Mathematical modeling with uncertainty in microelectronics

The necessity of mathematical modeling with uncertainty for processes and systems in microelectronics is discussed. In such modeling, in fact, evolution of attainable sets of the systems is considered. The cost of such transition to simulation with uncertainty is the increase in mathematics complexity under use. Two examples are considered: etching and deposition simulation; logic simulation for digital circuits.

Development of the Effective Reaction Model for Diamond Deposition Simulation within the Continuous Media Approach

Three models for diamond growth process by the chemical vapor deposition of methane are proposed. They differ in the degree of detail of the surface reaction description. The most complete model contains the reactions of deposition, etching and insertion. Gas-dynamic simulations have been performed for all those models. The species delivery to the substrate and the contribution from different species to the growth process is analysed. It is shown that different surface reaction models lead to different profiles of the species concentrations in the immediate vicinity of the substrate, thus, the experimental data on the growth rate may give information on the growth mechanism.

Effect of nanoparticles on the structure of thin films: atomistic simulation results

Предложена модель, описывающая влияние наночастиц на атомистическую структуру напыляемых тонких пленок. Модель основана на развитом ранее методе молекулярно-динамического моделирования процесса напыления тонких оптических покрытий и применена к пленкам диоксида кремния. Наночастица предполагается неподвижной, ее взаимодействие с атомами описывается сферически симметричным потенциалом. Структура пленки вблизи наночастицы исследуется с помощью радиальных функций распределения. Показано, что поведение этих функций около наночастицы существенно отличается для случаев высокоэнергетического и низкоэнергетического напыления. A model describing the effect of nanoparticles on the structure of thin films structure is proposed. The model is based on the previously developed molecular dynamics method of thin film deposition simulation and is applied to the study of silicon dioxide thin films. A nanoparticle is considered as a fixed object whose interaction with film atoms is described by a spherical symmetric potential. Radial distribution functions are used to study the film structure near the nanoparticle. It is shown that the behavior of these functions is essentially different near nanoparticles in the cases of high-energy and low-energy deposition processes.

Paint thickness simulation for painting robot trajectory planning: a review

Purpose The purposes of this paper are to review the progress of and conclude the trend for paint thickness simulation for painting robot trajectory planning. Design/methodology/approach This paper compares the explicit function-based method and computational fluid dynamics (CFD)-based method used for paint thickness simulation. Previous research is considered, and conclusions with the outlook are drawn. Findings The CFD-based paint deposition simulation is the trend for paint thickness simulation for painting robot trajectory planning. However, the calculation of paint thickness resulting from dynamically painting complex surface remains to be researched, which needs to build an appropriate CFD model, study approaches to dynamic painting simulation and investigate the simulation with continuously changing painting parameters. Originality/value This paper illustrates that the CFD-based method is the trend for the paint thickness simulation for painting robot trajectory planning. Current studies have been analyzed, and techniques of CFD modeling have also been summarized, which is vital for future study.

Modeling Particle Spray and Capture Efficiency for Direct Laser Deposition Using a Four Nozzle Powder Injection System

Powder capture efficiency is indicative of the amount of material that is added to the substrate during laser additive manufacturing processes, and thus, being able to predict capture efficiency provides capability of predictive modeling during such processes. The focus of the work presented in this paper is to create a numerical model to understand particle trajectories and velocities, which in turn allows for the prediction of capture efficiency. To validate the numerical model, particle tracking velocimetry experiments at two powder flow rates were conducted on free stream particle spray to track individual particles such that particle concentration and velocity fields could be obtained. Results from the free stream comparison showed good agreement to the trends observed in experimental data and were subsequently used in a direct laser deposition simulation to assess capture efficiency and temperature profile at steady-state. The simulation was validated against a single track deposition experiment and showed proper correlation of the free surface geometry, molten pool boundary, heat affected zone boundary and capture efficiency.

Surface roughness of thin film atomistic nanometer-size clusters

Предложен алгоритм расчета шероховатости поверхности тонких пленок, напыляемых в рамках численных экспериментов. Алгоритм применен к атомистическим кластерам диоксида кремния с характерным размером до 70 нм. Напыление пленки на подложку проводится с использованием метода, развитого ранее на основе классической молекулярной динамики с силовым полем DESIL, созданным специально для моделирования высокоэнергетических процессов напыления. Анализируется зависимость шероховатости от параметров алгоритма и от параметров напыления - температуры подложки и энергии осаждаемых атомов кремния. An algorithm of surface roughness calculation for the thin film atomistic clusters obtained in numerical experiments is proposed. The algorithm is applied to silicon dioxide films. The thickness of deposited films is up to 70 nm. The deposition process simulation is performed using the classical molecular dynamics method with the DESIL force field developed earlier specially for high-energy deposition simulation. The dependence of surface roughness on the algorithm parameters, the temperature of the substrate, and the energy of deposited silicon atoms is studied.