Control of Axial Resistivity Distribution in Bridgman Silicon Growth

Abstract

We propose the simple codoping method for improving the productivity of silicon single-crystal growth by controlling axial specific resistivity distribution. Numerical simulations have been performed to study the transport phenomena of dopant impurities in conventional and proposed Bridgman silicon growth using the finite element method and implicit Euler time integration. It has been demonstrated using mathematical models and by numerical analysis that the axial specific resistivity distribution can be modified in horizontal Bridgman silicon growth and relatively uniform its profile is feasible by the proposed doping method.

Resistivity distribution in bulk growth of silicon single crystals

“…Thus, we lose nothing by reformulating a problem in a weaker way and we gain the significant advantage of being able to consider problems with quite irregular solutions. The field equations are put into the weak form and boundary conditions are imposed in the normal manner [1,10,11]. Numerical ninepoint Gaussian quadrature for volume integrals and three-point Gaussian quadrature for surface integrals are used for calculating the residual equations and Jacobian matrix.…”

“…Wang et al [10] have proposed the simple codoping method for controlling the axial specific resistivity distribution in silicon single crystals by the mechanism of the complete recombination of conduction electron and hole. Two sorts of impurities (e.g., boron and phosphorus) are doped simultaneously in the meltdown stage in the melt growth process.…”

Ga segregation in Czochralski-Si crystal growth with B codoping

“…Wang and Im [6] have shown, using a mathematical model and numerical analysis, that the axial resistivity distribution in Si crystal growth can be controlled by simultaneously doping two different types of impurities, boron (B) and phosphorus (P). Recently, Lee [7] has demonstrated using numerical analysis that the axial distribution of the Ga concentration can be modified and made relatively uniform by codoping Ga and bismuth (Bi) in a CZ-Si crystal.…”

Quality evaluation of resistivity-controlled silicon crystals

“…Numerous studies have been reported to avoid macroscopic axial segregation in bulk crystal growth [1][2][3][4][5][6][7][8][9]. Wang and coworkers [10] have proposed the simple codoping method for controlling the axial specific resistivity distribution in silicon single crystals. Two sorts of impurities (e.g., boron and phosphorus) are doped simultaneously in the meltdown stage in the melt growth process.…”