Electronic cooling of a two-dimensional electron gas. Electronic states in an isolated island of 2DEG are filled to the chemical potential according to the Fermi-Dirac distribution. A quantum dot (not shown) is tunnel coupled to the right (left) side of the island and functions as an energy selective source (drain) of electrons. The quantum dot to the right of the island injects electrons into unoccupied states slightly below the chemical potential, while the quantum dot contacting the left side of the island removes electrons with energy slightly above the chemical potential. Transport of a single electron through the sample in this configuration removes of energy, cooling the 2DEG island.