Structure and Energetics of Si Nanocrystals Embedded in $a\mathrm{\text{−}}{\mathrm{S}\mathrm{i}\mathrm{O}}_2$

We develop realistic models of Si nanocrystals embedded in $a\mathrm{\text{−}}{\mathrm{S}\mathrm{i}\mathrm{O}}_2$ using a Monte Carlo approach. The interface structure and its energetics are studied as a function of the nanocrystal size. We find that the low-energy geometries at the interface are Si-O-Si bridge bonds. Remarkably, their fraction strongly declines as the size becomes smaller. Concurrently, the embedding causes substantial deformation in such small nanocrystals. Based on these findings, an alternative explanation is given for the reduced optical gaps in this size regime.

Figure 1

Ball and stick model (part of a thin slice cut) of a Si-NC embedded in $a\mathrm{\text{−}}{\mathrm{S}\mathrm{i}\mathrm{O}}_2$. Dark spheres show Si atoms in the NC. Large (small) gray spheres show Si (O) atoms in the oxide, respectively. Arrows indicate the formation of bridge bonds.

Figure 2

Variation of the (a) interface width and (b) interface energy with the Si-NC size. Solid lines are fits to the points. The dashed horizontal line in (a) indicates the width of the ideal planar interface. The dashed horizontal lines in (b) denote the energy of the planar interface without suboxides (bottom) and with suboxides (top).

Figure 3

Percentage of bridge bonding as a function of Si-NC size. The line is a fit to the points.

Figure 4

(a) The magnitude of the tetrahedral vector and (b) the strain energy of three different nanocrystals versus the distance from their center. The vertical solid lines denote the nominal position of the respective interfaces (see the text.)