Electron heating in a multiple-quantum-well structure below 1 K

Abstract

We have measured the electron-energy-loss rate in an $n$-doped $\mathrm{GaAs}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructure by finding the power required to establish a steady-state temperature offset between the electrons and the lattice. The measurement utilizes the temperature dependence of the resistance as a self-thermometer; heat is injected by an additional dc current. We find that for our sample the energy relaxation rate below 1 K is ${\tau }_{\varepsilon }^{-1\mathrm{}}=(2.5\mathrm{}\times {10}^6)T^3$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{K}}^{-3\mathrm{}}$.