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

Abstract

Prediction and adjustment of point defect (vacancies and self-interstitials) distribution in silicon crystals is of utmost importance for microelectronic applications. The simulation of growth processes is widely applied for process development and quite a few different sets of point defect parameters have been proposed. In this paper the transient temperature, thermal stress and point defect distributions are simulated for 300 mm Czochralski growth of the whole crystal including cone and cylindrical growth phases. Simulations with 12 different published point defect parameter sets are compared to the experimentally measured interstitial–vacancy boundary. The results are evaluated for standard and adjusted parameter sets and generally the best agreement in the whole crystal is found for models considering the effect of thermal stress on the equilibrium point defect concentration.

Application of the Alexander–Haasen Model for Thermally Stimulated Dislocation Generation in FZ Silicon Crystals

“…The numerical implementation of the heat transfer model is based on the open-source finite element library deal.II [19], which has been applied in the past for the modelling of transient temperature, stress, and point-defect fields [24]. The HF EM field was calculated beforehand using inductor current I = 1 A.…”

Impact of Thermal Stress on Intrinsic Point Defect in Czochralski Crystal Growth: Developing a Quantitative Model for Defect Formation and Distribution

“…Then true( V G true) normalc normalr normali normalt under thermal stress was obtained. Sabanskis et al have summarized several published parameter sets of point defects, and adopted them to numerical simulations with the effect of thermal stress considered. The obtained defect distribution, represented by the interstitial-vacancy boundary, was compared with experimental results.…”

“…Sueoka et al 20,23 calculated the stressdependent formation and migration enthalpies of vacancies and self-interstitials. These enthalpies were substituted into Voronkov criterion, 25 Sabanskis et al 26 have summarized several published parameter sets of point defects, and adopted them to numerical simulations with the effect of thermal stress considered. The obtained defect distribution, represented by the interstitialvacancy boundary, was compared with experimental results.…”