Quantum Mechanical Comparison between Lithiated and Sodiated Silicon Nanowires

Abstract

This computational research study will compare the specific charge capacity (SCC) between lithium ions inserted into crystallized silicon (c-Si) nanowires with that of sodium ions inserted into amorphous silicon (a-Si) nanowires. It will be demonstrated that the potential energy V(r) within a lithium–silicon nanowire supports a coherent energy state model with discrete electron particles, while the potential energy of a sodium–silicon nanowire will be discovered to be essentially zero, and, thus, the electron current that travels through a sodiated silicon nanowire will be modeled as a free electron with wave-like characteristics. This is due to the vast differences in the electric fields of lithiated and sodiated silicon nanowires, where the electric fields are of the order of 1010 V/m and 10−15 V/m, respectively. The main reason for the great disparity in electric fields is the presence of optical amplification within lithium ions and the absence of this process within sodium ions. It will be shown that optical amplification develops coherent optical interactions, which is the primary reason for the surge of specific charge capacity in the lithiated silicon nanowire. Conversely, the lack of optical amplification is the reason for the incoherent optical interactions within sodium ions, which is the reason for the low presence of SCC in sodiated silicon nanowires.