Microwave Caused Gas Heating and Radiation Heat Transfer in Resonant-type Microwave Plasma

Microwave Plasma Chemical Vapor Deposition (MPCVD) stands as the forefront method for producing large-size diamond, leveraging microwave energy to induce plasma from a $\mathrm{H}_{2} / \mathrm{CH}_{4}$ mixture, where activated species deposit to form diamond. Temperature regulation profoundly impacts diamond quality and uniformity during growth. Gas mixture temperatures can reach 2000-3000 K primarily through Ohmic heating via microwave-plasma interaction. Subsequently, high-temperature gas heats the solid substrate within the resonant cavity through radiation and conduction. While extensive research addresses the former process, the latter is often overlooked, directly impacting temperature uniformity on the seed crystal and thereby diamond quality. This study investigates microwave-induced gas heating, elucidating electric intensity and temperature distributions via multi-physics simulation. We solve a set of governing equations encompassing Maxwell’s equations for electromagnetics, electron number density equation for plasma, Ohmic heating equation for heating gas, and radiation and conduction heat transfer equations for heating solid. Simulation and comparison of different resonant cavity geometries, such as quartz-tube, cylindrical, and butterfly, reveal temperature non-uniformity across all structures. Manipulating the abutment shape, such as partial hollowing out, improves temperature uniformity. Additionally, adjusting water cooling designs proves effective in reducing non-uniformity further. These findings provide valuable insights for manufacturing high-quality and large-size diamond in MPCVD.