Bloch oscillations in superlattices: Monte-Carlo analysis using 2D scattering model (original) (raw)
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
Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices
Physical Review B, 2011
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. To demonstrate this, a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions is proposed and hydrodynamic equations for electron density, electric field and the complex amplitude of the Bloch oscillations are derived by singular perturbation methods. For appropriate parameter ranges, 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.
Coupled Bloch-phonon oscillations in GaAs/AlGaAs superlattices: theory and experiment
Physica E: Low-dimensional Systems and Nanostructures, 2000
We report on the femtosecond dynamics of coherent Bloch oscillations in GaAs=AlxGa1−xAs superlattices. In a superlattice with a miniband width equal to the optical phonon energy of GaAs the Bloch frequency can be tuned into resonance with the LO phonon by an applied electric ÿeld. We observe a strong coupling between Bloch oscillations and phonons leading to the coherent excitation of optical phonons when both are brought into resonance. This phenomenon is analyzed theoretically on the base of a microscopic Hamiltonian for the electron-phonon interaction in the superlattice. We show that coupled modes are described by a nonlinear pendulum coupled linearly to an oscillator representing the phonons. Under resonance condition the amplitudes of both modes increase and sidebands appear. The theoretical results are compared to the experimental observations.
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...
Time-resolved optical investigations of bloch oscillations in semiconductor superlattices
Solid-State Electronics, 1996
We present a complementary study of the interband and intraband dynamics of optically excited Bloch oscillations in GaAs/AI,Ga, _ ,As superlattices. Distinct differences in the frequency and dephasing of the oscillations give evidence for Bloch oscillations performed by electrons in continuum states and by excitonic wavepackets. The dephasing time of the electronic continuum states is found to be exceptionally long as compared to the excitonic dephasing time under identical excitation conditions. These observations are confirmed by THz emission experiments, where Bloch oscillations are detected under optical excitation well above the fundamental band gap. The experimental observations suggest that the electronic coherence may be partially maintained during relaxation and momentum scattering processes.
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.
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.
Internal field dynamics of coherent bloch oscillations in superlattices
Superlattices and Microstructures, 1994
Tbe dynamics of coherent wavepacket oscillations in GaAsiAIxGal_xAs superlattices are investigated by transmittive electro-optic sampling (TEDS) with femtosecond time resolution. Tbe internal polarization dynamics of coherently superposed Wannier-Stark states in an externally biased superlattice, denoted as Bloch oscillations, can be monitored with high sensitivity in TEDS experiments. The amplitude, dephasing, and frequency of Bloch oscillations are studied as a function of applied electric field. The increasing localization of Wannier-Stark states at higher fields results in a decreasing Bloch osciIlation amplitude.
Coupling of electromagnetic waves and Bloch oscillations in quantum superlattice
2003 Third IEEE Conference on Nanotechnology, 2003. IEEE-NANO 2003.
In this report we analyze, for the first time to our knowledge, the linear coupling of the Bloch oscillations and transversal electromagnetic waves in a quantum semiconductor superlattice (QSSL) towards the problem of realization of the tunable THz source. The analysis is implemented by means of wave equation for the electromagnetic field and the material equations with quasi-classic description of the electron transport in a biased QSSL. In the case when the Bloch frequency is greater than plasma frequency at the bottom of the lowest miniband of QSSL, the coupling leads to the reconnection of the dispersion curves at the region of their crossing, forming a slit between always stable high-frequency branch and lower frequency branch which has the region of an instability due to electron bunching in the momentum space. The last circumstance opens the great possibility to generate THz radiation in QSSL superimposed with an inhomogeneous dc field that is provided by the presence of the turning points for the electromagnetic waves. Such turning points play the role of the mirrors making up a resonator for the unstable waves. For the typical GaAslGaAlAs QSSL with miniband electron density IO"cmJ and superlattice period 5nm the critical strength of applied de electric field which leads to spectrum splitting is about 9kV/cm.
Damping of bloch oscillations in one-, two-, and three-dimensional quantum-dot superlattices
Semiconductors, 2002
In the preceding paper by the same authors, the density-matrix formalism was used to derive a quantum kinetic equation describing the damping of Bloch oscillations (BOs) in perfect one-, two-, and three-dimensional quantum-dot superlattices (QDSLs) and the conditions were determined under which the only process of the charge-carrier scattering by phonons in 2D and 3D QDSLs that contributes to the BO damping is the acoustic-phonon scattering within the transverse minibands of the Stark ladder of the carrier states. In this paper, the possibilities of suppressing this remaining scattering channel are analyzed. It is shown that the BO damping time in 2D and 3D QDSLs at room temperature may exceed the oscillation period by a factor of several hundreds and the conditions necessary for such strong suppression of the scattering are revealed. This makes a considerable difference between the QDSLs and the quantum-well superlattices, where, in reality, the BOs damping over a single oscillation period at room temperature. © 2002 MAIK "Nauka/Interperiodica".
Journal of Computational Physics, 2012
We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70 K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300 K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is * Corresponding author.
Electron-Phonon Scattering in Semiconductor Superlattices in a Quantizing Magnetic Field
Japanese Journal of Applied Physics, 1988
Total electron-phonon scattering rates are obtained in an ideal superlattice in a quantizing magnetic field. The dispersion of an electron along the superlattice axis is assumed to be of a tight-binding type. Compact analytical expressions are possible for acoustic and nonpolar optical phonon scattering. The numerical results for acoustic and nonpolar optical phonon scattering rates are presented for the GaAs/Ga1-x Al x As superlattice and the effect of miniband width parameters on these scattering rates is discussed.
Superradiant emission from Bloch oscillations in semiconductor superlattices
Physical review. B, Condensed matter, 1996
The superradiant character of submillimeter-wave emission from optically excited electronic Bloch oscillations in a GaAs/Al x Ga 1Ϫx As superlattice is investigated by time-resolved terahertz emission spectroscopy. The intensity of the radiation and its decay time are studied as a function of the density of excited charge carriers. From the measured emission efficiency, the spatial amplitude of the charge oscillations is estimated.
Damping of bloch oscillations in quantum dot superlattices: A general approach
Semiconductors, 2002
A quantum kinetic equation describing damping of the Bloch oscillations in ideal quantum-dot (QD) superlattices of various dimensionalities (1D, 2D, 3D) has been derived using the density matrix formalism. The possibility of suppressing completely single-phonon scattering by optical phonons and considerably suppressing the acoustic-phonon scattering in the QD superlattice by effectively controlling the spectrum by varying the DC electric field magnitude and orientation is demonstrated. Conditions ensuring that the only photon-scattering mechanism responsible for damping of the Bloch oscillations is scattering by acoustic phonons within transverse minibands of the Stark carrier-state ladder are obtained.
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.
Phonons in semiconductor superlattices
Superlattices and Microstructures, 1991
We present theoretical studies of phonon modes in semiconductor superlattices in a rigid-ion model. We examine the dispersion curves for phonone propagating in any directions, taking into account the long-range Coulomb interaction. We introduce an alternative approach which avoids direct computation of the Coulomb interaction in superlattices.
Theory of interface scattering of phonons in superlattices
2010
We present an atomic-scale theory of interface scattering of phonons in superlattices. In particular, we describe the scattering as a result of two features, mixing of atoms at interfaces and presence of dislocations at interfaces due to lattice mismatch. We apply the theory to quantitatively explain the thermal conductivity, and its variation with period and temperature, of Si/Ge superlattices.
Physical Review B, 1993
We analytically study phonon transmission and localization in random superlattices by using a Green's function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice structure factor. This is done by considering the backscattering of phonons, due to the complex mass density fluctuations, which incorporates all of the forward scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.
Phonon dispersion curves of GaAs/AlAs superlattices
Superlattices and Microstructures, 1988
The phonon properties of (GaAs)m(AlAs)n superlattices are studied with an eleven-parameter rigid-ion model. Short-range interactions up to the second neighbours are included, and the long-range Coulomb interaction is calculated exactly. Modes propagating both normal (k// = 0) oblique (k// ≡ 0) to the interfaces are studied. Anisotropy of zone center optical phonons is examined. The theoretical results are compared with the existing experimental data with favorable agreement.
Physical Review B, 1995
The ultrafast dynamics of photoexcited carriers in semiconductor superlattices is studied theoretically on the basis of a Monte Carlo solution of the coupled Boltzmann transport equations for electrons and holes. The approach allows a kinetic description of the relevant interaction mechanisms such as intraminiband and interminiband carrier-phonon scattering processes. The energy relaxation of photoexcited carriers, as well as their vertical transport, is investigated in detail. The effects of the multiminiband nature of the superlattice spectrum on the energy relaxation process are discussed with particular emphasis on the presence of Bloch oscillations induced by an external electric 6eld. The analysis is performed for different superlattice structures and excitation conditions. It shows the dominant role of carrierpolar-optical-phonon interaction in determining the nature of the carrier dynamics in the low-density limit. In particular, the miniband width, compared to the phonon energy, turns out to be a relevant quantity in predicting the existence of Bloch oscillations.