Modeling Phase Separation in Nonstoichiometric Silica

We have modeled the decomposition of nonstoichiometric amorphous ${\mathrm{S}\mathrm{i}\mathrm{O}}_x$ upon annealing into silicon and stoichiometric silica, using a new method based on mapping Metropolis Monte Carlo simulations onto rate equations. The concentrations of all oxidation states of silicon are derived as a function of time and found to attain steady-state values at long times dependent on temperature $T$ and oxygen content $x$. The degree of phase separation and the sizes of Si particles are predicted as a function of $T$ and $x$, enabling greater control over the size of silicon quantum dots in silica matrices.

Figure 1

Time evolution of OS concentrations in amorphous ${\mathrm{S}\mathrm{i}\mathrm{O}}_{0.33}$ and ${\mathrm{S}\mathrm{i}\mathrm{O}}_{1.7}$. Symbols: MC results for $kT=0.35\mathrm{e}\mathrm{V}({\mathrm{S}\mathrm{i}\mathrm{O}}_{0.33})$ and $kT=0.15\mathrm{e}\mathrm{V}({\mathrm{S}\mathrm{i}\mathrm{O}}_{1.7})$. Curves: RE results for the same temperatures. The time scale in the RE model is adjusted through the parameter $Z$ in Eq. (4) to give best fit to MC results. Curves are labeled according to OS.

Figure 2

Steady-state OS concentrations as a function of $x$. Curves labeled 0, 1, 2, 3, and 4 correspond to $\mathrm{S}\mathrm{i}(i)$, and were obtained within the RE model [using Eqs. (6, 7)] at $T=1250°\mathrm{C}$. Symbols represent experimental data for the content of $\mathrm{S}\mathrm{i}(0)$ in the bulk ${\mathrm{S}\mathrm{i}\mathrm{O}}_x$ annealed at $T=1250°\mathrm{C}$ [18]. The curve $0^{\prime }$ shows RE results for $\mathrm{S}\mathrm{i}(0)$ at $T\approx 600°\mathrm{C}$.

Figure 3

Lines: average Si cluster diameter as a function of $x$ at (1) $T=1250°\mathrm{C}$ and (2) $\sim 600°\mathrm{C}$, as calculated using Eqs. (6, 7). Symbols are experimental values of the average size of Si nanocrystals: circles [21] and crosses [18] are for bulk ${\mathrm{S}\mathrm{i}\mathrm{O}}_x$ annealed at $T=1250°\mathrm{C}$, triangles are for ${\mathrm{S}\mathrm{i}\mathrm{O}}_2/\mathrm{S}\mathrm{i}\mathrm{O}/{\mathrm{S}\mathrm{i}\mathrm{O}}_2$ superlattice annealed at $T=1100°\mathrm{C}$ [3].