Boundary Conditions for Simulations of Fluid Flow and Temperature Field during Ammonothermal Crystal Growth—A Machine-Learning Assisted Study of Autoclave Wall Temperature Distribution

Abstract

Thermal boundary conditions for numerical simulations of ammonothermal GaN crystal growth are investigated. A global heat transfer model that includes the furnace and its surroundings is presented, in which fluid flow and thermal field are treated as conjugate in order to fully account for convective heat transfer. The effects of laminar and turbulent flow are analyzed, as well as those of typically simultaneously present solids inside the autoclave (nutrient, baffle, and multiple seeds). This model uses heater powers as a boundary condition. Machine learning is applied to efficiently determine the power boundary conditions needed to obtain set temperatures at specified locations. Typical thermal losses are analyzed regarding their effects on the temperature distribution inside the autoclave and within the autoclave walls. This is of relevance because autoclave wall temperatures are a convenient choice for setting boundary conditions for simulations of reduced domain size. Based on the determined outer wall temperature distribution, a simplified model containing only the autoclave is also presented. The results are compared to those observed using heater-long fixed temperatures as boundary condition. Significant deviations are found especially in the upper zone of the autoclave due to the important role of heat losses through the autoclave head.

Numerical Simulation of Ammonothermal Crystal Growth of GaN—Current State, Challenges, and Prospects

“…It should, however, be noted that the adiabatic walls at the bottom and especially at the top of the enclosure may represent a major deviation from actual ammonothermal growth setups. As recently reported by Schimmel et al thermal losses through the autoclave head and head assembly appear to have a significant influence on the temperature distribution of the autoclave walls [57]. Therefore, both the experimental and the numerical model may not be an accurate representation of a typical solvothermal growth reactor.…”

“…It should be noted that there is still an active discussion on the need for 3D calculations and the limitations of 2D calculations for simulations of thermal field and flow field in ammonothermal systems. Several groups have so far focused on 2D calculations [25,27,29,57], taking advantage of their much lower computational cost. In their 2008 review on modeling of crystal growth processes in general, Chen et al suggest the coupling of a 2D axisymmetric global thermal field model with a 3D model for the fluid flow, among others, for ammonothermal growth modeling [58].…”

“…For their subsequent 3D simulation, Erlekampf et al chose the inner autoclave wall as the domain boundary, using the temperature distribution from their 2D model as the boundary condition [26]. Most recently, Schimmel et al reported a first 2D simulation that expands the domain boundary even further in order to investigate the temperature distribution in the autoclave walls [57].…”

“…However, there is no comprehensive information in the literature as to which choices are most reasonable and how they affect the results. Based on the recent publication by Schimmel et al [57], it appears that outer wall temperatures can be an effective and reasonably efficient choice but require knowledge of the temperature distribution in the outer autoclave walls rather than just knowledge of the heater set temperatures.…”

“…The relative importance of those effects depends on the choice of simulation domain. Specifically, radiation is relevant if the furnace is included in the simulation and if the setup features air-filled gaps in between heat sources and autoclave walls as in [57]. In most published studies, however, the border of the simulation domain was placed at the outer or inner autoclave walls, and radiation was not deemed to be relevant.…”