Quantum Confinement in Si and Ge Nanostructures

TL;DR

This study uses perturbative effective mass theory to model quantum confinement effects in Si and Ge nanostructures, comparing theoretical predictions with experimental data across different material states and geometries.

Contribution

It introduces a comprehensive application of effective mass theory to various nanostructures, distinguishing between crystalline and amorphous materials and correlating confinement strength with experimental observations.

Findings

Crystalline materials are best described by medium confinement models.

Amorphous materials exhibit strong confinement regardless of geometry.

Hole delocalization influences the magnitude of band gap expansion.

Abstract

We apply perturbative effective mass theory as a broadly applicable theoretical model for quantum confinement (QC) in all Si and Ge nanostructures including quantum wells (QWs), wires (Q-wires) and dots (QDs). Within the limits of strong, medium, and weak QC, valence and conduction band edge energy levels (VBM and CBM) were calculated as a function of QD diameters, QW thicknesses and Q-wire diameters. Crystalline and amorphous quantum systems were considered separately. Calculated band edge levels with strong, medium and weak QC models were compared with experimental VBM and CBM reported from X-ray photoemission spectroscopy (XPS), X-ray absorption spectroscopy (XAS) or photoluminescence (PL). Experimentally, the dimensions of the nanostructures were determined directly, by transmission electron microscopy (TEM), or indirectly, by x-ray diffraction (XRD) or by XPS. We found that crystalline materials are best described by a medium confinement model, while amorphous materials exhibit strong confinement regardless of the dimensionality of the system. Our results indicate that spatial delocalization of the hole in amorphous versus crystalline nanostructures is the important parameter determining the magnitude of the band gap expansion, or the strength of the quantum confinement. In addition, the effective masses of the electron and hole are discussed as a function of crystallinity and spatial confinement.