Modeling the Effect of Operating Parameters on Oxygen Content in Czochralski Growth of Silicon

Abstract

A model has been developed for the calculation of the axial oxygen profile in Czochralski-grown silicon crystals by extending the dynamic oxygen equilibrium model proposed by Carlberg, et al. (1). In this model the bulk of the melt is assumed to be well mixed and the transport of oxygen is described by mass transfer coefficients at the melt-crystal, meltcrucible, and melt-gas interfaces. In the present work, boundary layer considerations are used to define the dependency of these transport coefficients on the operating parameters. The current model therefore provides a means of assessing the effect of operating variables on the crystal oxygen content. Parametric studies, varying one parameter at a time while keeping others constant, indicate that the oxygen content is strongly influenced by the crucible rotation rate and is relatively insensitive to crystal rotation. The crucible temperature has a strong effect on the oxygen content while the effect of wall heat flux is minor. The effect of uncertainties in the physical properties on the predicted oxygen content was also examined. The equilibrium segregation constant, oxygen diffusivity in the melt, and the thermocapillarity constant were found to be the most important properties affecting the model predictions of crystal oxygen content.

Tailoring the oxygen distribution in 300 mm Czochralski crystal of pure silicon using cusp magnetic field

“…However, process control of this system is a crucial task for controlling quality of the crystal. Presence of oxygen in a grown crystal is one of the major factors for defects in the crystal or sometimes it is beneficial for controlling the crystal conductivity (Ramachandran et al, 1990). The materials used in producing semiconductor devices and microprocessors require precise control over the distribution of the oxygen in the crystals.…”

“…Rate of evaporation of oxygen is governed by two mechanisms: i) convective transport of the oxygen from the bottom of the crucible and ii) carry over rate of the oxygen by argon flow outside the melt through gas-melt interface. In earlier smaller size crucibles (Organ et al 1987, Ramachandran et al 1990and Ma and Walker, 1997, boundary layer analysis enables accurate prediction of oxygen distribution due to laminar nature of flow. For large crystal growth processes (>200mm), flow is more unstable due to high Grashof (Gr) or Rayleigh (Ra) numbers (Gr ∝ h 3 ) (Zhang et al 1999 andGrabner et al 2000).…”

M. P. Duduković: A Pioneer in Multiphase Reaction Engineering

“…From the early 1980s to the early 1990s, Mike's work in multiphase catalytic and noncatalytic systems was coupled with the development of reaction engineering methodologies for new environmentally benign processes and for the manufacture of advanced materials, such as semiconductor-grade silicon, [43][44][45][46][47][48][49] composites, [50][51][52][53][54][55][56][57] and iron particles. 58 In the late 1980s, the CREL group pioneered a prototype system for noninvasive flow mapping of gas-liquid bubble columns using Computer Automated Radioactive Particle Tracking (CARPT) with γ-rays.…”

“…From the early 1980s to the early 1990s, Mike's work in multiphase catalytic and noncatalytic systems was coupled with the development of reaction engineering methodologies for new environmentally benign processes and for the manufacture of advanced materials, such as semiconductor-grade silicon, − composites, − and iron particles . In the late 1980s, the CREL group pioneered a prototype system for noninvasive flow mapping of gas−liquid bubble columns using Computer Automated Radioactive Particle Tracking (CARPT) with γ-rays. , The CARPT experimental platform was expanded in the mid-1990s to include a Computer Assisted Tomography (CAT) system for measurement of the local voidage variations in bubble columns. , These two experimental innovations provided the basis for new insights into multiphase flows that were applied to various multiphase reactor types over the past decade, such as bubble columns, liquid−solid risers, gas−solid risers, ebullated beds, stirred tanks, and reactors containing structured packing .…”