k.p based closed form energy band gap and transport electron effective mass model for [1 0 0] and [1 1 0] relaxed and strained Silicon nanowire

In this paper, we address a physics based closed form model for the energy band gap (Eg) and the transport electron effective mass in relaxed and strained [1 0 0] and [1 1 0] oriented rectangular Silicon Nanowire (SiNW). Our proposed analytical model along [1 0 0] and [1 1 0] directions are based on the k.p formalism of the conduction band energy dispersion relation through an appropriate rotation of the Hamiltonian of the electrons in the bulk crystal along [0 0 1] direction followed by the inclusion of a 4 × 4 Lüttinger Hamiltonian for the description of the valance band structure. Using this, we demonstrate the variation in Eg and the transport electron effective mass as function of the cross-sectional dimensions in a relaxed [1 0 0] and [1 1 0] oriented SiNW. The behaviour of these two parameters in [1 0 0] oriented SiNW has further been studied with the inclusion of a uniaxial strain along the transport direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along [0 0 1] with the former one. In addition, the energy band gap and the effective mass of a strained [1 1 0] oriented SiNW has also been formulated. Using this, we compare our analytical model with that of the extracted data using the nearest neighbour empirical tight binding sp3d5s∗ method based simulations and has been found to agree well over a wide range of device dimensions and applied strain.