Envelope Function Formalism Research Articles

Temperature dependence analysis of intersubband absorption in asymmetric ZnO/MgZnO quantum wells: Potential for terahertz emission applications

In this paper, in ZnO/MgxZn1−xO quantum well structures, with 20% of Mg, we have calculated the electronic states of confined levels and the intersubband absorption coefficient with or without the effect of non-parabolicity. We use the finite difference approach to do our computations inside the envelope function formalism approximation. The results show that the wavelength range covered by the E12 transition (9–16 μm) is mid-infrared to far-infrared. According to our findings, ZnO/MgZnO quantum well structures, which have extremely similar lattice characteristics and the benefit of an unconstrained structure, have E23 transition energies that provide terahertz frequencies (1.1—20THz) that are utilized in airport security and explosives detection. This promotes intersubband photonic structure design and epitaxial development. Furthermore, we have examined the impact of temperature on the Fermi level and the load carrier population inside each level for these remarkable structures. In addition, each transition's oscillation force and intersubband absorption are considered.

Quantum magneto-transport properties of GaAs/AlxGa1-xAs Weakly coupled quantum wells for near wavelength infrared detection

We investigated here the GaAs(d1 = 184 Å)/Al0.18Ga0.82As (d2 = 42 Å) multiple quantum wells based on our enhanced numerical calculations in the envelope function formalism. We calculated the band structures and the effective mass mi* of charge carriers. When the well thickness d1 increases, the bandgap Eg decreases like m*. The calculated Fermi level energy and the density of states show n-type conductivity and a quasi-two-dimensional transport character. When the barrier thickness d2 increases the bandwidth decreases as a result of the weakening of interlayer tunnelling along the growth direction in the first Brillouin zone. We also interpreted theoretically the Shubnikov-de Haas and quantum Hall effects measurements reported by B. G. Tavares et al. These results are necessary for the design and engineering of multiple quantum wells infrared detectors.

GaAs-based strain-balanced GaNxAs1-x-yBiy type-I and -II multi-quantum wells for near-infrared photodetection range

Electronic band structure of t2-GaNx2As1-x2-y2Biy2/t1-GaNx1As1-x1-y1Biy1 strain-balanced quantum wells (QWs) elaborated on GaAs substrate was theoretically studied. Our study is based on the band anti-crossing model combined with the envelope function formalism. Using the zero stress balance model, the strain compensation criteria (N and Bi compositions, and thickness ratio (t1/t2) for the strain-balanced QWs is investigated. The critical thickness for each strained GaNAsBi layer is also discussed. Through the results, we found that the control of the compositions (x1,y1) and (x2,y2) for the tensile and compressive strained layers respectively, could modulate the band alignment of the strain-balanced QWs. The use of strain-balanced GaNx2As1-x2-y2Biy2/GaNx1As1-x1-y1Biy1type-II ”W” QWs is quite promising candidate for GaAs-based near-infrared photodetection range as compared to strain-balanced type-I QWs counterparts.

Long wavelength Infrared Detection, Bands Structure and effective mass in InAs/GaSb Nanostructure Superlattice

We have investigated in the bands structure and the effective mass, respectively, along the growth axis and in the plane of InAs (d1=48.5Å)/GaSb(d2=21.5Å) type II superlattice (SL), performed in the envelop function formalism. We studied the semiconductor to semimetal transition and the evolutions of the optical band gap, Eg(Γ), as a function of d1, the valence band offset Λ and the temperature. In the range of 4.2–300 K, the corresponding cutoff wavelength ranging from 7.9 to 12.6 µm, which demonstrates that this sample can be used as a long wavelength infrared detector. The position of the Fermi level, EF = 512 meV, and the computed density of state indicates that this sample is a quasi-two-dimensional system and exhibits n type conductivity. Further, we calculated the transport scattering time and the velocity of electrons on the Fermi surface. These results were compared and discussed with the available data in the literature.

Biaxial strain effects on the band structure and absorption coefficient of GaAs1-x-yNxBiy/GaAs MQWs calculated using k.p method

In this work, we derive the 16 band strain-dependent k·p Hamiltonian using finite difference method for dilute bismide-nitride compound GaNAsBi-based strained quantum wells (QWs). The effect of the biaxial strain (-0.57≤ε∥≤0.50%) on electronic band structure of GaNAsBi/GaAs double QWs (DQWs) operating at the near-infrared spectrum and telecommunications window (1.3 and 1.55 μm) are examined. We use the band anti-crossing model, envelop function formalism and Bir-Pikus theory in conjugation with k·p perturbation method to describe the optoelectronics properties (band offsets, absorption coefficient) behavior of the DQWs structures. Results show that the tensile strained GaNAsBi/GaAs DQWs can be used for the detection of 1, 0.95, and 0.80 eV energy range. This device seem be differentiated by higher carrier confinement and optical absorption compared to compressive strained one. The enhancement of spectral response is analyzed by increasing the QWs number and the coupling between them.

Correlation Between Bands Structure and Quantum Magneto Transport Properties in InAs/GaxIn1−xSb Type II Superlattice for Infrared Detection

We have used the envelope function formalism to investigate the bands structure of LWIR type II SL InAs(d1=2.18d2)/In0.25Ga0.75Sb(d2=21.5A). Thus, we extracted optical and transport parameters as the band gap, cut off wavelength, carriers effective mass, Fermi level and the density of state. Our results show that the higher optical cut-off wavelength can be achieved with smaller layer thicknesses. The semiconductor-semi metal transition was studied as a function of temperature. Our results permit us the interpretations of Hall and Shubnikov-de Haas effects. These results are in agreement with experimental results in literature and a guide for engineering infrared detectors.

Theoretical electronic band structures and transport in InAs/GaSb type II nanostructure superlattice for medium infrared detection

Abstract We report here the electronic band structure of nanostructure type II superlattice (SL) InAs(d1 = 21 A)/GaSb(d2 = 24 A) performed in the envelope function formalism. We calculated the energy E(d1), E(kz), E(kp) and the effective mass in the direction of growth kz and in plane kp of the SL. When the temperature increases, the band gap Eg decreases and the corresponding cutoff wavelength λc increases. We interpreted photoluminescence and transport measurements of Haugan et al. with an agreement in the calculated gaps. The computed density of states and Fermi energy position indicated that the sample is a p type semiconductor with a transition from bi-dimensional to tri-dimensional conductivity near 20 K. This sample is medium infrared detector (3.92 μm

GaAs quantum well in the non-parabolic case: the effect of hydrostatic pressure on the intersubband absorption coefficient and the refractive index

We investigated the effect of the hydrostatic pressure on the optoelectronic properties of a quantum well (QW) based on δ-doped GaAs sandwiched by Ga1-xAlxAs. We study the case of a non-parabolic conduction band where the aluminum content is set at 30%. We perform our calculations in the context of the approximation of the envelope function formalism using the finite difference method. Results show that the transition energies decrease with the increase of the hydrostatic pressure, which causes remarkable modifications on the optical properties of the QW nanostructure. The non-parabolicity effect is more important for small QW (Lw ≤ 5nm) and less marked in narrow and large QW. In addition, we study the absorption coefficient for 8 nm/4 nm/8 nm geometry. On the one hand, the pressure increase creates a displacement of the optical absorption coefficient towards low energies and a decrease of the absorption peak value. On the other hand, the refractive index moves towards higher energies. We show that in the presence of a hydrostatic pressure and following its effect on intersubband transitions, these optical properties also depend on the dopant concentration rate and the quantum well width. Our study finds interests for the nano-fabrication of quantum wells and in particular for those used in optical and electronic applications.

Calculation of Energy States of Excitons in Square Quantum Wells

The ground and excited energy states of excitons in single square GaAs-based quantum wells are found by the numerical solution of the three-dimensional Schrodinger equation. This equation is obtained within the envelope-function formalism from the exciton energy operator using the spherical approximation of the Luttinger Hamiltonian. Precise results for the exciton states are achieved by the finite-difference method. The radiative decay rates of the calculated states are also determined.

Investigations in electronic quantum transport of quasi two dimensional InxGa1-xAs/InP nanostructure superlattice for infrared detection

We investigated, theoretically, the electronic band structures, transport and magneto-transport properties of In0.53Ga0.47As(d1 = 10 nm)/InP(d2 = 5 nm) lattice matched superlattice (SL) at 1.7 K. These studies were performed in the envelope function formalism with effects of well thickness d1. The SL has a direct band gap of 849 meV and the cut-off wavelength of 1.46 μm indicates that it can be used as a short infrared detector. The computed density of states and position of Fermi level, predict that this sample is a quasi two-dimensional system and exhibits n type conductivity. We have interpreted the oscillations in the magneto-resistance observed by Pusep et al. in this superlattice. These results were compared and discussed with the available data in the literature.

Effect of conduction band non-parabolicity on the intersubband transitions in ZnO/MgxZn1-xO quantum well heterostructures

In this paper, we have calculated the electronic states and the coefficient of transmission in ZnO/MgxZn1-xO quantum well structures (QW), with 20% of Magnesium in both the parabolic and the non-parabolic cases. Our calculations are performed in the context of the approximation of the envelope function formalism, and using the finite difference method. The results show that the intersubband transition energy increases rapidly with well width until Lw=5nm and becomes almost constant (specially transitions E13 et E23). Wavelength λ23 decreases with well width until Lw=5nm and becomes constant. The non-parabolicity effect is more pronounced for small QW (Lw ≤ 5nm) and less marked in narrow and large QW. Also, we are studied the coefficient of transmission. We notice that when the height of barrier increases the coefficient of transmission decreases. It will be necessary to provide more energy to the electron so that it can cross the barrier. We also notice the variations related to a phenomenon of reflection quantum.

Spin filtering via resonant reflection of relativistic surface states

A microscopic approach is developed to scattering of surface states from a non-magnetic linear defect at a surface with strong spin-orbit interaction. Spin-selective reflection resonances in scattering of Rashba-split surface states by an atomic stripe are theoretically discovered in a proof-of-principle calculation for a model crystal potential. Spin-filtering properties of such linear defects are analyzed within an envelope-function formalism for a perturbed surface based on the Rashba Hamiltonian. The continuous Rashba model is found to be in full accord with the microscopic theory, which reveals the essential physics behind the scattering resonance. The spin-dependent reflection suggests a novel mechanism to manipulate spins on the nanoscale.

Calculation of energy states of excitons in square quantum wells

AbstractThe ground and excited energy states of excitons in single square GaAs-based quantum wells are found by the numerical solution of the three-dimensional Schrödinger equation. This equation is obtained within the envelope-function formalism from the exciton energy operator using the spherical approximation of the Luttinger Hamiltonian. Precise results for the exciton states are achieved by the finite-difference method. The radiative decay rates of the calculated states are also determined.

Correlation between electronic bands structure and magneto-transport properties of nanostructure type II superlattice for terahertz detection

We have used the envelope function formalism (EFF) to investigate the bands structure, energy subbands and carrier's effective mass in the growth direction and in-plan of InAs(d1 = 160 Å)/GaSb(d2 = 105 Å) semimetallic superlattice. The photodetector parameters like optical band-gap, Eg, cut-off frequency, |fc|, and in-plan electron effective mass, m∗E1, were calculated as a function of d1 and/or d2 and temperature T. Eg(R = d1/d2) indicates that the semiconductor-to-semimetal transition goes to lower R when T increases. The range of 11.6 ≤|fc(THz)|≤ 23.8, demonstrates that this sample can be used as a terahertz (THz) detector. For T ≤ 141 K, our results agree with the available experimental data. Using the Boltzmann magnetic-field-dependent Hall coefficient and the magnetoresistance results of D. M. Symons et al., we have deduced the SL electronic parameters. At 141 K, the p to n-type conductivity transition was observed at B0 = 32 T. The Fermi level, EF = 515 meV, reveal a p-type conductivity at 300 K.

Inhomogeneous GaInNAs quantum wells: their properties and utilization for improving of p-i-n and p-n junction photodetectors

Abstract A theoretical study of electronic structures and optical properties of GaInNAs/GaAs quantum wells has been performed. The inhomogeneous distributions of indium and nitrogen atoms along the growth direction were discussed as the main factors having significant impact on the QWs absorption efficiency. The study was performed by applying the band anticrossing model combined with the envelope function formalism and based on the material parameters which can be found in the literature. Indeed, the electronic band structure of 15 nm thick uniform Ga0.7In0.3N0.02As0.98/GaAs QW was computed together with electronic structures of several types of inhomogeneous QWs, with the same total content of In and N atoms. It was found that presented inhomogeneities lead to significant quantum wells potential modifications and thus to spatial separation of the electrons and holes wave functions. On the other hand, these changes have a significant impact on the absorption coefficient behavior. This influence has been studied on the basis of simulated photoreflectance spectra, which probe the absorption transitions between QW energy subbands. The electronic structure of inhomogeneous QWs under the influence of electric field has also been studied. Two different senses of electric field vector (of p-i-n and n-i-p junctions) have been considered and thus, the improvement of such types of QWs-photodetectors based on inhomogeneous GaInNAs QWs has been proposed.

Investigation in band structures of GaAs/Al x Ga1−x As nanostructures superlattices at high magnetic field and low temperatures

We have investigated in the band structures E(d 1), E(k z , k p ) and the effective mass m*/m 0, respectively, along the growth axis and in the plane of GaAs (d 1 = 19 nm)/Al0.3Ga0.7As (d 2 = 5 nm) superlattice, performed in the envelope function formalism. Our results show the effect of the well thickness d 1 and the temperature on the electronic structures of this superlattice. The latter has a direct band gap of 1.529 eV, and the corresponding cutoff wavelength indicates that it can be used as a near-infrared detector. The position of Fermi level, based on the magnetoresistance measurements of Smrcka et al. and Fermi–Dirac integral computation at 0.4 K, predicts that this sample exhibits n-type conductivity with a two-dimensional electron gas.

Electronic transport and band structures of GaAs/AlAs nanostructures superlattices for near-infrared detection

We report here the theoretical calculations of band structures E(d 1), E(k z , k p ) and effective mass along the growth axis and in the plane of GaAs/Al x Ga1−x As superlattices, in the envelope function formalism. The effect of valence band offset, well thickness and temperature on the band structures, has been also studied. Our results show that a transition from indirect to direct band gap in (GaAs) m /(AlAs)4 takes place between m = 5 and 6 monolayers at room temperature. Samples (GaAs)9/(AlAs)4 and GaAs(d 1 = 10 nm)/Al0.15Ga0.85As(d 2 = 15 nm) have a direct band gap of 1.747 eV at room temperature and 1.546 eV at T = 30 mK, respectively. Their corresponding cutoff wavelengths are located in the near infrared region. We have interpreted the photoluminescence measurements of Ledentsov et al. in GaAs(d 1 = 2.52 nm)/AlAs (d 1 = 1.16 nm) and the oscillations in the magnetoresistance observed by Kawamura et al. in GaAs/Al0.15Ga0.85As superlattice. In the later, the existence of discrete quantized levels along the growth direction z indicates extremely low interactions between adjacent wells leading to the use in parallel transport. The position of Fermi level predicts that this sample exhibits n-type conductivity. These results were compared and discussed with the available data in the literature and can be used as a guide for the design of infrared nanostructured detectors.

Renormalization of optical transition strengths in semiconductor nanoparticles due to band mixing

Unique optical properties of semiconductor nanoparticles (SN) make them very promising in the multitude of applications including lasing, light emission and photovoltaics. In many of these applications it is imperative to understand the physics of interaction of electrons in a SN with external electromagnetic fields on the quantitative level. In particular, the strength of electron–photon coupling determines such important SN parameters as the radiative lifetime and absorption cross section. This strength is often assumed to be fully encoded by the so called Kane momentum matrix element. This parameter, however, pertains to a bulk semiconductor material and, as such, is not sensitive to the quantum confinement effects in SNs. In this work we demonstrate that the quantum confinement, via the so called band mixing, can result in a significant suppression of the strength of electron interaction with electromagnetic field. Within the envelope function formalism we show how this suppression can be described by introducing an effective energy-dependent Kane momentum. Then, the effect of band mixing on the efficiencies of various photoinduced processes can be fully captured by the conventional formulae (e.g., spontaneous emission rate), once the conventional Kane momentum is substituted with the renormalized energy-dependent Kane momentum introduced in here. As an example, we evaluate the energy-dependent Kane momentum for spherical PbSe and PbS SNs (i.e., quantum dots) and show that neglecting band mixing in these systems can result in the overestimation of absorption cross sections and emission rates by a factor of ∼2.

Application of the transition semiconductor to semimetal in type II nanostructure superlattice for mid-infrared optoelectronic devices

The present work is devoted to the study of band structure and band gap in symmetric InAs (d 1 = 25 A)/GaSb (d 2 = 25 A) type II superlattice. Our calculations were performed in the envelope function formalism with the valence band offset Λ = 570 meV. We discussed the semiconductor to semimetal transition and the evolutions of the fundamental band gap, E g (Γ), as a function of d 1, Λ and the temperature. This study suggests that a wide range of wavelength can be reached by adjusting d 1. In addition, E g (Γ, T) decreases from 288.7 to 230 meV in the range of 4.2–300 K, corresponding to the cutoff wavelength ranging from 4.3 to 5.4 µm. These latter results explain the recent experimental ones realized by C. Cervera et al. for our Λ = 588 meV.

Electronic band structure and Shubnikov–de Haas effect in two-dimensional semimetallic InAs/GaSb nanostructure superlattice

We have investigated the band structure E(d = d1 + d2), E(kz) and E(kp), respectively, as a function of the SL period, d, in the growth direction and in plan of InAs(d1 = 160 A)/GaSb(d2 = 105 A) type II superlattice, performed in the envelope function formalism with the valence band offset, Λ, of 510 meV at 4.2 K. For the ratio d1/d2 = 1.52, d and Λ dependence of the SL energy band gap show that the semiconductor-to-semimetal transition takes place at dc = 173 A and Λc = 463 meV. Therefore, this sample is semimetallic. The position of the Fermi level, EF = 500.2 meV, indicates n type conductivity. The spectra of energy, E(kz, kp), show a negative band gap of −48.3 meV. The cutoff wavelength |λc| = 25.7 µm indicates that this sample can be used as a far-infrared detector. Further, we have interpreted the minima of the magnetoresistance oscillations, Shubnikov–de Haas effect, observed by D. M. Symons et al.