Quantum-kinetic theory for electron-diffusion and phonon-drag thermoelectric powers from drifting electrons in a quantum wire*

Thermal conditions during an ultrafast femtosecond-scale laser pulse are difficult to resolve due to phonon vibration drag behind an electron excitation. The motivation behind this study is to establish a ground-up quantum dynamics model to predict elastic wave effects in a confined electron-phonon state. We established transient collision equations from three-phonon coupled anharmonic interactions to obtain the evolution of hot phonon species distribution and thermoelectric response in a confined-size semiconductor material, such as a GaAs nanowire subjected to a spatially uniform DC electric field. A simplified diatomic chain model was chosen to represent longitudinal phonon dispersion. A quasi-steady state was observed in electron-phonon drift-drag response and settling of low frequency phonon-phonon scattering. We also studied the effects from phonon-surface boundary parameters, such as fluctuation strength and interaction length. As new materials with surprising measured transport properties are being found, further development of this unifying theory of carrier-lattice dynamics has potential for capturing ephemeral excitations in various solids.