Theory of optical-phonon limited hot-electron transport in quantum wires

We present a kinetic theory of a nonequilibrium electron gas in a one-dimensional circular quantum wire interacting with acoustic and polar optical phonons. Besides these scattering mechanisms we also include an elastic interaction with interface roughness for the electron momentum relaxation. We have solved the Boltzmann kinetic equation analytically and obtained different distribution functions for a one-dimensional electron gas. A detailed kinetic analysis of the limiting case of the electron gas interacting solely with optical phonons is undertaken and the distribution function is found when this system can be described in a self-consistent way. Our analytical results are in good agreement with previous numerical studies of a similar system using Monte Carlo techniques. As an application of the developed theory we have calculated the electric-field dependences of electron mobility and average energy for different parameters of the quantum wire. It is shown that at high lattice temperature the electron mobility is a nonmonotonous function of the applied electric field and has its maximum value at intermediate electric fields when the transition from acoustic-phonon-limited to optical-phonon-limited transport takes place.