Envelope Function Theory Research Articles

Envelope-function theory of inhomogeneous strain in semiconductor nanostructures

Envelope-function theory of inhomogeneous strain in semiconductor nanostructures

Theory of silicon spin qubit relaxation in a synthetic spin-orbit field

We develop the theory of single-electron silicon spin qubit relaxation in the presence of a magnetic field gradient. Such field gradients are routinely generated by on-chip micromagnets to allow for electrically controlled quantum gates on spin qubits. We build on a valley-dependent envelope function theory that enables the analysis of the electron wave function in a silicon quantum dot with an arbitrary roughness at the interface. We assume the presence of single-layer atomic steps at a Si/SiGe interface and study how the presence of a gradient field modifies the spin-mixing mechanisms. We show that our theoretical modeling can quantitatively reproduce results of experimental measurements of qubit relaxation in silicon in the presence of a micromagnet. We further study in detail how a field gradient can modify the EDSR Rabi frequency of a silicon spin qubit. While this strongly depends on the details of the interface roughness, interestingly, we find that adding a micromagnet on top of a spin qubit with an ideal interface can even reduce the EDSR frequency within some interval of the external magnetic field strength.

Atypical dependence of excited exciton energy levels and electron-hole correlation on emission energy in pyramidal InP-based quantum dots

We calculate the spectrum of excited exciton states in application-relevant self-assembled pyramidal quantum dots grown in InAs/InP and InAs/AlGaInAs material systems. These types of dots have been recently shown to combine the emission in the third optical fiber window with low surface density and a reasonable level of in-plane symmetry of emitters, which predestines them for studies on single- and entangled-photon emission and for corresponding applications. The spectrum of optically active excited states is crucial for successful resonant and quasi-resonant excitation of emitters, allowing for conservation of angular momentum and addressing individual selected quantum states. Here, we show that in both types of studied dots, due to their specific morphology of truncated pyramid, the density of excited-state ladder, especially the s–p shell splitting may follow an unconventional dependence on emission energy, opposite to the one typically met in regular quantum dots. We obtain this result via modeling based on available morphological data and calculation within the multi-band {{varvec{k}} {cdot } {varvec{p}}} envelope-function theory combined with the configuration-interaction method used to calculate exciton states. Then, we explain this observation in purely geometric terms, as a result of an increasing effective quantum confinement width in a pyramid that is progressively cut from the top. Additionally, we show that the inverted trend is also manifested in the amount of electron-hole correlation in the exciton ground state, which also shows an anomalous dependence on emission energy and quantum dot volume.

Effects of laser field and electric field on exciton states in InAs/InxAl1-xAs quantum wells

Based on the effective mass approximation and envelope function theory, the exciton binding energy in a single InAs / InxAl1 − xAs quantum well is calculated by the variational method under the applied electric field and laser field. The effects of material composition, well width, laser parameters, and electric field intensity on the exciton binding energy are calculated. The results show that the confinement potential is distorted by the laser field and the barrier is tilted by the electric field. The exciton binding energy is reduced by the presence of laser field or electric field. It is also shown that the exciton binding energy increases with the decrease of the indium component within a certain range. In addition, the effect of the well width on the exciton binding energy is not linear, and the exciton binding energy increases to a maximum first and then decreases with the decrease of the well width. The binding energy of excitons depends on the interaction of several parameters.

Relaxation of single-electron spin qubits in silicon in the presence of interface steps

We develop a valley-dependent envelope function theory that can describe the effects of arbitrary configurations of interface steps and miscuts on the qubit relaxation time. For a given interface roughness, we show how our theory can be used to find the valley-dependent dipole matrix elements, the valley splitting, and the spin-valley coupling as a function of the electromagnetic fields in a Si/SiGe quantum dot spin qubit. We demonstrate that our theory can quantitatively reproduce and explain the result of experimental measurements for the spin relaxation time with only a minimal set of free parameters. Investigating the sample dependence of spin relaxation, we find that at certain conditions for a disordered quantum dot, the spin-valley coupling vanishes. This, in turn, completely blocks the valley-induced qubit decay. We show that the presence of interface steps can in general give rise to a strongly anisotropic behavior of the spin relaxation time. Remarkably, by properly tuning the gate-induced out-of-plane electric field, it is possible to turn the spin-valley hot spot into a ``cold spot'' at which the relaxation time is significantly prolonged and where the spin relaxation time is additionally first-order insensitive to the fluctuations of the magnetic field. This electrical tunability enables on-demand fast qubit reset and initialization that is critical for many quantum algorithms and error correction schemes. We therefore argue that the valley degree of freedom can be used as an advantage for Si spin qubits.

Effect of thickness on the electronic structure and optical properties of quasi two-dimensional perovskite CsPbBr3 nanoplatelets

The effect of thickness of cesium lead halide perovskite CsPbBr3 nanoplatelets (NPLs) on their electronic structure and optical properties are investigated using an effective-mass envelope function theory based on the 8-band k·p model with the consideration of exciton binding energy. We first reported the CsPbBr3 nanoplatelets’ band structure and optical gain with exciton effect. As the thickness of NPLs decreases, their bandgap increases and the band mixing is more obvious which influences the transition matrix element (TME). The optical gain of CsPbBr3 nanoplatelets is calculated by taking into account of TME, Fermi factor, injected carrier density and thickness. A blue shift of peak position in optical gain can be observed as the thickness of NPLs decreases. As the injected carrier density arises, the maximum optical gain of thicker NPLs reach saturation much faster than the thinner ones. To obtain high differential gain, NPLs with less thickness are better choices. Experimental work is carried out and the results agree with our theoretical results very well.

Collinear orbital antiferromagnetic order and magnetoelectricity in quasi-two-dimensional itinerant-electron paramagnets, ferromagnets, and antiferromagnets

We develop a comprehensive theory for magnetoelectricity in magnetically ordered quasi-2D systems whereby in thermal equilibrium an electric field can induce a magnetization $m$ and a magnetic field can induce a polarization. This effect requires that both space-inversion and time-reversal symmetry are broken. Antiferromagnetic (AFM) order plays a central role in this theory. We define a N\'eel operator $\tau$ such that a nonzero expectation value $\langle \tau \rangle$ signals AFM order, in the same way $m$ signals ferromagnetic (FM) order. While $m$ is even under space inversion and odd under time reversal, $\tau$ describes a toroidal moment that is odd under both symmetries. Thus $m$ and $\langle \tau \rangle$ quantify complementary aspects of magnetic order in solids. In quasi-2D systems FM order can be attributed to dipolar equilibrium currents that give rise to $m$. In the same way, AFM order arises from quadrupolar currents that generate the moment $\langle \tau \rangle$. The electric-field-induced magnetization can then be attributed to the electric manipulation of the quadrupolar currents. We develop a $k \cdot p$ envelope-function theory for AFM diamond structures that allows us to derive explicit expressions for the operator $\tau$. Considering FM zincblende and AFM diamond, we derive quantitative expressions for the magnetoelectric responses due to electric and magnetic fields that reveal explicitly the inherent duality of these responses required by thermodynamics. Magnetoelectricity is found to be small in realistic calculations for quasi-2D electron systems. The magnetoelectric response of quasi-2D hole systems turns out to be sizable, however, with moderate electric fields being able to induce a magnetic moment of one Bohr magneton per charge carrier. Our theory provides a broad framework for the manipulation of magnetic order by means of external fields.

A WKB approach to the quantum multiband electron dynamics in the kinetic formalism

We derive a WKB-like asymptotic expansion of the multiband Wigner function. The model, derived in the envelope function theory, is designed to describe the dynamics in semiconductor devices when the interband conduction-valence transition cannot be neglected. We derive a hierarchy of equations that to lowest order consist of two HamiltonJacobi equations corresponding to the classical dynamics of point particles with positive and negative kinetic energy. Our methodology is based on the Van Vleck approach and a WKB-like asymptotic expansion procedure is used to reduce the numerical complexity of the Wigner multiband evolution system. An approximate closed-form solution is obtained by an iterative procedure that exploits the different time scales on which the intraband and interband dynamical variables evolve. The interband tunneling mechanism appearing to the first order of the expansion is expressed in a very simple mathematical form. By exploiting the highly oscillating behaviour of the multiband Wigner functions we derive a asymptotic expression of the interband transition probability. The resulting formulation reveals particularly close to the classical description of the particles motion and this formal analogy is useful to gain new physical insight and to profit of the numerical method developed for classical systems. The approximates evolution equations are used to simulate the evolution of the Wigner quasi-distribution function in a IRTD diode.

Effect of Size on the Electronic Structure and Optical Properties of Cubic CsPbBr3 Quantum Dots

The size effect on the electronic structure and optical properties of cubic CsPbBr3 perovskite quantum dots is investigated by using an 8-band ${k}\cdot{p} $ model based on effective-mass envelope function theory with exciton binding energy consideration. Quantum dots with smaller size have larger bandgaps due to quantum confinement. The transition matrix element (TME) is also influenced by the size. The optical gain of such material is calculated by considering TME, Fermi factor, injected carrier density, quantum dot size, and dephasing rate. Higher density of injected carrier is needed for smaller quantum dot to get a positive optical gain. The peak of optical gain has a blue shift as the size of quantum dot decreases. When the carrier density increases for a quantum dot with certain size, a blue shift in emission peak position can be observed due to band filling effect. Smaller quantum dots have higher differential optical gain at carrier densities within certain range.

Finite Element Method Linear Triangular Element for Solving Nanoscale InAs⁄GaAs Quantum Ring Structures

This paper concerned with the solution of the nanoscale structures consisting of the with an effective mass envelope function theory, the electronic states of the quantum ring are studied. In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of quantum rings are studied by the one electronic band Hamiltonian effective mass approximation, the energy- and position-dependent on electron effective mass approximation, and the spin-dependent on the Ben Daniel-Duke boundary conditions. In the description of the Hamiltonian matrix elements, the Finite elements method with different base linear triangular element is adopted. The non-linear energy confinement problem is solved approximately by using the Finite elements method with linear triangular element, to calculate the energy of the electron states for the quantum ring.

Finite Element Method withPiecewise Linear Function for Solving NanoscaleInAs⁄GaAsQuantum RingStructures

In this paper concerned with the solution of the nanoscale structures consisting of the with an effective mass envelope function theory, the electronic states of the quantum ring are studied.In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of quantum rings are studied by the one electronic band Hamiltonian effective mass approximation, the energy-and position-dependent on electron effective mass approximation, and the spin-dependent on the Ben Daniel-Duke boundary conditions. In the description of the Hamiltonian matrix elements, the Finite elements method with different base piecewise linear function is adopted. The non-linear energy confinement problem is solved approximately by using the Finite elements method with piecewise linear function, to calculate the energy of the one electron states for the quantum ring. The results of numerical example are compared for accuracy and efficiency with the finite element method of linear triangular element. This comparison shows that good results of numerical example.

G‐Factor Anisotropy Inversion in InGaAs 2D Nanostructures

The inversion or sign change of the electron g‐factor anisotropy in thin‐layer semiconductor nanostructures is investigated theoretically and gauged for InGaAs asymmetric single and double quantum wells (QWs). The g‐factor anisotropy in these 2D nanostructures is given by the difference between the longitudinal and transverse components; it is a fine sensor of the confining potential and in InGaAs structures it is determined by the Rashba spin–orbit coupling. In the presence of structure inversion asymmetry (SIA) the g‐factor anisotropy is expected to invert at a critical well width. This effect can be useful technologically and is here analyzed in detail with InGaAs/InP asymmetric multi‐layer structures. The g‐factor anisotropy in these structures is calculated in a fine grid around the inversion point, using 8‐band kp Kane model based envelope function theory for the nanostructure, and perturbation theory for the calculation of the effective g factor. It is shown that the anisotropy inversion can be seen only in asymmetric structures with very thin layers, near the limit of no bound states allowed, and corresponding to the electron being pushed out of the confining region. The inversion point, or critical well width for the g‐factor anisotropy inversion in Insulator/InGaAs/InP QWs is determined to be ≈4 nm. For double or coupled QWs it is found that the inversion can be observed only with very thin tunneling barriers around 1 nm wide.

Third nonlinear optical susceptibility of CdS/ZnS core-shell spherical quantum dots for optoelectronic devices

In this paper, we have investigated the optical properties of CdSe/ZnS core shell quantum dot. The carriers wave functions and eigenenergies have been obtained by solving the three dimensional Schrödinger equation under the frame work of the effective-mass envelope-function theory. Then we have calculated the nonlinear susceptibilities associated with intersubbandtransitions in the conduction band for CdS/ZnS spherical quantum dots. In addition, we have also investigated theoretically the third order susceptibilities for quadratic electro-optic effects as a function of the core, shell radii, pump photo-energy and time relaxation. Numerical calculations revealed that susceptibilities have one peak (resonance) and depend on the parameters already mentioned. Indeed, by increasing the width of shell, the peaks of susceptibilities will be red shifted and the intensities will in fact increase as functions of pump photon energy. The obtained results can give a new degree of freedom in optoelectronic device applications.

Finite Element Method With Linear Rectangular Element for Solving Nanoscale InAs⁄GaAs Quantum Ring Structures

This paper is concerned with the solution of the nanoscale structures consisting of the with an effective mass envelope function theory, the electronic states of the quantum ring are studied. In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of quantum rings are studied by the one electronic band Hamiltonian effective mass approximation, the energy- and position-dependent on electron effective mass approximation, and the spin-dependent on the Ben Daniel-Duke boundary conditions. In the description of the Hamiltonian matrix elements, the Finite elements method with different base piecewise linear function is adopted. The non-linear energy confinement problem is solved approximately by using the Finite elements method with piecewise linear function, to calculate the energy of the one electron states for the quantum ring. The results of numerical example are compared for accuracy and efficiency with the finite element method of linear triangular element. This comparison shows that good results of numerical example.

External electric field effect on the binding energy of a hydrogenic donor impurity in InGaAsP/InP concentric double quantum rings

Within the framework of effective-mass envelope-function theory, the ground state binding energy of a hydrogenic donor impurity is calculated in the InGaAsP/InP concentric double quantum rings (CDQRs) using the plane wave method. The effects of geometry, impurity position, external electric field and alloy composition on binding energy are considered. It is shown that the peak value of the binding energy appears in two rings with large gap as the donor impurity moves along the radial direction. The binding energy reaches the peak value at the center of ring height when the donor impurity moves along the axial direction. The binding energy shows nonlinear variation with the increase of ring height. With the external electric field applied along the z-axis, the binding energy of the donor impurity located at z[Formula: see text] decreases while that located at z[Formula: see text] increases. In addition, the binding energy decreases with increasing Ga composition, but increases with the increasing As composition.

Comparison of external electric and magnetic fields effect on binding energy of hydrogenic donor impurity in different shaped quantum wells

The effects of external electric and magnetic fields on the ground state binding energy of hydrogenic donor impurity are compared in square, V-shaped, and parabolic quantum wells. With the effective-mass envelope-function approximation theory, the ground state binding energies of hydrogenic donor impurity in InGaAsP/InP QWs are calculated through the plane wave basis method. The results indicate that as the quantum well width increases, the binding energy changes most fast in SQW. When the well width is fixed, the binding energy is the largest in VQW for the donor impurity located near the center of QWs. For the smaller and larger well width, the electric field effect on binding energy is the most significant in VQW and SQW, respectively. The magnetic field effect on binding energy is the most significant in VQW. The combined effects of electric and magnetic fields on the binding energy of hydrogenic donor impurity are qualitative consistent in different shaped QWs.

Optoelectronics of inverted type-I CdS/CdSe core/crown quantum ring

Inverted type-I heterostructure core/crown quantum rings (QRs) are quantum-efficient luminophores, whose spectral characteristics are highly tunable. Here, we study the optoelectronic properties of type-I core/crown CdS/CdSe QRs in the zincblende phase—over contrasting lateral size and crown width. For this, we inspect their strain profiles, transition energies, transition matrix elements, spatial charge densities, electronic bandstructures, band-mixing probabilities, optical gain spectra, maximum optical gains, and differential optical gains. Our framework uses an effective-mass envelope function theory based on the 8-band k ⋅ p method employing the valence force field model for calculating the atomic strain distributions. The gain calculations are based on the density-matrix equation and take into consideration the excitonic effects with intraband scattering. Variations in the QR lateral size and relative widths of core and crown (ergo the composition) affect their energy levels, band-mixing probabilities, optical transition matrix elements, emission wavelengths/intensities, etc. The optical gain of QRs is also strongly dimension and composition dependent with further dependency on the injection carrier density causing the band-filling effect. They also affect the maximum and differential gain at varying dimensions and compositions.

Optical properties of CdSe/ZnTe type II core shell nanostructures

CdSe/ZnTe core shell nanoparticles present original optical and electronic properties because of the spatial separation of electrons and holes caused by the type-II alignment of energy states. Such structure permits access to optical transition energies that are not limited to band gap energies and hence can provide narrow emission spectra and a broad absorption range.In this study, we have investigated the nanostructure size effect on the electronic and optical properties of type II CdSe/ZnTe core shell quantum dot. The carriers wave functions and eigenenergies have been achieved by solving the Schrödinger equation, in the framework of the effective-mass envelope-function theory. The impact of core radius R1 and the shell radius R2 on electron and hole energies has been studied for the fundamental and the first excited states. The Coulomb interaction has been calculated and the exciton energy has been deduced. Then, the absorption coefficient has been examined by means of the compact density matrix, the pick of the absorption increases with R2 and is red shifted. Good excitonic radiative life time in this type II core shell quantum dot has been obtained. The photoluminescence from the CdSe/ZnTe core shell can be adjusted to covers practically all the visible wavelength, which is very important for biomedical and photovoltaics.

Temperature-dependent optoelectronic properties of quasi-2D colloidal cadmium selenide nanoplatelets.

Colloidal cadmium selenide (CdSe) nanoplatelets (NPLs) are a recently developed class of efficient luminescent nanomaterials suitable for optoelectronic device applications. A change in temperature greatly affects their electronic bandstructure and luminescence properties. It is important to understand how and why the characteristics of NPLs are influenced, particularly at elevated temperatures, where both reversible and irreversible quenching processes come into the picture. Here we present a study of the effect of elevated temperatures on the characteristics of colloidal CdSe NPLs. We used an effective-mass envelope function theory based 8-band k·p model and density-matrix theory considering exciton-phonon interaction. We observed the photoluminescence (PL) spectra at various temperatures for their photon emission energy, PL linewidth and intensity by considering the exciton-phonon interaction with both acoustic and optical phonons using Bose-Einstein statistical factors. With a rise in temperature we observed a fall in the transition energy (emission redshift), matrix element, Fermi factor and quasi Fermi separation, with a reduction in intraband state gaps and increased interband coupling. Also, there was a fall in the PL intensity, along with spectral broadening due to an intraband scattering effect. The predicted transition energy values and simulated PL spectra at varying temperatures exhibit appreciable consistency with the experimental results. Our findings have important implications for the application of NPLs in optoelectronic devices, such as NPL lasers and LEDs, operating much above room temperature.

Electron g factor anisotropy in asymmetric III–V semiconductor quantum wells

The electron effective g factor tensor in asymmetric III–V semiconductor quantum wells (AQWs) and its tuning with the structure parameters and composition are investigated with envelope-function theory and the Kane model. The spin-dependent terms in the electron effective Hamiltonian in the presence of an external magnetic field are treated as a perturbation and the g factors and , for the magnetic field in the QW plane and along the growth direction, are obtained analytically as a function of the well width L. The effects of the structure inversion asymmetry (SIA) on the electron g factor are analyzed. For the g-factor main anisotropy in AQWs, a sign change is predicted in the narrow well limit due to SIA, which can explain recent measurements and be useful in spintronic applications. Specific results for narrow-gap and AQWs are presented and discussed with the available experimental data; in particular InAs QWs are shown to not only present much larger g factors but also a larger g-factor anisotropy, and with the opposite sign with respect to GaAs QWs.