In this work,1 we investigated the changes of the electronic structures of silicon under external strain in a supercell model. The use of a supercell model is a common practice in modern first-principles calculations to study the systems with impurities or lattice distortions. (Figure Presented). Based on Bloch's theorem in condensed matter physics, the band folding effect occurs when using a supercell model and gives rise to complicated band structures.2 As illustrated in Fig. 1, when the primitive cell extends three times in a specific direction and forms a supercell model, the corresponding reciprocal direction in the Brillouin zone shrinks to 1/3 and the original primitive cell bands (Figure Presented). in the first Brillouin zone will be folded into the compressed supercell first Brillouin zone. This artificial band folding effect may result in the misleading of the valence band maximum (VBM) or conduction band minimum (CBM) positions. We found that the band folding effect is particularly significant on the Si(110)-orientation case. For the Si(110) band structures, we showed in the original paper that the indirect-To-direct bandgap transition can be achieved at 4% strain using supercell calculations. However, in the ?110?-orientation supercell model, we found that the band folding effect makes the X point overlap the G point (the position of VBM). Instead of using the supercell model in the original paper, the strained band structure evolutions by using primitive cell models are shown in Fig. 2. For the external strains applied along ?110?-orientation, as shown in Fig. 2(c), the CBM position gradually shifts toward the X point. It reaches the X point at 4% (not shown in the figure). This causes a false judgment of indirect-To-direct bandgap transition at 4% strain in supercell calculations since the X point overlaps the ? point and both the CBM and VBM positions would seem to be located at the ? point. Actually, the strain effect only induces a shift of the CBM point from the position between the ? and X points to the X point. The strain along (110) orientation does not induce indirect-direct bandgap transition on silicon. These correct band structure plots of strained silicon by using primitive cell calculations should replace Fig. 4 in the original publication. This correction does not alter other results and the primary conclusions in the paper.
Li, S., Chou, J-P., Zhang, H., Lu, Y., & Hu, A. (2019). Erratum: A study of strain-induced indirect-direct bandgap transition for silicon nanowire applications (Journal of Applied Physics (2019) 125 (082520) DOI: 10.1063/1.5052718). Journal of Applied Physics, 126(17). https://doi.org/10.1063/1.5129793