Phonon-Drag thermopower in a quantum wire with parabolic confinement potential for electrons

Background and Objectives: A quantitative theory of the phonondrag thermopower for one-dimensional degenerate electron gas in a quantum wire with parabolic confinement potential is presented. The temperature gradient is directed along the axis of the quantum wire. Due to the confinement, the energy spectrum and the wave function of the electron change substantially. It is assumed that the Fermi level is located between the zeroth and the first of the size quantization. Results: The analysis shows that the dominant scattering mechanism at low temperatures for a highly degenerate electron gas is the scattering by ionized impurities, and for the phonons it is the scattering on the sample boundary. In the temperature range, 1–2 K, the diffusion thermopower exceeds the phonon one. With increasing temperature, the phonon thermopower increases sharply, exceeding the diffusion one by an order of magnitude. The diffusion component of the thermopower varies approximately in inverse proportion to the concentration, and the phonon component is inversely proportional to the square of the concentration. It is shown that in the temperature interval 1–20 K the main contribution to the thermopower is given by the phonon-drag effect.