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

Abstract

During the standard ac lock-in measurement of the resistance of a two-dimensional electron gas (2DEG) applying an ac current I = 2 I 0 sin (ω t), the electron temperature T e oscillates with the angular frequency 2 ω due to the Joule heating ∞I 2. We have shown that the highest (T H) and the lowest (T L) temperatures during a cycle of the oscillations can be deduced, at cryogenic temperatures, exploiting the third-harmonic (3 ω) 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 T e. The temperatures T H and T L thus obtained allow us to roughly evaluate the thermal conductivity κ x x of the 2DEG via the modified 3 ω method, in which the method originally devised for bulk materials is modified to be applicable to a 2DEG embedded in a semiconductor wafer. κ x x thus deduced is found to be consistent with the Wiedemann-Franz law. The method provides a convenient way to access κ x x using only a standard Hall-bar device and the simple experimental setup for the resistance measurement.