Computer Simulation of Concentration Distribution of Intrinsic Point Defect Valid for All Pulling Conditions in Large-Diameter Czochralski Si Crystal Growth

Abstract

To explain and engineer intrinsic point defect behavior in large-diameter single crystal Si grown using the Czochralski (CZ) method, a unified model valid for all pulling processes, crystal resistivities, and electrically inactive impurity concentrations that couples the effects of thermal stress, dopants, and interstitial oxygen (O i ) atoms is needed. We determined the thermal equilibrium concentration of intrinsic point defects (vacancy V and self-interstitial Si I) in CZ-Si crystal as functions of thermal stresses, type and concentration of dopant, and the concentration of O i atoms. Global heat transfer during crystal growth in a puller was simulated using STR Group's CGSim software package. A visual distribution of V and I concentrations inside a growing doped and thermally stressed Si ingot is very useful for improving the quality of large-diameter CZ-Si crystals.

Effect of thermal stress on point defect behavior during single crystal Si growth

“…16,17) However, in these reports of Sueoka et al [8][9][10][11][12] and Nakamura et al 13) the point defect behavior due to thermal stress was confirmed by the change in ξ cri . In the studies by both Kamiyama et al 14) and Sueoka et al 15) it was difficult to verify the impact of stress effect on point defect behavior. This was because of the low stress conditions and no comparison between experimental and simulation grown-in defect patterns in Sueoka's study 15) and due to the discrepancy between the actual crystal-melt interface shape and the simulation in Kamiyama's study.…”

“…13) Sueoka et al and Kamiyama et al introduced the thermal stress effect on the point defect simulation, wherein the concentration distributions of V and I in the crystal during the growth process were calculated by solving the advection diffusion equation and considering the pair annihilation of V and I. 14,15) On the other hand, Abe et al put a unique interpretation on the determination of defect type V-or I-dominant from the experimental data, i.e. the growth interface is filled with only vacancies, and self-interstitials are generated when the thermal stress exceeds a critical value.…”

Evaluation of the Performance of Published Point Defect Parameter Sets in Cone and Body Phase of a 300 mm Czochralski Silicon Crystal

“…Depending on whether the stress is isotropic or planar, the theoretically predicted dH f dσ can vary significantly [19,22]. The latter parameter set with larger dH f V dσ is more realistic, as confirmed experimentally by analyzing the relationship ξ crit (σ ave ) [18].…”

“…Stress changes PD formation enthalpy, affecting the equilibrium concentration and the critical value of v/G, which has been confirmed experimentally [18] and explained theoretically [19]. Since the stress generally increases with the crystal size, this effect is more important for large crystals and is actively investigated nowadays [20][21][22][23].…”

Numerical and experimental investigation of effect of oxygen concentration on grown-in defects in a Czochralski silicon single crystal

“…A wide range of oxygen concentrations can be investigated as changes in solid-liquid interface shapes and thermal stress can be considered to determine α. Although there are cases wherein PDSim was used to investigate the impact of α on the point defect behavior and tendency (x cri ), [21][22][23] there has been no investigation on determining α by using PDSim.…”