  The cooling of two-dimensional electrons in silicon-metal-oxide semiconductor
field effect transistors is studied experimentally. Cooling to the lattice is
found to be more effective than expected from the bulk electron-phonon coupling
in silicon. Unexpectedly, the extracted heat transfer rate to phonons at low
temperatures depends cubically on electron temperature, suggesting that
piezoelectric coupling (absent in bulk silicon) dominates over deformation
potential. According to our findings, at 100 mK, electrons farther than 0.1 mm
from the contacts are mostly cooled by phonons. Using long devices and low
excitation voltage we measure electron resistivity down to 100 mK and find that
some of the "metallic" curves, reported earlier, turn insulating below about
300 mK. This finding renders the definition of the claimed 2D metal-insulator
transition questionable. Previous low temperature measurements in silicon
devices are analyzed and thumb rules for evaluating their electron temperatures
are provided.
