Modeling and perspectives of the Si nanocrystals–Er interaction for optical amplification

In the present article, a detailed study of the optical properties of the Er-doped Si nanocrystals system, obtained through ion implantation of Er in samples containing Si nanocrystals formed by plasma enhanced chemical vapor deposition is reported. In particular, we present a phenomenological model based on an energy level scheme taking into account the strong coupling between each Si nanocrystal (NC) and the neighboring Er ions, and considering the interactions between pairs of Er ions too, such as the concentration quenching effect and the cooperative up-conversion mechanism. Based on this model, we wrote down a system of coupled first order differential rate equations describing the time evolution of the population of both the Si NC and the Er related excited levels. By studying the steady state and time resolved luminescence signals at both the 1.54 and 0.98 μm Er lines and at the Si nanocrystals emission (at around 0.8 μm), we were able to fit the experimental data in a wide range of Er concentration (between $3\times {10}^{17}/{\mathrm{cm}}^3$ and $1.4\times {10}^{21}/{\mathrm{cm}}^3)$ and excitation pump power (in the range $1–{10}^3\mathrm{mW}),$ determining a value of $3\times {10}^{-15}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ for the coupling constant describing the interaction between Si NC and Er ions, and of $7\times {10}^{-17}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ for the cooperative up-conversion coefficient. Moreover, an energy transfer time of ∼1 μs has been estimated, confirming that Si nanocrystals can actually play a crucial role as efficient sensitizers for the rare earth. In addition, the role of Si nanocrystals and of strong gain limiting processes, such as cooperative up-conversion and confined carriers absorption from an excited NC, in determining positive gain at 1.54 μm will be investigated in details. The impact of these results on the fabrication of optical amplifiers will be finally addressed.