| Nonlinear quantum transport theory and its linear limit are examined here for semiconductor microstructures, including quantum wells and superlattices. The problem of linear cyclotron resonance is treated using a memory function approach for a type I semiconductor superlattice with interacting quantum wells subject to impurity and phonon scatterings. Furthermore, we develop a fully microscopic quantum field theoretical description of transport in terms of nonequilibrium generating Green's functions, culminating in the analysis of the transient time development of negative absolute minority electron mobility at low temperature in an electron-hole plasma in a quantum well. In this connection, we set forth the microscopic dynamics for a coupled electron-hole-phonon system with electron-electron and hole-hole interactions, as well as the electron-hole attraction responsible for drag phenomena. The coupled fields equations for the one-electron and one-hole Green's functions, and for the electron-hole Green's function, and for the two-electron and two-hole Green's functions, which involve the mixed Green's function for the one electron or one hole and phonon state variable are derived. The effective interactions are also derived on this basis as well as the dressed phonon propagator. A generalized shielded potential approximation is propounded and we developed an exact variational differential counterpart of the GKB ansatz after separating off the gauge dependence of the physical Green's function in the presence of interactions. Our examination of the transient and steady state current response of an electron-hole system in a quantum well is undertaken on the basis of nonlinear coupled quasi-2D transport equations for the electron and hole Wigner functions which we derive from our Green's function equations. Electron-hole drag effects result in negative absolute minority electron mobility at low temperature in the steady state d.c. limit, and we show that in the linear limit, the phonon mediated electron-hole interaction introduces a small irregularity-oscillation in the knee of the electron mobility curve as function of temperature at about 60 K, which nicely parallels the data of Hopfel, Shah, Wolff and Gossard. Finally, our linearized time-dependent coupled electron and hole Wigner function transport equations are analyzed numerically to study the transient time development of negative electron mobility, including both electron and hole overshoot phenomena, and the approach to steady state subject to dynamic nonlocal electron and hole screening effects. |
