
K. Scheerschmidt and M. Werner
Carbon supersaturation and high density of twin lamellae influence the physical properties of multicrystalline silicon and restrict its applicability as a material in photovoltaics. To understand, e.g., the resulting structural modifications and the stress relief, the carbon incorporation in silicon has to be investigated by total energy minimizations using molecular dynamics simulations either at abinitio level (DFT) or applying classical methods with empirical potentials. The relaxed structure models support the interpretation of transmission electron micrographs by contrast simulations and thus the analysis of carbon incorporation at twins or elsewhere in silicon
Fig. 1 Models resulting from abinitio structure simulations (DFT) to minimize the total energy: a) Si twin structure (T) with a {111} lattice plane distance of 3.14Å as average of the two adjacent atom layers (numbers indicate the important next neighbor distances in Å); b) Half of (111) twin double plane (C@T) occupied with C (brighter spheres); c) One Clayer parallel to the twin (Cseparate); d) Randomly distributed C substitutions (Crandom); e) Double layer of C occupation (2C@T) at the twin yielding an additional lattice shift; f) Half twin C occupation and randomly distributed C near the twin (C@T&random).
 
Fig. 2 MDrelaxed model (54,000 atoms, TS potential) with (111)twins (T), half (C@T) or double (2C@T) layer Coccupation, and random Csubstitution (R) . Inset: relative total and potential energy per atom during equilibration at the different temperature steps. 
 Fig. 3 Image simulations of Si{111}twin structures: (a) relaxation using empirical MD with the TS potential and 54000 atoms according to Fig.2, (b) nonrelaxed twin, (c) abinitio relaxed twin (T), (d) Clayer outside the twin, (e) half (C@T) layer Coccupation, (f) double (2C@T) layer Coccupation, (g) random Csubstitution (R) from Fig. 1. 