Papers by Keyword: Precipitate Growth

Abstract: Materials microstructural evolution can be effectively investigated with physics-based mod els, such as phase-field modeling. Nevertheless, the need to generate fine mesh systems in order to obtain numerical solutions of complex partial differential equations(PDEs) systems makes it compu tationally expensive. Therefore, the focus of this work is on Fourier Neural Operators (FNO), a quick and generalizable machine learning model that serves as a surrogate model. In this study, we have demonstrated the capability of FNO to learn the dynamics of precipitate growth. For interpolation settings, FNO could accurately predict the two coupled phase-field variables(c and η) which represent the evolutionary state of the precipitate growth. It could also predict microstructure evolutions based on unseen initial conditions in extrapolation settings that is, outside the training set’s distribution of initial conditions. However, the error increases as we deviate further away from the distribution of the initial conditions used during training. For the case of precipitate growth in 1D with a system size of (X,T)=(4096*101), the Fourier neural operator has an inference time of only 0.027s compared to 0.21s of the pseudo-spectral method. We have also shown the capability of FNO in predicting the coupled phase-field variables at a higher resolution(4096*101) using the same model trained with low resolution data(64*101).

Abstract: Nitrogen doping of CZ silicon results in an early formation of large precipitate nuclei during crystal cooling, which are stable at 900°C. These are prone to develop stacking faults and high densities of defects inside defect denuded zones of CZ silicon wafers. Simultaneous doping of FZ silicon with nitrogen and oxygen results in two main stages of precipitate nucleation during crystal cooling, an enhanced nucleation around 800°C, which is nitrogen induced, and a second enhancement around 600°C, which depends on the concentration of residual oxygen on interstitial sites. A combined technique of ramping with 1K/min from 500-1000°C with a final anneal at 1000°C for 2h and lateral BMD measurement by SIRM provides a possibility to delineate v/G on nitrogen-doped silicon wafers. Surface segregation of nitrogen and oxygen during out-diffusion can explain the enhanced BMD formation in about 105m depth and the suppressed BMD formation in about 405m depth below the surface. The precipitate growth is enhanced in regions where nitrogen is filled up again after a preceding out-diffusion.

Abstract: Thermal treatments to enhance precipitation like RTA, ramp anneal and argon anneal were performed on low oxygen 300 mm wafers without vacancy or interstitial agglomerates (“so called” defect-free material). Best results were achieved using high temperature argon anneal leading to a homogenous BMD and denuded zone formation. Furthermore the getter efficiency was positively tested by intentional Ni-contamination. Concepts to overcome the slip danger like improved support geometries and nitrogen codoping were also evaluated and are seen to be beneficial.