Impact of local atomic stress on oxygen segregation at tilt boundaries in silicon

Abstract

Using the atom probe tomography, transmission electron microscopy, and ab initio calculations, we investigate the three-dimensional distributions of oxygen atoms segregating at the typical large-angle grain boundaries (GBs) (Σ3{111}, Σ9{221}, Σ9{114}, Σ9{111}/{115}, and Σ27{552}) in Czochralski-grown silicon ingots. Oxygen atoms with a covalent radius that is larger than half of the silicon's radius would segregate at bond-centered positions under tensile stresses above about 2 GPa, so as to attain a more stable bonding network by reducing the local stresses. The number of oxygen atoms segregating in a unit GB area NGB (in atoms/nm2) is hypothesized to be proportional to both the number of the tensilely-stressed positions in a unit boundary area nbc and the average concentration of oxygen atoms around the boundary [Oi] (in at. %) with NGB∼50nbc[Oi]. This indicates that the probability of oxygen atoms at the segregation positions would be, on average, fifty times larger than in bond-centered positions in defect-free regions.

Nanoscopic analysis of oxygen segregation at tilt boundaries in silicon ingots using atom probe tomography combined with TEM and ab initio calculations

“…By using a [100] bicrystal seed prepared by combining two square prisms of Si with nearly (100), SATBs with the tilt axis of [100] were introduced (Ohno et al ., ). Σ3{111} GBs without GB dislocations were intentionally introduced by applying thermal shocks during CZ growth (Ohno et al ., ), and Σ9{221}, Σ9{114}, Σ9{111}/{115} and Σ27{552} GBs were spontaneously formed as a result of the interaction of Σ3{111} GBs (Ohno et al ., ). Oxygen atoms were inevitably introduced from the silica crucible, and the concentration in as‐grown ingots [O i ] was, on average, about 0.002 at.%.…”

“…As model GBs, the atomic stress of symmetric Σ9 GBs with different GB planes, i.e. Σ9{221} and Σ9{114} GBs, were examined by ab initio calculations (Ohno et al ., ). A cuboid cell with two Σ9{221} GBs consisting of 64 atoms (1.16 × 2.92 × 0.39 nm 3 ) and one with two Σ9{114} GBs consisting of 248 atoms (4.09 × 1.64 × 0.77 nm 3 ) were constructed with high‐angle annular dark‐field data, and they were relaxed by ab initio calculations with the projector‐augmented wave method based on the generalized gradient approximation implemented by the Quantum Materials Simulator package (Ishibashi et al ., ).…”

“…In a 3D Si map viewed normal to the needle axis, we barely observed Si{220} lattice planes with the spacing of 0.19 nm when the needle axis was almost normal to {220} (Ohno et al ., ). Thus, the depth resolution along the needle axis was estimated to be about 0.2 nm.…”

“…Recently, we have systematically examined the 3D distribution of oxygen atoms at tilt boundaries by atom probe tomography (APT), which has a low detection limit, lower than the limit of TEM (about 0.01 at.% on a GB plane) simultaneously with a spatial resolution comparable to the resolution of TEM (0.4 and 0.2 nm in lateral and depth resolutions at best) (Akutsu et al ., ). Oxygen distributions at SATBs (Ohno et al ., ; ), at LATBs (Ohno et al ., ; ; ) and at arrays of GB dislocations in LATBs (Ohno et al ., ) were systematically examined. The 3D distribution was correlated with the atomic hydrostatic stress around the GBs; the stress around LATBs was estimated by ab initio calculations based on atomic‐resolution scanning TEM data (Ohno et al ., ), and SATBs and GB dislocation arrays was calculated with the standard elastic theory based on dark‐field TEM data (Ohno et al ., ).…”

“…Oxygen distributions at SATBs (Ohno et al ., ; ), at LATBs (Ohno et al ., ; ; ) and at arrays of GB dislocations in LATBs (Ohno et al ., ) were systematically examined. The 3D distribution was correlated with the atomic hydrostatic stress around the GBs; the stress around LATBs was estimated by ab initio calculations based on atomic‐resolution scanning TEM data (Ohno et al ., ), and SATBs and GB dislocation arrays was calculated with the standard elastic theory based on dark‐field TEM data (Ohno et al ., ). In the present work, we have summarized all the APT data and constructed the comprehensive mechanism for the oxygen segregation at GBs: it is hypothesized that oxygen atoms preferentially segregate at the atomic sites under specific atomic stress so as to attain more stable bonding network by reducing the local stress.…”