
Author(s):
N. Hirayama, A. Endo, K. Fujita, Y. Hasegawa, N. Hatano, H. Nakamura, R. Shirasaki and K. Yonemitsu

Title:
CurrentInduced Cooling Phenomenon in a TwoDimensional Electron Gas under a Magnetic Fiel

Date of publication:
June 22, 2011

Key words:
magnetothermoelectric effect, transport equation, nonlinear Poisson equation, finite difference method, two dimensional electron gas, Ettingshausen effect, cooling phenomenon

Abstract:
We investigate the spatial distribution of temperature induced by a dc current in a twodimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential φ and the temperature T in a 2DEG enclosed in a square area surrounded by insulatedadiabatic (top and bottom) and isopotentialisothermal (left and right) boundaries (with φ left < φ right and Tleft = Tright), using a pair of nonlinear Poisson equations (for φ and T) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and RighiLeduc effects. We find that, in the vicinity of the leftbottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, a downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.
