Quantum confinement of carriers in the type-I quantum wells structure

Quantum confinement is recognized to be an inherent property in low-dimensional structures.Traditionally,it is believed that the carriers trapped within the well cannot escape due to the discrete energy levels.However,our previous research has revealed efficient carrier escape in low-dimensional structures,contradicting this conventional understanding.In this study,we review the energy band structure of quantum wells along the growth direction considering it as a superposition of the bulk material dispersion and quantization energy dispersion resulting from the quantum confinement across the whole Brillouin zone.By accounting for all wave vectors,we obtain a certain distribution of carrier energy at each quantized energy level,giving rise to the energy subbands.These results enable carriers to escape from the well under the influence of an electric field.Additionally,we have compiled a comprehensive summary of various energy band scenarios in quantum well structures relevant to carrier transport.Such a new interpretation holds significant value in deepening our comprehension of low-dimensional energy bands,discovering new physical phenomena,and designing novel devices with superior performance.

Reanalysis of energy band structure in the type-II quantum wells

Band structure analysis holds significant importance for understanding the optoelectronic characteristics of semiconductor structures and exploring their potential applications in practice. For quantum well structures, the energy of carriers in the well splits into discrete energy levels due to the confinement of barriers in the growth direction. However, the discrete energy levels obtained at a fixed wave vector cannot accurately reflect the actual energy band structure. In this work, the band structure of the type-II quantum wells is reanalyzed. When the wave vectors of the entire Brillouin region(corresponding to the growth direction) are taken into account, the quantized energy levels of the carriers in the well are replaced by subbands with certain energy distributions. This new understanding of the energy bands of low-dimensional structures not only helps us to have a deeper cognition of the structure, but also may overturn many viewpoints in traditional band theories and serve as supplementary to the band theory of low-dimensional systems.

Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism

Herein,a physical and mathematical model of the voltage−current characteristics of a p−n heterostructure with quantum wells(QWs)is prepared using the Sah−Noyce−Shockley(SNS)recombination mechanism to show the SNS recombination rate of the correction function of the distribution of QWs in the space charge region of diode configuration.A comparison of the model voltage−current characteristics(VCCs)with the experimental ones reveals their adequacy.The technological parameters of the structure of the VCC model are determined experimentally using a nondestructive capacitive approach for determining the impurity distribution profile in the active region of the diode structure with a profile depth resolution of up to 10Å.The correction function in the expression of the recombination rate shows the possibility of determining the derivative of the VCCs of structures with QWs with a nonideality factor of up to 4.

Plasmons in a free-standing nanorod with a two-dimensional parabolic quantum well caused by surface states

The collective charge density excitations in a free-standing nanorod with a two-dimensional parabolic quantum well are investigated within the framework of Bohm-Pine＇s random-phase approximation in the two-subband model.The new simplified analytical expressions of the Coulomb interaction matrix elements and dielectric functions are derived and numerically discussed.In addition,the electron density and temperature dependences of dispersion features are also investigated.We find that in the two-dimensional parabolic quantum well,the intrasubband upper branch is coupled with the intersubband mode,which is quite different from other quasi-one-dimensional systems like a cylindrical quantum wire with an infinite rectangular potential.In addition,we also find that higher temperature results in the intersubband mode（with an energy of 12 meV（～ 3 THz）） becoming totally damped,which agrees well with the experimental results of Raman scattering in the literature.These interesting properties may provide useful references to the design of free-standing nanorod based devices.

Erratum:“Study of quantum well mixing induced by impurity-free vacancy in the primary epitaxial wafers of a 915 nm semiconductor laser”[J.Semicond.,2023,44(10),102302]

The thickness and composition of the external laminae contain errors,leading to inaccuracies in the theoretical calculations and simulations associated with Fig.3,Fig.4,and Fig.5.However,as these theoretical calculations merely illustrate a trend and do not contradict the experimental results,a request for modification has been submitted.

Bose–Einstein distribution temperature features of quasiparticles around magnetopolaron in Gaussian quantum wells of alkali halogen ions

We have applied strong coupling unitary transformation method combined with Bose–Einstein statistical law to investigate magnetopolaron energy level temperature effects in halogen ion crystal quantum wells.The obtained results showed that under magnetic field effect,magnetopolaron quasiparticle was formed through the interaction of electrons and surrounding phonons.At the same time,magnetopolaron was influenced by phonon temperature statistical law and important energy level shifts down and binding energy increases.This revealed that lattice temperature and magnetic field could easily affect magnetopolaron and the above results could play key roles in exploring thermoelectric conversion and conductivity of crystal materials.

Binding Energies of Screened Excitons in a Strained(111)-Oriented Zinc-Blende GaN/AlGaN Quantum Well Under Hydrostatic Pressure

We investigate the binding energies of excitons in a strained （111）-oriented zinc-blende GaN/Al0.3 Ga0.7 N quantum well screened by the electron-hole （e-h） gas under hydrostatic pressure by combining a variational method and a selfconsistent procedure. A built-in electric field produced by the strain-induced piezoelectric polarization is considered in our calculations. The result indicates that the binding energies of excitons increase nearly linearly with pressure,even though the modification of strain with hydrostatic pressure is considered, and the influence of pressure is more apparent under higher e-h densities. It is also found that as the density of an e-h gas increases,the binding energies first increase slowly to a maximum and then decrease rapidly when the e-h density is larger than about 1 ×10^11 cm^-2. The excitonic binding energies increase obviously as the barrier thickness decreases due to the decrease of the built-in electric field.

Material Growth and Device Fabrication of GaAs Based 1.3μm GaInNAs Quantum Well Laser Diodes

Material growth and device fabrication of the first 1.3μm quantum well （QW） edge emitting laser diodes in China are reported. Through the optimization of the molecular beam epitaxy （MBE） growth conditions and the tuning of the indium and nitrogen composition of the GalnNAs QWs, the emission wavelengths of the QWs can be tuned to 1.3μm. Ridge geometry waveguide laser diodes are fabricated. The lasing wavelength is 1.3μm under continuous current injection at room temperature with threshold current of 1kA/cm^2 for the laser diode structures with the cleaved facet mirrors. The output light power over 30mW is obtained.

GSMBE-Grown InGaAs/InGaAsP Strained Quantum Well Lasers at 1.84 Micron Wavelength

GSMBE grown 1 84 micron wavelength InGaAs/InGaAsP/InP strained quantum well lasers are reported. Lasers with 800 micron long cavity and 40 micron wide planar electrical stripe have been operated under the pulsed regime at room temperature. At 20℃, the threshold current density is 3 8kA/cm 2 and the external different quantum efficiency is 9 3%.

Electronic States of a Shallow Hydrogenic Donor Impurity in Different Shaped Semiconductor Quantum Wells

The shallow hydrogenic donor impurity states in square, V-shaped, and parabolic quantum wells are studied in the framework of effective-mass envelope-function theory using the plane wave basis. The first four impurity energy levels and binding energy of the ground state are more easily calculated than with the variation method. The calculation results indicate that impurity energy levels decrease with the increase of the well width and decrease quickly when the well width is small. The binding energy of the ground state increases until it reaches a maximum value, and then decreases as the well width increases. The results are meaningful and can be widely applied in the design of various optoelectronie devices.

Finite size effects on helical edge states in HgTe quantum wells with the spin orbit coupling due to bulk- and structure-inversion asymmetries

There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.

Solitons in nonlinear systems and eigen-states in quantum wells

We study the relations between solitons of nonlinear Schro¨dinger equation and eigen-states of linear Schro¨dinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for the coupled system with attractive interactions correspond to the identical eigen-states with the ones of the coupled systems with repulsive interactions. Although their energy eigenvalues seem to be different, they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases.Meanwhile, we demonstrate that soliton solutions in nonlinear systems can also be used to solve the eigen-problems of quantum wells. As an example, we present the eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having parity–time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as a water wave tank, nonlinear fiber, Bose–Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another way to understand the stability of solitons in nonlinear Schro¨dinger equation described systems, in contrast to the balance between dispersion and nonlinearity.

Polar Quasi-Confined Optical Phonon Modes in Wurtzite Quasi-One-Dimensional GaN/Al_xGa_(1-x)N Quantum Well Wires

Based on the dielectric continuum model and Loudon＇s uniaxial crystal model,quasi-confined （QC） optical phonon modes and electron-QC phonon coupling functions in quasi-one-dimensional （QID） wurtzite quantum well wires （QWWs） are deduced and analyzed. Numerical calculations on an AIN/GaN/AIN wurtzite QWW are performed. The results reveal that the dispersions of the QC modes are quite obvious only when the free wavenumber kz in the z-direction and the azimuthal quantum number m are small. The reduced behavior of the QC modes in wurtzite quantum systems is clearly observed. Through the discussion of the electron-QC mode coupling functions,it is found that the lower-frequency QC modes in the high-frequency region play a more important role in the electron-QC phonon interactions. Moreover,our computations also prove that kz and m have a similar influence on the electron-QC phonon coupling properties.

A Fractional-Dimension Variational Approach for the Bound Polaron in Parabolic Quantum Wells

The binding energy of a bound polaron in a finite parabolic quantum well is studied theoretically by a fractional- dimensional variational method. The numerical results for the binding energies of the bound polaron and longitudinal-optical phonon contributions in GaAs/Al0.3 Ga0.7 AS parabolic quantum well structures are obtained as functions of the well width. It is shown that the binding energies of the bound polaron are obviously reduced by the electron-phonon interaction and the phonon contribution is observable and cannot be neglected.

Oscillatory electron phonon coupling in Pb/Si（111）deduced by temperature-dependent quantum well states

Photoemission study of atomically flat Pb films with a thickness from 15 to 24 monolayers （ML） have been performed within a temperature range 75-270K. Well-defined quantum well states （QWSs） are observed, which exhibit interesting temperature-dependent behaviours. The peak position of the QWSs shifts towards higher binding energy with increasing substrate temperature, whereas the peak width broadens linearly due to enhanced electron-phonon coupling strength （λ）. An oscillatory A with a period of 2ML is deduced. Preliminary analysis shows that the oscillation can be explained in terms of the interface induced phase variations, and is thus a manifestation of the quantum size effects.

Light propagation characteristics in quantum well structures of photonic crystals

Two-dimensional （2D） closed-cavity single quantum well （SQW） and multiple quantum well （MQW） structures are proposed based on the traditional 2D open-cavity SQW structures of photonic crystals. The numerical calculation results show that the proposed structures can greatly improve the optical characteristics compared with the traditional structures. It is found that the barrier thickness has a great impact on the optical characteristics of the closed-cavity MQW structures： when the barrier thickness is narrower, each resonant peak which appears in the SQW would split, the number of split times is just equal to the number of wells, and each well in the MQW structures is a travelling-wave-well, similar to the well in the open-cavity SQW structures; when the barrier thickness is wider, there is no effect of spectral splitting, and each well in the MQW structures is a standing-wave-well, just like the well in the closed-cavity SQW. The physical origin of different field distributions and the effect of the spectral splitting are provided.

Finite size effects on the quantum spin Hall state in HgTe quantum wells under two different types of boundary conditions

The finite size effect in a two-dimensional topological insulator can induce an energy gap Eg in the spectrum of helical edge states for a strip of finite width. In a recent work, it has been found that when the spin--orbit coupling due to bulk-inversion asymmetry is taken into account, the energy gap Eg of the edge states features an oscillating exponential decay as a function of the strip width of the inverted HgTe quantum well. In this paper, we investigate the effects of the interface between a topological insulator and a normal insulator on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. Two different types of boundary conditions, i.e., the symmetric and asymmetric geometries, are considered. It is found that due to the existence of the interface between topological insulator and normal insulator this oscillatory pattern on the exponential decay induced by bulk-inversion asymmetry is modulated by the width of normal insulator regions. With the variation of the width of normal insulator regions, the shift of the Dirac point of the edge states in the spectrum and the energy gap Eg closing point in the oscillatory pattern can occur. Additionally, the effect of the spin-orbit coupling due to structure-inversion asymmetry on the finite size effects is also investigated.

A dual-blue light-emitting diode based on strain-compensated InGaN-AlGaN/GaN quantum wells

A strain-compensated InGaN quantum well（QW） active region employing a tensile AlGaN barrier is analyzed.Its spectral stability and efficiency droop for a dual-blue light-emitting diode（LED） are improved compared with those of the conventional InGaN/GaN QW dual-blue LEDs based on a stacking structure of two In0.18Ga0.82N/GaN QWs and two In0.12Ga0.88N/GaN QWs on the same sapphire substrate.It is found that the optimal performance is achieved when the Al composition of the strain-compensated AlGaN layer is 0.12 in blue QW and 0.21 in blue-violet QW.The improvement performance can be attributed to the strain-compensated InGaN-AlGaN/GaN QW,which can provide a better carrier confinement and effectively reduce leakage current.

Spectra of Hydrogenic Donor States in Quantum-Dot Quantum Well Structures

The series expansion approach has been employed to calculate the exact energy spectra of hydrogenic donor states in a quantum-dot quantum well(QDQW). The result shows that the hydrogenic donor energy levels are very different from those in a quantum dot. In a QDQW, the donor energy levels depend on not only the radius of core and the barrier, but also the numbers of small wells. When there exist two small wells outside the core, the “band gap”exists between donor levels, and its width depends on the depth of the small wells.

Magnetic-Field Effects on Donor Impurity States in a Quantum Well

Green’s function technique is used to obtain the solution of Shredinger equation for impurity states in a quantum well (QW) under the magnetic field. Binding energy of impurity states is defined as poles of the wave function. We studied effects of the magnetic field magnitude and impurity position on the binding energy. The calculations were performed for both ground and excited states. The dependences of binding energies versus impurity position and magnetic field are presented for GaAs/Al0.3Ga0.7As QW.