3D modeling of doping from the atmosphere in floating zone silicon crystal growth

Abstract Three-dimensional numerical simulations of the inert gas flow, melt flow and dopant transport in both phases are carried out for silicon single crystal growth using the floating zone method. The mathematical model allows to predict the cooling heat flux density at silicon surfaces and realistically describes the dopant transport in case of doping from the atmosphere. A very good agreement with experiment is obtained for the radial resistivity variation profiles by taking into account the temperature dependence of chemical reaction processes at the free surface.

Piemaisījumu transporta kausējumā 3D matemātiskā modelēšana peldošās zonas silīcija monokristāla audzēšanas procesā

Darbs ir veltīts silīcija monokristāla audzēšanas peldošās zonas procesa, izmantojot adatas acs tehniku, skaitliskajai modelēšanai. Pamatojoties uz to, ka uz atklātās kušanas frontes eksistē plāns šķidrā silīcija slānis, kas ieplūst kausējumā pa kakliņa ārējo daļu, un ka piemaisījumu ievadīšana notiek caur argona atmosfēru, tiek ievesti precizēti robežnosacījumi kausējuma ātrumam un piemaisījumu koncentrācijai, un tiek pētīta to ietekme uz piemaisījumu koncentrācijas sadalījumu kausējumā. Aprēķini tiek veikti ar iepriekš izstrādātām programmām FZone un FZSiFOAM (uz atvērtā koda bibliotēkas OpenFOAM bāzes), tiek iegūti īpatnējās pretestības radiālie sadalījumi izaudzētajā monokristālā, un ve…

Hydrodynamical aspects of the floating zone silicon crystal growth process

Abstract 3D numerical modeling of dopant transport in the melt is carried out for the 100 mm floating zone silicon single crystal growth process. The axis-symmetric shape of the molten zone is calculated with the program FZone considering the coil and the high frequency (HF) electromagnetic (EM) field in 3D. Time dependent melt flow, temperature and dopant concentration fields are modeled using a specialized solver based on the open source code library OpenFOAM ® . The influence of the Marangoni coefficient in the boundary conditions on the melt velocity field is analyzed. The obtained shapes of the crystallization interface and resistivity profiles in the grown crystal are compared with ex…

Numerical modelling for the diameter increase of silicon crystals grown with the pedestal method

Abstract The pedestal method is one of crucible-free crystal growth methods, that has been less researched than the well-known floating zone (FZ) method. However, the pedestal method may be a cost-effective alternative to FZ, if large diameter feed rods are available. The investigated system contains two electromagnetic inductors: high-frequency inductor for pedestal top surface melting and middle-frequency inductor for pedestal side heating. The present work describes recent advances in numerical modelling of heat transfer and phase boundaries in axially symmetrical approximation, neglecting the melt flow. The shape of high-frequency inductor was optimized with the algorithm of gradient de…

Float zone single crystals for testing rods, pulled under electron beam heating