The heating and cooling of 2D electrons at low temperatures

Abstract: We present measurements of the cooling length $\ell_E$ for hot electrons in a GaAs-based high mobility two-dimensional electron gas (2DEG). The thermal measurements are performed on a long 60 $\mu$m-wide channel, which is Joule-heated at one end, along which there are three similar hot-electron thermocouples, spaced 30 $\mu$m apart. The thermocouples measure an exponentially decaying temperature profile with a characteristic length $\ell_E$, which decreases from 23 to 16 $\mu$m as the lattice temperature increases from 1.8 to 5 K. From a simple one-dimensional model of heat diffusion, we measure an inelastic scattering time which decreases from $\tau_i \approx$ 0.36 to 0.18 ns. The measured $\tau_i$ 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.