Energetics of Self-Interstitial Clusters in Si

The transient supersaturation in a system undergoing Ostwald ripening is related to the cluster formation energy $E_{\mathrm{fc}}$ as a function of cluster size $n$. We use this relation to study the energetics of self-interstitial clusters in Si. Measurements of transient enhanced diffusion of B in Si-implanted Si are used to determine $S\left(t\right)$, and inverse modeling is used to derive $E_{\mathrm{fc}}\left(n\right)$. For clusters with $n>\mathrm{}15\mathrm{}$, $E_{\mathrm{fc}}\approx 0.8\mathrm{eV}$, close to the fault energy of $\{113\}$ defects. For clusters with $n<\mathrm{}10\mathrm{}$, $E_{\mathrm{fc}}$ is typically 0.5 eV higher, but stabler clusters exist at $n\approx 4$ ( $E_{\mathrm{fc}}\approx 1.0\mathrm{eV}$) and $n\approx 8$ ( $E_{\mathrm{fc}}\approx 0.6\mathrm{eV}$).