The heating and cooling of 2D electrons at low temperatures

We present measurements of the cooling length ℓE for hot electrons in a GaAs-based high mobility two-dimensional electron gas (2DEG). Measurements are performed on a long 60 µm-wide channel, which is Joule-heated at one end, along which there are three similar hot-electron thermocouples, spaced 30 µm apart. The thermocouples measure an exponentially decaying temperature profile with characteristic length ℓE, which decreases from 23 to 16 µm as the lattice temperature increases from 1.8 to 5 K. From a simple one-dimensional model of heat diffusion, we measure the inelastic scattering time decreasing from τi ≈ 360 to 180 ps. The measured τi has a magnitude and temperature dependence consistent with acoustic phonon scattering times. We discuss how the sample design can be varied for further thermal investigations. Knowledge of the temperature profile and its gradient will prove useful in measurements of the thermal conductivity and the Nernst effect.