\textbf{\textit{In Situ}}\textbf{ Resistivity of Endotaxial FeSi}$_{\mathrm{\mathbf{2}}}$\textbf{ Nanowires on Si(110)}

We present \textit{in situ} Ultra-High Vacuum (UHV) measurements of the resistivity $\rho $ of self-assembled endotaxial FeSi$_{\mathrm{2}}$ nanowires (NWs) on Si(110) using a variable-spacing two-point method with a moveable Scanning Tunneling Microscope (STM) tip and fixed contact pad. The resistivity at room temperature was found to be nearly constant down to NW width W $=$ 4 nm, but rose sharply to nearly double the bulk value at W $=$ 3nm. These data are not well-fit by a simple Fuch-Sondheimer model for boundary scattering, suggesting that other factors, possibly quantum effects, may be significant at the smallest dimensions. For a NW width of 4 nm, partial oxidation increased $\rho $ by approximately 50{\%}, while cooling from 300K to 150K decreased $\rho $ by approximately 10{\%}. The relative insensitivity of $\rho $ to NW size or oxidation or cooling is attributed to a high concentration of vacancies in the FeSi$_{\mathrm{2}}$ structure, with a correspondingly short length for inelastic electron scattering, which obscures boundary scattering except in the smallest NWs. It is remarkable that the vacancy concentration persists in very small structures.