Step Quantum Wells Research Articles

Computation of the near-infrared electro-absorption in GeSn/SiGeSn step quantum wells

In this study, we propose a theoretical simulation of the type-I step quantum well obtained from GeSn/SiGeSn to scan a wide range of telecommunication wavelengths and obtain near-infrared optical modulators. At T = 300 K, the band discontinuities and energy gap between stretched Ge1−xSnx and relaxed Si0.1Ge0.9−ySny due to the acquisition of the heterostructure were calculated.Then, optimization of this heterostructure based on (Si) GeSn was performed using the solid theory model to balance out the composition y of Si0.1Ge0.9-ySny relaxed and thickness of Ge0.91Sn0.09 QWs. The eigenenergies and their related wavefunctions are computed by solving the Schrödinger equation using the finite difference method under the framework of the effective mass approximation. Depending on the y concentration, the energy levels of the electron and the heavy hole, the change of transition energies and oscillator strength were examined for different well widths. Additionally, the absorption coefficient with y concentration and structure parameters were examined.From the findings obtained, it was determined that this material group is very important to obtain high efficiency from electro-absorption modulators covering the 1.55 μm wavelength range.

A particular behavior of levels energy evolution and theoretical study of the quantum probability distribution in GaAs/AlGaAs asymmetric stepped semiconductor quantum wells for terahertz optoelectronics

The study of the evolution of the energy levels as a function of the step layer’s width Lw2 in an asymmetric stepped quantum well AlxGa1-xAs/GaAs/AlyGa1-yAs/AlxGa1-xAsx=24%,y=14%, revealed a particular behavior, marked by the presence of plateaus within certain deep well’s width, Lw2, ranges. We initially computed the eigenenergies and eigenfunctions by numerically solving the Schrödinger equation. This was done within the effective mass and envelope function approximation, taking into account the influence of non-parabolicity. To explain the origin of the plateaus and their impact on intersubband transition energies, we determined the distribution of the probability density of the presence of the electron in each region of the stepped quantum well. The results of these calculations demonstrated that the electron's probability density is higher in the step well than in the deep one, particularly for electrons with energy levels above 113.47 meV. This elevation in probability density exhibits maximum values that remain nearly constant within specific Lw2 domains, providing an explanation for the observed energy plateaus. Such plateaus allow more energy tunability and thus open up additional possibilities for applications in the THz domain either in the linear or nonlinear optics.

The inner barrier mediated spin–orbit control in stepped quantum wells

The inner barrier in stepped quantum wells, which embrace an intrinsic structural inversion asymmetry (SIA), offers more possibilities for the multi-band spin–orbit (SO) control. By varying the inner band offset [Formula: see text], which adjusts the quantum confinement for electrons and also the SIA, we reveal that both the Rashba ([Formula: see text]) and Dresselhaus ([Formula: see text]) SO coeffcients of the two subbands exhibit contrasting dependence on [Formula: see text]. Also, [Formula: see text] and [Formula: see text] may have opposite signs, depending on the value of [Formula: see text]. By fine tuning the inner offset, there may even exist a scenario in which [Formula: see text] identically vanishes but [Formula: see text] is finite, offering a knob on how to subband-selectively suppress spin relaxation induced by SO coupling. In addition, by resorting to an external gate [Formula: see text], we reveal that in the regime of [Formula: see text] and [Formula: see text] having opposite signs, their magnitudes also vary with [Formula: see text] in an opposite manner. This, together with the engineered inner barrier of stepped wells, will facilitate flexible spin manipulation. Finally, the interband SO couplings, which depend on the spatial overlap of wave functions of distinct subbands and the corresponding parities, are also discussed.

A 5.7 THz GaN/AlGaN quantum cascade detector based on polar step quantum wells

We report on a GaN/AlGaN quantum cascade detector operating in the terahertz spectral range. The device was grown by metal organic chemical vapor deposition on a c-sapphire substrate and relies on polar GaN/AlGaN step quantum wells. The active region thickness is in micrometer range. The structural, electrical, and optical investigations attest of high structural quality of the synthetized nitride material. The detector exhibits a peak photocurrent at 5.7 THz (23.6 meV) with a responsivity of 0.1 mA/W at 10 K under surface normal irradiation through a 10 μm period grating. The photocurrent persists up to 20 K.

Detailed analysis of the intersubband absorption in a GaAs stepped quantum well for quadratic detection and second harmonic generation

We focus on intersubband transitions tunability in GaAs stepped quantum wells through the step's width variation. A double resonance can then occur due to two-photon absorption with possible promising nonlinear optics applications in absorption or emission. In this work, we identified five structures where the equidistant two-photon absorption (ETPA) is possible. We have evaluated the potential of each structure for quadratic detection (QD) and/or second harmonic generation (SHG). This was accomplished quantitatively through the analysis of the calculations results of the main terms of the nonlinear factors involved in both processes. These calculations are based on those of the optical physical parameters linked to the intersubband absorption, namely the individual absorption coefficients and the corresponding dipolar momentum couplings. To highlight the enhancing effect of the asymmetry degree on the total absorption, an investigation of the optical absorption properties of symmetrical quantum wells was done in parallel.

Lattice strain influence on conduction band nonparabolicity in GaAs and InAs: Application to intraband optical absorption in InGaAs-GaAs asymmetric step quantum wells

We use empirical sps*d5 tight-binding calculations to determine the effects of compressive biaxial lattice strain, perpendicular to the [001] crystal direction, in zinc blende GaAs and InAs. Under that approach, we have been able to compute the behavior of quantities such as the average valence band energy, the energy band gap, the conduction band effective mass, and the spin-orbit split-off energy, as functions of the biaxial strain, within a range from 0 to −7%. Expressions governing these dependencies are reported for both materials. With such information at hand it is possible to calculate the variation of the coefficient of conduction band nonparabolicity due to the presence of strain. Also, the outcome for such quantities allows to evaluate the valence band offset in GaAs/InGaAs heterointerfaces as a consequence of the strain appearing from the difference between the lattice constants of the involved materials. Taking advantage of the above mentioned results, we have performed the calculation of confined conduction band states in step-like asymmetric quantum wells of the GaAs/Inx1Ga1-x1As/Inx2Ga1-x2As/GaAs prototype, using a k→⋅p→ formalism that solves the effective mass equation arising from a bi-cuadratic (nonparabolic) dispersion law. We report the calculation of the optical absorption coefficient related with intraband transitions that involve the ground and first excited energy levels. For that purpose, the study takes into account the variation of the layer widths and compositions.

Intra-band Raman scattering and gain in a double quantum well wire with asymmetrical barriers

In this paper we present a study on electron states in a double quantum well wire with asymmetrical barriers, also emission spectra are analyzed for a process of electron Raman scattering in this system, for which we calculate the differential cross section. The model we use considers the system to be at a temperature of T=0K and the presence of a single electron in the conduction band. In addition, the conduction band is assumed to be parabolic, which splits into a system of sub-bands due to confinement. On the other hand, in this work we study the net Raman gain of the system, illustrating the results through the transition rate since they are directly proportional. The results obtained in this work are compared to those of previous works and we show that the net Raman gain of the double quantum well wire with asymmetrical barriers is greater than that of the step-quantum well wire, and than that of the core/shell quantum well wire, obtaining the results of these systems as limit cases. We also showed that the system studied here is slightly more efficient than the double quantum well with asymmetrical barriers. These results can be applied in the manufacture of electronic and optoelectronic devices as quantum cascade lasers.

Selective asymmetric gate control of the Rashba spin-orbit coupling in GaInAs/AlInAs stepped wells

Resorting to ordinary GaInAs/AlInAs stepped quantum wells subjected to an external gate, which allows for adjusting the well symmetry and electron occupancy, we demonstrate that the Rashba spin-orbit (SO) strengths of the first (${\ensuremath{\alpha}}_{1}$) and second (${\ensuremath{\alpha}}_{2}$) subbands exhibit opposite gate dependence, triggered by the inner barrier, of which the structural potential energy for electrons is sandwiched between energy levels of two subbands. This opens a route towards selective and opposite SO control, greatly fascinating for spintronic applications. Moreover, we find that ${\ensuremath{\alpha}}_{1}$ and ${\ensuremath{\alpha}}_{2}$ may have opposite signs, in favor of hosting topological matter of persistent skymion lattice in conventional semiconductor heterostructures that we recently proposed [J. Y. Fu, P. H. Penteado, M. O. Hachicya, D. Loss, and J. C. Egues, Phys. Rev. Lett. 117, 226401 (2016)]. Finally, while the interband Rashba term ($\ensuremath{\eta}$) is found to be essentially gate independent, it may lead to the energy dispersion anticrossing or maintaining crossing, depending on intraband Rashba couplings.

Terahertz intersubband absorption of GaN/AlGaN step quantum wells grown by MOVPE on Si(111) and Si(110) substrates

We demonstrate terahertz intersubband absorptions in nitride step quantum wells (SQWs) grown by metal organic vapor phase epitaxy simultaneously on two different substrate orientations [Si(111) and Si(110)]. The structure of the SQWs consists of a 3 nm thick Al0.1Ga0.9N barrier, a 3 nm thick GaN well, and an Al0.05Ga0.95N step barrier with various thicknesses. This structure design has been optimized to approach a flatband potential in the wells to allow for an intersubband absorption in the terahertz frequency range and to maximize the optical dipole moment. Structural characterizations prove the high quality of the samples. Intersubband absorptions at frequencies of 5.6 THz (λ ≈ 54 μm), 7 THz (43 μm), and 8.9 THz (34 μm) are observed at 77 K on both substrate orientations. The observed absorption frequencies are in excellent agreement with calculations accounting for the depolarization shift induced by the electron concentration in the wells.

Electron states and electron Raman scattering in a semiconductor quantum well with step-barriers: Electric field effect

In this work, we present the study of an intra-band electron Raman scattering process for a semiconductor quantum well with step-barriers, developed in a GaAs/AlxGa1−xAs matrix. For the solution of this problem, the existence of an electron in a single conduction band and a system under the effect of an external electric field in the direction of confinement were considered. In addition, we will study the electron states for this system. In this study, we calculate the differential cross-section and the net Raman gain, so that the corresponding emission spectra (which are interpreted and discussed) are obtained. For this, we consider a simple parabolic conduction band, which is unfolded into a sub-band system due to confinement. Moreover, the exact solutions of the electron states considering the approximation of the envelope function are obtained. In like manner, we make a comparison between the quantum well with step-barriers with other systems such as the asymmetric double quantum well and the step-quantum well with the objective of studying the differences between these three systems.

The effect of intense laser field on the nonlinear optical features in asymmetric multiple step and inverse V-shaped multiple step quantum wells

For asymmetric multiple step quantum wells (AMS QWs) and asymmetric inverse V-shaped multiple step quantum wells (AIVSMS QWs), the nonlinear optical features, such as the nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) coefficients are analyzed as according on the intense laser field (ILF). The found consequences indicate that the ILF parameter confirms a vital influence on the shape and height of the confined potential profile of both AMS QWs and AIVSMS QWs, and the alterations of the dipole moment matrix elements and the energy levels are adhered on the profile of the confined potential. According to the results, the potential profile and height of the AIVSMS QWs compared to AMS QWs were affected differently from ILF intensity. These results indicate that NOR, SHG, and THG coefficient of AMS QWs and AIVSMS QWs may be regulated in a preferred energy range and the magnitude of the resonance peak (RP) by tuning the ILF parameter. By varying the ILF parameter, it is feasible to classify blue or red shifts in RP locations of NOR, SHG and THG coefficients. Our results can be valuable in investigating new ways of manipulating the opto-electronic properties of semiconductor QW devices.Highlights•The electro-optical properties of AMS QWs and AIVSMS QWs vary by increasing ILF.•The change of AIVSMS QWs compared to AMS QWs is more affected by ILF.•NOR, SHG, and THG coefficients change with rising ILF.•RP spectrums show blue or red shifts as according to ILF.

Bias-Polarity-Dependent Photocurrent Spectra of Terahertz Stepped-Quantum-Well Photodetectors

The authors study the photoresponse of a broadband THz-frequency detector with stepped quantum wells in the absorption layer. Due to the asymmetric distribution of the wave function of the second excited subband ${E}_{2}$, the escape probability for photoexcited electrons is strongly dependent on bias polarity, which is responsible for the different shapes of photocurrent spectra under positive and negative bias voltages. These results show that not only band structure but also the nature of the wave function itself plays a key role in designing these high-performance quantum-well photodetectors.

Theory of electron Raman scattering in a semiconductor core/shell quantum well wire

A study of the electron states of a semiconductor core/shell quantum well wire and the electron Raman scattering are presented. Thus, the system has been modeled considering a GaAs/AlxGa1−xAs/AlAs structure. To carry out this study, the exact mathematical expressions that describe the electron states and the Raman differential cross-section in the aforementioned system were obtained. Our model considers T=0K and that, as a consequence of the presence of the confinement, the electron bands unfold in a subband system. In addition, the expressions that describe the differential cross-section and the selection rules for the emission spectra are shown. On the other hand, the net gain of Raman is studied through the transition rate, since they are directly proportional. It should be point out that our results are compared with the results obtained in previous works, especially with the step-quantum well wire. Finally, it is shown that although the core/shell quantum well wire and the step-quantum well wire are very similar systems, the Raman net gain for the step-quantum well wire is much greater than the one for the core/shell quantum well wire.

Linear and nonlinear optical properties in the terahertz regime for multiple-step quantum wells under intense laser field: Electric and magnetic field effects

We present a theoretical study on the linear and nonlinear optical properties in AlrGa1-rAs/GaAs asymmetric multiple step quantum wells (AMSQW) under the effects of a non-resonant intense laser field (ILF), electric, and magnetic field. Calculations are for the linear optical absorption and refractive index relative changes combined with the second and third harmonic generation. The potential profile is constructed as a function of the Aluminum concentration, so that the heterostructure has four steps of different concentration, width and height. The energy levels and corresponding wavefunctions are obtained by solving the Schördinger equation, for an electron, in the envelope function approach, with parabolic bands, and the effective mass approximations. The results show that variations in ILF, electric field and magnetic field have significant influences on the magnitude and peak energy positions of the SHG and THG coefficients. Therefore, we can conclude that the effects of ILF, electric and magnetic fields can be used to tune and control the SHG and THG in the range of the terahertz electromagnetic spectrum.Keywords: Multiple-step quantum wells; Linear optical properties; Second and third harmonic generation; Terahertz radiation; Intense laser field; Electric and magnetic fields.

Tunability of the optical absorption and refractive index changes in step-like and parabolic quantum wells under external electric field

In this paper, the effects of an external electric field on the energy transitions and optical absorption lineshape in step and parabolic GaAs quantum wells are theoretically investigated. The energy separations between the three lowest energy levels E1, E2 and E3 and their corresponding wavefunctions are calculated by solving the Schrödinger equation. Our theoretical findings show that the intersubband transitions and the optical absorption in the step-like quantum well can be tuned and controlled by an applied electric field (F). Especially the optical absorption coefficient α12(ω) presents a blue shift by increasing the intensity of F. Contrary to the case of step-like quantum well, the energy transition and the optical absorption coefficient α12(ω) are less sensitive to the applied electric field F in the case of parabolic quantum well. In the latter case α12(ω) presents a small red-shift variation. The obtained behavior in the optical absorption coefficient and refractive index changes can be used to design and fabricate new optical devices such as optical modulators.

Significant internal quantum efficiency enhancement of GaN/AlGaN multiple quantum wells emitting at ~350 nm via step quantum well structure design

Significant internal quantum efficiency (IQE) enhancement of GaN/AlGaN multiple quantum wells (MQWs) emitting at ~350 nm was achieved via a step quantum well (QW) structure design. The MQW structures were grown on AlGaN/AlN/sapphire templates by metal-organic chemical vapor deposition (MOCVD). High resolution x-ray diffraction (HR-XRD) and scanning transmission electron microscopy (STEM) were performed, showing sharp interface of the MQWs. Weak beam dark field imaging was conducted, indicating a similar dislocation density of the investigated MQWs samples. The IQE of GaN/AlGaN MQWs was estimated by temperature dependent photoluminescence (TDPL). An IQE enhancement of about two times was observed for the GaN/AlGaN step QW structure, compared with conventional QW structure. Based on the theoretical calculation, this IQE enhancement was attributed to the suppressed polarization-induced field, and thus the improved electron–hole wave-function overlap in the step QW.

Electron states and electron Raman scattering in a semiconductor step-quantum well wire

The differential cross-section for an electron Raman scattering process in a semiconductor GaAs/AlGaAs step-quantum well wire is calculated and expressions for the electron states are presented. The system is modeled by considering T=0K and also by a single parabolic conduction band, which is split into a sub-band system due to confinement. The net Raman gain for an electron Raman scattering process is obtained. Also, the emission spectra for several scattering configurations are discussed, and the interpretation of the singularities found in the spectra is given. The results obtained in this study are compared with those obtained for other structures, and so it has been demonstrated that the wire shows greater efficiency.

Electron states and electron Raman scattering in semiconductor step-quantum well: Electric field effect

In this work we determine and show the expressions of the electron states of a step-quantum well with the presence of an external electric field, developed in a GaAs/AlGaAs matrix. The electron states are obtained using the envelope function approximation. In this work it is only necessary to consider a single conduction band, which due to the confinement is divided into a subband system, with T=0K. Expressions for the electron states and the differential cross-section for an intraband electron Raman scattering process of are presented, the net Raman gain is also calculated. In addition, the interpretation of the singularities found in the emission or excitation spectra is given, since several dispersion configurations are discussed. Furthermore, the effects of an electric field on the electron states and on the differential cross section are studied.

The electron-longitudinal optical phonon scattering rate in GaInAsP/InP stepped quantum well

Within the framework of effective mass approximation, the scattering rate via longitudinal optical (LO) phonon emission for an electron and the mean scattering rate via LO phonons emission for electrons initially in the first excited sub-band and finally in the ground sub-band in [Formula: see text] stepped quantum well (QW) is calculated adopting the shooting method and Fermi’s golden rule. The results show that the scattering rate and the mean scattering rate are highly dependent on alloy compositions, well width, initial electron energy, electron temperature and sub-band separation [Formula: see text] between the ground sub-band and the first excited sub-band. When [Formula: see text] is larger than the LO phonon energy, the scattering rate and the mean scattering rate increases with increasing Ga composition, decreasing As composition and increasing well width. However, when [Formula: see text] is smaller than the LO phonon energy, its change tendency is contrary. The scattering rate increases with decreasing initial electron energy if the separation between the initial electron energy and the ground state energy [Formula: see text] is not smaller than the LO phonon energy. The scattering rate and the mean scattering rate increases with rising electron temperature. The mean scattering rate reaches the maximum value when [Formula: see text] is equal to the LO phonon energy. The interruption in the scattering rate happens when the separation between the initial electron energy and [Formula: see text] is smaller than the LO phonon energy. The rapid decrease of the mean scattering rate happens when [Formula: see text] is smaller than the LO phonon energy if [Formula: see text] continues decreasing. In addition, both the scattering rate and the mean scattering rate show little change with different stepped layer widths.

The effects of doping layer location on the electronic and optical properties of GaN step quantum well

In the present work, the intersubband transition and the optical absorption coefficient between the ground and the first excited states in the Si-δ-doped step AlGaN/GaN quantum well were theoretically studied by solving Schrödinger-Poisson equations self-consistently within the framework of effective mass approximation. The delta-doped layer was inserted in three different locations (middle of the quantum well, middle of the step quantum well and middle of the left barrier). The obtained results show that the energy difference between the ground and the first excited state and the optical absorption depend not only on the doping layer concentration but also on its location. The shape of the confining potential and the wavefunctions were also changed depending on the doped layer location. It was found that doping in the middle quantum well is advantageous to obtain an optical absorption with a higher energy separation; however, doping in the left barrier gives us an optical absorption with a lower energy separation. The obtained results in optical absorption give us a new degree of freedom in optoelectronic devices based on intersubband transitions.