Wannier-Stark Localization Research Articles

Bloch oscillations and Wannier-Stark localization in a tight-binding lattice with increasing intersite coupling

The onset of Bloch oscillations in an exactly solvable one-dimensional tight-binding lattice model with increasing hopping rates between adjacent sites is theoretically investigated. In particular, it is shown that Wannier-Stark localization is attained at a finite value of the applied dc field. An optical realization of the lattice model, based on light transport in engineered waveguide arrays, is also proposed.

Bistability operation of photocurrent due to wave‐function coupling of Wannier‐Stark localization states in a GaAs/AlAs superlattice

AbstractWe have investigated effects of the resonant wave‐function coupling between Wannier‐Stark localization states on photocurrent properties in a GaAs (6.8 nm)/Al0.1Ga0.9As (4.0 nm) superlattice. The resonant coupling, which causes an anticrossing behavior of the relevant transition energies, were clearly detected by electroreflectance spectroscopy and analyzed by calculating the Wannier‐Stark localization states as a function of electric field strength. It is found that the photocurrent‐voltage characteristics exhibit a peak structure, which results in a negative differential resistance, owing to a change of the optical transition probability under the resonant‐coupling condition between the first and second quantized electron states in adjacent quantum wells. Utilizing this negative differential resistance property, we have demonstrated a photocurrent‐bistability operation of a self‐electro‐optic effect device. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Wannier-stark effect in Ge/Si quantum dot superlattices

Deep level transient spectroscopy (DLTS) measurements were performed to study electron emission from quantum states in a 20-layer Ge quantum-dot superlattice (QDSL) in a Ge/Si p-n heterostructure. It was established that the changes in the DLTS spectra depend heavily on the magnitude of the applied reverse bias Ur. Three regions of the reverse bias Ur were identified, corresponding to the manifestation of the three modes of the Wannier-Stark effect: Wannier-Stark ladder mode, Wannier-Stark localization, and nonresonant Zener tunneling mode. Furthermore, it was found that the appearance of DLTS peaks for all three modes is associated with electron emission from deep-level defects via Wannier-Stark localized states arising as a result of the splitting of the electron miniband of the Ge/Si QDSL.

Transformation process from quantum beats of miniband excitons to Bloch oscillations in aGaAs∕AlAssuperlattice under applied electric fields

We have investigated the coherent dynamics of excitonic wave packets from the viewpoint of the electric-field-induced transformation from the minibands to the Wannier-Stark (WS) localization in a GaAs $(6.8\phantom{\rule{0.3em}{0ex}}\mathrm{nm})∕\mathrm{Al}\mathrm{As}$ $(0.9\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ superlattice embedded in a $p\text{\ensuremath{-}}i\text{\ensuremath{-}}n$ diode structure with the use of a reflection-type pump-probe technique. It is clearly confirmed that the coherent-dynamics profile changes from the quantum beat of the miniband excitons to the Bloch oscillation in the WS localization with an increase in an applied bias voltage, producing an internal electric field. The key finding is that the Bloch oscillation with the frequency of ${\ensuremath{\nu}}_{\mathrm{BO}}=2eFD∕h$ appears in a weak-localization regime in addition to the ordinary Bloch oscillation with ${\ensuremath{\nu}}_{\mathrm{BO}}=eFD∕h$ in a strong-localization regime, where $F$ is the electric field and $D$ is the superlattice period. The experimental results of the coherent dynamics are reasonably explained by the electric-field-strength dependence of the excitonic-transition energies observed by electroreflectance spectroscopy and that of the localization profiles of the envelope functions of the electron and hole states calculated by a transfer-matrix method.

DLTS study of the Wannier–Stark effect in Ge/Si QD superlattices

Deep-level transient spectroscopy (DLTS) has been applied to study the emission of electrons from quantum states in a 20-layer quantum-dot superlattice (QDSL) of Ge in a Ge/Si p–n heterostructure. Changes in the DLTS spectra of this structure strongly depend on the applied bias U r. There are three bias ranges corresponding to three modes of the Wannier–Stark effect: Wannier–Stark ladder mode, Wannier–Stark localization and non-resonant Zener tunneling. The DLTS peaks for all the three modes are associated with emission of electrons from deep-level defects into the Wannier–Stark localized states resulting from the splitting of the electron miniband of the Ge/Si QDSL.

Photocurrent bistability in a GaAs∕AlxGa1−xAs superlattice under resonant-coupling conditions of Wannier-Stark localization states

We have investigated the effects of the resonant coupling between the Wannier-Stark localization states on photocurrent properties in a GaAs (6.8nm)∕Al0.1Ga0.9As (4.0nm) superlattice embedded in a p-i-n structure. The resonant-coupling profiles were confirmed with electroreflectance spectroscopy and analyzed by calculating the Wannier-Stark localization states as a function of electric field. It is found that the photocurrent-voltage characteristics exhibit peak structures, which results in negative differential resistance, owing to the changes of the optical-transition probabilities under the first- and second-nearest-neighbor resonant-coupling conditions between the first and second quantized electron states in the Wannier-Stark localization. Utilizing the negative differential resistance properties under the resonant-coupling conditions, we have demonstrated photocurrent-bistability operations of a self-electro-optic effect device.

Wannier-Stark ladder conditions in 4H-SiC p-n junctions grown on off axis substrates

4 H - Si C p+-n−-n+ junctions have been prepared on 8° off oriented plane aiming to investigate conditions of Wannier-Stark localization (WSL), and respectively the occurrence of a negative temperature coefficient of avalanche breakdown voltage (TCABV). A method is proposed that can enable obtaining important results without reaching the regime of destructive avalanche breakdown. By analyzing the photocurrent of light with different wavelengths and at strong electric fields, a negative differential photoconductance has been discovered testifying that the WSL is not suppressed at the field inclination in 8° off axis, and a negative TCABV is expected in commercial p-n junctions.

Wannier-Stark Ladder and Negative Differential Conductance in 4H-SiC

The work deals with the highly important problem of the qualitative temperature dependence of avalanche breakdown voltage in p-n junctions based on 4H-SiC. As it has been shown before, the temperature coefficient of avalanche breakdown voltage (TCABV) is negative in seven SiC polytypes, including 4Н-SiC. This effect has been explained by the Wannier-Stark localization (WSL). It is worth noting that the plane of the investigated p-n junctions coincided with the basal plane (0001). However the current SiC device technology prefers 4H-SiC p-n junction formation on a plane that has 8о disorientation from (0001). This may result in a weakening of the WSL and, correspondingly, in a positive TCABV. This problem has been elucidated in the present paper. The photocurrent of 4H-SiC p-n junctions in a strong electric field has been scrutinized, that has allowed to discover a negative differential conductivity region and it has testified to the WSL process and negative TCABV.

Miniband-width effects on Wannier–Stark localization of the first and second quantized states in a GaAs/AlAs superlattice

We performed electroreflectance (ER) measurements in order to reveal the transformation processes from the minibands to the Wannier–Stark (WS) localization states in a GaAs (6.8 nm)/AlAs (0.9 nm) superlattice. The high sensitivity of ER spectroscopy enabled us to observe the interband optical transitions associated with the second ( n=2) minibands in addition to those associated with the first ( n=1) minibands. It is found that the electric field strengths for the formation of the WS-localization states of the n=2 minibands are considerably higher than those of the n=1 minibands. The experimental results are quantitatively analyzed on the basis of the theoretical calculation of the electric-field-strength dependence of the miniband states using a transfer-matrix method. It is concluded that the critical electric field strengths for the formation of the WS-localization states clearly correlate with the miniband widths.

Electroreflectance Observation of Transformation Processes of the First and Second Minibands to Wannier–Stark Localization States in a GaAs/AlAs Superlattice

We have investigated the transformation processes of the first (n=1) and second (n=2) minibands to the Wannier–Stark (WS) localization states in a GaAs (6.8 nm)/AlAs (0.9 nm) superlattice embedded in a p–i–n structure by electroreflectance spectroscopy. The high sensitivity of electroreflectance enabled us to observe the interband optical transitions associated with the n=2 minibands in addition to those associated with the n=1 minibands. The systematic results of the electroreflectance spectra as a function of electric field strength demonstrate that the electric field strength for the formation of the WS-localization state of the n=2 miniband is higher than that of the n=1 miniband, which reflects a difference in the energy widths of the n=1 and n=2 minibands. The experimental results are quantitatively discussed on the basis of the electric-field-strength dependence of the energies and envelope functions of the n=1 and n=2 minibands calculated using a transfer-matrix method. We find a clear correlation between the miniband widths and the critical electric field strengths for the formation of the WS-localization states.

Spin accumulation in lateral semiconductor superlattices induced by a constant electric field

The electric-field dependence of the spin accumulation in strongly coupled lateral superlattices subject to Rashba spin-orbit interaction is studied by the density-matrix approach. At low fields, the spin accumulation depends linearly on the electric field. In this field regime, the magnitude of the homogeneous magnetization is larger in the lateral superlattice than in the corresponding two-dimensional electron gas. The magnetization exhibits a maximum as a function of the electric field. In the region of Wannier-Stark localization, the field-induced magnetization decreases with increasing electric field strength. Field-mediated resonant-tunneling transitions between different spin states manifest themselves in a spin depolarization.

Wannier-Stark Localization Effects in 6H-SiC JFETs

The dependence of short-circuit photo-current on the voltage applied to the source-gate (or drain-gate) junction Vg was studied. One should consider the fact that the photo-current begins to drop with voltage exceeding certain threshold value. Thus the 6H-SiC JFET behaves uncommonly. Moreover Isd ~Vg dependence shows a drop Isd to zero at a condition that there is a non-pinched-off part of the channel. For a comparison parallel investigations were conducted with two industrial Si JFETs with a structure similar to that of 6H-SiC JFET under study. The results obtained for Si JFETs are trivial for photocurrent and Isd. We believe that the effects observed in 6H-SiC JFET should be attributed to the Wannier-Stark localization regime.

Nonequilibrium Green's function approach to resonant transport in semiconductor superlattices

We present a theoretical and computational investigation of resonant electron transport in GaAs/AlAs superlattices in the presence of electric and magnetic fields applied along the direction perpendicular to the interfaces. Our calculation focuses on the form of the velocity—electric-field curve in the region of increasing Wannier–Stark localization. We find that the current flow is strongly modulated by a subtle interplay of Stark cyclotron resonance and optical-phonon resonance.

Electric‐field‐induced hopping transport in superlattices

AbstractA strong electric field applied parallel to the superlattice axis leads to Wannier–Stark localization. There are two formally equivalent pictures for the drift velocity and the diffusion coefficient, the hopping model, which is most suitable for localized states, and the band picture, which is applicable to extended states. Complete localization of carriers is achieved by strong electric and magnetic fields. In these molecule‐like systems, there is a strong interdependence between the carrier spectrum and its statistical properties, the description of which requires a new approach. The related double‐time character of the transport gives rise to interesting quantum effects in the current–voltage characteristics. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

New Wannier-Stark localization effects in natural 6H-SiC superlattice

A premature electric breakdown caused by the formation of a strong-field domain under conditions of negative differential conductivity in the 6H-SiC n+-n−-n+ structure optimized for ultrahigh-frequency measurements was observed in the range of electric fields corresponding to the Bloch oscillation regime in a natural 6H-SiC superlattice. The experimental results and ensuing estimates indicate that this domain is mobile and, hence, oscillating, allowing the microwave oscillations that are rapidly damped under conditions of avalanche break-down in a natural 6H-SiC superlattice to be forecasted. Crystal perfectness of a natural 6H-SiC superlattice made it possible to directly observe the Wannier-Stark localization up to electric breakdown, i.e., during the natural crystal lifetime. This was accomplished by the optical photoelectric transformation method in the multiplication regime for a photocurrent created by photons with above-bandgap energy. It was shown that the Wannier-Stark localization, which involves only electrons, occurs in natural 6H-SiC superlattice up to fields that are almost equal to the breakdown field in 6H-SiC, unresponsively to band mixing, i.e., to the fundamental destroyer of the Wannier-Stark localization.

Wannier-Stark localization in the natural superlattice of silicon carbide polytypes

Results of a study of silicon carbide polytypes under high electric fields are presented. The presence of a natural superlattice in silicon carbide polytypes is shown to introduce a miniband structure into the conduction band, which leads to a number of effects: negative differential conductivity in the Bloch oscillation mode, electron-phonon resonances, localization in the lower miniband, resonance tunneling between the first and second minibands, prevalence of holes in the impact ionization in a wide range of fields, anomalously high avalanche breakdown fields (with a negative temperature dependence of the breakdown field) and other unusual effects. Notice that all the phenomena mentioned above are parts of a single Wannier-Stark localization process, which sets in as the mean electric field increases from 100 to 2900 kV/cm (the maximal field magnitude achieved in an abrupt p-n junction is twice larger).

Semiconductor superlattices: artificial crystals with unique electronic and transport properties

Semiconductor superlattices are artificial crystals with a periodicity much larger than lattice constants of the constituent materials. Applying an electric field parallel to the superlattice axis, i.e., perpendicular to the layers, results in unique electronic and transport properties such as miniband transport and Wannier-Stark localization, which are the basis for the observation of Bloch oscillations. At larger field strengths, resonant tunneling between different mini- or subbands dominates the electronic transport properties. Miniband transport and resonant tunneling are highly nonlinear process resulting in interesting phenomena of self-organization of the field distribution.

Quantum tunneling of Bose-Einstein condensates in optical lattices under gravity.

We investigate the quantum tunneling of Bose-Einstein condensates in optical lattices under gravity in the "Wannier-Stark localization" regime and "Landau-Zener tunneling" regime. Our results agree with experimental data [B. P. Anderson et al., Science 282, 1686 (1998); F. S. Cataliotti et al., Science 293, 843 (2001)]. We obtain the total decay rate which is valid over the entire range of temperatures, and show how it reduces to the appropriate results for the classical thermal activation at high temperatures, the thermally assisted tunneling at intermediate temperatures, and the pure quantum tunneling at low temperatures. We design an experimental protocol to observe this new phenomenon in further experiments.

Dynamical properties of one-dimension quantum dot array in a DC electric field

We have investigated theoretically dynamical properties of two electrons confined to one-dimension quantum dot array in a DC electric field. We find that Wannier–Stark localization still occurs in the system. Coulomb interaction between electrons does not destroy Wannier–Stark localization, but can result in significant changes to the dynamical behavior of the system. In particular, when the Coulomb interaction is weak, there is a beat phenomenon in the self-propagation. When the strength of Coulomb interaction is equal to the integer times of the Bloch frequency, the dynamics of the system is dominated by resonant oscillations between the initial site and one nearest-neighbor site, which is associated with avoided crossing in energy spectrum. The effect is more favorable for experimental investigations of coherent oscillations of charged carries.

Electron transport in silicon carbide natural superlattices under the Wannier-Stark quantization conditions: Basic issues and application prospects

Hot-electron transport in silicon carbide natural superlattices was investigated. Almost all of the theoretically predicted effects related to the Wannier-Stark localization, such as Bloch oscillations, Stark-phonon resonances, miniband-state localization, and resonance tunneling between the minibands, were observed for the first time. In n+-n−-n+ structures optimized for the measurements at microwave frequencies, the formation of the mobile electric domain was observed in the electric-field range corresponding to the Bloch oscillation conditions; thus, the onset of the microwave oscillations in the 6H-SiC natural superlattice can be stated with a high degree of confidence.