Cooling of Electrons in a Silicon Inversion Layer

Low temperature cooling of two-dimensional electrons in silicon-metal-oxide semiconductor field effect transistors is studied experimentally and found to be more effective than expected from the bulk electron-phonon coupling in silicon. The extracted heat transfer rate to phonons depends cubically on electron temperature, suggesting that piezoelectric coupling, which is absent in bulk silicon, dominates over deformation potential. As a result, at 100 mK, electrons farther than $\sim 100\mu \mathrm{m}$ from the contacts are mostly cooled by phonons. Using long devices and low excitation voltage we measure electron resistivity down to $\sim 100\mathrm{mK}$ and find that some of the “metallic” curves turn insulating below $\sim 300\mathrm{mK}$.