Quantum confinement in Si and Ge nanostructures

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.

Carrier multiplication in germanium nanocrystals

“…On the theoretical side, Barbagiovanni et al 26 provide a comparison between calculations for weak/medium and strong confinement regimes that agree nicely with the experimental results obtained by Takeoka et al 23 and us, respectively. The average NC diameter can also be estimated from the width and/ or shift of the Raman spectrum (Figure 2b).…”

“…[26][27][28] Nevertheless, there are clear discrepancies in the theoretical modeling and experimental results concerning germanium NCs, and therefore, no well-established generally accepted relationship between germanium NC size and optical bandgap exists. [26][27][28][29][30] In particular Takeoka et al 23 reports that a PL energy of 1.25 eV corresponds to a relatively small NC diameter of ,2 nm, whereas Niquet et al 28 reports the formation of much larger germanium NCs with diameters of ,8 nm upon annealing at the same temperature. However, it is unclear whether the amount of excess germanium and/or sputtering conditions were similar in these two studies.…”

Tunneling of electrons between Si nanocrystals embedded in a SiO2matrix

“…Similar simple-cubic arrangements have been studied for cubic Si quantum dots together with the effective-mass approximation (EMA), bulk effective electron masses, and model parameters for the energy barriers between Si, SiC, SiO 2 , and Si 3 N 4 27,28 . However, there are several theoretical 29 and experimental 30 indications that the effective-mass concept is simply not valid in nanostructured systems, or at least, size-dependent effective masses have to be taken into account. First-principles methods are parameter-free and do not need questionable approximations as the EMA for small NCs or input from experiment.…”

Structural parameters effect on the electrical and electroluminescence properties of silicon nanocrystals/SiO2 superlattices

“…Actually, considering that the origin of this emission is tightly related to the quantum confinement of carriers within the nanostructures [23], the structural parameters effect on the Normalized electroluminescence spectra acquired from the devices containing the SL structure under study: (a) different t SiO2 at a fixed Si excess of 17 at% and (b) different Si excess at a constant t SiO2 = 1 nm. A device containing a reference bulk sample has been employed for the sake of comparison.…”