Computer Simulation of Boron Transport in Magnetic Czochralski Growth of Silicon

Abstract

Finite difference computations were used to follow boron migration in the melt and segregation in CZ Si crystal growth. With no applied magnetic field, transport near the growth interface was dominated by advection, resulting in a nearly uniform radial distribution of boron. Application of a 1 kG axial field calmed the melt motion enough that advection and diffusion appeared to play equal roles in transport near the crystal: the boron profile under the interface showed some characteristics of a diffusion boundary layer, but was quite shallow. Increasing to 2 kG further suppressed the melt motion until transport near the growth interface appeared to be strongly dominated by diffusion. Before equilibrium was reached, there was a fully developed diffusion boundary layer and a pronounced radial variation of boron concentration at the interface and in the Si crystal.

Theory of transport processes in single crystal growth from the melt

“…Hoshikawa et al (1980) first demonstrated the control of oxygen concentration in CZ-grown silicon using an applied magnetic field also see Kim and Smetana (1986). More recent analysis by Kim and Langlois (1986) of boron transport in CZ growth with an axial magnetic field shows large radial variations in boron concentration when bulk convection is weak. Such large variations have been reported in several unpublished experimental studies.…”

Magnetically Damped Convection During Solidification of a Binary Metal Alloy

“…Magnetic damping has been studied both experimentally (e.g., Hoshikawa et al, 1984;Hirata and Inoue, 1985;Kim and Smetana, 1985) and numerically (e.g., Oreper and Szekely, 1984;Langlois, 1984;Lee etal., 1984;Mihelcic and Wingerath, 1985;Organ, 1985;Kim and Langlois, 1986) for the growth of single crystals, as in the Czochralski or Bridgman-Stockbarger processes. The effect of magnetic damping on the metallurgical grain structure in a solidified metal alloy has been investigated experimentally (Uhlmann et al, 1966), and experiments have been performed under more controlled conditions to study the effects of a magnetic field on convection during solidification (Vives and Perry, 1987).…”

Computer Simulation of Oxygen Segregation in CZ/MCZ Silicon Crystals and Comparison with Experimental Results

“…Computer simulation of the fluid flow and dopant transfer/segregation in CZ and MCZ silicon crystal growth (4), developed over the years, has achieved a quantitative agreement with experimental results in gallium-doped silicon (5). In the present paper, the model is further developed and applied to the solute oxygen in CZ/MCZ silicon growth.…”

“…The radial, azimuthal, and axial components of electrical current are related to the velocity and the electrical potential ~ according to Jr = (l(-c)(b/Or ~-Bo~/r ) [3] Jo = -crBou [4] Jz --~a~b/az [5] where a denotes the electrical conductivity and B0 is the magnetic induction of the applied axial field.…”