Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices (original) (raw)
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Modulated Bloch Waves in Semiconductor Superlattices
European Consortium for Mathematics in Industry, 2014
We show that in a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. In order to demonstrate this, we propose a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions and we derive by singular perturbation methods hydrodynamic equations for electron density, electric field, and the complex amplitude of the Bloch oscillations. Numerical solutions of these equations show stable Bloch oscillations with spatially inhomogeneous field, charge, current density, and energy density profiles. These Bloch oscillations disappear as scattering times become sufficiently short. For sufficiently low lattice temperatures (70 K), Bloch and Gunn type oscillations mediated by electric field, current, and energy domains coexist for a range of voltages. For larger lattice temperatures (300 K), there are only Bl...
Spatially confined Bloch oscillations in semiconductor superlattices
EPL (Europhysics Letters), 2011
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that convective nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. In this case, numerical solutions show that there are stable Bloch oscillations confined to a region near the collector with inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear when damping due to inelastic collisions becomes sufficiently strong.
Nonlinear Electronic Transport in Semiconductor Superlattices
Applied and Industrial Mathematics in Italy Ii, 2007
We propose novel BGK models for inelastic collisions in the kinetic theory of electron transport in semiconductor superlattices. The Chapman-Enskog method produces a drift-diffusion equation describing the behavior of the electric field F and the electron density n in an appropriate hyperbolic limit. Under voltage bias, stable solutions thereof include stable self-sustained oscillations of the current through the superlattice due to periodic injection of electric field pulses at one end of the device that move to the other end. For almost elastic collisions, the model has a local equilibrium that oscillates rapidly in time and the resulting balance equations describe for the first time the annihilation of the Bloch oscillations due to scattering.
Bloch oscillations in superlattices: Monte-Carlo analysis using 2D scattering model
Physica E-low-dimensional Systems & Nanostructures, 2003
We studied the behavior of Bloch oscillations (BO) in AlGaAs/GaAs superlattices by Monte-Carlo method. Two different scattering models based on effective mass approximation were used for studying of electron miniband transport. Scattering on polar optical and acoustic phonons as well as impurities were taken into account. Behavior of BO was studied under different conditions such as the intensity of electric field, temperature and ionized impurity density.
Miniband transport and oscillations in semiconductor superlattices
Nanotechnology, 2004
We present and analyse solutions of a recent derivation of a drift-diffusion model of miniband transport in strongly coupled superlattices. The model is obtained from a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term by means of a consistent Chapman-Enskog expansion. The reduced drift-diffusion equation is solved numerically and travelling field domains and current oscillations are obtained. A broad range of frequencies can be achieved, depending on the model parameters, in good agreement with available experiments on GaAs/AlAs superlattices.
Bloch oscillations in superlattice simulated by the Monte Carlo method
1997
The Monte Carlo based semiclassical model for the vertical electron transport in superlattice including most important features of electron transport through the superlattice minibands is presented. Inelastic acoustic phonon, polar optical phonon and ionized impurity scattering are considered in the bulk formalism. The model has been applied on GaAs/GaAlAs superlattice simulation with one miniband for gamma electrons. The simulation is performed by different conditions defined by temperature, electric field and ionized impurity concentration. Bloch oscillations of miniband electrons with different lifetimes, frequencies and amplitudes are observed in the simulation results
Bloch Oscillations of Excitonic Wave-Packets in Semiconductor Superlattices
Physical Review B, 1994
Vfe present a detailed investigation of the coherent dynamics of excitonic wave packets composed of heavy/light-hole, electron miniband, and Wannier-Stark states in GaAs/Al Gai As superlattices. Using transient degenerate four-wave mixing, we study the dependence of Bloch oscillations and heavy/light-hole beats on the applied field, miniband width, lattice temperature, and excitation conditions. Bloch oscillations are observed in samples with minibandwidths varying from 13 to 46 meV and at lattice temperatures up to 200 K. Under certain excitation conditions, we observe higher harmonics of the Bloch oscillation frequency. Spectrally resolved transient four-wave mixing experiments show unambiguously that quantum-mechanical interference is the origin of the oscillations. The experimental four-wave mixing traces are compared with a theoretical model based on many-level third-order density-matrix theory.
Nonlinear Electron and Spin Transport in Semiconductor Superlattices
SIAM Journal on Applied Mathematics, 2008
Nonlinear charge transport in strongly coupled semiconductor superlattices is described by Wigner-Poisson kinetic equations involving one or two minibands. Electron-electron collisions are treated within the Hartree approximation whereas other inelastic collisions are described by a modified BGK (Bhatnaghar-Gross-Krook) model. The hyperbolic limit is such that the collision frequencies are of the same order as the Bloch frequencies due to the electric field and the corresponding terms in the kinetic equation are dominant. In this limit, spatially nonlocal drift-diffusion balance equations for the miniband populations and the electric field are derived by means of the Chapman-Enskog perturbation technique. For a lateral superlattice with spin-orbit interaction, electrons with spin up or down have different energies and their corresponding drift-diffusion equations can be used to calculate spin-polarized currents and electron spin polarization. Numerical solutions show stable self-sustained oscillations of the current and the spin polarization through a voltage biased lateral superlattice thereby providing an example of superlattice spin oscillator. PACS numbers:
Journal of Physics: Condensed Matter, 2002
Nonlinear charge transport in semiconductor superlattices under strong electric fields parallel to the growth direction results in rich dynamical behaviour including the formation of electric field domains, pinning or propagation of domain walls, self-sustained oscillations of the current and chaos. Theories of these effects use reduced descriptions of transport in terms of average charge densities, electric fields, etc. This is simpler when the main transport mechanism is resonant tunnelling of electrons between adjacent wells followed by fast scattering between subbands. In this case, we will derive microscopically appropriate discrete models and boundary conditions. Their analyses reveal differences between low-field behaviour where domain walls may move oppositely or parallel to electrons, and high-field behaviour where they can only follow the electron flow. The dynamics is controlled by the amount of charge available in the superlattice and doping at the injecting contact. When the charge inside the wells becomes large, boundaries between electric field domains are pinned resulting in multistable stationary solutions. Lower charge inside the wells results in self-sustained oscillations of the current due to recycling and motion of domain walls, which are formed by charge monopoles (high contact doping) or dipoles (low contact doping). Besides explaining wave motion and subsequent current oscillations, we will show how the latter depend on such controlling parameters as voltage, doping, temperature, and photoexcitation.