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

Abstract

Silicon devices currently require silicon wafers that are free of grown-in defects. Point-defect simulation for silicon crystal growth, which is performed using the advection-diffusion equation considering the pair annihilation of vacancies and self-interstitials, is improved in this study by considering the effect of thermal stress during the growth process. This effect is introduced into the point-defect simulation as the stress term of the formation enthalpy. The stress coefficients in the stress term are determined by analyzing the correlation between the grown-in defect patterns obtained from the actual pulling tests and simulations. The defect patterns obtained from the simulations performed using the improved point-defect simulation method in this study were congruent with the experimental results, particularly for crystals with large diameters and high stress. The improved simulation method proposed in this study shall be useful for designing new hot-zone conditions and enhancing the understanding of point-defect behavior.

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

“…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].…”

“…While the PD parameter sets proposed by different groups are validated and finetuned to improve agreement with experiments in the body phase [3,4,20,[23][24][25][26] (we are not aware of works comparing simulation results with experiment in the cone), they vary considerably. One of the possible reasons for such discrepancies is uncertainties in the global heat transfer (e.g., due to imprecise material properties) since the point defect distribution is sensitive to the temperature field in the crystal.…”

The Structural Modulation of Amorphous 2D Tungsten Oxide Materials in Magnetron Sputtering

“…Hence, the stress related defects are created. [ 28 ] Furthermore, the defects develop into macrocracks in parallel with the silicon substrate, resulting in a formation of 2D monolayers. In order to study this hypothetical explanation, two devices were designed in this paper.…”

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

“…The P I −L/DL boundary (hereinafter referred to as the L/DL boundary) was obtained using the Cu decoration and Wright etch methods. 24) 2.2. Point defect concentration simulation method and determination of a and C V free 2.2.1.…”

“…Point defect concentration simulation method. A point defect concentration simulation (PDSim), 24) which calculates the concentration distributions of V and I in the crystal during crystal growth, was used to investigate the effect of oxygen concentration on the grown-in defects behavior. Temperature distribution and thermal stress in the crystal were obtained considering the actual solid-liquid interface shape.…”