Phonon-emission spectroscopy of a two-dimensional electron gas

A two-dimensional electron gas (2D EG) was created in a metal-oxide-semiconductor structure on a (100) surface of Si at a temperature of 1 K. Transport of electric current through the 2D EG led to power dissipation and the emission of acoustical phonons. We used superconducting tunnel junctions as phonon detectors and found that the phonon-frequency spectrum had a 2$k_F$ cutoff. As a consequence of the reduced dimensionality of the electrons the cutoff frequency depended also on the phonon-emission angle. The phonon intensity emitted under oblique angles was asymmetric and depended on the current direction (phonon-drag effect). These properties are in contrast to what one would expect from a 3D blackbody source. We calculated the expected spectra using the energy and momentum conservation laws applied to the interaction between 2D electrons and 3D phonons and found good agreement with the experimental results as long as the electron densities did not exceed 4×${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$. At larger densities additional features were observed which are not yet understood.