodeposition of polycrystalline copper on both a copper and a gold substrate. With this model, the early-stage nucleation and the grain growth after impingement of nuclei can be simulated; as such the entire growth history is reconstructed in terms of the evolution of microstructure, grain statistics and grain boundary misorientation. The model is capable of capturing some key aspects of nucleation and growth mechanisms including the nucleation type (e.g. homogeneous or heterogeneous), texture development, the growth of grains and higher energetic state of grain boundaries. The model has also proven capable of capturing the effects of deposition parameters including applied electrode potential, concentration of cupric ions and temperature. Their effects are largely dependent on the substrates. The early-stage electrocrystallization of Cu on polycrystalline Au has been studied by ex-situ AFM observations. The evolution of surface morphology of the electrodeposited copper on a sputtered Au seed layer from 16ms to 1000s was observed and their formation mechanism discussed. The heterogeneous nucleation phenomenon, the competitive growth both longitudinally and laterally, and the dominant growth of some nuclei were experimentally observed, which are also visualized by the relevant KMC simulation results at a smaller size scale and a shorter time scale. A heuristic model is therefore proposed to describe the mechanism of the early-stage electrocrystallization of Cu on a polycrystalline Au seed layer. Electroplated copper columns plated for different times have been characterized in terms of the evolution of their external morphology, cross-sectional microstructure and crystal structure. The microstructure of electroplated copper columns is characteristic of bi-modal or tri-modal grain size distribution. The results indicate that recrystallization has occurred during or after the plating, top-down and laterally. Slight changes of the crystal structure were observed by in-situ XRD and it was found that the changes of the (111) and (200) planes occurred at different stages of self-annealing. Finally, the results indicate the presence of organic additives is not essential for self-annealing of a copper column to occur

Simulation of Metal Electrodeposition Using the Kinetic Monte Carlo and Embedded-Atom Methods

The effects of the microstructure of metal films on electric component performance and longevity have become increasingly important with the recent advances in nanotechnology. Depending on the application of the metal films and interconnects, certain microscopic structures and properties are preferred over others. A common method to produce these films and interconnects is through electrodeposition. As with every process, the ability to control the end product requires a detailed understanding of the system and the effect of operating conditions on the resulting product. To address this problem, a three-dimensional on-lattice kinetic Monte Carlo (KMC) method is developed to conduct atomistic simulations of single crystal and polycrystalline metal electrodeposition. The method utilizes the semi-empirical multi-body embedded-atom method (EAM) potential that accounts for the cohesive forces in a metallic system. The resulting computational method, KMC-EAM, enables highly descriptive simulations of electrodeposition processes to be performed over experimentally relevant scales. In this work, kinetically controlled copper electrodeposition onto single crystal copper under galvanostatic direct-current conditions and polycrystalline copper under potentiostatic direct-current conditions is modelled using the aforementioned KMC method. Four types of surface processes are considered during electrodeposition: deposition, dissolution, surface diffusion and grain boundary diffusion. The equilibrium microstructures from single crystal experiments were validated using molecular dynamics (MD) simulations through the comparison of energy per atom and average coordination number. The growth mode observed is in agreement with experimental results for the same orientation of copper. MD simulation relaxes constraints and approximations resulting from the use of KMC. Results indicate that collective diffusion mechanisms are essential in order to accurately model the evolution of coating morphology during electrodeposition. In the polycrystalline simulations, the effect of surface energy is taken into account in the propensities of deposition and dissolution. Sub-surface grain volume measurements were obtained from simulation results and the grain volume evolution with time is in agreement with both qualitative observations based on the deposit morphology and surface energy calculations. Simulations of polycrystalline deposition agree with findings from experimental studies that the evolution of the root-mean-squared roughness of the deposit during the early stages of deposition follows a power law relationship with respect to time $\approx t^{n}$. Furthermore, the power law exponent on time is determined to be $n \approx 0.5$, also in agreement with the experimental values reported in the literature

Mathematical Modeling of Rechargeable Hybrid Aqueous Batteries

A rechargeable hybrid aqueous battery (ReHAB) system was recently developed by our research group. It has been improved via different experimental approaches, but nobody yet has tried to use mathematical modeling techniques to further understand the system. This thesis tries to investigate the ReHAB system using a few current modeling methods. The study is categorized into empirical level, electrochemical engineering level and atomistic level. At the empirical level, a battery is simply viewed as a whole system, which means detailed descriptions in terms of the cathode, anode or electrolyte are ignored. By using the historical experimental data, researchers can predict the future behavior of a battery regardless of its internal phenomena. They usually employ some general mathematical functions, such as polynomial, logarithmic, exponential or other nonlinear functions. Currently automatic curve fitting and predicting algorithms are commonly used in the battery management system, due to the advantage in coping with the system nonlinearity. The first study in this thesis implements a tracking method called particle filter method on the ReHAB experimental data. The basic math function in the simulation is an empirical formula between the battery capacity and the Coulombic efficiency. The study confirms this correlation in the ReHABs, and proves that particle filter method can be a good option in battery performance tracking and prediction. At the electrochemical engineering level, battery performance is simulated in the continuum models, by incorporating chemical or electrochemical reactions, transport phenomena or interfacial kinetics. This level of simulation can help observe battery electrodes in details. It is more accurate than the empirical level model, and more versatile in simulating various electrochemical problems. This thesis secondly focuses on the ReHAB system cathode and anode using finite element method, which is implemented in COMSOL Multiphysics. The study includes a design of battery system model, investigation of species distribution during cell operation, side-reaction effects and anode corrosion issues. The models designed at this level give consistent results compared with the experimental data, and illustrate some guidance for the potential experiments. At the atomistic level, molecular simulation can model the system dynamics via step-by-step computation. Stochastic method is an efficient molecular method to investigate electrochemical problems coupled with species diffusion and chemical reactions. Atomistic simulation commonly spends longer time, but it can be very accurate regarding the evolution of a dynamic physical system. The study at this level employs the classical stochastic method on the electrochemical deposition of Zn atoms. It is focused on the dendrite formation via implementing diffusion-limited aggregation techniques and the remaining metal ions by using stochastic simulation methods. The simulation schematically illustrates the overpotential influence on the dendrites and ion distribution at the metal surface. These findings prove that overpotential is an important factor and can also help further design of experiments

Zn二次電池負極におけるZn析出成長のマルチスケールシミュレーション及び実験的解析

早大学位記番号:新9147早稲田大