Materials when structured as low-dimensional systems are known to exhibit new behaviour relative to their macroscopic properties. In the case of silicon nanowires, quasione-dimensional structures, band folding can result in an electronic structure with a direct band gap. The increased surface to volume ratio permits the surface chemistry to significantly alter the value of band gaps.
In our work, we demonstrate that reduced dimensionality in silicon nanowires also has a significant impact on electron-phonon (e-ph) interactions that has not been previously anticipated. We derive a new form for deformation potentials in Si nanowires that enables a general approach to the calculation of e-ph couplings, an approach that may be readily extended to other semiconductor nanowires. The validity of such macroscopic theories at the nanoscale is central to advancing semiconductor technology (see, e.g., the developments in the effective mass approximation). For this purpose, we employ density functional theory (DFT) to calculate the band structure of Si nanowires andapply strain to extract the deformation potentials.
We find that contrary to common assumption, the tabulated deformation potentials not only vary as a function of size and orientation but also vary with respect to the direction of the applied strain. This has a direct influence on the strength of the scattering of electrons by phonons travelling in different directions. We have developed a simple theory to take into account the full anisotropy of the deformation potentials and its impact on electron mobility. The effect of the direction of growth of the wires and surface passivation are also studied. Notably, the deformation potentials in -oriented wires are found to be highly anisotropic when compared to those of  wires or bulk silicon. This results in the suppression of the scattering from breathing modes and, coupled to their lower effective mass, leads to much higher mobilities for  wires.