In this paper, the relationship between various physical and chemical dynamics included in a gas cutting process was analyzed and a mathematical model was presented. To express the gas cutting process in a formula that could reflect the physics and chemical reaction dynamics, the entire process was classified into three stages: flame spurt, metal oxidation, and metal oxide melting. Flame spurt is caused by combustion of fuel gas and oxygen. It was modeled through fluid dynamics, chemical species transport, and reaction kinetics. Metal oxidation was modeled as a chemical reaction of surface oxidation and oxide growth based on temperature and concentration of species of the metal surface obtained through flame and cutting oxygen spurt results. Finally, the melting of metal oxide was expressed as a rate equation based on melting conditions, heat flux obtained in the previous two stages, and changed properties of the metal. The presented mathematical model could analyze dynamic relationships for each stage of a gas cutting process and connect them into one process. Results of this study can be used as basic data for future finite element analysis and simulations.

Chemical mechanical planarization (CMP) is a semiconductor process which is necessary for multi-layer interconnection structure. CMP pad is a consumable used in the process and with numerous asperities on the surface that wear out by the load applied from the contact with the wafer. Also, it has a patterned wafer, the step height is gradually removed by contact of the asperities with upper and lower layers. The contact state would be different according to the step height reduction. Likewise, depending on the pattern size at the specific step height, the maximum radius of the asperity curvature differs whether it reaches the down area. In this study, the height distribution of asperities was expressed as a function of time and asperity height taking into account the wear of asperities, and based on the Greenwood-Williamson theory, a mathematical model for material removal rate considering pattern size was derived. The consistency of the novel model is verified with the CMP experiment conducted using oxide patterned wafers, and the experimental data were compared with the residual step height using theoretical removal rate. The root mean square error of the step height reduction was 19.84 nm.