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The efficiency of multiple quantum well (QW) light emitting diodes (LEDs) to a large degree depends on uniformity of hole distribution between the QWs. Typically, transport between the QWs takes place via carrier capture into and thermionic emission out of the QWs. In InGaN/GaN QWs, the thermionic hole transport is hindered by the high quantum confinement and polarization barriers. To overcome this drawback, hole injection through semipolar QWs located at sidewalls of V-defects had been proposed. However, in the case of the V-defect injection, strong lateral emission variations take place. In this work, we explore the nature of these variations and the impact of the V-defects on the emission spectra and carrier dynamics. The study was performed by mapping electroluminescence (EL) and photoluminescence (PL) with a scanning near-field optical microscope in LEDs that contain a deeper well that can only be populated by holes through the V-defects. Applying different excitation schemes (electrical injection and optical excitation in the far- and near-field), we have shown that the EL intensity variations are caused by the lateral nonuniformity of the hole injection. We have also found that, in biased structures, the PL intensity and decay time in the V-defect regions are only moderately lower that in the V-defect-free regions thus showing no evidence of an efficient Shockley-–Read–Hall recombination. In the V-defect regions, the emission spectra experience a red shift and increased broadening, which suggests an increase of the In content and well width in the polar QWs close to the V-defects. [ABSTRACT FROM AUTHOR]

Organic–inorganic hybrid perovskite quantum wells exhibit electronic structures with properties intermediate between those of inorganic semiconductors and molecular crystals. In these systems, periodic layers of organic spacer molecules occupy the interstitial spaces between perovskite sheets, thereby confining electronic excitations to two dimensions. Here, we investigate spectroscopic line broadening mechanisms for phonons coupled to excitons in lead-iodide layered perovskites with phenyl ethyl ammonium (PEA) and azobenzene ethyl ammonium (AzoEA) spacer cations. Using a modified Elliot line shape analysis for the absorbance and photoluminescence spectra, polaron binding energies of 11.2 and 17.5 meV are calculated for (PEA)2PbI4 and (AzoEA)2PbI4, respectively. To determine whether the polaron stabilization processes influence the dephasing mechanisms of coupled phonons, five-pulse coherent Raman spectroscopies are applied to the two systems under electronically resonant conditions. The prominence of inhomogeneous line broadening mechanisms detected in (AzoEA)2PbI4 suggests that thermal fluctuations involving the deformable organic phase broaden the distributions of phonon frequencies within the quantum wells. In addition, our data indicate that polaron stabilization primarily involves photoinduced reorganization of the organic phases for both systems, whereas the impulsively excited phonons represent less than 10% of the total polaron binding energy. The signal generation mechanisms associated with our fifth-order coherent Raman experiments are explored with a perturbative model in which cumulant expansions are used to account for time-coincident vibrational dephasing and polaron stabilization processes. [ABSTRACT FROM AUTHOR]

Gallium nitride (GaN)- based lasers are extensively employed in display, lighting, and communication applications due to their visible laser emission. Despite notable advancements in their performance and reliability, sustained device functionality over extended periods remains a challenge. Among the diverse mechanisms contributing to degradation, the deterioration of quantum wells poses a persistent obstacle. In this study, we investigated the atomic-level degradation of quantum wells within GaN-based laser diodes utilizing atom probe microscopy. Our analysis revealed a substantial increase in indium fluctuation, accompanied by the formation of indium protrusions at the quantum well interfaces, which provides a credible explanation for the observed increase in FWHM (full width at half maximum) of the spontaneous spectra of lasers following prolonged operation. Additionally, magnesium analysis yielded no evidence of diffusion into the quantum well region. Combined with prior studies, we attribute the degradation of quantum wells primarily to the formation of indium-related non-radiative recombination centers. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D)/three-dimensional (3D) halide perovskite heterostructures have been extensively studied for their ability to combine the outstanding long-term stability of 2D perovskites with the superb optoelectronic properties of 3D perovskites. While current studies mostly focus on vertically stacked 2D/3D perovskite heterostructures, a theoretical understanding regarding the optoelectronic properties of 2D/3D perovskite lateral heterostructures is still lacking. Herein, we construct a series of 2D/3D perovskite lateral heterostructures to study their optoelectronic properties and interfacial charge transfer using density functional theory (DFT) calculations. We find that the band alignments of 2D/3D heterostructures can be regulated by varying the quantum-well thickness of 2D perovskites. Moreover, decreasing the 2D component ratio in 2D/3D heterostructures can be favorable to form type-I band alignment, whereas a large component ratio of 2D perovskites tends to form type-II band alignment. We can improve the amount of charge transfer at the 2D/3D perovskite interfaces and the light absorption of 2D perovskites by increasing quantum-well thickness. These present findings can provide a clear designing principle for achieving 3D/2D perovskite lateral heterostructures with tunable optoelectronic properties. [ABSTRACT FROM AUTHOR]

The static electric dipole–dipole coupling between donor–acceptor pairs (DAPs) in wide-bandgap semiconductors has recently emerged as a means of realizing a quantum science platform through optically controllable, long-range interactions between defects in the solid state. In this work, we generalize DAPs to consider arbitrary dopant populations and demonstrate that the charge of the NV center in diamond is well suited for quantum science. Explicitly, we leverage experimental results [see Z. Yuan et al., PRR 2, 033263 (2020)] to show that shallow NV centers can be efficiently initialized to a given relative population of the negative and neutral charge states and that modulating the surface termination would allow for control of the timescale over which the initialization and subsequent computations would occur. Furthermore, we argue that the observation of electroluminescence from the neutral charge state of the NV center [see N. Mizuochi et al., Nat. Photon. 6, 299 (2012)], but not from the negative charge state, implies the ability to interface with the NV center's charge in a manner analogous to the spin interface enabled by the spin-state dependent fluorescence of the NV center. [ABSTRACT FROM AUTHOR]

In this paper, mole fraction dependent strain in a III-nitride alloy and its effects on built-in polarization and quantized states in multi-quantum-wells (MQWs) have been investigated. The internal electric field arising out of spontaneous and piezoelectric polarizations in the presence of strain has been calculated. Then, the energy eigenvalues and wavefunctions of carriers in the modified potential well configurations have been computed by solving a time-independent Schrödinger equation using a finite difference method. Next, the overlap integrals between the wavefunctions of bound states in conduction and valence bands, an important consideration for optical transitions, have been computed and plotted. The results are shown taking three nitride-based MQW structures InGaN/GaN, GaN/AlGaN, and InGaN/InAlN as examples. The study helps choose suitable mole fractions for the improved and desired performance of the nitride MQW based devices. [ABSTRACT FROM AUTHOR]

Asymmetric quantum wells (AQWs) utilizing interband transitions enhance second-order susceptibility over a wide wavelength range compared to natural crystals. The nonlinear susceptibility is further enhanced in AQWs with type-II band alignment as compared to type-I band alignment, a result of the larger interband charge shift. This enhancement is demonstrated in this work by analyzing three type-I and type-II AQW designs based on the lattice-matched InP/AlGaInAs materials systems using the envelope wavefunction approximation. The calculated interband second-order susceptibility tensor elements in type-II structures range between 20 and 1.60 × 103 pm/V for nearly resonant optical rectification and difference frequency generation applications at near-infrared and terahertz wavelengths, an improvement of nearly 1 order of magnitude over the type-I structures and 1–2 orders of magnitude over natural crystals such as LiNbO3, KTiOPO4 (KTP), or GaAs. A factor of 2–3 further enhancement of the tensor elements is achieved by optimizing the well widths and band offsets of the type-II asymmetric quantum wells. The type-II structure can be implemented in other material systems spanning the longwave infrared to visible wavelengths, enhancing nonlinear susceptibility for various applications, including photonic integrated circuits. [ABSTRACT FROM AUTHOR]

In this study, we investigate the tradespace between the improvement of mid-infrared light-emitting diode efficiency through microcavity enhancement vs reduction of Auger recombination for different W-superlattice thicknesses. Several sample designs are modeled and then grown and fabricated to test the tradespace at different W-superlattice thicknesses down to the quantum well limit. In a half-cavity, with a single reflector from the top metal contact, intermediate thickness W-superlattices gave the highest efficiencies, outperforming those in the W-quantum well limit across the entire measured current range. Experimentally, we report wallplug efficiencies of 0.4% for a room temperature 3.2 μm device. W-superlattices of intermediate thickness were also found to be optimal for a full-cavity device with a bottom distributed Bragg reflector added. The resonant full cavity did strongly improve the peak spectral radiance, with a measured increase of four to five times for a 3.6 μm device, and a value that is >250 times larger than previously reported. [ABSTRACT FROM AUTHOR]

Wurtzite ScxAl1−xN/GaN (x = 0.13–0.18) multi-quantum wells grown by molecular beam epitaxy on c-plane GaN are found to exhibit remarkably strong and narrow near-infrared intersubband absorption in the technologically important 1.8–2.4 μm range. Band structure simulations reveal that, for GaN wells wider than 3 nm, the quantized energies are set by the steep triangular profile of the conduction band caused by intrinsic polarization fields. As a result, the intersubband transition energies provide unique and direct access to essential ScAlN polarization parameters. Measured infrared absorption indicates that the spontaneous polarization difference of the presumed lattice-matched Sc0.18Al0.82N/GaN heterostructure is smaller than the theoretically calculated value. The intersubband transition energies are relatively insensitive to the barrier alloy composition indicating negligible variation of the net polarization field in the probed 0.13–0.18 Sc composition range. [ABSTRACT FROM AUTHOR]

A wire-on-well (WoW) structure was fabricated using InGaAs/GaAs/GaAsP superlattice device growth technology. This structure modifies the local concentration of carriers in the quantum well and lengthens the carrier lifetime to increase carrier transport efficiency. However, the reason for this remains unclear. Therefore, we investigated the detailed carrier transition properties using photoluminescence (PL) and photoreflectance measurements. Regarding the PL spectra at 4 K, two characteristic peaks at 1.39 and 1.34 eV were observed. Both transitions are attributed to the recombination between the first quantum level of the electron (e1) and that of the heavy hole (hh1). We also discussed the carrier distribution in the WoW structure and found that the maximum carrier existing probabilities for e1 and hh1 are located at different positions. The less overlapping of the wavefunctions causes low transition probability and results in the observed long carrier lifetime. An additional prominent result in the WoW structure is the blue shift attributed to the 1.34 eV PL peak induced by increasing laser excitation power. We found that the blue shift occurred by the screening of the electric field caused by the compressive strain, as in the case of the quantum-confined Stark effect. [ABSTRACT FROM AUTHOR]

Nonvolatile memory using intersubband transitions and quantum-well electron accumulation in GaN/AlN resonant tunneling diodes (RTDs) is a promising candidate for high-speed nonvolatile memory operating on a picosecond timescale. This memory has been fabricated on sapphire(0001) substrates to date because of the high affinity between the nitride materials and the substrate. However, the fabrication of this memory on Si(111) substrates is attractive to realize hybrid integration with Si devices and nonvolatile memory and three-dimensional integration such as chip-on-wafer and wafer-on-wafer. In this study, GaN/AlN RTDs are fabricated on a Si(111) substrate using metal-organic vapor phase epitaxy. The large strain caused by the differences in the thermal expansion coefficients and lattice constants between the Si(111) substrate and nitride materials are suppressed by a growth technique based on the insertion of low-temperature-grown AlGaN and thin AlN layers. The GaN/AlN RTDs fabricated on Si(111) substrates show clear GaN/AlN heterointerfaces and a high ON/OFF ratio of >220, which are equivalent to those for devices fabricated on sapphire(0001) substrates. However, the nonvolatile memory characteristics fluctuate by repeated write/erase memory operations. Evaluation of the ON/OFF switching time and endurance characteristics indicates that the instability of the nonvolatile memory characteristics is caused by electron leakage through deep levels in the quantum-well structure. Possible methods for suppressing this are discussed with an aim of realizing high-speed and high-endurance nonvolatile memory. [ABSTRACT FROM AUTHOR]

A band design of a quantum cascade laser with a generation frequency higher than 6 THz and an active region based on four GaAs/Al0.14Ga0.86As quantum wells is proposed. Calculations were carried out based on the solution of the Schrödinger equation taking into account the dephasing of quantum states, as well as a closed system of balance equations. The temperature dependences of the gain at frequencies of 6.3–6.6 THz were calculated for the proposed quantum cascade laser with a double metal waveguide. Features of the proposed laser structure include two injection quantum wells and the suppression of non-radiative transitions between laser levels. According to calculations, this provides the maximum operating temperature of up to 81 K at 6.4 THz. The results of this study open up the way for quantum cascade lasers based on GaAs/AlGaAs to operate at frequencies above 6 THz. [ABSTRACT FROM AUTHOR]

The authors investigate the influence of local polarization on the thermoelectric properties of monolayer MoS2 using a tight-binding approach. It is found that strain-induced polarization in armchair monolayer MoS2 can be easily embedded to strongly enhance the thermoelectric efficiency ZT for quantum wells. The structure we proposed can achieve a figure of merit ZT of 0.8 at room temperature in an armchair MoS2 nanoribbon, and ZT achieves 1 at 500 K. The results facilitate insight and understanding of strain modulated thermoelectric properties of monolayer MoS2 nanodevices, provide theoretical guidance for experiments, and indicate their great potential in thermoelectric devices. [ABSTRACT FROM AUTHOR]

The authors investigate the influence of local polarization on the thermoelectric properties of monolayer MoS2 using a tight-binding approach. It is found that strain-induced polarization in armchair monolayer MoS2 can be easily embedded to strongly enhance the thermoelectric efficiency ZT for quantum wells. The structure we proposed can achieve a figure of merit ZT of 0.8 at room temperature in an armchair MoS2 nanoribbon, and ZT achieves 1 at 500 K. The results facilitate insight and understanding of strain modulated thermoelectric properties of monolayer MoS2 nanodevices, provide theoretical guidance for experiments, and indicate their great potential in thermoelectric devices. [ABSTRACT FROM AUTHOR]

The coupling of an electron gas confined by a harmonic potential and submitted to a strong magnetic field tilted in relation to the confining direction creates an excitation called here magneto-polariton. This work describes the origin of this excitation and calculates the energy eigenvalues for different tilted angles. It presents the reasons leading to the crossings and repulsions of the energy bands, the degeneracy of the states, the way the Fermi levels change with the magnetic field, the influence of an external electric field, and how the Hall resistance plateaus change with the change in the tilted angle. [ABSTRACT FROM AUTHOR]

This review concentrates on the microstructure of InxGa1−xN layers and quantum wells (QWs) in relation to their optical properties. The microstructure of InxGa1−xN, with a constant In(x) concentration, shifts with layer thickness. Only layers below 100 nm for x = 0.1 are nearly defect-free. A photoluminescence peak is observed at 405 nm, in line with ∼10% In, suggesting band-edge luminescence. Layers with greater thickness and In content present a corrugated surface with numerous structural defects, including V-defects, causing redshifts and multi-peaks in photoluminescence up to 490 nm. These defects, resembling those in GaN, lead to a corrugated sample surface. Atomic force microscopy shows a 3.7-fold larger corrugation in samples with 20 QWs compared to those with 5 QWs measured on 2 × 2 μm2 areas. Like in GaN, dual growth on different crystallographic planes results in varied QW thicknesses, influencing optical traits of devices made from InxGa1−xN layers. The purpose of this review and the chosen subject is to highlight the significant contribution of Wladek Walukiewicz and his group to the current research on the properties of InxGa1−xN, which are crucial alloys in the field of optoelectronics. [ABSTRACT FROM AUTHOR]

GaN/AlxGa1−xN quantum wells were grown by molecular beam epitaxy on high quality bulk (0001) GaN substrates. The quantum well thickness was set in the 6–8 nm range to favor the photoluminescence emission of indirect excitons. Indeed, such excitons are known to be spatially indirect due to the presence of the internal electric field which spatially separates the electron and hole wave functions. The growth conditions were optimized in view of minimizing the photoluminescence peak broadening. In particular, the impact of growth temperature (up to 900 °C) on the surface morphology, structural, and photoluminescence properties was studied. The diffusion of indirect excitons on the scale of tens of micrometers was measured with a micro-photoluminescence setup equipped with a spatially resolved detection. A dedicated model and its analysis allow us to extract from these measurements the exciton diffusion constant and to conclude on the optimum growth conditions for the GaN/AlxGa1−xN quantum well structures suited for studies of quantum collective effects in indirect exciton liquids. [ABSTRACT FROM AUTHOR]

Alkali metal dosing has nowadays been extensively used in angle-resolved photoemission spectroscopy (ARPES) for the in situ surface electron doping of materials to provide access to the unoccupied states. This technique also gives rise to nontrivial physical phenomena, such as the appearance of quantum well states and effects due to alkali metal intercalation. Here, we uncovered a previously unobserved type of electronic behavior induced by alkali metal dosing. By employing ARPES to study the evolution of the electronic structure of the Ti2O3 thin film upon rubidium (Rb) dosing, we found that the electron chemical potential of the system remains unchanged throughout the process. Interestingly, a series of electron-like band dispersions first appear with Rb dosing. A further increase in the Rb dosage leads to the eventual disappearance of the electron-like bands and the emergence of a set of hole-like bands. Our finding enriches the phenomenology brought about by alkali metal surface dosing, suggesting a novel functionality of this popular surface doping technique. [ABSTRACT FROM AUTHOR]

The effect of the GaAsP strain-compensating layer on type-II GaAs1−xSbx/InyGa1−yAs was investigated. GaAsSb/InGaAs multiple quantum wells (MQWs) without and with GaAsP strain-compensating layers were grown by molecular beam epitaxy. Increasing Sb or In compositions can extend photoluminescence (PL) emission at longer wavelength along with the highly induced compressive strain in the QWs. The power-dependent PL measured at low temperature reveals the type-II band characteristics of the GaAs1−xSbx/InyGa1−yAs system. A detailed analysis of the experimental data reveals that the GaAsP layers compensate the compressive strain of GaAsSb/InGaAs. The type-II QWs with GaAsP layers, (8 nm) GaAs0.84Sb0.16/(2.5 nm) In0.3Ga0.7As/(10 nm) GaAs0.85P0.15, emits PL at ∼1.1 μm, up to 210 K, while the PL of those strained sample without GaAsP vanishes at lower temperature. In view of the described sample, x-ray diffraction (XRD) analysis along with the simulation shows the validity of the procedure, resulting in nearly matched parameters of QW thicknesses and material compositions—(8.9 nm) GaAs0.835Sb0.165/(2.3 nm) In0.3Ga0.7As/(10.3 nm) GaAs0.85P0.15, with those of the designed QW. The thicknesses of QW from the TEM image, (8.6 nm) GaAsSb/(3.1 nm) InGaAs/(10.1 nm) GaAsP, agree well with the XRD results. [ABSTRACT FROM AUTHOR]

We introduce a multiple-carrier-lifetime model (MCLM) for light-emitting diodes (LEDs) with non-uniform carrier distribution, such as in multiple-quantum-well (MQW) structures. By employing the MCLM, we successfully explain the modulation response of V-pit engineered MQW LEDs, which exhibit an S21 roll-off slower than −20 dB/decade. Using the proposed model and employing a gradient descent method, we extract effective recombination and escape lifetimes by averaging the carrier behavior across the quantum wells. Our results reveal slower effective carrier recombination and escape in MQW LEDs compared with LEDs emitting from a single QW, indicating the advantages of lower carrier density achieved through V-pit engineering. Notably, the effective carrier recombination time is more than one order of magnitude lower than the effective escape lifetime, suggesting that most carriers in the quantum wells recombine, while the escape process remains weak. To ensure the reliability and robustness of the MCLM, we subject it to a comprehensive threefold validation process. This work confirms the positive impact of spreading carriers into several quantum wells through V-pit engineering. In addition, the MCLM is applicable to other LEDs with a non-uniform carrier distribution, such as micro-LEDs with significant surface recombination and non-uniform lateral carrier profiles. [ABSTRACT FROM AUTHOR]

The effect of inserting a nm-scale layer of Zn(Si,Ge)N2 into an AlGaN quantum well structure designed for light emission in the wavelength range from 255 to 305 nm is investigated here. The enhanced confinement of the hole within the quantum well results in an enhancement of the overlap of the hole and electron wave functions, resulting in an enhancement of the radiative recombination rate. In this theoretical calculation, for emission at a 270 nm wavelength, the enhancement in the wavefunction overlap can reach a factor of 7 when compared to an AlGaN quantum well device specifically engineered for optimal emission at the identical wavelength. Increases of almost an order of magnitude in both the peak spontaneous emission intensity and the radiative recombination rate are predicted. The peak emission wavelength can be tuned from 255 to 305 nm by adjusting the width and/or the composition of the inserted layer. The proposed structures provide a route to higher efficiency ultraviolet practical light emitting diodes and lasers. [ABSTRACT FROM AUTHOR]

The semiconductor quantum well based on mercury telluride is characterized by two distinct phases: conventional insulating phase and topological insulating phase with helical edge states. The system undergoes a topological quantum phase transition from one phase to the other, tuned by the critical geometric parameters of the quantum well. It is shown that the quantum states in each phase exhibit distinct flavors of Bloch oscillations, depending strongly on the geometric parameters and crystal momentum of the system. In particular, the group and Berry velocities and the real-space trajectories exhibit pronounced Bloch oscillations. Interestingly, the x - and y -components of the group velocity are interchanged by interchanging their corresponding components of the crystal momentum. In addition, a Gaussian wave packet undergoes distinct time evolution in each quantum phase of the HgTe quantum well. Moreover, the effects of applied in-plane electric and transverse magnetic fields are determined within the framework of Newtonian mechanics, leading to the geometric visualization of such an oscillatory motion. We find that in the presence of both applied in-plane electric and transverse magnetic fields simultaneously, the system undergoes a dynamic phase transition between confined and de-confined states, tuned by the relative strength of the fields. It is argued that the distinct Bloch oscillations originate from the peculiar band structure of HgTe quantum wells in each quantum phase. Furthermore, we find that the direct-current drift velocity in each quantum phase exhibits negative differential conductivity, a hallmark of the Bloch oscillation regime. [ABSTRACT FROM AUTHOR]

The high built-in polarization field is a fingerprint of III-nitride heterostructures. Alloy composition and doping profile significantly affect the magnitude of the electric field present in subsequent layers, but the sign of the electric field is usually defined by substrate polarity and external bias. Here, we propose to utilize acceptor and donor doping concentrations exceeding 1020 cm−3 to obtain a high junction field that can solely abolish built-in polarization for a polar (0001) InGaN/GaN quantum well (QW). We have used photoluminescence (PL), time-resolved PL (TRPL), and contactless electroreflectance in order to gain insight into the strength of the electric field present in the grown heterostructures. Good match between expected and measured electric field values was obtained. A dramatic decrease in the luminescence lifetime for a flat QW was confirmed using TRPL. The presented results open a way to realize devices that profit from the low built-in field, like photodetectors, using abundant polar substrates. [ABSTRACT FROM AUTHOR]

The quantum well diode (QWD) performs a dual role, functioning both as an emitter and a detector due to its unique feature of spectral overlap between emission and detection spectra. This dual functionality positions QWDs as promising candidates in the realm of multifunctional sensors. Furthermore, the well-established maturity of optical fiber communication, grounded in its intrinsic property of total reflection, makes it an ideal transmission medium for QWD sensing signals. Leveraging the coexisting emission and detection capabilities of QWDs, we have constructed a sensing system in this article. This system utilizes a QWD, which is stimulated to emit light, with the emitted light traveling through a specified length of optical fiber. A specialized load-bearing film, featuring an aluminum membrane on its rear to act as a mirror and an object of known weight on its front, induces deformation in the film, thereby altering the characteristics of the reflected light. This modulated light is subsequently captured by the QWD via the optical fiber, enabling the computation of the weight of the object. In this article, the QWD's emission peak is around 522 nm, and its detection range extends from 370 to 530 nm. Furthermore, by employing the appropriate approach, integrating QWD with optical fibers can be extended to sensing and measuring various physical quantities such as temperature, solution concentration, wind speed, and more. The advantages of QWDs include cost-effectiveness, multifunctionality, portability, and environmental friendliness. This technology represents a promising avenue for sensor control in the era of the Internet of Things. [ABSTRACT FROM AUTHOR]

We have studied the epitaxial growth of Si thin films on the Cd(0001) surface using low-temperature scanning tunneling microscopy. When deposited at low temperatures (100 K), Si atoms form dendritic islands with triangular shapes, indicating the existence of anisotropic edge diffusion in the process of Si film growth. After annealing to elevated temperatures, the triangular dendritic Si islands become hexagonal compact islands. Moreover, the 2D Si islands located on two different substrate terraces exhibit different heights due to the influence of quantum-well states in Cd(0001) films. Based on high-resolution scanning tunneling microscopy images, it is observed that the first, second, and third Si layers show the pseudomorphic 1 × 1 structure. In particular, the first and second layer islands reveal the opposite triangles, indicating the hexagonal close-packed stacking of Si atoms. These results provide important information for the growth of pristine Si films on metal substrates and the understanding of Si–metal interaction. [ABSTRACT FROM AUTHOR]

The luminescence efficiency of AlxGa1−xN quantum dots (QDs) and quantum wells (QWs), buried in AlN cladding layers and emitting in the ultraviolet range between 234 and 310 nm, has been investigated. The growth and optical properties have been done using similar aluminum composition (varying from 0.4 to 0.75) for both QDs and QWs. In order to compare as much as possible the optical properties, the QWs were fabricated with a growth time tuned such that the QW width is similar to the average height of the QDs. The photoluminescence (PL) showed emission ranging from 4 to 5.4 eV, putting into evidence differences in terms of full width at half maximum, PL intensity, and asymmetry of the line shape between QDs and QWs. The results show shorter wavelengths and a slightly narrower PL linewidth for QWs. To determine the light emission dependence with the electric field direction in the crystal, the evolutions of the emission diagrams for all samples were recorded along two orthogonal directions, namely, the "in-plane" (growth) and the "on-side" directions, from which the light emission was collected. For the whole QDs and QWs samples' series, the shapes of the emission diagram indicate emission in both in-plane and on-side directions, as evidenced by intra-valence band mixings caused by strain effects combined with the anisotropic Coulomb interactions that are particularly contributing to the polarization at wavelengths below 260 nm. Furthermore, the degree of polarization, determined for each sample, showed good agreement with results from the literature. [ABSTRACT FROM AUTHOR]

The polarization-induced quantum confined Stark effect has been recognized as a significant factor contributing to the Internal Quantum Efficiency (IQE) droop in light-emitting diodes (LEDs). This study focuses on the design of LEDs by investigating the InAlN/AlGaN interface. By incorporating InAlN quantum wells, a polarization-matched (PM) multi-quantum well (MQW) LED architecture was developed. While the flat conduction and valence bands on PM MQWs indicate an improved recombination rate, it is crucial to examine the impact on IQE, considering carrier confinement and injection efficiency influenced by the band offsets. This paper presents a numerical analysis comparing two LEDs emitting at 245 and 275 nm, respectively. The results demonstrate that the PM LED operating at 275 nm exhibits enhanced performance, benefiting from high probability density overlap. Conversely, the PM LED emitting at 245 nm demonstrates poor confinement, resulting in an overall low performance, regardless of polarization matching. [ABSTRACT FROM AUTHOR]

We present a setup for fast, low-bias (≤ 1 mV) DC transport measurements with μs time resolution for high ohmic resistance (≈ 20 k Ω) semiconducting samples. We discuss the circuitry and instrumentation for the measurement approach that can be applied to any kind of semiconductor device or (gated) two-dimensional material and demonstrate the main measurement artifacts in typical measurements by means of circuit simulation. Based on the latter, we present a simple two-step protocol for eliminating the measurement artifacts reliably. We demonstrate the technique by measuring the transitions between quantum Hall plateaus in the HgTe quantum wells and resolve plateaus as short-lived as 100 μs. [ABSTRACT FROM AUTHOR]

The characteristic polytype behaviors of SiC and accompanying low stacking fault energies are known to cause engineering issues, including polytype inclusions and bipolar degradation. The dependence of the relative stability of SiC polytypes and stacking fault energies on excess carrier concentration was investigated using first-principles calculations. The relative energy of 2H-, 4H-, and 6H-SiC to 3C-SiC increased with the excess electrons over 2 × 1019 cm−3, while the energy variation with excess holes was small. The stacking fault energies in 4H-SiC also exhibited a significant decrease with excess electrons over 1.0 × 1019 cm−3, whereas this change was minor with excess holes. These excess carrier dependencies were attributed to variations in the bandgap between polytypes. The energy level of the excess electrons was at the conduction band minimum; this was lowest in 3C-SiC, which had the lowest bandgap energy. Consequently, the energy of 3C-SiC with excess electrons was lower than that of other polytypes. Conversely, the valence band maximum lacked electrons when excess holes were present, resulting in a small difference among the Fermi levels of the polytypes. Hence, the energy difference between the SiC polytypes was similar for excess holes. Similarly, the stacking faults in SiC exhibited quantum-well structures by incorporating other polytypes with different bandgaps. With excess electrons, the Fermi level within the stacking faults was lower than that in the bulk crystals. Consequently, the stacking fault energy decreased for the same reason that the energy in 3C-SiC decreased under excess electron conditions. [ABSTRACT FROM AUTHOR]

This paper presents a novel physics-based analytical model for the injection recombination current in micro-light emitting diodes (μLEDs) with multiple quantum wells (MQWs), specifically excluding trap-assisted tunneling contributions at low forward voltages. The model simplifies the complex MQW structure by representing MQWs as a single equivalent quantum well (EQW). The μLED current is attributed to the recombination of injected holes and electrons within this EQW. Key parameters of the model encompass the EQW's position within the depletion region, hole diffusion coefficient, series resistance, and thermal resistance of the device. Experimental validation of the model is performed using current–voltage characteristics obtained from InGaN/GaN QW μLEDs. [ABSTRACT FROM AUTHOR]

Strain-related piezoelectric polarization is detrimental to the radiative recombination efficiency for InGaN-based long wavelength micro-LEDs. In this paper, partial strain relaxation of InGaN multiple quantum wells (MQWs) on the wafer scale has been demonstrated by adopting a partially relaxed InGaN superlattice (SL) as the pseudo-substrate. Such a pseudo-substrate was obtained through an electro-chemical etching method, in which a sub-surface InGaN/InGaN superlattice was etched via threading dislocations acting as etching channels. The degree of strain relaxation in MQWs was studied by x-ray reciprocal space mapping, which shows an increase of the in-plane lattice constant with the increase of etching voltage used in fabricating the pseudo-substrate. The reduced strain in the InGaN SL pseudo-substrate was demonstrated to be transferable to InGaN MQWs grown on top of it, and the engineering of the degree of strain relaxation via porosification was achieved. The highest relaxation degree of 44.7% was achieved in the sample with the porous InGaN SL template etched under the highest etching voltage. Morphological and structural properties of partially relaxed InGaN MQWs samples were investigated with the combination of atomic force and transmission electron microscopy. The increased porosity of the InGaN SL template and the newly formed small V-pits during QW growth are suggested as possible origins for the increased strain relaxation of InGaN MQWs. [ABSTRACT FROM AUTHOR]

This work is devoted to finding the optimal parameters of the HgTe/CdHgTe multi-quantum-well structure for the generation of two-dimensional plasmon-phonons under optical excitation. It is shown that a decrease in the bandgap and an increase in the number of quantum wells lead to two consequences. The first is a decrease in the nonequilibrium carrier threshold concentration and the threshold power density of optical excitation required for the plasmon-phonon gain. The second is a significant (tens of times) decrease in the effective refractive index of the generated plasmon-phonons, which improves the output of the plasmon-phonon radiation from the edge of the structure. The value of the optimal bandgap and the optimal number of quantum wells in the structure for plasmon-phonon gain are discussed. [ABSTRACT FROM AUTHOR]

The carrier recombination behavior of GaN-based blue laser diodes (LDs) is studied and analyzed by experiments and simulation calculations before lasing, with a particular focus on the role of Auger recombination. It is found that Auger recombination plays a crucial role in the decrease in differential efficiency and threshold current of GaN-based blue LDs. The theoretical calculation results show that a large Auger recombination rate may lead to a dominant recombination channel before lasing, which could exceed the radiation recombination and result in an obvious decrease in the differential efficiency. Such a high Auger recombination will dissipate a large number of carriers in the quantum well, resulting in deterioration of device performance, a higher threshold current and a lower efficiency. This work presents a method to evaluate Auger recombination through differential efficiency and also provides evidence that suppressing the Auger recombination rate is beneficial to improve the performance of blue LDs. [ABSTRACT FROM AUTHOR]

The photovoltaic performance of inverted perovskite solar cells (PSCs) is often hindered by trap‐induced non‐radiative recombination and photochemical degradation occurring at the upper interfaces and the grain boundaries of perovskite films. Herein, ortho‐, meta‐, and para‐isomers of fluorophenylethylammonium iodine (F‐PEAI) organic spacer molecules are evaluated for the construction of perovskite quantum wells (2D or quasi‐2D, PQWs) to encapsulate 3D perovskites. Among the three variants, p‐F‐PEAI leads to the most symmetric charge distribution and the weakest steric hindrance which resulting in reinforced interactions with PbI2 and perovskite, the enhanced out‐of‐plane orientation is confirmed by Grazing incidence wide‐angle X‐ray scattering (GIWAXS) results. Density functional theory and crystal orbital Hamilton population (COHP) calculations further confirm that p‐F‐PEAI engages most strongly with the perovskite structure. Moreover, transmission electron microscopy (TEM) characterization is used to illustrate that p‐F‐PEAI‐assisted 2D PQWs effectively passivate both the grain boundaries and surfaces of perovskites. This configuration facilitates effective surface passivation, improves charge carrier transport, and significantly suppresses non‐radiative recombination. The resultant inverted PSCs achieve an excellent power conversion efficiency (PCE) of 25.03% with a fill factor (FF) of 85.11%. The unencapsulated devices exhibit enhanced long‐term stability under ambient environments and continuous light illumination. [ABSTRACT FROM AUTHOR]

ABSTRACT Quantum computers comprising large‐scale arrays of qubits will enable complex algorithms to be executed to provide a quantum advantage for practical applications. A prerequisite for this milestone is a power‐efficient qubit control and detection system operating at cryogenic temperatures. Implementing such systems in complementary metal‐oxide‐semiconductor (CMOS) technology offers clear advantages in terms of scalability. Here, we present a fully integrated quantum dot array in which silicon quantum wells are co‐located with control and detection circuitry on the same die in a commercial 22‐nm fully depleted silicon‐on‐insulator (FDSOI) process. Our system comprises a two‐dimensional quantum dot array, integrated with 8 detectors and 32 injectors, operating at 3 K inside a cryo‐cooler. The power consumption of the control and detection circuitry is 2.5 mW per qubit without body biasing. The design utilizes 0.8‐V nominal Vt$$ {V}_t $$ devices. The setup allows us to verify discrete charge injection control and detection at the quantum dot array and demonstrate the feasibility of this architecture for scaling up the existing quantum core to hundreds and thousands of physical qubits. [ABSTRACT FROM AUTHOR]

The aim of the present work is to demonstrate the applicability of machine learning techniques and in particular neural network quantum states in the context of loop quantum gravity, albeit for a simplified theory. We consider 3-dimensional Euclidean gravity in a gauge theoretical formulation in a certain weak coupling limit due to Smolin, and show that the gauge group becomes Abelian, resulting in U (1) 3 BF-theory. The theory is quantised using loop quantum gravity methods. The kinematical degrees of freedom are truncated, on account of computational feasibility, by fixing a graph and deforming the algebra of the holonomies to impose a cutoff on the charge vectors. This leads to a quantum theory related to U q (1) 3 BF-theory. The effect of imposing the cutoff on the charges is examined. We also implement the quantum volume operator of 3d loop quantum gravity. Most importantly we compare two constraints for the quantum model obtained: a master constraint enforcing curvature and Gauß constraint, as well as a combination of a quantum Hamilton constraint constructed using Thiemann's strategy and the Gauß master constraint. The two constraints are solved using the neural network quantum state ansatz, demonstrating its ability to explore models which are out of reach for exact numerical methods. The solutions spaces are quantitatively compared and although the forms of the constraints are radically different, the solutions turn out to have a surprisingly large overlap. We also investigate the behavior of the quantum volume in solutions to the constraints. [ABSTRACT FROM AUTHOR]

We study the formation of a superradiant optical mode in the room temperature reflection spectra from resonant Bragg structures (RBSs) composed of single and double (In,Ga)N quantum wells (QWs) in the unit cell. The appearance of the mode manifests itself by a significant increase in the resonant optical reflectivity due to the electromagnetic coupling of quasi-two-dimensional excitons in the QWs. The implementation of the supercells with double (In,Ga)N QWs results in an increase in the oscillator strength of the quasi-2D excitons and corresponding rise of the radiative broadening parameter to the value as high as 0.3 ± 0.02 meV. We also show that the supercells with double QWs are preferable for RBS with large number of periods due to better tolerance to deviations from the exact periodicity. [ABSTRACT FROM AUTHOR]

Solid‐state infrared sources designed to emit wavelengths above 2 µm often face challenges in achieving high emission efficiency, minimizing power consumption, and reducing fabrication costs. In response, a 2.4 µm wavelength light emitting diode (LED) is developed using metamorphic In0.83Ga0.17As/InAs0.3P0.65Sb0.05 multiple quantum well (MQW) heterostructures. The substantial conduction (94 meV) and valence band offsets (300 meV) within this type‐I MQW LED architecture result in strong carrier confinement, improving electron and hole wavefunction overlap. Despite a notable lattice mismatch of 2.0% between the MQWs and InP substrate, the resulting LED wafer exhibits exceptionally low surface roughness (1.1 nm) and well‐defined, sharp interfaces within the heterostructures. Furthermore, this MQW LED exhibits favorable emission properties, including a low turn‐on field, minimal efficiency droop, and stable emission wavelength across varying injection currents. These advancements underscore the potential of such short‐wave infrared emitters for scalable applications in fields such as inspection, optical on‐chip communication, and biomedical diagnostics. [ABSTRACT FROM AUTHOR]

In this study, the lasing characteristics of GaInAsP laser diodes (LDs) grown on directly bonded InP/Si substrates with a gas out channel (GOC) structure are investigated. GOC InP/Si substrates are fabricated using hydrophilic direct bonding and metal–organic vapor phase epitaxy growth methods and subsequently their surface conditions, bonding strength, and lasing performance are examined. Herein, it is observed that the introduction of a GOC substantially reduces void formation and improves the threshold current density of the LDs. In the results, it is demonstrated that the performance of the GOC InP/Si substrates is comparable to that of InP substrates, highlighting their potential for use in high‐performance optical devices. [ABSTRACT FROM AUTHOR]

In the case of finite confinement potential, the average energies and corresponding wave functions for the 1s2nl configurations, in which nl = 2s, 2p, 3d, and 4f, of three‐electron GaAs/AlxGa1−xAs quantum dot with and without impurity are computed by using a new variational approach which is a combination of Quantum Genetic Algorithm procedure and Hartree–Fock–Roothaan method. Using the calculated average energies and wave functions, a detailed investigation of the linear, third‐order nonlinear and total absorption coefficients (ACs) and the refractive index changes (RICs) for the quantum dot is performed, and the obtained results are presented as a function of dot radius and photon energies. The results show that the dot radius, the impurity charge, and the height of potential barrier have a strong influence on the average energies and absorption spectra of the system. As the potential barrier height increases, the peak positions of the ACs and RICs shift toward higher energy, and there is a significant increase in the amplitudes of the absorption spectra as the potential barrier height increases. In addition, the electron wave functions begin to enter the quantum well at smaller dot radii with increasing barrier height. [ABSTRACT FROM AUTHOR]

A scheme is proposed to enhance quantum correlation, including entanglement and steering, for two magnon modes in a cavity‐magnon hybrid system through coherent quantum feedback. The hybrid system consists of a microwave cavity and two YIG spheres, which incorporates a nonlinear flux‐driven Josephson parametric amplifier in order for the generation of two photons within the cavity simultaneously. A quantum coherent feedback loop is used for the reduction of effective dissipation. By modulating feedback parameters, optimal bipartite and tripartite entanglement, as well as quantum steering are derived. Importantly, compared with the same setup without coherent feedback, the proposed scheme significantly improves quantum correlation. Furthermore, by optimizing the feedback reflectivity and the ratio of cavity‐magnon coupling strength, the enhancement of asymmetric steering can be controlled. Notably, incorporating the feedback loop effectively increase its robustness against thermal noise, thus the scheme offer better prospect for experimental development. This study paves the way for advancements in quantum information processing and quantum entanglement within cavity‐magnonics. [ABSTRACT FROM AUTHOR]

Excitons are expected to be a high‐efficiency emission source in UV light‐emitting devices. However, the damping of the excitonic laser oscillation has been reported under conditions where the excitonic states are expected to be populated in the conventional theory. In order to understand the exciton dynamics under the thermal nonequilibrium state, a theoretical model including various energy species in semiconductors such as electrons, phonons, and photons is required. Herein, a 2D phononic–excitonic–radiative model is constructed to analyze the exciton dynamics in a 2D system. 2D excitons with four principal quantum number states and the continuum in the lowest energy level of the AlN/GaN/AlN quantum wells are considered. It is found that the 2D phonon significantly augments the excitation transition rate. When the high recombination rate corresponding to stimulated emission is considered, the exciton binding energy of 108 meV is not enough to reduce the population in the high‐order discreet states and the continuum states, while the binding energy of 215 meV corresponding to the one monolayer GaN has an advantage of reducing these populations. The analysis of population flux has an advantage in discussing the increase in the kinetic energy transfer to the 1S exciton. [ABSTRACT FROM AUTHOR]

To investigate nonradiative recombination processes in indium gallium nitride (InGaN)‐based red light‐emitting diodes (LEDs), an InGaN‐based red LED with a hybrid quantum well (QW) structure consisting of red and blue single quantum wells (SQWs) is characterized by micro‐photoluminescence (μ‐PL) spectroscopy. The μ‐PL mapping of the red emission reveals numerous dark spots with various sizes and contrasts. Not only the red and blue (from a blue SQW) but green emission bands are observed at some red dark spots, suggesting that indium (In) segregation is one of the causes of nonradiative recombination in the red emission. Comparing the blue and green emission images to the red emission image reveals that the dark spots in the intensity map of the red emission can be classified into four types. Through this correlative analysis, the red dark spots associated with the dark areas in the intensity map of the blue emission are attributed to the major nonradiative recombination centers in the red emission. [ABSTRACT FROM AUTHOR]

Radiative and nonradiative recombination processes are investigated in the temperature range from 10 to 500 K for AlGaN quantum wells on epitaxially laterally overgrown AlN/sapphire templates. Time‐integrated photoluminescence (PL) spectroscopy under selective excitation conditions demonstrates that the decrease in the radiative recombination efficiency with increasing temperature is one of the causes of the thermal droop in AlGaN‐based deep‐ultraviolet (DUV) light‐emitting diodes. Time‐resolved PL spectroscopy indicates that not only the decreasing nonradiative recombination lifetime but increasing radiative recombination lifetime with increasing temperature contributes to the thermal droop. The temperature dependence of the radiative recombination lifetime is discussed, revealing that luminescence linewidth is a valuable criterion for designing efficient AlGaN‐based DUV emitters. [ABSTRACT FROM AUTHOR]

The internal quantum efficiency (IQE) and cathodoluminescence intensity line profile of AlGaN multiple quantum well (MQW) structures on low‐dislocation face‐to‐face annealed sputtered AlN (FFA Sp‐AlN) and on conventional metalorganic vapor‐phase epitaxy‐grown AlN (MOVPE‐AlN) templates are evaluated and the effect of the number of quantum wells (QWs) on the IQE is discussed. The higher IQE in the FFA samples is probably due to the lower threading dislocation (TD) density; however, the IQE also increases with the number of QWs although the TD density remains constant. Effective diffusion length increases with the number of QWs, indicating that the AlGaN MQW layer helps to suppress point defect diffusion, resulting in IQE increase. Furthermore, the segregation of point defects into the TDs and point defect diffusion via the TDs may explain the difference in the IQE improvement rate between the MQWs on the FFA Sp‐AlN and MOVPE‐AlN templates. [ABSTRACT FROM AUTHOR]

Topological photonics shows considerable promise in revolutionizing photonic devices through the use of topological phases, leading to innovations like topological lasers that enhance light control. One of the recent breakthroughs is reducing the size of these systems by utilizing lower‐dimensional boundary states, notably via higher‐order topological phases. This paper presents the experimental demonstration of a topological laser in an anomalous quadrupole topological phase, an instance of higher‐order phases. To facilitate this, a topological nanocavity with a quality factor near 6000 is engineered through a twisting operation. The topological nature of this system is validated by the calculation of nested Wannier centers and the emergency condition of corner states. The experimental observations reveal the manifestation of corner states and the achievement of single‐mode pulsed laser, driven by an optical gain from multiple quantum wells at telecommunication wavelengths and a temperature of 4 K. A lasing threshold of 23 µW and a cold quality factor of 1500 are deduced through rate equation. This work gives a new potential in the application of topological principles to advance nanophotonic technologies. [ABSTRACT FROM AUTHOR]

Herein, the wavelength dependence of the efficiency and the lifetime of far UV‐C light‐emitting diodes (LEDs) on a single‐crystal AlN substrate is systematically analyzed from experiments and simulations. A positive relation between efficiency and emission wavelength is observed. The wall‐plug efficiency reaches 0.47, 1.0, 2.1, and 2.4% at 227, 230, 233, and 235 nm wavelengths, respectively. The simulation results show that carrier injection plays a critical role in the efficiency change in the far UV‐C region rather than in the internal quantum or light extraction efficiency. The lifetime test clearly demonstrates a trade‐off between the L70 lifetime and the emission wavelength, although the initial optical power increases with the longer wavelength. The measurement results under various wavelengths and stress currents indicate that the carriers injected in quantum wells motivate power reduction during current stress. Moreover, the internal quantum efficiency affects the degradation rate because the influence of defects becomes stronger during stress. Finally, the reliability of a 231 nm LED is investigated at a reduced current of 35 mA. The projected L70 and L50 lifetimes are 11 000 and 28 000 h, respectively, from the fitting model based on the defect generation during aging. [ABSTRACT FROM AUTHOR]

Far‐ultraviolet‐C (far‐UVC) light emitting diodes (LED) emitting at an emission wavelength of 226 nm with different n‐AlGaN contact layers, quantum well barriers, and quantum well numbers are compared regarding their emission power, operation voltage, and lifetime. Electroluminescence measurements show higher emission power but also an increased operation voltage with increasing Al mole fraction in the n‐AlGaN contact layer. Furthermore, it is found that both the mean emission power and the device lifetime decrease with increasing Al mole fraction (82–89%) of the quantum well barriers and therefore with increasing barrier height. Finally, 226 nm LEDs with 6 and 9 quantum wells are compared. It is observed that the sample with 9 quantum wells shows an around 30% lower mean emission power but, in contrast, the L70 lifetime of these LEDs is higher by a factor of around five. Based on these optimizations, 226 nm LEDs with a maximum external quantum efficiency of 0.28% (wall plug efficiency of 0.18%) as well as an emission power of 2.1 mW and an operation voltage of 9.6 V at 200 mA are realized. [ABSTRACT FROM AUTHOR]

Doping semiconductor nanomaterials with manganese ion (Mn2+) introduce a well‐defined photoactive d‐d level within the band structure, paving the way for diverse applications. Although Mn doping in single‐layer 2D hybrid perovskites (n = 1) has been extensively studied, limited research has been conducted on doping with modulation of the layer thickness. Herein, Mn2+ doping in hybrid 2D perovskite nanoplatelets (NPLs), L2An‐1[Pb1‐xMnx]nBr3n+1 (where L = butylammonium, A = methylammonium), with variations in Mn concentration (x = 0–0.60) and layer thickness (n = 1–3) is reported. Substitutional doping of Mn significantly increases the photoluminescence quantum yield as well as the rate of energy transfer efficiency, which strongly depends on the layer thickness of NPLs. The Mn concentration in 2D NPLs determines the rate of forward and backward energy transfer. Low‐temperature emission spectra allow to determine thickness‐dependent exciton binding energy for Mn‐doped 2D NPLs (x = 0.5) with values of 410 ± 11 meV (n = 1), 188 ± 9 meV (n = 2), and 151 ± 17 meV (n = 3). The faster dissociation of band‐edge excitons into free carriers at Mn2+ sites results in high brightness with an excellent CRI of 89.2 for the white light‐emitting diode. [ABSTRACT FROM AUTHOR]

This research provides a flexible approach to manipulate formation of InGaAs nanostructures on the GaAs (100) surface by varying arsenic (As4) beam equivalent pressure (BEP). By selecting the As4/(In+Ga) BEP ratio to be 4, 8, 20, 50 and 100, we were able to obtain different quantum structures from quantum well (QW) to quantum dots (QDs), then to spatially ordered quantum dot chains (QD-chains), and finally to quantum wires (QWRs), respectively. This transformation of nanostructures was explained by anisotropic surface diffusion coupled with the strain relieving Stranski–Krastanov growth mode, while the anisotropy was modulated by increasing As4 flux and subsequently enhanced by multilayer-stacking growth with a suitable spacer thickness. Photoluminescence characteristics show correlation to the nanostructure morphology for each sample. In particular, the formation of QD-chains and QWRs results in anisotropic features that offer potential device applications. [ABSTRACT FROM AUTHOR]