Curvature effects on optical response of Si nanocrystals in ${\text{SiO}}_2$ having interface silicon suboxides

Several models of oxygenated and hydrogenated surfaces of Si quantum wells and Si nanocrystals (NCs) of variable shapes have been constructed in order to assess curvature effects on energy gaps due to the three Si suboxides. Si suboxides in partially oxydized models of nanocrystals of spherical shapes (or quantum dots) are shown to reduce energy gaps compared to the hydrogenated nanocrystals, consistent with previous results in the literature. This trend is shown to be reversed when planar interfaces are formed in Si NC inside ${\text{SiO}}_2$ thin films, as in Si quantum wells. At planar interfaces (or surfaces) the electronic charge density is shown to become extended and to distribute among the Si suboxides, thus generating along these planar interfaces extended, or delocalized, states. This delocalization of the electronic states then increases the energy gap compared to equivalent hydrogenated interfaces (or surfaces). Determination of geometric effects of curvature on the band gaps are based on density-functional theory (DFT) using the real-space numerical approach implemented in the “Pseudopotential Algorithm for Real-Space Electronic Structure” (PARSEC) program. A method for measuring interface effects due to Si suboxides in Si NC in ${\text{SiO}}_2$ is also suggested by comparing photoluminescence (PL) between as-grown and annealed Si-NC samples. The DFT calculations suggest that blueshift of more than 0.2 eV of the PL should be observed in as-grown samples having Si suboxides at their planar interfaces, in comparison to annealed samples above $950°\text{C}$ that have fewer or no Si suboxides once annealed, providing that the bulk of Si NC remains unaltered.

Figure 1

(Color online) Side view of the disklike Si QD containing 126 Si atoms. The surface is made of 26 double-bond oxygens and 48 hydroxides. Silicon atoms are light (yellow) spheres, oxygen atoms are dark (red) spheres, and hydrogen atoms are small (white) spheres.

Figure 2

(Color online) Top view of three models containing the three Si suboxides, with variable geometries. (a) The Si-QD model is made of 66 Si atoms, containing four of each ${\text{Si}}^{3+}$, ${\text{Si}}^{2+}$, and ${\text{Si}}^{1+}$ suboxides, for a total of 16 O atoms and 56 H atoms (among which eight are bonded to O atoms). (b) The planar Si(100) nanocrystal model is made of 178 Si atoms, 16 of each ${\text{Si}}^{3+}$, ${\text{Si}}^{2+}$, and ${\text{Si}}^{1+}$ suboxides, for a total of 64 O atoms and 104 H atoms. (c) The Si-QW model is made of 52 Si atoms and the same number of O and H atoms as in the Si QD. Image mirror atoms outside the periodic unit cell have been repeated for clarity. All three models have nine Si monolayers that separates the Si suboxides visible at the top to the invisible Si suboxides at the bottom. Colors are defined in Fig. 1. Interface model is based on the surface model from Pasquarello et al. (Ref. 32).

Figure 3

(Color online) LDA HOMO-LUMO gap results for the first set of models. (To retrieve calculated LDA energy-gap value subtract 0.6 eV—the LDA band-gap correction for Si—to the numbers in the graph.) The horizontal dotted line at 2.5 eV arbitrarily separates two general domains, one containing gaps of hydrogenated models (above the dotted line) and one containing gaps of the double-bond oxygen and hydroxide models (below that line). Square symbols are connected in order to indicate the trends of energy gaps in both hydrogenated (thick blue line) and oxygenated (thin red line) spherical Si QD, as discussed in the text. Diamond and filled-triangle symbols are energy gaps of oblong and disklike Si QD with hydrogen or Si suboxides, respectively. The difference of four Si atoms between the disklike (126 Si atoms) dots and oblong or spherical dots (122 Si atoms) is kept so as to ensure uniformity of shapes.

Figure 4

(Color online) Total charge density for the oxygenated Si(100) nanocrystal shown in Fig. 2b, along the plane defined by the Si atoms at the surface. The grid points where the charge density $\rho$ (in units of electron charge) is less than 0.001 corresponds to the background mesh (symbol $+$). Light (yellow) area: $0.001<\rho <0.02$. Darker (red) area: $0.02<\rho <0.1$. Darkest (black) area: $0.1<\rho <1.0$.