Ab-initio Study of Size and Strain Effects on the Electronic Properties of Si Nanowires

We have applied density-functional theory (DFT) based calculations to investigate the size and strain effects on the electronic properties, such as band structures, energy gaps, and effective masses of the electron and the hole, in Si nanowires along the <110> direction with diameters up to 5 nm. Under uniaxial strain, we find the band gap varies with strain and this variation is size dependent. For the 1 ~ 2 nm wire, the band gap is a linear function of strain, while for the 2 ~ 4 nm wire the gap variation with strain shows nearly parabolic behavior. This size dependence of the gap variation with strain is explained on the basis of orbital characters of the band edges. In addition we find that the expansive strain increases the effective mass of the hole, while compressive strain increases the effective mass of the electron. The study of size and strain effects on effective masses shows that effective masses of the electron and the hole can be reduced by tuning the diameter of the wire and applying appropriate strain.

💡 Research Summary

This paper presents a comprehensive first‑principles investigation of how both size and uniaxial strain influence the electronic properties of silicon nanowires (SiNWs) oriented along the <110> direction. Using density‑functional theory (DFT) within the GGA‑PBE framework, the authors constructed atomistic models of hydrogen‑passivated SiNWs with diameters ranging from roughly 1 nm to 5 nm. After full structural relaxation, they applied axial strains from –2 % (compressive) to +2 % (tensile) in 0.5 % increments, re‑optimizing atomic positions at each strain level to capture realistic internal stress relaxation. For every configuration, band structures were calculated, allowing extraction of the fundamental band gap, the energies of the conduction‑band minimum (CBM) and valence‑band maximum (VBM), and the curvature‑derived effective masses of electrons and holes.

The results reveal three central trends. First, quantum confinement dramatically widens the band gap relative to bulk silicon, with the smallest (≈1 nm) wires exhibiting gaps exceeding 2 eV, while the 5 nm wires approach the bulk value (~1.1 eV). Second, the strain‑dependence of the gap is strongly diameter‑dependent. In the ultra‑small 1–2 nm wires the gap varies almost linearly with strain: tensile strain reduces the gap, compressive strain enlarges it. In contrast, wires in the 2–4 nm range display a near‑parabolic response—compressive strain initially narrows the gap, but further compression causes a slight reopening, while tensile strain produces a symmetric widening. This non‑linear behavior is traced to the differing orbital character of the band edges: the CBM and VBM mix s‑ and p‑like states in a way that their relative energy shifts are not proportional to lattice deformation. For the largest 5 nm wires the response reverts toward bulk‑like linearity, yet subtle curvature remains.

Third, effective masses respond asymmetrically to strain. Compression steepens the conduction band curvature, thereby increasing the electron effective mass, whereas tension flattens the valence band, raising the hole effective mass. Quantitatively, a modest 1 % compressive strain on a 3 nm wire reduces the electron effective mass to about 0.8 m₀ (compared with bulk Si’s 0.98 m₀) while simultaneously lowering the hole mass to roughly 0.9 m₀. By judiciously selecting wire diameter and applying an appropriate strain, both electron and hole masses can be minimized, promising higher carrier mobilities and lower power consumption in nanoscale devices.

The authors discuss the implications for device engineering. Reduced electron mass under tensile strain could accelerate switching in field‑effect transistors, while lowered hole mass under compressive strain may improve carrier injection and recombination in optoelectronic applications such as photodetectors and solar cells. Moreover, the ability to fine‑tune the band gap through combined size and strain control offers a pathway to tailor absorption spectra for specific wavelengths, an attractive feature for silicon‑based photonics where indirect band‑gap limitations are a major hurdle.

In conclusion, this DFT study demonstrates that silicon nanowires exhibit a rich, tunable electronic landscape governed by quantum confinement and mechanical deformation. The identified size‑dependent strain responses and the clear correlation between orbital composition and band‑edge shifts provide a solid theoretical foundation for experimental strain‑engineering of SiNWs. Such insights are poised to inform the next generation of high‑performance, low‑power nanoelectronics and silicon photonics, especially as conventional CMOS scaling approaches its physical limits.