Valence Subbands Research Articles

Valence subband structure of 〈011〉-oriented quantum wells

We present semianalytical calculations of the valence subband structure for 〈011〉-oriented quantum wells of cubic semiconductors. Working in the Kohn–Luttinger formalism [Phys. Rev. 97, 869 (1955)], we present analytic expressions for the effective mass tensor and show the full subband dispersion for GaAs and InAs. In addition to the usual extremum at k∥=0, 〈011〉-oriented wells support saddle point spectra. In this case, the effective mass changes sign as a function of in-plane crystallographic direction.

Study on symmetry forbidden transitions in an InxGa1−xAs/GaAs single quantum well by temperature dependence

The photoreflectance (PR) spectroscopy of the single quantum well InxGa1−xAs/GaAs system has been measured at various temperatures. The selection rules for the interband transitions are Δn=0, where n is the quantum number of the nth subband in the quantum well. The symmetry forbidden transitions (Δn≠0), such as 12H (where mnH denotes transition between the mth conduction to nth valence subband of heavy hole), were often observed in the experiments and it was attributed to the existence of the built-in electric field in the quantum well. In this work, we change the strength of the built-in electric field by varying the temperatures of the samples. By varying the temperatures of the samples, the strength of the field can be changed by the effect of photo-induced voltages. The measured ratios of the intensities of 12H to 11H transitions decrease as the temperatures are lowered. Therefore, the existence of the built-in electric field may account for the observations of the symmetry forbidden transition 12H in the experiments.

Duality of Stark-ladder optical transitions in a double-period [formula omitted] superlattice under high electric fields

Stark effects have been investigated on the photocurrent spectra of a double-period GaAs AlAs superlattice with a specially designed barrier configuration, thin and thick, for a fixed well width. Under applied high electric fields, a duality of the Stark ladder optical transitions is observed and rigorously explained in terms of the inequivalence between the neighboring wells of the barrier confinement effect. The field-induced evolution of eigenenergies and wavefunctions calculated by the transfer matrix method confirms the duality of conduction and valence subband states, which give different energies due to the asymmetry for -1st and 0th order Stark ladder transitions in good agreement with the experimental results.

Theory of carrier gain dynamics in InGaAs/AlGaAs strained-layer single-quantum-well diode lasers

Calculations of the femtosecond gain dynamics in InGaAs/AlGaAs strained-layer single-quantum-well diode lasers are presented and compared to experiments which use a novel multiple-wavelength pump probe technique. We develop a detailed theoretical model for the gain dynamics in a quantum well laser diode structure to aid in the interpretation of gain dynamics induced by both interband absorption and stimulated emission of photons. In the model, transient gain and differential transmission are computed in a multiband effective mass model including biaxial strain, valence subband mixing, and scattering both within and between subbands. The transient photogeneration of electron-hole pairs by the pump pulse and subsequent relaxation of carriers by both polar optical phonon scattering and carrier-carrier scattering are calculated within a Boltzmann equation framework. A relaxation approximation for the carrier-carrier scattering is made making the coupled Boltzmann equations an effective one dimensional model which are then solved using an adaptive Runge-Kutta technique rather than a more computationally intensive Monte Carlo approach.

Valence band offsets in strained GaAs1−xPx/GaAs heterojunctions

Valence band offsets at [100]-oriented heterojunctions between tensile-strained GaASj1−xPx and unstrained GaAs are studied experimentally and theoretically. Light-hole (LH) and heavy-hole (HH) offsets are first extracted from the well-width dependence of valence subband splittings observed in luminescence spectra of tensile-strained GaAs1−xPx/GaAs quantum wells of various compositions (x = 0.06,0.09, and 0.19). This data is then combined with results from two other laboratories, yielding a set of 30 independent experimental offset values for junctions with compositions throughout the range 0.06≤x ≤0.32. The data are found to be highly consistent, with linear fits δELH = −140x (meV) and δEHH= −401x (meV) describing the measured offsets to within less than 5 meV on average. Experimental results are then compared with theoretical predictions for the GaAs1−x Px/GaAs system obtained from a tight-binding model for strained heterojunctions. Predictions from the tight-binding calculations are found to lie within experimental scatter for the LH offsets, which define the valence band edge in these heterostructures, while magnitudes of the tight-binding HH offsets exceed measured values by ~20% on average.

Absorption Spectra of Type I and Type II Strained-Layer Superlattices

Absorption spectra which originate from direct valence-band-to-conduction-band transitions in strained-layer superlattices (SLSs) are studied theoretically. The electronic structures are calculated by using the Luttinger-Kohn Hamiltonian in the Kronig-Penney model. The absorption coefficients are evaluated by taking the mixing of heavy- and light-hole states into account. As a result of calculation, firstly, origins of fine structures in the absorption spectra observed at a room temperature for type I ZnSe(22 A)–ZnS(23 A) SLS are clarified satisfactorily. Secondly, novel properties of type II ZnTe–ZnSe are predicted, i.e. it is revealed that the absorption intensity is one order of magnitude less in type II SLS than in type I SLS, and that in type II SLS the strength for any transitions to the higher conduction and from the higher valence subbands is greatly enhanced, in sharp contrast to the type I SLS.

Optical nonlinearities in multiple quantum wells: Generalized Elliott formula.

Excitonic nonlinearities due to plasma effects in quantum-well structures under quasistationary excitation can be reproduced by appropriate many-body treatments, which usually require numerical calculations that may become computationally intensive. An alternative approach is based on analytical approximations; however, this has not been examined carefully so far. In this paper we present the analytical calculation of the optical properties of quasi-two-dimensional, type-I semiconductor quantum wells, at varying plasma densities and accounting for one conduction band and two valence subbands. This has been developed based on the two-dimensional version of the Elliott formula and on some analytical approximations already known in part. The obtained analytical results are scalable to a considerable range of constituent materials and of quantum-well thicknesses. These results are compared with the numerical solutions achieved within a more complete many-body approach, based on the Bethe-Salpeter equation, and with experimental results obtained in a pump-probe experiment. The comparison provides general guidelines on the accuracy and on the limitations of the analytical approach applicable to the case of quasi-two-dimensional excitons when multisubband and finite-size effects are included.

Donor states in Te-Doped GaAs l−xP x

We have investigated the level configuration of the valence subbands in GaAs/GaAs1−xPx (x = 0.23) strained-barrier quantum well structures as a function of the well width. Circularly polarized photoluminescence excitation (CPPLE) spectroscopy was used to identify the heavy- or light-hole character of the optical transitions. Distinct polarization properties were observed in the strain-split heavy- and light-hole bands in the GaAsP barriers, which indicates the photoexcited electrons in the barriers retain spin orientation well even after the capture into the well and the relaxation process. Utilizing this polarization tendency of the transitions in the barriers, we could distinguish unequivocally the heavy- and light-hole character of the quantum well-related transitions. By varying the well width systematically, we observed the level crossing between n = 1 heavy- and light-hole transitions around the well width of 4 nm. This is in good agreement with the calculation based on the effective mass approximation.

Spectroscopic study of beryllium related acceptors in silicon

We have investigated the level configuration of the valence subbands in GaAs/GaAs1−xPx (x = 0.23) strained-barrier quantum well structures as a function of the well width. Circularly polarized photoluminescence excitation (CPPLE) spectroscopy was used to identify the heavy- or light-hole character of the optical transitions. Distinct polarization properties were observed in the strain-split heavy- and light-hole bands in the GaAsP barriers, which indicates the photoexcited electrons in the barriers retain spin orientation well even after the capture into the well and the relaxation process. Utilizing this polarization tendency of the transitions in the barriers, we could distinguish unequivocally the heavy- and light-hole character of the quantum well-related transitions. By varying the well width systematically, we observed the level crossing between n = 1 heavy- and light-hole transitions around the well width of 4 nm. This is in good agreement with the calculation based on the effective mass approximation.

Absorption Spectra and Electronic Structures in ZnSe–ZnS and ZnTe–ZnSe Strained-Layer Superlattices

Absorption spectra which originate from vertical valence-band-to-conduction-band transitions in type I ZnSe-ZnS and type II ZnTe-ZnSe strained-layer superlattices (SLSs) are studied theoretically. It has been found that the absorption in the type II SLS is one order of magnitude less than that in the type I SLS, and that in the type II SLS the strength for any transitions to the higher conduction and from the higher valence subbands is greater than that to the lower conduction and from the lower valence subbands, in sharp contrast to the type I SLS.

Finite-element analysis of valence band structure and optical properties of quantum-wire arrays on vicinal substrates

The valence subband dispersion of quantum-wire arrays grown on vicinal substrates in GaAs-Al/sub x/Ga/sub 1-x/As material system is calculated using a finite-element method with periodic boundary conditions. The variational functional for the Luttinger-Kohn Hamiltonian is derived using the integration by parts with proper boundary conditions. The validity of this method is confirmed by calculating subband structure of quantum wells and rectangular quantum wires. Along with the electronic band structure, a detailed study of gain in the quantum-wire arrays with rectangular and serpentine shapes is presented, including the effect of coupling between wires and polarization dependence of the momentum matrix element. Finally, these results are compared to those of quantum wells. >

Intersubband absorption of TE and TM waves in p-type semiconductor superlattice including the effects of continuum states

We present theoretical results for the absorption coefficients for both TE and TM waves due to intersubband transitions within the valence subbands of a p-type superlattice. Both the bound and continuum states are included in our calculation. The continuum states are discretized by applying a periodic boundary condition. Numerical results are illustrated for different well and barrier widths. The results show that the intersubband transitions among the bound states result in sharp resonance absorption while the intersubband transitions between bound states and continuum states give a broad maximum at a photon energy larger than the barrier height. The TE and TM absorption coefficients are comparable in magnitude. Our theoretical results are in agreement with recent experimental observations on bound states to continuum states transitions. >

Absorption and population inversion in p-type InGaAs strained layers based on intervalence subband transition at FIR frequencies

A tensile strained p-InGaAs/InP heterostructure was employed to investigate the feasibility of THz-lasers experimentally. The internal strain induced by the lattice-mismatched epitaxy splits the degenerate valence bands and provides two separate subbands for laser action in the FIR. Strong absorption associated with the direct free hole transition between the LH- and HH-valence bands has been observed and the characteristics of the absorption spectra is discussed. It is shown that when the applied electric field is above 6 × 10 4 V/cm light holes are in streaming motion and the redistribution of holes could result in population inversion in the split valence subbands.

Band structure and optical properties of alkali metal halides

Optical spectra, photoemission spectra, and photoconductivity spectra of alkali metal halides are analyzed using energy band structure calculations and selection rules for direct and indirect transitions. The main feature of the band structure of MeN3 (Me: Na, K, Rb, Cs) as proposed by the authors is the presence of two conductivity bands, one anionic and the other cationic in nature. A weak dispersion of the valence subband indicates that phonons may yield a significant contribution to the observed spectra. All of the optical and photoemission spectra so far reported for the metal azides may be explained on the basis of the proposed band model.

Characterization of GaP / InGaP and GaP / GaAsP strained-layer quantum wells grown by metalorganic chemical vapor deposition

GaP/InGaP and GaP/GaAsP strained-layer quantum well (QW) structures with 3.0–5.0 nm thick well layers in the direct gap region were grown on GaP substrates by metalorganic chemical vapor deposition (MOCVD) using triethylgallium (TEGa) and ethyldimethylindium (EDMIn) for the column III sources and 100% AsH 3 and PH 3 for the column V sources. The strained QW structures were characterized using TEM and 4.2 K photoluminescence (PL). Transmission electron microscope (TEM) images indicate that the structures are uniform with sharp, defect-free interfaces. The QW layers are clearly resolved and appear to be free of misfit dislocations or other defects. The InGaP QW structures exhibit improved 4.2 K PL linewidths and a shift of the peak energies to shorter wavelengths compared to InGaP bulk layers of the same compositions. The GaAsP QW structures also exhibit sharp PL emission linewidths. The band alignments for the GaP/InGaP and GaP/GaAsP strained heterojunctions were calculated using local-density-functional pseudopotential formalism and the model-solid approach. Optical transition energies between the conduction band and valence subbands at the Γ point were calculated for the InGaP and GaAsP strained QWs, taking into account both the strain-modified band structures and quantum confinement effects. By employing the results derived from the theoretical predictions, we show that the 4.2 K PL spectra of the InGaP strained wells exhibit both the n = 1 heavy-hole and light-hole related transitions. We also show that the degree of removal of valence band degeneracy can be determined from the PL spectra.

Analyses of localized confinement potential in semiconductor strained wires and dots buried in lattice-mismatched materials

Analytical and finite-element-method calculations have been conducted for obtaining strain distributions and consequent carrier confinement potential changes in semiconductor strained wires and dots made of lattice-mismatched materials. The inhomogeneous strain distribution modifies the confinement potentials locally, which causes carrier wave function localization. First, to obtain a fundamental strain distribution and band-structure change semiquantitatively, analytical calculations are performed in simple, symmetrical structures such as an InP cylinder and an InP ball buried in GaAs or InGaP matrices assuming isotropic valence bands and isotropic elastic characteristics. Here, strain is found to exist in the surrounding matrices as well as in the wires and dots. This effect is peculiar to the strained wire and dot because in pseudomorphic strained layers there is no strain in surrounding matrices. Thus, the band structures are found to be greatly modified in the surrounding matrix as well as in the wire or dot. Hole effective masses at the band edge are also calculated by diagonalizing a 4×4 orbital strain Hamiltonian. Furthermore, to calculate the effects in a realistic structure, finite-element-method calculations are performed for a triangle-shaped InP wire along the 〈110〉 direction, including anisotropic elastic characteristics. Calculated nonuniform strain within the wire is found to modify the confinement potential, which localizes electrons near the base. Valence subbands are largely split near the vertices. From these results, the strained wires and dots are found to be applicable for quantum wires and dots, in which the quantum confinement effect will be enhanced by the modified confinement potential due to the inhomogeneous strain.

Dependence of optical gain on crystal orientation in surface-emitting lasers with strained quantum wells

We analyze theoretically optical gains in vertical-cavity surface-emitting lasers (VCSELs) for various crystal orientations. The calculation based on the multiband effective-mass theory takes into account the effects of anisotropy and nonparabolicity on the valence subband dispersion. It is found that in VCSELs employing InGaAs/InP strained quantum wells (QWs) with non-(001) orientations except (111), the polarization in the QW plane can be controlled and high gains are obtained. In particular, the gains in VCSELs with (NN1)-oriented (N≥2) strained QWs are markedly higher than those in the equivalent (001) lasers.

Carrier-gain dynamics in InxGa1-xAs/AlyGa1-yAs strained-layer single-quantum-well diode lasers: Comparison of theory and experiment.

We present measurements and calculations of femtosecond gain dynamics in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As strained-layer single-quantum-well diode lasers using a multiple-wavelength pump-probe technique. To aid in the interpretation of gain dynamics induced by both interband absorption and stimulated emission of photons, we develop a detailed theoretical model for gain dynamics in quantum-well laser diode structures and compare it with experimental measurements. In the model, transient gain and differential transmission are computed in a multiband effective-mass model including biaxial strain, valence subband mixing, and polar-optical-phonon scattering both within and between subbands. Transient photogeneration of electron-hole pairs by the pump pulse and subsequent relaxation of carriers by polar-optical-phonon scattering are calculated in a Boltzmann-equation framework.

Tensile-strained multiple quantum-well structures for a large refractive index change caused by current injection

Tensile-strained multiple quantum-well (MQW) structures with camel-back shaped first valence sub-bands are proposed as structures with a large refractive index change caused by current injection. These structures have a high joint density of states at the absorption edge, and the injected carriers in the structures have a long lifetime because of separation in the k-space between electrons and holes. The refractive index change caused by current injection is calculated for camel-back InGaAs/InGaAsP strained MQW structures for 1.55 μm-wavelength light. These structures show a larger refractive index change than the other InGaAs/InGaAsP strained/unstrained MQW structures.

Strain effects on the energy bands of ZnSe films grown on GaAs substrates by spectroscopic ellipsometry

Room-temperature spectroscopic ellipsometry measurements were carried out on ZnSe thin films grown on (001)GaAs substrates by molecular-beam epitaxy for the study of the lattice mismatch-induced strain at the interface. The magnitude of the absorption coefficient at the E0+Δ0 critical point is very sensitive to the strain in the film. The variation in the magnitude of the absorption coefficient is used to estimate the critical thickness for the onset of dislocation generation. Almost complete relaxation of the films was obtained for thicknesses higher than 500 nm. Also, the strain-induced coupling between the valence subbands was found to cause additional shifting of the light-hole subband.