A solid solution composed of two or more elements, after melting at high temperature, will recrystallize as the temperature decreases to form a solid solution. During the recrystallization process, the concentration of elements with low concentration and high concentration of element crystals in the solution is different. During the crystallization of solid solution, if the solid phase and liquid phase are close to the equilibrium state, that is, at an infinitely slow speed from the melt The solid is solidified, and the concentration of an impurity in the solid phase is Cs and the concentration of the impurity in the liquid phase is C1, then the ratio (k0) of the two is called the equilibrium segregation coefficient of the impurity in this crystal. Different metal impurities have different segregation coefficients, and the smaller the equilibrium segregation coefficient of metal impurities, the easier it is to remove.
In fact, it is very difficult to achieve equilibrium. The equilibrium in solids is mainly accomplished by the diffusion of atoms, and the equilibrium in liquids is mainly accomplished by the diffusion and convection of atoms. As long as it is relatively stable, it is ideal. The equilibrium segregation coefficients of metal impurities iron, titanium and copper in silicon are very small, 6.4×10-24, 2×10-24, 8×10-24 respectively, which can be well removed by directional solidification, while oxygen, phosphorus, boron, carbon The equilibrium segregation coefficients are very large, 0.5, 0.35, 0.8, and 0.7, respectively, which are difficult to remove by this method.
In actual crystal growth, it is impossible to reach an equilibrium state; that is, it is impossible for the solid to precipitate out of the melt at an infinitely slow rate, and therefore, the impurities in the melt are not uniformly distributed. For impurities with k0<1, since more impurities are discharged into the melt from the solid-liquid interface when the Cs<C1 crystal solidifies, if the diffusion rate of impurities in the melt is lower than the rate of crystal solidification, then at the solid-liquid interface The accumulation of impurities will appear on one side of the melt, forming an impurity-enriched layer. The ratio of the solid impurity concentration Cs at the solid-liquid interface to the impurity concentration C1 in the liquid is called the effective segregation coefficient ke.
where R is the growth rate; B is the thickness of the diffusion layer; D is the liquid diffusion coefficient.
Figure 1 shows the effective partition coefficients of the main metal impurities in silicon. It can be seen from the figure that the effective segregation coefficients of the metal impurities are very small and can be effectively removed.