We study the mitigation of Si nanocrystal (Si-nc) free carrier absorption (FCA) loss at telecom wavelengths in a concentric microdisk design. The concentric microdisk design relies on using the Si-nc emission as an optical pump for the surrounding Er-based lasing media without subjecting the lasing mode to the FCA loss present in the Si-ncs. We analyze the FCA loss as a function of overhang width in this design and show that for large enough overhang width the FCA loss is negligible. We also compute the FCA cross section from the FCA loss and number of excited Si-ncs, modeled by a four-level system, and show ${\sigma }_{\mathrm{FCA}}=1.08\pm 2.3\times {10}^{-17}{\mathrm{cm}}^2$ , which is in good agreement with reported cross sections for similar films.