Invited; Stress and Doping Impact on Intrinsic Point Defect Behavior in Growing Single Crystal Silicon

For the further development of 450 mm-diameter defect-free Si crystals, one has to take into account the impact of thermal stress on intrinsic point defect properties and behavior during single crystal growth from a melt. In this study, we evaluate the impact of thermal stress between -30 MPa (tensile) and 30 MPa (compressive), which probably covers the actual values in mass production for 450 mm-diameter crystals, on the so-called Voronkov criterion of dominant point defects.The dependence of the formation and migration enthalpies of vacancy V and self-interstitial I on the stress is evaluated by density functional theory (DFT). The obtained results are used to more accurately describe the impact of thermal stress on the critical (v/G)0. The impact of compressive thermal stress on (v/G)0 is predicted to shift the growing Si crystal more vacancy-rich, as recently confirmed experimentally by Nakamura et al (ECS Solid State Letters, 3 (2014) N5-N7). Furthermore, the dependence on the thermal stress of the process window for defect-free Si growth is clarified, which is important for the development of the pulling process of future large-diameter defect-free Si crystals.

Also the mechanisms behind the experimentally observed impact of the type and concentration of substitutional dopants on intrinsic point defect behavior and formation of grown-in defects (voids and interstitial clusters) in a Si single crystal growing from a melt, are clarified. DFT calculations with 216-atom supercells are carried out to obtain the formation energies of V and I at all sites within a sphere around the dopant atom with 6 A radius for V and 5 A radius for I. P-type (B and Ga), neutral (C, Ge, and Sn) and n-type (P, As, Sb, and Bi) dopants are considered. The formation energies of V and I around dopant atoms change depending on the types and sizes of dopants. On the basis of the calculated results, an appropriate model of intrinsic point defect behavior in heavily doped Si is proposed. (1) The incorporated total V and I concentrations at the melting point depend on the types and concentrations of dopants. (2) Most of the total V and I concentrations contribute to Frenkel pair recombination during Si crystal growth at temperatures much higher than those to form grown-in intrinsic point defect clusters. The Voronkov model, while taking into account the present improvements, clearly explains all reported experimental results on grown-in defects for heavily doped Si.

The proposed improved Voronkov model uniformly explains point defect behavior for all dopant types and concentrations, taking into account also thermal stress levels.