Thermal relaxation in titanium nanowires: signatures of inelastic electron-boundary scattering in heat transfer

We have employed noise thermometry for investigations of thermal relaxation between the electrons and the substrate in nanowires patterned from 40-nm-thick titanium film on top of silicon wafers covered by a native oxide. By controlling the electronic temperature $T_e$ by Joule heating at the base temperature of a dilution refrigerator, we probe the electron-phonon coupling and the thermal boundary resistance at temperatures $T_e= 0.5 - 3$ Kelvin. Using a regular $T^5$-dependent electron-phonon coupling of clean metals and a $T^4$-dependent interfacial heat flow, we deduce a small contribution for the direct energy transfer from the titanium electrons to the substrate phonons due to inelastic electron-boundary scattering.