Physics-Based Band Gap Model for Relaxed and Strained [100] Silicon Nanowires

In this paper, we propose a physics-based simplified analytical model of the energy band gap and electron effective mass in a relaxed and strained rectangular [100] silicon nanowires (SiNWs). Our proposed formulation is based on the effective mass approximation for the nondegenerate two-band model and 4 × 4 Lüttinger Hamiltonian for energy dispersion relation of conduction band electrons and the valence band heavy and light holes, respectively. Using this, we demonstrate the effect of the uniaxial strain applied along [100]-direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along [001] followed by a uniaxial one along the [100]-direction, respectively, on both the band gap and the transport and subband electron effective masses in SiNW. Our analytical model is in good agreement with the extracted data using the extended-Hückel-method-based numerical simulations over a wide range of device dimensions and applied strain.