Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals

The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing.

[1]  Lijun Liu,et al.  Effect of cusp magnetic field on the turbulent melt flow and crystal/melt interface during large-size Czochralski silicon crystal growth , 2021 .

[2]  J. Jung,et al.  Optimal Cooling System Design for Increasing the Crystal Growth Rate of Single-Crystal Silicon Ingots in the Czochralski Process Using the Crystal Growth Simulation , 2020, Processes.

[3]  K. Kakimoto,et al.  Numerical analysis of dopant concentration in 200 mm (8 inch) floating zone silicon , 2020 .

[4]  Sabine Zakel,et al.  A new generation of 99.999% enriched 28Si single crystals for the determination of Avogadro’s constant , 2017 .

[5]  A. Muiznieks,et al.  Hydrodynamical aspects of the floating zone silicon crystal growth process , 2014 .

[6]  R. Menzel Growth Conditions for Large Diameter FZ Si Single Crystals , 2013 .

[7]  H. Riemann,et al.  Float-Zone silicon crystal growth at reduced RF frequencies , 2012 .

[8]  E. Cardoso,et al.  Determination of the effective distribution coefficient (K) for silicon impurities , 2012 .

[9]  K. Shim,et al.  Distribution coefficient of boron in Si crystal ingots grown in cusp-magnetic Czochralski process , 2008 .

[10]  J. Garandet New Determinations of Diffusion Coefficients for Various Dopants in Liquid Silicon , 2007 .

[11]  Bok-Cheol Sim,et al.  Boron segregation control in silicon crystal ingots grown in Czochralski process , 2006 .

[12]  G. Gerbeth,et al.  Breakdown of Burton-Prim-Slichter approach and lateral solute segregation in radially converging flows , 2005, physics/0605139.

[13]  T. Wetzel,et al.  Numerical study of transient behaviour of molten zone during industrial FZ process for large silicon crystal growth , 2004 .

[14]  A. Mühlbauer,et al.  Modelling of phase boundaries for large industrial FZ silicon crystal growth with the needle-eye technique , 2003 .

[15]  A. Mühlbauer,et al.  Influence of the three dimensionality of the HF electromagnetic field on resistivity variations in Si single crystals during FZ growth , 2000 .

[16]  F. Durand,et al.  Oxygen and carbon transfer during solidification of semiconductor grade silicon in different processes , 2000 .

[17]  K. Mills,et al.  Thermophysical Properties of Silicon , 2000 .

[18]  A. Mühlbauer,et al.  Numerical modelling of the microscopic inhomogeneities during FZ silicon growth , 1999 .

[19]  A. Muiznieks,et al.  Analysis of the dopant segregation effects at the floating zone growth of large silicon crystals , 1997 .

[20]  D. Hurle,et al.  Effective Distribution Coefficient of Silicon Dopants During Magnetic Czochralski Growth , 1985 .

[21]  S. Sze Semiconductor Devices: Physics and Technology , 1985 .

[22]  B. Kolbesen,et al.  Carbon in silicon: Properties and impact on devices , 1982 .

[23]  L. Wilson Analysis of microsegregation in crystals , 1980 .

[24]  V. Eremenko,et al.  Dissolution of polycrystalline silicon carbide in liquid silicon , 1972 .

[25]  K. Milliken Simplification of a Molten Zone Refining Formula , 1955 .

[26]  R. Prim,et al.  The Distribution of Solute in Crystals Grown from the Melt. Part I. Theoretical , 1953 .

[27]  A. Sabanskis,et al.  3D modeling of doping from the atmosphere in floating zone silicon crystal growth , 2017 .

[28]  B. Nacke,et al.  3D unsteady modelling of the melt flow in the FZ silicon crystal growth process , 2007 .