  Heat dissipation in current-carrying cryogenic nanostructures is problematic
because the phonon density of states decreases strongly as energy decreases. We
show that the Coulomb interaction can prove a valuable resource for carrier
cooling via coupling to a nearby, cold electron reservoir. Specifically, we
consider the geometry of an electron bilayer in a silicon-based
heterostructure, and analyze the power transfer. We show that across a range of
temperatures, separations, and sheet densities, the electron-electron
interaction dominates the phonon heat-dissipation modes as the main cooling
mechanism. Coulomb cooling is most effective at low densities, when phonon
cooling is least effective in silicon, making it especially relevant for
experiments attempting to perform coherent manipulations of single spins.
