Numerical Modeling of Crystal of ZnSe by Physical Vapor Transport - Towards a more Comprehensive Formulations

Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of PVT growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided. The effect of gravity on the process from numerical computations shows subtle effects although experimental evidence from vertically and horizontally grown samples show dramatic evidence of gravitational effects. The shortcomings of the problem formulation will be discussed and a framework will be provided leading up towards a more comprehensive model of PVT systems.