Biased Semiconductor Superlattices Research Articles

Generalized framework for the step response of semiconducting materials to optically switched electrical bias input in terahertz emission spectroscopy

In this paper, a generalized framework for the step response of semiconducting materials to optically switched electrical bias input in terahertz emission spectroscopy was developed, introducing a complex response function into the frequency domain. A comprehensive formula was obtained for calculating the transient current from the poles of the response function under bias field. This formula was found to give transient currents of an exponentially saturated, overshooting, or oscillating nature for three different regimes of charge transport in an isolated energy band. Furthermore, it was clarified how the transient terahertz emission is linked to the response function and its retarded contribution. When either true current or polarization current is linear with respect to bias field and dominates the transient current, the retarded contribution is identified as the small-signal ac complex conductivity. Two different spectral examples of the retarded contribution were given for actual terahertz Bloch oscillations in biased semiconductor superlattices, describing the small-signal response of polarization current under the Wannier–Stark localization and the large-signal response of true current under interminiband mixing.

Effects of initial three-dimensional electron energy distribution on terahertz Bloch oscillations in a biased semiconductor superlattice

We investigate how the initial three-dimensional energy distribution of electrons created by femtosecond pump pulses in a biased semiconductor superlattice affects terahertz Bloch oscillations, which imitate a step response to a bias electric field. The emitted terahertz waveforms are well reproduced from a damped oscillation current with capacitive nature, exhibiting shorter relaxation times and worse temporal resolutions for central pump photon energies that are outside the range of ordinary electron excitation into the conduction first miniband. This indicates that in-plane excess energy changes the relaxation time via scattering processes, while partial use of the pump pulse spectrum reduces the temporal resolution.

Electronic states underlying peculiar Bloch oscillations in a biased semiconductor superlattice with interminiband mixing

We simulate the energy eigenstates of electrons and holes, which underlie terahertz Bloch oscillations observed recently with a peculiar phase shift, in a biased semiconductor superlattice with interminiband mixing. Electron wavefunctions are extended downstream, while some of them have a moderately first-miniband-like nature that partly resembles Wannier–Stark localization upstream. When a typical heavy-hole wavefunction is chosen, a few first-miniband-like electron wavefunctions prove to have large overlap integrals with it under relatively low bias fields. These electron wavefunctions are thus essential for the optical excitation of the Bloch oscillations, supported experimentally by the peak patterns of dc photocurrent spectra.

Harmonic Generation in Biased Semiconductor Superlattices.

Semiconductor superlattices are proven nanomaterials for THz nonlinear optics by means of high order harmonic generation. Seminal approaches leading to a perfectly antisymmetric current-voltage (I–V.) curve predict the generation of odd harmonics only in the absence of a bias. However, even harmonics at high orders have been detected in several experiments. Their generation has been explained by considering deviations from the current flow symmetry that break the exact antisymmetry of the I–V. curve. In this paper, we focus on another issue found experimentally that has also not been explained, namely the harmonic power output asymmetry from negative to positive applied bias. Once more, breaking the I–V. flow symmetry explains the experiments and leads to a further tool to design the power output of these materials. Furthermore, a new approach for the Boltzmann Equation under relaxation-rate approximation eliminates numerical difficulties generated by a previous theory. This leads to very efficient analytical expressions that can be used for both fundamental physics/optics/material sciences and realistic device development and simulations.

Interaction between two Bloch oscillating electron groups in a biased semiconductor superlattice created by a pair of temporally shifted optical pulses

We investigate the interaction between two Bloch oscillating electron groups in a GaAs-based superlattice created by a pair of temporally shifted optical pulses, observing terahertz waveforms emitted by the second group in the presence of the first group. The terahertz emission exhibits gradual reductions in its resonance frequency and dephasing time as the temporal difference increases to a few hundred ps. This suggests that the first group interacts with the second group mainly via field screening and phonons. The initial oscillation phase of the second group, corresponding to its inversionless terahertz gain, is not affected by the first group.

Phase shift of terahertz Bloch oscillations induced by interminiband mixing in a biased semiconductor superlattice

We investigate terahertz waveforms emitted from a GaAs-based superlattice with interminiband mixing under various dc bias electric fields, injecting electrons into the conduction first miniband with femtosecond optical pulses. Bloch oscillations are observed under relatively low bias fields; surprisingly, the oscillation phase is found to shift by π/2 from those reported previously for Wannier–Stark ladder states in nearly isolated minibands. The oscillatory feature of terahertz emission is gradually destroyed under higher bias fields. We show that the observed π/2 phase shift can be ascribed to significant delocalization of electron wavefunctions driven by interminiband mixing.

Temperature-dependent spectral linewidths of terahertz Bloch oscillations in biased semiconductor superlattices

We investigate temperature-dependent spectral linewidths of Bloch oscillations in biased semiconductor superlattices experimentally and theoretically. The spectral linewidth in a GaAs-based superlattice determined by terahertz emission spectroscopy becomes larger gradually as temperature increases from 80 to 320 K. This behavior can be quantitatively reproduced by a microscopic theory of the spectral linewidth that has been extended to treat the phonon scattering and interface roughness scattering of electrons on a Wannier-Stark ladder. A detailed comparison between the terahertz measurements and theoretical simulations reveals that the LO phonon absorption process governs the increase in the spectral linewidth with increasing temperature.

Manifestation of anomalous Floquet states with longevity in dynamic fractional Stark ladder with high AC electric fields

We examine a resonance structure of Floquet state in dynamic fractional Stark ladder (DFSL) realized in biased semiconductor superlattices driven by a terahertz cw laser on the basis of the R-matrix Floquet theory. To do this, we calculate an excess density of state ρ(ex)(E) corresponding to lifetime of the Floquet state with a fractional matching ratio η, where η is the ratio of a Bloch frequency ΩB to a laser frequency ω, namely, η=ΩB/ω. The results for η=3/2 demonstrate the appearance of discernibly large peaks associated with Floquet states with longevity in a region of relatively high laser-intensity. The underlying physics is discussed in terms of an analytical expression of ρ(ex)(E) and the associated Green function in which ponderomotive couplings are included in a non-perturbative way.

Dissipative transport in superlattices within the Wigner function formalism

We employ the Wigner function formalism to simulate partially coherent, dissipative electron transport in biased semiconductor superlattices. We introduce a model collision integral with terms that describe energy dissipation, momentum relaxation, and the decay of spatial coherences (localization). Based on a particle-based solution to the Wigner transport equation with the model collision integral, we simulate quantum electronic transport at 10 K in a GaAs/AlGaAs superlattice and accurately reproduce its current density vs field characteristics obtained in experiment.

Enhanced terahertz emission by Landau quantization in semiconductor superlattices

We present a theoretical description of the process of therahertz emission in biased semiconductor superlattices that follows an ultra-fast interband excitation. The results show that the average current performs Bloch oscillations whose amplitude depends on the intrinsic characteristic of the superlattice as well as on the light pulse parameters. In these calculations we use a fully three-dimensional picture and include the excitonic effects. We also studied the terahertz intensity when the sample is subjected to a magnetic field parallel to its axis. We considered in detail the high magnetic field regime, where the in-plane motion is frozen in Landau orbits spectrally well separated. In this regime, a set of quasi one-dimensional Bloch oscillators can be ideally generated (oscillators with decoupled vertical and lateral electron motions), making the terahertz emission more intense and more coherent.

Optimizing biased semiconductor superlattices for terahertz amplification

Over the past 15 yr or more, researchers have been trying to achieve gain for electromagnetic fields in the terahertz frequency region using biased semiconductor superlattices, but with little success. In this work, we employ our model of the excitonic states in biased GaAs/Al0.3Ga0.7As semiconductor superlattices to find the optimal structures for amplification of terahertz radiation. In particular, we determine the optimum well width, barrier width, and bias field for terahertz fields with frequencies ranging from 1 to 4 terahertz. We find that gain coefficients on the order of 40 cm−1 should be achievable over most of this frequency range.

Variation of Dynamic Fano Resonances in Semiconductor Superlattices Driven by Dc and THz Fields

We describe the dynamic Fano resonances in a biased three-dimensional semiconductor superlattice driven by combined dc and THz fields. The Fano resonances on the Wannier Stark ladders are dominantly changed by the THz field via the band collapse phenomenon. The Fano coupling matrix is closely related to the separated energy distance between the two types of exciton resonances produced by the dc and the THz fields. The dynamic Fano coupling strength increases as the exciton resonance induced by the THz field approaches the Wannier exciton states.

Intraband dynamics and terahertz emission in biased semiconductor superlattices coupled to double far-infrared pulses

This paper studies both the intraband polarization and terahertz emission of a semiconductor superlattice in combined dc and ac electric fields by using the superposition of two identical time delayed and phase shifted optical pulses. By adjusting the delay between these two optical pulses, our results show that the intraband polarization is sensitive to the time delay. The peak values appear again for the terahertz emission intensity due to the superposition of two optical pulses. The emission lines of terahertz blueshift and redshift in different ac electric fields and dynamic localization appears. The emission lines of THz only appear to blueshift when the biased superlattice is driven by a single optical pulse. Due to excitonic dynamic localization, the terahertz emission intensity decays with time in different dc and ac electric fields. These are features of this superlattice which distinguish it from a superlattice generated by a single optical pulse to drive it.

Controlling and enhancing terahertz collective electron dynamics in superlattices by chaos-assisted miniband transport

We show that a tilted magnetic field transforms the structure and THz dynamics of charge domains in a biased semiconductor superlattice. At critical field values, strong coupling between the Bloch and cyclotron motion of a miniband electron triggers chaotic delocalization of the electron orbits, causing strong resonant enhancement of their drift velocity. This dramatically affects the collective electron behavior by inducing multiple propagating charge domains and GHz-THz current oscillations with frequencies ten times higher than with no tilted field.

Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain

We present a careful analysis of the coherent terahertz emission from an undoped biased semiconductor superlattice excited via an ultrashort optical pulse. We use both a semiclassical model and a fully quantum-mechanical model that includes the excitation process and excitonic effects to analyze emission. We conclude that, in contrast to what has recently been claimed, it is not possible to deduce whether there is terahertz gain from the analysis of the emitted coherent terahertz pulse.

Tunable terahertz amplification in optically excited biased semiconductor superlattices: Influence of excited excitonic states

We simulate the coherent carrier dynamics of an optically excited, undoped AlGaAs superlattice in the presence of a terahertz pulse using an excitonic formalism that includes $1s$ excitonic states as well as higher in-plane excited states and allows for dephasing and population decay. We show that this system exhibits tunable terahertz gain due to excitonic effects, even in the presence of a large number of unbound excitons. We find that gain coefficients greater than $20\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ can be achieved over a tuning range of $3--11\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$ and that due to the coherent cascading of the carriers down the excitonic Wannier-Stark ladder, the gain coefficients have much higher gain saturation fields than comparable two-level systems.

Ultrafast Fiske effect in semiconductor superlattices induced by the coupling of electron Bloch oscillations to longitudinal optical phonons and coherent plasmons

We show that resonant coupling of coherent electron Bloch oscillations to longitudinal optical phonons in a wide-miniband semiconductor superlattice induces a unidirectional transient electron current in the system. This effect has a profound analogy to the DC Fiske effect observed when a superconductor Josephson junction or a superfluid weak link is coupled, respectively, to an electromagnetic or acoustic resonator. In the ultrafast Fiske effect, the coupling opens an elastic rectifying channel which exists only during the coherence time of the electron wave packets involved. In the considered ultrafast coupling effect, the longitudinal optical phonons in the superlattice play the role of the resonator coupled to the free damped electron Bloch oscillations, via both their amplitude and phase. We also show that similar unidirectional transient current, but with the opposite sign, is induced by non-resonant coupling of electron Bloch oscillations to coherent electron plasma oscillations. This unidirectional transient current can probably explain the origin, the sign and the carrier-density dependence of the self-induced coherent unidirectional current, which was observed in an undoped biased semiconductor superlattice with photo-excited carriers.

Excitonic approach to the ultrafast optical response of semiconductors

We present a theoretical approach to treating the coherent dynamics of optically generated charge carriers in semiconductors using an excitonic basis. In contrast to the semiconductor Bloch equations, our approach treats intraband correlations without factorization. It also includes phase space filling effects that have generally been omitted in previous excitonic treatments of coherent dynamics. We show that, in the coherent limit, where the intraband dephasing time and population decay time are both equal to half of the interband dephasing time, our excitonic approach agrees with the semiconductor Bloch equations to at least third order in the optical field, but that it differs significantly in more general situations. Our excitonic equations are shown to be particularly applicable in systems, such as biased semiconductor superlattices, where bound excitons dominate the optical response and where intraband correlations play a central role. Using a simple model of a nanoring, we show how the spectral shifts in the interband response can be explained in terms of phase-space-filling-induced excitonic population dynamics.

Interminiband Rabi oscillations in biased semiconductor superlattices

Carrier dynamics at energy level anticrossings in biased semiconductor superlattices was studied in the time domain by solving the time-dependent Schr\"odinger equation. The resonant nature of interminiband Rabi oscillations has been explicitly demonstrated to arise from the interference of intrawell and Bloch oscillations. We also report a simulation of direct Rabi oscillations across three minibands, in the high-field regime, due to interaction between three strongly coupled minibands.

Acoustic Analogue of Electronic Bloch Oscillations and Resonant Zener Tunneling in Ultrasonic Superlattices

We demonstrate the existence of Bloch oscillations of acoustic fields in sound propagation through a superlattice of water cavities and layers of methyl methacrylate. To obtain the acoustic equivalent of a Wannier-Stark ladder, we employ a set of cavities with different thicknesses. Bloch oscillations are observed as time-resolved oscillations of transmission in a direct analogy to electronic Bloch oscillations in biased semiconductor superlattices. Moreover, for a particular gradient of cavity thicknesses, an overlap of two acoustic minibands occurs, which results in resonant Zener-like transmission enhancement.