Adaptive phase field modeling of morphological instability and facet formation during directional solidification of SiGe alloys

Abstract An adaptive phase field model is used to study the morphological instability and the facet formation during a directional solidification of SiGe alloys. Using highly anisotropic surface free energy and cusp kinetic functions, as well as a proper temperature gradient, the simulated critical growth velocity for various alloy concentrations is in good agreement with classical theories and experimental observations. The simulated facet formation and kinetics are also consistent with the experiments as well.

[1]  K. Fujiwara,et al.  Formation mechanism of a faceted interface: In situ observation of the Si(100) crystal-melt interface during crystal growth , 2009 .

[2]  Chih-Jen Shih,et al.  Adaptive phase field simulation of non-isothermal free dendritic growth of a binary alloy , 2003 .

[3]  C. W. Lan,et al.  An Adaptive Finite Volume Method for Incompressible Heat Flow Problems in Solidification , 2002 .

[4]  K. A. Jackson,et al.  Monte Carlo modeling of silicon crystal growth , 2000 .

[5]  H. Nguyen-Thi,et al.  Phase-field Modeling of the Initial Transient in Directional Solidification of Al-4wt%Cu Alloy , 2010 .

[6]  C. Lan,et al.  Phase field modeling of growth competition of silicon grains , 2008 .

[7]  Peter W Voorhees,et al.  A phase-field model for highly anisotropic interfacial energy , 2001 .

[8]  K. Nakajima,et al.  Floating zone growth of Si-rich SiGe bulk crystal using pre-synthesized SiGe feed rod with uniform composition , 2005 .

[9]  Cellular growth of Ge1-xSixGe1-xSix single crystals , 2008 .

[10]  W. Tiller,et al.  The redistribution of solute atoms during the solidification of metals , 1953 .

[11]  S. Uda,et al.  Formation mechanism of cellular structures during unidirectional growth of binary semiconductor Si-rich SiGe materials , 2012 .

[12]  Y. Sung,et al.  Nonlinear size-dependent melting of the silica-encapsulated silver nanoparticles , 2012 .

[13]  R. Sekerka Equilibrium and growth shapes of crystals: how do they differ and why should we care? , 2005 .

[14]  D. Herlach,et al.  Solidification of highly undercooled Si and Si–Ge melts , 2007 .

[15]  S. Patankar Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[16]  N. Abrosimov,et al.  The critical growth velocity for planar-to-faceted interfaces transformation in SiGe crystals , 2012 .

[17]  A. Popescu,et al.  Grain growth of silicon , 2012 .

[18]  A. Karma,et al.  Quantitative phase-field modeling of dendritic growth in two and three dimensions , 1996 .

[19]  A. Karma,et al.  Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  W. Miller Numerical simulations of bulk crystal growth on different scales: silicon and GeSi , 2010 .

[21]  K. Fujiwara,et al.  In-situ observations of melt growth behavior of polycrystalline silicon , 2004 .

[22]  R. Sekerka,et al.  Stability of a Planar Interface During Solidification of a Dilute Binary Alloy , 1964 .