There is some experimental evidence that the c(4 x 2) structure is the low-temperature phase of the Si(001) surface. The critical temperature for the order-disorder transition was experimentally determined as about 200 K. This structural phase transition was studied by using a two-dimensional Ising spin model whose interaction parameters were estimated by first-principles total-energy calculations. Monte Carlo simulations were then performed. The sects of dimer defects on the nature of the phase transition are discussed.Intensive studies have been performed for elucidating the basic properties of the low-temperature phase of the Si(001) surface. In order to interpret the insulating nature of the surface at low temperatures, two possibilities have been proposed. One is the asymmetric dimer model proposed by Chadi2 and another is the antiferromagnetic order model. s'4 The clear c(4 x 2) pattern observed below 200 K by low-energy-electron diffraction ' (LEED) may support the asymmetric dimer model, because the observed superstructure spots may be too strong to be attributed to the antiferromagnetic ordering for the spin-unpolarized LEED. On the other hand, scanning-tunneling-microscope (STM) images at room temperature ' seem to suggest that the dimers are symmetric on most of the Bat surface. This fact has been taken as evidence for antiferromagnetic ordering. However, a recent STM measurement at low temperature (( 200 K) (Ref. 10) clearly showed asymmetric dimers that order in a c(4 x 2) pattern over a wide region of the surface. It is therefore believed that a room-temperature STM image may correspond to the time average of the Hip-Hop motion of the asymmetric dimers.The temperature dependence of the LEED intensity profile for the quarter-order spot characteristic of the c(4x2) structure was carefully studied recently. s The intensity of the quarter-order spots rapidly decreases around 200 K as the temperature increases, suggesting that the surface undergoes an order-disorder phase transtion at the critical temperature T, 200 K. As the temperature exceeds T" the quarter-order spot becomes broad in the direction perpendicular to the dimer row but remains fairly sharp in the direction parallel to the dimer row. The presence of a streak pattern associated with the quarter-order spot even at temperatures twice as high as T, implies a strong short-range order along the dimer row even at such high temperatures. A similar order-disorder transition on the Ge(001) surface was studied recently by using x-ray scattering.A theoretical study of the order-disorder phase transition on the Si(001) surface was performed by Ihm et al.~2and Saxena et al. They adopted an Ising spin model where the two degrees of &eedom of an Ising spin correspond to the two possible orientations of an asymmetric Si-Si dimer. The interaction parameters in the model were estimated &om the total energies of four different arrangements of the asymmetric dimers calculated by the tight-binding approximation. This analysis incorrectly predicted the p(2 x 2)...

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.

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