  A simple bulk model of electron-phonon coupling in metals has been
surprisingly successful in explaining experiments on metal films that actually
involve surface- or other low-dimensional phonons. However, by an exact
application of this standard model to a semi-infinite substrate with a free
surface, making use of the actual vibrational modes of the substrate, we show
that such agreement is fortuitous, and that the model actually predicts a
low-temperature crossover from the familiar T^5 temperature dependence to a
stronger T^6 log T scaling. Comparison with existing experiments suggests a
widespread breakdown of the standard model of electron-phonon thermalization in
metals.
