Study On Evaporation And Distribution Of Phosphorus In N-Type Multicrystalline Silicon

N-type multicrystalline silicon ingot,with doping element of phosphorus,is the development direction of solar cell material.During directional solidification process,distribution of phosphorus in silicon ingot is inhomogeneous because of the segregation and evaporation of phosphorus,which makes the electrical properties inhomogeneous.However,researches about the evaporation and segregation of phosphorus were limit.In this paper,the evaporation and distribution of phosphorus were studied.We proposed two mathematical models,considering the evaporation,segregation,melt flow field and solid-liquid interface,to describe the distribution of phosphorus.In the vertical dimension,A formula similar to Scheil equation was established to calculate the longitudinal distribution of phosphorus in silicon.In the horizontal dimension,numerical simulation method and mathematical model,considering the melt flow field and solid-liquid interface,were applied to describe the horizontal distribution of phosphorus.The conclusion is as follows.In the vertical dimension,the distribution of phosphorus in the n-type multicrystalline ingot is considered to be affected by the joint action of evaporation and segregation.During melting process,the mass transfer of phosphorus were influenced by mass transfer in liquid boundary layer and evaporation in melt surface.Phosphorus removal efficiency in ingot a and b were 33.1% and 9.8%,respectively.During solidification process,a formula similar to Scheil equation was established to calculate the longitudinal distribution of phosphorus in silicon.The effective segregation coefficient of phosphorus in ingot a and b were 0.31 and0.33 respectively,which could be obtained from the fitting result.This research provide theoretical foundation for uniform distribution of phosphorus in vertical dimension.In the horizontal dimension,Thickness of diffusion layer and instantaneous effective segregation coefficient of phosphorus were investigated by the numerical simulation method.Furthermore,a mathematical model considering the evaporation and segregation of phosphorus was built to predict phosphorus content at arbitrary position of the silicon ingot.At earlier stage of solidification process,the results show that the melt flow rate and solid-liquid interface shape have great impacts on the uniform distribution of phosphorus in multicrystalline silicon ingot.The fluctuation rate of phosphorus content is less than 5.7% for concave solid-liquid interface by controlling the thermal field and theshape of solid-liquid interface.At final stage of solidification process,the horizontal distribution of phosphorus was only influenced by the shape of solid-liquid interface.The results show that concave solid-liquid interface is benefit to horizontal uniform distribution of phosphorus in n-type multicrystalline silicon ingot.