Numerical Simulation Of Czochralski Single Silicon Crystal Growth Process

The rapid development of ultra-large-scale,ultra-high-speed integrated circuits has put more and more stringent requirements on silicon single crystal materials.Accordingly,large-size silicon crystals with high-quality have become the development trend for semiconductor industry.Czochralski method is the most widely used process for silicon single crystal growth in past decades,and its significant advantage is the ability to produce high-quality,large-size semiconductor grade or solar grade monocrystalline silicon wafers.However,stringent requirements for silicon substrate on cost and quality render the research and development of Czochralski furnace,hotzone and associated growth process a very time-consuming and expensive task.Accordingly,numerical simulation has become an essential and indispensable tool to shorten the R&D cycle and to reduce cost as well.Therefore,employing numerical simulation tool to investigate the Czochralski silicon single crystal growth process plays key role for further cost reduction,quality improvement,device performance and lifetime in semiconductor industry.In this paper,investigations of 18-inch and 12-inch Czochralski silicon single crystal growth process are presented by numerical simulations using finite element analysis software FEMAG-CZ.The purpose of our research is to further reduce the silicon single crystal production cost and improve the crystal quality.The numerical simulation process is based on the actual furnace structure,and all hotzone components as well as major physical phenomena such as radiative,conductive and convective heat transfer,and mass transfer are considered in our simulations,which can accurately predict the results.Firstly,three-dimensional numerical simulations on Czochralski 18-inch silicon ingot growth process were performed taking into account horizontal magnetic field with different strengths.The numerical simulation results show that both the temperature field and oxygen distribution in the silicon melt exhibit the fully three-dimensional asymmetric feature due to three dimensional asymmetric characteristic of melt flow under horizontal magnetic field.Meanwhile,the strength of horizontal magnetic field strongly affects the flow pattern and flow characteristic in the silicon melt,particularly beneath the melt/crystal growth interface,and accordingly changes the melt/crystal interface shape and oxygen transport process from the silicon melt to the growing crystal substantially.Secondly,three-dimensional numerical simulations on the influences of pulling rate,crystal rotation and crucible rotation of single crystal growth are further investigated as well under the horizontal magnetic field.The results show that with the increase of pulling rate,the area of the high temperature zone in the sidewall of the crucible decreases,and the low temperature region below the solid-liquid interface increase,and the solid-liquid interface gradually becomes convex to the crystal by the concave melt.Meanwhile,the V/G in the crystal near the interface increases,and there is no obvious change on the melt flow.With the increase of crystal rotation rate(or crucible rotation rate),the low temperature region below the solidification interface decreases and the temperature gradient increases,the solid-liquid interface gradually becomes convex to the crystal from the concave melt,and the V/G does not change significantly.Lastly,global modeling and dynamical simulations of heat transfer and point defects for Czochralski 12-inch silicon single crystal growth were performed.The numerical simulation results show that the core of growing crystal is dominated by vacancies when the growth rate is high,and the diameter of vacancy-dominated core decreases when the growth rate is gradually reduced.At enough low growth rate the whole core of growing crystal becomes interstitial-dominated.Point-defect dynamical simulations can provide an efficient way to grow silicon single crystals with specific point defect distribution or even defect-free crystals through appropriate control of pulling rate.