Struggle between inner atoms of ultra-thin silicon film and both its dimer surfaces

Nanometer scale ultra-thin silicon films were investigated by using first principles calculation method in thickness upto 36 layers with three different constraint conditions of atoms and cells. The deformations of atoms in the film, accompanied by the dimer formations at both surfaces, were evaluated by the total energies, and were compared among their constraint conditions. The models with the free constraint conditions of atoms and cells had the highest energy gains due to the dimer formation. This trend was clear when the number of layers was equal to or less than 20. This is because the cells are free and can absorb the deviations of surface atoms in dimers by the deformation of internal atoms from the bulk positions, and these deviations propagate into the internal atoms. As a result, the deformations happened in the entire cell, which showed tilting of the z-axis. This means the models with no constrained atoms and cells exhibit an interaction between dimers on both surfaces intermediated by the atoms inside the films. The amount of deviation of this type of model was the largest among the models studied in this work. However, the differences in the energy gains among the three types of models were lower than 0.025 eV when the number of layers was equal to or larger than 24.