Multiscale modeling of point defect dynamics in a silicon crystal

Abstract

The quality of silicon wafers used as substrates for semiconductor and photovoltaic devices is measured in the type, size and density of defects formed during crystal growth process or device process. The native point defects such as vacancies, self interstitials and impurities such as oxygen are diffusing, reacting, and aggregating to form intrinsic micro scale defects in silicon crystal. The methods to expect crystal defects through simulation are indirect interpreting method which forecasts the defects through temperature interpretation and direct interpreting method which forecasts defect directly. In the indirect method, defects are expected through the ratio between cooling rate G($\degC$/cm) and crystal pulling rate V(mm/cm) based on Voronkoy’s theory by using temperature interpretation. As the wafer demand high quality according to the design rule reduction was getting raised, recently the studies to direct defects expectation are popularized. Direct method of crystal defects can be divided as macroscopic method, mesoscopic method and microscopic method depending on interpreting length scale and time scale. Macroscopic method can interpret whole system but, it’s hard to get accurate thermophysical property. Mesoscopic method is only applied for several tens to hundreds $\mum^2$ of system, but it only required the interatomic potential and diffusivity of clusters. Microscopic method has been extensively used to explore the fundamental interactions between point defects, which the cluster formation energy and particle dynamics are well understood. In spite of their efficiency, micro scopice method is limited to the nano_scale in both length and time scale. In order to interpret micro scale defect formation, a coarser description must be used. In this study, we didn’t consider microscopic method. Many researches performed direct defect simulations for crystal growth process and device process. But, these models were optimized in their laboratory con...