On the effects of ampoule tilting during vertical Bridgman growth: three-dimensional computations via a massively parallel, finite element method

Advanced Modeling of InP Crystal Growth by the MLEK Process

“…In most cases, the flow in the liquid melt is unsteady and three-dimensional due to instabilities caused by thermal convection, Kakimoto et al (1993), and are mainly concerned with the onset of threedimensionality and flow structure with only thermal convection. 3-D melt flows during the Czochralski growth of oxide materials were reported by Xiao & Derby (1995), and effects of ampoule tilting on melt convection during Bridgman growth were studied by Xiao et al (1996). More recently, results from 3-D simulations have been reported at international workshops, Ben Hadid et al (1997), Tanaka et al (1997).…”

Computer Modelling of Bulk Crystal Growth

“…This boundary condition applies to long growth vessels in which a well-mixed region at the far-field boundary is isolated from the influence of the interface region. Xiao et al [93] discuss issues with the validity of this boundary condition when these assumptions do not hold. The QSS segregation model can predict radial segregation, but only under conditions of no axial segregation, a significant restriction.…”

Simulating Interface Growth and Defect Generation in CZT – Simulation State of the Art and Known Gaps

“…The energy equation can be numerically solved by the traditional methods, such as the FD, FV, and FE method, and it also can be solved in lattice-based schemes. The distribution of chemical components, such as zinc in CZT or Ga in GaSe, in liquid phases is described by a convective diffusion equation, and the fraction in solid phase is governed by a diffusion equation [46,47]. The convective diffusion and diffusion equations can be solved by the traditional FD, FV, and FE methods or in latticebased schemes as well.…”

“…Figure 4 shows the simulation results from a continuum crystal growth model that coupled a LBM fluid flow solver with a phase-field interface capturing method. Xiao et al [46] were among the first to compute crystal growth in a vertical solidification system whose axis is tilted away from the gravitational vector. They showed that the flows generated by tilting leads to better mixing of solute and could reduce radial segregation in the melt.…”

“…In continuum crystal growth models, the flow behavior in melt domains is governed by fluid mass and momentum conserve equations, such as Navier-Stokes (NS) equations [46,47] and Boltzmann equations [48][49][50]. Navier-Stokes equations are the most widely studied method for solving fluid dynamic problems, and there are various numerical methods to solve it in different applications, such as finite difference (FD), finite volume (FV), and finite element (FE) methods.…”