Direct measurement of the thermal conductivity of a two-dimensional electron gas

The temperature decay along a silicon inversion layer, heated at one end by a DC current, has been measured at liquid helium temperatures by using the electron gas as its own thermometer. The decay profile was obtained by solving the heat diffusion equation with energy loss by phonon emission. Using experimental values of the energy loss rate, the measured temperature decay was fitted to the theoretical profile to obtain values for the thermal conductivity of a two-dimensional electron gas. The values found are in agreement with those predicted by the Weidemann-Franz law.