Joule heating and the thermal conductivity of a two-dimensional electron gas at cryogenic temperatures studied by modified 3ω method

Abstract

During the standard ac lock-in measurement of the resistance of a two-dimensional electron gas (2DEG) applying an ac current I=2I0sin(ωt), the electron temperature Te oscillates with the angular frequency 2ω due to the Joule heating ∝I2. We have shown that the highest (TH) and the lowest (TL) temperatures during a cycle of the oscillations can be deduced, at cryogenic temperatures, exploiting the third-harmonic (3ω) component of the voltage drop generated by the ac current I and employing the amplitude of the Shubnikov–de Haas oscillations as the measure of Te. The temperatures TH and TL thus obtained allow us to roughly evaluate the thermal conductivity κxx of the 2DEG via the modified 3ω method, in which the method originally devised for bulk materials is modified to be applicable to a 2DEG embedded in a semiconductor wafer. κxx thus deduced is found to be consistent with the Wiedemann–Franz law. The method provides a convenient way to access κxx using only a standard Hall-bar device and the simple experimental setup for the resistance measurement.