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When impurity and phonon scattering coexist, the Boltzmann equation has beensolved accurately for nonlinear electron transport in a quantum wire. Based onthe calculated non-equilibrium distribution of electrons in momentum space, thescattering effects on both the non-differential (for a fixed dc field) anddifferential (for a fixed temperature) mobilities of electrons as functions oftemperature and dc field were demonstrated. The non-differential mobility ofelectrons is switched from a linearly increasing function of temperature to aparabolic-like temperature dependence as the quantum wire is tuned from animpurity-dominated system to a phonon-dominated one [see T. Fang, {\em et al.},\prb {\bf 78}, 205403 (2008)]. In addition, a maximum has been obtained in thedc-field dependence of the differential mobility of electrons. The low-fielddifferential mobility is dominated by the impurity scattering, whereas thehigh-field differential mobility is limited by the phonon scattering [see M.Hauser, {\em et al.}, Semicond. Sci. Technol. {\bf 9}, 951 (1994)]. Once aquantum wire is dominated by quasi-elastic scattering, the peak of themomentum-space distribution function becomes sharpened and both tails of theequilibrium electron distribution centered at the Fermi edges are raised by thedc field after a redistribution of the electrons is fulfilled in a symmetricway in the low-field regime. If a quantum wire is dominated by inelasticscattering, on the other hand, the peak of the momentum-space distributionfunction is unchanged while both shoulders centered at the Fermi edges shiftleftward correspondingly with increasing dc field through an asymmetricredistribution of the electrons even in low-field regime [see C. Wirner, {\emet al.}, \prl {\bf 70}, 2609 (1993)].

Comparison of inelastic and quasi-elastic scattering effects on nonlinear electron transport in quantum wires