Fast Prediction of Transport Structures in the Melt by Physics Informed Neural Networks during 'VMCz' Crystal Growth of Silicon

Abstract

Fast prediction of fluid flow and thermal fields during the growth of bulk silicon single crystals by the 'Vertical Magnetic Field Applied Czochralski (VMCz) Method' was successfully achieved by the application of Physics Informed Neural Networks (PINNs) without any answer-labeled training data generated by a numerical simulation. The PINNs' results are in good agreement with those of the numerical simulation. The prediction time by PINNs was significantly reduced; to less than 0.1 seconds compared with about 30 minutes required by the numerical simulation. Moreover, being mesh-free techniques, PINNs do not require mesh reconstruction to accommodate the change in the growth melt volume during growth. This shows that PINNs have great potential, as real-time simulation techniques, for future applications in various areas.