Electrons In Semiconductor Superlattices Research Articles

Multistability, chaos, and random signal generation in semiconductor superlattices.

Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable device for random signal generation to fill the THz gap. The interplay among noise, multistability, and chaos is also investigated.

Resonance splitting effect through magnetic superlattices in graphene

Using the transfer-matrix formalism, the resonance splitting effect of Dirac electrons through two types of magnetic superlattices in graphene is studied theoretically. The numerical results show that the transmission presents (n − 1)-fold resonance splitting for the both magnetic superlattices with n-barrier, similar to Schrödinger electrons in semiconductor superlattices. It is believed that the Dirac electrons possess a general (n − 1)-fold splitting rule for n-barrier magnetic superlattices, of which the corresponding vector potential is periodic field. The magnetic superlattices with strong magnetic field can be used as a very efficient wave-vector filter for Dirac electrons. The splitting feature of the transmission probability also reflects in the conductance and shot noise. These properties should be useful for the design of graphene-based electronic devices.

Resonant peak splitting through magnetic Kronig–Penney superlattices in graphene

Abstract The resonance splitting effect of Dirac electrons through magnetic Kronig–Penney superlattices with delta-function barriers in graphene is studied theoretically. It is found that both transmission probability and conductance present ( n − 1 ) - fold resonant peak splitting in n vector potential barriers, which is the same as that of standard electrons in semiconductor superlattices [R. Tsu, L. Esaki, Appl. Phys. Lett. 22 (1973) 562]. The resonant peak splitting and wave-vector filtering could be controlled by adjusting the transverse wave vector and structural parameters. These properties may be useful for the design of graphene-based electronic devices.

Magnetic-field-enhanced transient and stationary drift currents of oscillating Bloch electrons in superlattices and limits of average-particle description in relation to Monte Carlo simulations

We theoretically investigate transient and stationary drift currents of Bloch electrons in semiconductor superlattices subjected to an electric field along the growth axis and a magnetic field tilted with respect to the electric field. The magnetic-field-induced nonlinear coupling between the Bloch oscillations along the axis and in-plane cyclotron oscillations leads to a resonant phase-sensitive self-rectification of the oscillating currents. Both the transient motion of the particles after pulse excitation and the motion in the stationary state show this phenomenon. The effects have already been demonstrated experimentally but were discussed on the basis of different concepts. Here, we treat the transient and the stationary effect on equal footing using the model of the coupled oscillators. The relaxation and dephasing of the oscillations are explored with a Monte Carlo method and compared with results of models which use average-particle variables. It is found that average-particle-type models are not adequate to describe the resonance and relaxation effects of the ensemble satisfactorily. In the long-time limit and for strong coupling, they lead to some artifacts such as self-sustained oscillations or hysteresis effects, which do not exist in the Monte Carlo approach. The average-particle description is a qualitative approximation for weak coupling and if elastic scattering dominates. The shapes of the resonance curves in the Monte Carlo simulation sensitively depend on the details of the scattering mechanisms and allow us to identify their relative importance.

DYNAMIC LOCALIZATION AND ELECTROMAGNETIC TRANSPARENCY OF SEMICONDUCTOR SUPERLATTICE IN MULTIFREQUENCY ELECTRIC FIELDS

We consider the dynamics of electrons in semiconductor superlattices in intense multifrequency electric fields. We examine the conditions for dynamic localization and electromagnetic transparency. We investigate processes of formation, destruction, and stabilization of electromagnetic transparency in biharmonic field. The stable states with static fields are determined.

Wannier functions of isolated bands in one-dimensional crystals

We present a simple procedure to obtain the maximally localized Wannier function of isolated bands in one-dimensional crystals with or without inversion symmetry. First, we discuss the generality of dealing with real Wannier functions. Next, we use a transfer-matrix technique to obtain nonoptimal Bloch functions which are analytic in the wave number. This produces two classes of real Wannier functions. Then, the minimization of the variance of the Wannier functions is performed, by using the antiderivative of the Berry connection. In the case of centrosymmetric crystals, this procedure leads to the Wannier-Kohn functions. The asymptotic behavior of the Wannier functions is also analyzed. The maximally localized Wannier functions show the expected exponential and power-law decays. Instead, nonoptimal Wannier functions may show reduced exponential and anisotropic power-law decays. The theory is illustrated with numerical calculations of Wannier functions for conduction electrons in semiconductor superlattices.

Bloch Oscillations in Superlattices: The Problem of a Terahertz Oscillator

The feasibility of designing a terahertz oscillator based on the Bloch oscillations of electrons in semiconductor superlattices is studied. It is shown that superlattices with high-Q Bloch oscillations can be used to generate a terahertz emission in pulsed electric fields with an off-duty factor that ensures the thermalization of electrons heated by the field. It is suggested that a terahertz oscillator is designed with a frequency that is tuned continuously by an electric field on the basis of anharmonic Bloch oscillations of electrons in semiconductor superlattices that have special miniband characteristics in which the major part of the effective electron mass is positive and increases as the electron energy increases. This circumstance makes it possible to eliminate the development of undesired domain instability (the Gunn effect).

Geometrical approach to scattering in one dimension

The transfer matrix technique is much used to study one-dimensional scattering, such as electrons in semiconductor superlattices. We elaborate on the geometrical interpretation of the transfer matrix, in particular its relation to conformal mapping in the unit disc, and the analogy to Lorentz transformations on a Dirac spinor in 2 + 1 dimensions.

Optimal band-pass filter for electrons in semiconductor superlattices

An analytic solution is presented to the problem of designing anantireflection coating to be added to an arbitrary periodicsuperlattice, so as to create an optimal electron mini-band-pass filter.

Photonic Bloch oscillations in laterally confined Bragg mirrors

We show that the photons in laterally confined Bragg mirrors may experience Bloch oscillations similar to those of electrons in semiconductor superlattices subjected to electric fields. An effective electric field is produced in the photonic case by variation of the lateral size of the structure as one moves along the structure axis. The temporal behavior of a short pulse of light oscillating within a miniband of such an optical superlattice made from the porous silicon has been modeled by a proper scattering-state simulation scheme.

Photon Bloch oscillations in laterally confined Bragg mirrors

We show that photons in laterally confined Bragg mirrors may experience Bloch oscillations similar to those of electrons in semiconductor superlattices. In particular, Bloch oscillations of light within a photonic miniband of a porous silicon Bragg mirror is modelled by a proper scattering-state simulation scheme.

Transport in semiconductor superlattices in quantizing parallel electric and magnetic fields

Transport of electrons in semiconductor superlattices in high electric and magnetic fields applied parallel to the symmetry axis is studied within a quantum-kinetic approach. Scattering on acoustic and optic phonons as well as impurities is taken into account. Cyclotron-Stark resonances in the current density are much more pronounced in the magnetic field dependence than in the current–voltage characteristic. This theoretical result agrees qualitatively with experiments. Cyclotron-Stark-phonon resonances are strongly enhanced by the magnetic field, but are predicted to be observable only in samples, where the elastic scattering is weak compared to scattering on polar-optical phonons.

Cyclotron-Stark-phonon-photon resonances in semiconductor superlattices under terahertz irradiation

High-field transport of electrons in semiconductor superlattices under intense parallel magnetic and time-dependent electric fields is investigated within a quantum-kinetic approach. Intra-collisional field effects of all fields are taken into account. In a biased superlattice subject to an intense radiation field of terahertz frequency, cyclotron-Stark-phonon-photon current resonances are predicted to occur for particular ratios of the Bloch , cyclotron , and terahertz frequencies . Under strong irradiation, pronounced maxima appear at resonance positions given by , where l, n, m are integers and the phonon frequency. Electro-phonon resonances are enhanced by a magnetic field but strongly weakened by an intense terahertz electric field.

Direct measurement of the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices

We present a novel experimental technique which allows to precisely measure the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices as a function of time: The dipole field caused by the motion of the electrons is traced by small shifts of the Wannier–Stark ladder states. The electron wave packet displacement can then be derived from these shifts with the excitation density as the only free parameter. Using this method, we show that the optically generated electron wave packets perform harmonic oscillations, as predicted by Zener for the semiclassical motion of electrons in 1934. The absolute amplitudes of the wave packets depend inversely on the static field and are close to the values expected from semiclassical theory.

Direct Measurement of the Spatial Displacement of Bloch-Oscillating Electrons in Semiconductor Superlattices

Direct Measurement of the Spatial Displacement of Bloch-Oscillating Electrons in Semiconductor Superlattices

Quasistatic and dynamic interaction of high-frequency fields with miniband electrons in semiconductor superlattices

We studied the interaction of high-frequency (HF) fields with the miniband electrons in semiconductor superlattices that show (at room temperature) negative differential conductance. We observed a field-induced reduction of current through the superlattices, with a different bias dependence for fields below and above a characteristic frequency (1 THz). An analysis based on Bloch oscillations, indicating that the electrons relaxed within one cycle of the HF field (quasistatic interaction) or followed the field adiabatically (dynamic interaction), allows one to extract the intraminiband relaxation time ${(10}^{\ensuremath{-}13}\mathrm{s}).$

Direct Measurement of the Spatial Displacement of Bloch-Oscillating Electrons in Semiconductor Superlattices

The absolute spatial displacement of Bloch-oscillating electrons in semiconductor superlattices is measured as a function of time with a few angstrom resolution using a novel experimental technique: The oscillating Bloch wave packet creates a small dipole field which can be determined using the field shift of the Wannier-Stark ladder transitions as a sensitive detector. The total amplitudes and their dependence on the static electric field are in good agreement with a theory including excitonic effects.

Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices.

We solve the time-dependent Schr\"odinger equation based on the complete Hamiltonian for independent electrons in ideal GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As superlattices, described by the conventional one-dimensional flat-band picture, subject to a uniform electric field F. Our approach consists of using high-accuracy numerical methods, thereby enabling us to avoid truncating the Hamiltonian or adopting other uncontrolled approximations. In suitable circumstances the electrons exhibit long-lived, time-periodic Bloch oscillations, in the form of either sinusoidal center-of-mass oscillations or a coherent breathing mode. Depending on the miniband structure of the superlattice, the value of F, and the form of the initial wave function, other dynamical phenomena can coexist with or even totally mask the Bloch oscillations. These are unbounded acceleration of a portion of the electron wave packet antiparallel to the electric field and intrawell oscillations. We provide the conditions under which each of these three basic dynamical elements occurs. We summarize the major results of our systematic investigation of the dependence of the electron dynamics on the entire parameter space of periodic potentials, field strengths, and initial wave functions.

Bloch and localized electrons in semiconductor superlattices

The energy spectrum of electrons in semiconductor superlattices consists of Bloch-like miniband states and localized impurity states. Optical transitions between these states are investigated by infrared spectroscopy. The inter-miniband absorption spectrum is dominated by the van Hove singularities of the quasi one-dimensional joint density of states. The detailed shape of the absorption can be understood in terms of the relevant transition matrix elements and the electron concentration, i.e. it depends on whether the first miniband is full or half-filled. We show that this has implications for intra-miniband absorption and the optical sum rules. In addition, a transition between the states localized at the lower edge of the minibands occurs, which can be traced back to the 1s-2pz hydrogenic donor transition in the low-doping limit. Finally, we discuss the relevance of our observations for the study of the metal-insulator transition in superlattices.

Three-dimensional properties of conduction electrons in semiconductor superlattices

The deviation of electron scattering probability in semiconductor superlattices from its bulk value is proposed as an index of 3-D properties of conduction electrons in semiconductor superlattices. The relative deviation of scattering probability is numerically calculated for acoustic-phonon scattering, ionized-impurity scattering, and polar-optical phonon scattering in GaAs/Al 0.45Ga 0.55As superlattices. By comparing the three scattering processes, it is found that the probability of acoustic-phonon scattering in the superlattices deviates to the largest extent, and that the difference in the relative deviations of the scattering probabilities is due to the wave-vector dependences of the respective scattering processes.