On the Calculation of Gas Distribution Function by Utilizing TIME Dependent Temperature

The method for determining gas distribution function is reconstructed. In this study, theBoltzmann equation is bypassed by converse method. The temperature change is specified first inorder to determine the distribution function. The argument of this method is explained both byanalytically solving Bolztmann equation and pure probabilistic consideration in statisticalthermodynamics. Boltzmann equation is solved by modeling collision terms with severalassumptions and It is found that the results are similar. On the other hand, probabilistic methodgives no rigorous physical understanding so it offer several justifications about the resultingdistribution function. The calculation shows that the distribution function is totally Maxwellian inall cases. The temperature dependency only affects the peak value and the shape curve. It is foundthat more slender curve is resulted in higher temperature and quick sampling data is required toprobe the rapidly change temperature processes

Combining Monte Carlo Transport and Level Set Surface Evolution for Modeling Vapor Phase Deposition of Thin Films over Sub-Micron Features

A hybrid scheme is used to model the vapor phase deposition of thin films at the feature scale. The transport of the chemical species to the substrate surface is modeled with a Collisionless Direct Simulation Monte Carlo (DSMC) method. The Level Set Method is used to model the growth of the thin-film on the substrate. The convergence criteria for these methods were not found in literature. The governing equations for the Level Set Method are, in general, non-linear partial differential equations. The coupling of the DSMC Method with the Level Set Method results in a set of non-Gaussian stochastic non-linear partial differential equations. Developing general convergence criteria proved exceedingly difficult, and only qualitative results are presented to support our convergence criteria. Simulation results are in qualitative agreement with experiments and other results from literature

ON THE CALCULATION OF GAS DISTRIBUTION FUNCTION BY UTILIZING TIME DEPENDENT TEMPERATURE

The method for determining gas distribution function is reconstructed. In this study, theBoltzmann equation is bypassed by converse method. The temperature change is specified first inorder to determine the distribution function. The argument of this method is explained both byanalytically solving Bolztmann equation and pure probabilistic consideration in statisticalthermodynamics. Boltzmann equation is solved by modeling collision terms with severalassumptions and It is found that the results are similar. On the other hand, probabilistic methodgives no rigorous physical understanding so it offer several justifications about the resultingdistribution function. The calculation shows that the distribution function is totally Maxwellian inall cases. The temperature dependency only affects the peak value and the shape curve. It is foundthat more slender curve is resulted in higher temperature and quick sampling data is required toprobe the rapidly change temperature processes.Key words : Boltzmann equation, modeling collision, probabilistic method, the distributionfunctio

Multi-scale Modeling of Chemical Vapor Deposition: From Feature to Reactor Scale

Multi-scale modeling of chemical vapor deposition (CVD) is a very broad topic because a large number of physical processes affect the quality and speed of film deposition. These processes have different length scales associated with them creating the need for a multi-scale model. The three main scales of importance to the modeling of CVD are the reactor scale, the feature scale, and the atomic scale. The reactor scale ranges from meters to millimeters and is called the reactor scale because it corresponds with the scale of the reactor geometry. The micrometer scale is labeled as the feature scale in this study because this is the scale related to the feature geometries. However, this is also the scale at which grain boundaries and surface quality can be discussed. The final scale of importance to the CVD process is the atomic scale. The focus of this study is on the reactor and feature scales with special focus on the coupling between these two scales. Currently there are two main methods of coupling between the reactor and feature scales. The first method is mainly applied when a modified line of sight feature scale model is used, with coupling occurring through a mass balance performed at the wafer surface. The second method is only applicable to Monte Carlo based feature scale models. Coupling in this second method is accomplished through a mass balance performed at a plane offset from the surface. During this study a means of using an offset plane to couple a continuum based reactor/meso scale model to a modified line of sight feature scale model was developed. This new model is then applied to several test cases and compared with the surface coupling method. In order to facilitate coupling at an offset plane a new feature scale model called the Ballistic Transport with Local Sticking Factors (BTLSF) was developed. The BTLSF model uses a source plane instead of a hemispherical source to calculate the initial deposition flux arriving from the source volume. The advantage of using a source plane is that it can be made to be the same plane as the coupling plane. The presence of only one interface between the feature and reactor/meso scales simplifies coupling. Modifications were also made to the surface coupling method to allow it to model non-uniform patterned features. Comparison of the two coupling methods showed that they produced similar results with a maximum of 4.6% percent difference in their effective growth rate maps. However, the shapes of individual effective reactivity functions produced by the offset coupling method are more realistic, without the step functions present in the effective reactivity functions of the surface coupling method. Also the cell size of the continuum based component of the multi-scale model was shown to be limited when the surface coupling method was used. Thanks to the work done in this study researchers using a modified line of sight feature scale model now have a choice of using either a surface or an offset coupling method to link their reactor/meso and feature scales. Furthermore, the comparative study of these two methods in this thesis highlights the differences between the two methods allowing their selection to be an informed decision