Electron transport in quantum wire superlattices

Electronic transport is theoretically investigated in laterally confined semiconductor superlattices using the formalism of nonequilibrium Green's functions. Velocity-field characteristics are calculated for nanowire superlattices of varying diameters, from the quantum dot superlattice regime to the quantum well superlattice regime. Scattering processes due to electron-phonon couplings, phonon anharmonicity, charged impurities, surface and interface roughness, and alloy disorder are included on a microscopic basis. Elastic scattering mechanisms are treated in a partial coherent way beyond the self-consistent Born approximation. The nature of transport along the superlattice is shown to depend dramatically on the lateral dimensionality. In the quantum wire regime, the electron velocity-field characteristics are predicted to deviate strongly from the standard Esaki-Tsu form. The standard peak of negative differential velocity is shifted to lower electric fields, while additional current peaks appear due to integer and fractional resonances with optical phonons.

Figure 1

Schematic of superlattices with different lateral geometries. Panel (a) shows a standard quantum well superlattice consisting of 2D ($x$,$y$) infinite layers of various materials stacked periodically along the $z$ direction. Panels (b), (c), and (d) represent nanowire superlattices of different lateral sizes. Dotted arrows are sketched of classical trajectories of charge carriers through the various superlattices under an electric field applied along the $z$ direction. Scattering processes occur due to various effects (interaction with phonons, structural disorder, etc.). It illustrates the transition from transport involving 3D scattering processes towards a pure 1D motion with increasing quantum lateral confinement. Cylindrical coordinates ($\rho$,$\theta$,$z$) used in the calculations are indicated for the (b) nanowire.

Figure 2

Drift velocity in a nanowire superlattice as a function of the nanowire diameter for various electric fields. The superlattice period consists of 5 nm GaAs followed by 5 nm AlGaAs. The temperature is set to 300 K.

Figure 3

Spectral function $A_{\text{lat}}\left(E\right)$ (upper panel) and electron density $n_{\text{lat}}\left(E\right)$ (lower panel) for various nanowire diameters (see text for definitions). The electric field is 20 kV/cm and the temperature is 300 K.

Figure 4

Drift velocity–voltage characteristics at 300 K for various diameters of the nanowire superlattice.

Figure 5

Drift velocity–voltage characteristics at 300 K for different treatments of the scattering mechanisms.

Figure 6

Drift velocity–voltage characteristics at 300 K with and without the inclusion of phonon anharmonicity.