The energy balance at substrate surfaces during plasma processing

\n Physics-informed neural networks (PINNs) have gained popularity across different engineering fields due to their effectiveness in solving realistic problems with noisy data and often partially missing physics. In PINNs, automatic differentiation is leveraged to evaluate differential operators without discretization errors, and a multitask learning problem is defined in order to simultaneously fit observed data while respecting the underlying governing laws of physics. Here, we present applications of PINNs to various prototype heat transfer problems, targeting in particular realistic conditions not readily tackled with traditional computational methods. To this end, we first consider forced and mixed convection with unknown thermal boundary conditions on the heated surfaces and aim to obtain the temperature and velocity fields everywhere in the domain, including the boundaries, given some sparse temperature measurements. We also consider the prototype Stefan problem for two-phase flow, aiming to infer the moving interface, the velocity and temperature fields everywhere as well as the different conductivities of a solid and a liquid phase, given a few temperature measurements inside the domain. Finally, we present some realistic industrial applications related to power electronics to highlight the practicality of PINNs as well as the effective use of neural networks in solving general heat transfer problems of industrial complexity. Taken together, the results presented herein demonstrate that PINNs not only can solve ill-posed problems, which are beyond the reach of traditional computational methods, but they can also bridge the gap between computational and experimental heat transfer.

Physics-Informed Neural Networks for Heat Transfer Problems

Global modelling of heat transfer in crystal growth furnaces

Gas flow effect on global heat transport and melt convection in Czochralski silicon growth

Modern microelectronic device manufacture requires single-crystal silicon substrates of unprecedented uniformity and purity, As the device feature lengths shrink into the realm of the nanoscale, it is becoming unlikely that the traditional technique of empirical process design and optimization in both crystal growth and wafer processing will suffice for meeting the dynamically evolving specifications. These circumstances are creating more demand for a derailed understanding of the physical mechanisms that dictate the evolution of crystalline silicon microstructure and associated electronic properties. This article describes modeling efforts based on the dynamics of native point defects in silicon during crystal growth, which are aimed at developing comprehensive and robust tools for predicting microdefect distribution as a function of operating conditions. These tools are not developed independently of experimental characterization but rather are designed to take advantage of the very detailed information database available for silicon generated by decades of industrial attention. The bulk of the article is focused on two specific microdefect structures observed in Czochralski crystalline silicon, the oxidation-induced stacking fault ring (OSF-ring) and octahedral voids; the latter is a current limitation on the quality of commercial CZ silicon crystals and the subject of intense research. (C) 2000 Published by Elsevier Science S.A.

Defect engineering of Czochralski single-crystal silicon

Numerical-method for Reducing Stress Level in Gaas Crystals

Numerical-simulation of Crystal-growth - Influence of Melt Convection On Global Heat-transfer and Interface Shape

Semiconductor crystal growth is a very complex process occurring on a small geometrical scale. One of the major concerns is the dislocation density which, in the case of gallium arsenide, must remain below an acceptable level for its use as a substrate in electronic devices. The authors show how numerical simulation is able to predict the level of thermal stresses which cause dislocations and to demonstrate the consequences of geometrical modifications of the furnace. They also discuss natural convection in the melt and compare recent numerical results to experimental measurements.

P. Nicodeme

Papers

Global modelling of heat transfer in crystal growth furnaces

Numerical-method for Reducing Stress Level in Gaas Crystals

Numerical-simulation of Crystal-growth - Influence of Melt Convection On Global Heat-transfer and Interface Shape

Numerical simulation of heat transfer in LEC growth of gallium arsenide