A Selective Review of the Quantification of Defect Dynamics in Growing Czochralski Silicon Crystals

A vast majority of modern microelectronic devices are built on the monocrystalline silicon substrates produced from the crystals grown by the Czochralski (CZ) process and the float-zone (FZ) process. Silicon crystals inherently contain various precipitates known as microdefects that often affect the yield and the performance of many devices. Hence, the quantitative understanding and the control of the microdefect formation and the microdefect distributions in silicon crystals play a central role in determining the quality of silicon substrates. This paper reviews significant developments in the field of the quantification of the defect dynamics in growing CZ and FZ crystals. The breakthrough discovery of the initial point defect incorporation in the vicinity of the melt/crystal interface made in the early 1980s allowed a simplified quantification of the CZ and the FZ defect dynamics. A deeper insight into the formation and the growth of microdefects was provided over the past decade by various treatments of the agglomeration of the intrinsic point defects of silicon. In particular, a rigorous quantification of the agglomeration of the point defects using the classical nucleation theory, a recently developed lumped model that captures the microdefect distribution by representing the actual population of microdefects by an equivalent population of identical microdefects, and another rigorous treatment involving the Fokker−Planck equations are discussed in detail.