Energy Band Calculation of Si/Si0.7 Ge0.3 Nanopillars in k➙ Space

Abstract

In this work, we explore the energy band of the well-aligned silicon (Si) nanopillars (NPs) embedded in $\mathrm{S}\mathrm{i}_{0.7}\mathrm{G}\mathrm{e}_{0.3}$ matrix fabricated by neutral beam etching. Instead of real-space modeling, we formulate and solve the Schrödinger equation with an effective mass approach using 3D finite-element simulation in $\vec{k}$ space. This approach enables us to calculate the electronic structure in a computationally effective manner. The effects of the height, radius, separation, and shape of Si NPs on the energy band and density of states are calculated and discussed. The effect of the radius on the electron energy band control is significant while that of the shape is marginal owing to high geometry aspect ratio. In contrast with the results of electrons, both the radius and separation play crucial role in tuning the energy band of holes; consequently, they govern the variation of energy band gap of $\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}_{0.7}\mathrm{G}\mathrm{e}_{0.3}$ NPs.