We will focus on the horizontal Bridgman growth system to analyze the transport phenomena numerically, because the simple furnace system and the confined growth environment allow for the precise understanding of the transport phenomena in solidification process. In conventional melt growth process, the dopant concentration tends to vary significantly along the crystal. In this work, we propose the modification of crucible geometry for improving the productivity of silicon single-crystal growth by controlling axial specific resistivity distribution. Numerical analysis has 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 proposed method is useful for obtaining crystals with superior uniformity along the growth direction at a lower cost than can be obtained by the conventional melt growth process.