We report a detailed analytical, numerical, and experimental study of microdisk resonators doped with nanometer sized silicon quantum dots (nanocrystals). An intuitive analytical ray-optics-based model is developed and used to capture the behavior of the quality factor $\left(Q\right)$ as a function of the disk size and the attenuation coefficient. Two regimes in the behavior of $Q$ with the disk size establish a simple design rule for optimizing the performance of these cavities. The validity of our analytical model is verified by full-vectorial finite element method calculations of the microcavity modes. Based on the predictions of the analytical and numerical calculations, we have fabricated microdisk resonators with diameters ranging between 2 and $8\mu \mathrm{m}$. $Q>{10}^3$ are obtained for disk radii as small as $4\mu \mathrm{m}$—highest observed for Si-nanocrystal-doped microdisk resonators. The fundamental limit on $Q$ is estimated by quantifying all of the potential optical loss processes through a careful analysis which includes the effects of nanocrystal size distribution. Our theoretical calculations match well with experiments and reveal that the line-edge roughness scattering and radiation loss can be minimized sufficiently to enable study and quantification of more fundamental optical loss processes of this material due to band-to-band absorption, Mie scattering, and free-carrier absorption in the Si nanocrystals. Using the experimental $Q$’s and the mode volumes, we predict the maximum low-temperature Purcell enhancement factor in our structures on the order of 6 and with some design improvements enhancements up to 50 can be realized.

• Received 2 January 2008

DOI:https://doi.org/10.1103/PhysRevA.78.023829