Transition Energies In Quantum Wells Research Articles

Verification of band offsets and electron effective masses in GaAsN/GaAs quantum wells: Spectroscopic experiment versus 10-band k·p modeling

Optical transitions in GaAs1−xNx/GaAs quantum wells (QWs) have been probed by two complementary techniques, modulation spectroscopy in a form of photoreflectance and surface photovoltage spectroscopy. Transition energies in QWs of various widths and N contents have been compared with the results of band structure calculations based on the 10-band k·p Hamiltonian. Due to the observation of higher order transitions in the measured spectra, the band gap discontinuities at the GaAsN/GaAs interface and the electron effective masses could be determined, both treated as semi-free parameters to get the best matching between the theoretical and experimental energies. We have obtained the chemical conduction band offset values of 86% for x = 1.2% and 83% for x = 2.2%, respectively. For these determined band offsets, the electron effective masses equal to about 0.09 mo in QWs with 1.2% N and 0.15 mo for the case of larger N content of 2.2%.

Electronic and optical properties of quantum wells embedded in wrinkled nanomembranes

The authors theoretically investigate quantum confinement and transition energies in quantum wells (QWs) asymmetrically positioned in wrinkled nanomembranes. Calculations reveal that the wrinkle profile induces both blue- and redshifts, depending on the lateral position of the QW probed. Relevant radiative transitions include the ground state of the electron (hole) and excited states of the hole (electron). Energy shifts as well as stretchability of the structure are studied as a function of wrinkle amplitude and period. Large tunable bandwidths of up to 70 nm are predicted for highly asymmetric, wrinkled QWs.

Fourier transform infrared surface photovoltage spectroscopy for the investigation of mid‐infrared semiconductor lasers

AbstractA novel application of the surface photovoltage spectroscopy (SPS) technique, using a Fourier transform infrared (FTIR) interferometer, has been developed for the investigation of narrow‐gap mid‐infrared semiconductor quantum well (QW) laser structures. We demonstrate the FTIR‐SPS technique at room temperature for a GaInSb/AlGaInSb type I QW laser structure, grown on GaAs, emitting in the mid‐infrared at ∼4 μm, revealing an unambiguous detection of the ground and excited state transitions of the GaInSb QW, as well as the AlGaInSb barrier bandgap energy. As a further corroboration of the new technique, the FTIR‐SPS spectrum of a ∼1.5 μm communication laser structure has also been measured and shown to be in good agreement with conventional grating‐based electro‐modulated reflectance and SPS spectroscopic measurements on this sample. A detailed numerical analysis of the room temperature FTIR‐SPS results for the mid‐infrared semiconductor laser structure is also presented, including a comparison with theoretical predictions of the QW transition energies. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Room temperature contactless electroreflectance of the ground and excited state transitions in Ga0.76In0.24As0.08Sb0.92∕GaSb single quantum wells of various widths

The optical transitions in Ga0.76In0.24As0.08Sb0.92∕GaSb quantum wells with the width varying from 10to21nm were studied by room temperature contactless electroreflectance (CER). In addition to the quantum well (QW) ground state transition (11H), the 22H and 33H transitions (where klH denotes transition between the kth heavy hole and the lth electron subbands) have been clearly observed in CER spectra. The experimental QW transition energies were compared with theoretical predictions based on an effective mass formalism model. It has been concluded that this QW is type I for both electron and holes and the conduction band offset for the unstrained Ga0.76In0.24As0.08Sb0.92∕GaSb interface equals ∼90%.

Optical Properties of a Wrinkled Nanomembrane with Embedded Quantum Well

A wrinkled nanomembrane with embedded quantum well (QW), fabricated by the partial release and bond back of epitaxial layers upon underetching, is investigated by spatially resolved micro-photoluminescence spectroscopy. From the observed QW transition energies and calculations based on the linear deformation potential theory, we find that the bonded back regions are fully relaxed and act on the strain state of the wrinkled QW. Light emission enhancement observed in the wrinkled QW is explained by interference contrast theory.

Ground and excited state transitions in as-grown Ga0.64In0.36N0.046As0.954 quantum wells studied by contactless electroreflectance

The optical transitions of as-grown Ga0.64In0.36N0.046As0.954 multiple quantum wells grown at the low temperature of 375°C were studied by contactless electroreflectance (CER). The investigation was carried out at room temperature for a set of samples having quantum well (QW) widths ranging from 3.9to8.1nm. The ground and the excited state transitions were clearly observed in CER spectra (the ground state transition was observed at the wavelength of 1.9μm for the 8.1nm wide QW). The experimental QW transition energies were compared with theoretical predictions based on an effective mass formalism model. Good agreement between experimental data and theoretical calculations has been obtained assuming that the conduction band offset for GaInNAs∕GaAs interface is 80% and the electron effective mass is 0.09m0.

Characterisation of a 760 nm vertical‐cavity surface‐emitting laser structure by reflectance and photomodulated reflectance

AbstractPhotomodulated reflectance (PR) studies are conducted on the wafer of a vertical‐cavity surface‐emitting laser (VCSEL) designed for oxygen sensing up to high temperatures. By varying the angle of incidence, the VCSEL cavity mode (CM) is tuned through the positions of two static PR features, revealing the ground‐state electron to heavy‐hole and light‐hole quantum well (QW) transition energies. The PR is also measured over a large temperature range, revealing that the CM becomes tuned to the heavy‐hole QW transition at a temperature of 115 ± 1 °C, where the energies coincide at ∼1.631 eV (760 nm). It is observed that when tuned, the width of the CM feature in the reflectance spectrum is maximised. Reflectance simulations confirm that this broadening occurs when the CM is tuned with an excitonic transition, where the cavity absorption is maximised. Therefore, monitoring this broadening as the energies of the CM and QW are varied relative to each other could provide an additional, non‐destructive technique for determining the VCSEL ground‐state QW transition energy and the conditions under which it is tuned to the CM. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Boundary conditions for the electron wavefunction in GaInNAs-based quantum wells and modelling of the temperature-dependent effective bandgap

The boundary conditions were investigated for the electron wavefunction in Ga1−xInxNyAs1−y-based heterostructures described by the band anticrossing model. Among other advantages, the utilisation of these boundary conditions simplifies the calculation of, for example, transition energies in quantum wells. The derived equations were applied to model the temperature-dependence of the effective bandgap in Ga1−xInxNyAs1−y/GaAs quantum well structures with high indium concentration. From a fit to the experimental photoreflectance data, evidence was found to show that the nitrogen level EN in the band anticrossing Hamiltonian, measured with respect to the valence band edge, shifts to higher energies with decreasing temperature. This extends similar results reported in the literature for low indium content epilayers.

Boundary conditions for the electron wavefunction in GaInNAs-based quantum wells andmodelling of the temperature-dependent bandgap

In this paper we derive and discuss the boundary conditions for the electron wavefunction in generalGa1−xInxNyAs1−y-based heterostructures described by the band anticrossing model. The use of these boundaryconditions greatly simplifies the calculation of, for example, transition energies in quantumwells. We then apply the derived equations to model the temperature-dependent bandgap ofGa1−xInxNyAs1−y/GaAs quantum well structures with high indium concentrations. From a fit to ourexperimental photoreflectance data we find evidence that the effective nitrogen levelEN in the band anticrossing Hamiltonian, measured with respect to the valence bandedge, shifts to higher energies with decreasing temperature. This supports andextends similar results reported in the literature for low indium content epilayers.

Spectroscopic characterization of 1450 nm semiconductor pump laser structures for Raman amplifiers

In order to characterize various different epilayer designs for semiconductor Raman amplifier pump lasers, combined electromodulated reflectance (ER) and photoluminescence (PL) studies were performed on wafer samples of InP / InGaAsP / InGaAsP edge-emitter laser structures in the infrared spectral region. Information about the quantum well (QW) transitions is obtained primarily from the ER, with additional corroboration provided by the PL. The ER spectra are fitted with a line shape model to obtain the ground-state and higher-order QW transition energies, which are found to agree well with theoretically calculated values. The ER spectra also provide the waveguide core and barrier compositions and built-in electric fields in the laser structures. The information provided by ER studies on the prefabrication wafers is found to corroborate well with diagnostic spontaneous emission measurements performed on actual laser devices fabricated from the same wafer batches.

Piezoelectric Field Influence on GaN/Al x Ga 1—x N Quantum Well Optical Properties

The absorption and luminescence properties of hetero-polarization GaN/AlxGa1—xN (x = 0.12 and 0.165) quantum well (QW) structures are studied by photoreflectivity, photoluminescence excitation spectroscopy (PLE), and photoluminescence at low temperature. The QW transition energy as a function of well thickness exhibits a quantum-confined Stark effect (QCSE) due to the presence of a strong built-in electric field (piezoelectricity and spontaneous polarization). An electric field strength of 120 kV/cm in the barrier and between 600 and 800 kV/cm in the well are obtained from the analysis of Franz-Keldysh oscillations in photoreflectivity spectra. These values are in good agreement with results from the fit of the QW transition energy versus the thickness, using the electric field as a parameter.

Built-in electric-field effects in wurtzite AlGaN/GaN quantum wells

AlGaN/GaN quantum well (QW) structures are grown on c-plane sapphire substrates by molecular beam epitaxy. Control at the monolayer scale of the well thickness is achieved and sharp QW interfaces are demonstrated by the low photoluminescence linewidth. The QW transition energy as a function of the well width evidences a quantum-confined Stark effect due to the presence of a strong built-in electric field. Its origin is discussed in terms of piezoelectricity and spontaneous polarization. Its magnitude versus the Al mole fraction is determined. The role of the sample structure geometry on the electric field is exemplified by changing the thickness of the AlGaN barriers in multiple-QW structures. Straightforward electrostatic arguments well account for the overall trends of the electric-field variations.

Self-limitation of AlGaN/GaN quantum well energy by built-in polarization field

Wurtzite AlGaN/GaN quantum well (QW) structures were grown by molecular beam epitaxy on c-plane sapphire substrates and the QW transition energies were measured by low temperature photoluminescence. Both the well widths and the Al mole fraction in the AlxGa1−xN(0<x<0.3) 100-Å-thick barriers have been varied in order to assess the built-in electric field present in the quantum heterostructures. It is found that the electric field increases linearly with the Al composition. The magnitude of this electric field is as high as 1 MV/cm for an Al mole fraction of 0.27. The main consequence is that whatever the investigated Al composition range, the well thickness must be lower than 30 Å in order to get a transition energy greater than the band gap of GaN.

Photomodulated reflectance ofInxGa1−xAs/GaAs/AlAsmicrocavity vertical-cavity surface emitting laser structures: Monitoring higher-order quantum well transitions

In the previous paper, a line shape model was developed to describe photomodulated reflectance (PR) spectra of vertical-cavity surface emitting laser (VCSEL) structures in the vicinity of the resonance between the cavity mode and ground-state quantum well (QW) exciton, in the weak cavity exciton coupling regime. Here, this model is extended to cavity mode resonances with higher-order QW transitions, both allowed and forbidden. In addition, the model's validity is further confirmed by demonstrating a way of obtaining ``pseudo-PR'' spectra of the QW ground-state and higher-order transitions. These spectra are derived by monitoring changes in PR line shape, as the cavity mode energy is tuned through the QW transitions. These spectra are virtually free of VCSEL cavity effects, and represent plots of the energy dependence of the imaginary part of the modulated QW dielectric function, $\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{2}.$ The $\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{2}$ spectra can be fitted using conventional excitonic PR line shapes to extract the energies and linewidths of the ground-state and higher-order QW transitions. Examples are given for two InGaAs/GaAs/AlAs VCSEL structures. The results of this technique are confirmed by comparing with those obtained in two other experimental approaches: (i) measuring sets of complete PR spectra, at different positions on the sample, of the resonances between the cavity mode and various QW excitons, and fitting these with the new line shape model; (ii) measuring the PR spectrum of the exposed QW after removal of the top Bragg stack by etching, and fitting in the conventional way. All the results are found to be in good agreement both with each other and with the ground-state and higher-order QW transition energies calculated using a three-band $\mathit{k}\ensuremath{\cdot}\mathit{p}$ model.

Optical and Structural Properties of AlGaN/GaN Quantum Wells Grown by Molecular Beam Epitaxy

AlGaN/GaN quantum well (QWs) were grown on (0001) sapphire substrates by molecular beam epitaxy (MBE) using ammonia as nitrogen precursor. The Al composition in the barriers was varied between 8 and 27 % and the well thickness from 4 to 17 monolayers (MLs, 1ML = 2.59Å). X-ray diffraction (XRD) experiments are used to investigate the strain state of both the well and the barriers. The QW transition energy are measured by low temperature photoluminescence (PL). A large quantum confined Stark effect is observed leading to QW luminescence much lower than the emission line of the GaN buffer layer for well width above a certain critical thickness. The built-in electric field responsible for such a phenomenon is deduced from fit of the PL data. Its magnitude is of several hundred kV/cm and increases linearly with the Al composition.

Analysis of strained InGaAs/InGaAsP single quantum wells using room temperature photoreflectance

Room temperature photoreflectance (PR) has been performed on five nominally 90 Å wide undoped single quantum well (QW) structures in barriers, lattice matched to an InP substrate. The nominal QW Ga composition varies between x = 0.47 and x = 0.68, corresponding to tensile strains between zero and 1.47%, respectively. Room temperature photoluminescence measurements are also performed on the same position on the sample as the PR. Allowed and forbidden interband QW transition energies, given by least-squares fitting to the PR, are found to agree well with theoretical predictions based on an effective mass formalism, including excitonic binding energies and quantum-confined Stark effects. In achieving this agreement, values for the QW composition, thickness and band offset are determined by refining their nominal values. The conduction band offsets are found to range from 0.35 to 0.14 for tensile strains between zero and 1.40%. The energies of the ground state light- and heavy-hole QW transitions increase roughly linearly with tensile strain.

Optical and Structural Properties of AlGaN/GaN Quantum Wells Grown by Molecular Beam Epitaxy

AbstractAIGaN/GaN quantum well (QWs) were grown on (0001) sapphire substrates by molecular beam epitaxy (MBE) using ammonia as nitrogen precursor. The Al composition in the barriers was varied between 8 and 27 % and the well thickness from 4 to 17 monolayers (MLs, 1ML = 2.59Å). X-ray diffraction (XRD) experiments are used to investigate the strain state of both the well and the barriers. The QW transition energy are measured by low temperature photoluminescence (PL). A large quantum confined Stark effect is observed leading to QW luminescence much lower than the emission line of the GaN buffer layer for well width above a certain critical thickness. The built-in electric field responsible for such a phenomenon is deduced from fit of the PL data. Its magnitude is of several hundred kV/cm and increases linearly with the Al composition.

Excited states of hydrogenic impurities in quantum wells in magnetic fields

Quasi-two-dimensional hydrogenic impurity levels in quantum wells under the influence of magnetic fields are investigated. Experimentally, 1s to np (n=2, 3, 4) transition energies in quantum wells of various widths are measured by the photoconductivity technique for magnetic fields up to 9 T. Theoretically, these energies are calculated by a new variational method that is valid for the whole range of magnetic field strengths, from the zero-field limit to the high-field limit. Good agreement is achieved for every transition for well widths up to approximately 300 AA, for which the confinement effect is appreciable. Consistent discrepancies found for 450 AA are expected to be accounted for by including subband mixing because of the wide width and small subband separation. Our study demonstrates that the simple variational method can produce good results for highly excited levels in magnetic fields provided that the confinement due to the quantum well is sufficiently strong.

Interface-phonon-mediated magnetopolaronic effect on impurity transition energies in quantum wells.

Electron interactions with interface phonon modes and strictly confined bulk phonon modes are considered to calculate the resonant magnetopolaronic 1s-2${\mathit{p}}_{+}$ transition energy of a hydrogenic impurity in the quantum well of a double heterostructure. An interaction gap is predicted between the bulk LO and TO frequencies, in constrast to the Fr\"ohlich-type interaction. These results are in good agreement with recent experimental data.