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

Abstract

We have measured the electron-energy-loss rate in an $n$-doped $\mathrm{GaAs}\ensuremath{-}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ 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 ${\ensuremath{\tau}}_{\ensuremath{\varepsilon}}^{\ensuremath{-}1}=(2.5\ifmmode\times\else\texttimes\fi{}{10}^{6}){T}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ${\mathrm{K}}^{\ensuremath{-}3}$.