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 \(T_\mathrm{e}\) by Joule heating at the base temperature of a dilution refrigerator, we probe the electron–phonon coupling and the thermal boundary resistance at temperatures \(T_\mathrm{e}= 0.5\)–3 K. 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.