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Resonant photoluminescence studies of carrier localisation in c-plane InGaN/GaN quantum well structures.
... Furthermore, carrier localization is essential to explain the optical properties of this mate- rial system in detail. For example, the photoluminescence (PL) spectra of these (In,Ga)N/GaN QWs exhibit large line widths [3,17], an "S-shaped" temperature dependence of the PL peak energy [1,6], a mobility edge [18], and a time- decay behavior where the explanation depends crucially on localization effects [2,9]. The cause, nature, and consequence of this localization have generated significant debate over the years. ...
In this work, we present a detailed analysis of the interplay of Coulomb effects and different mechanisms that can lead to carrier-localization effects in c-plane (In,Ga)N/GaN quantum wells. As mechanisms for carrier localization, we consider here effects introduced by random alloy fluctuations as well as structural inhomogeneities such as well-width fluctuations. Special attention is paid to the impact of the well width on the results. All calculations have been carried out in the framework of atomistic tight-binding theory. Our theoretical investigations show that independent of the well widths studied here, carrier-localization effects due to built-in fields, well-width fluctuations, and random-alloy fluctuations dominate over Coulomb effects in terms of charge-density redistributions. However, the situation is less clear cut when the well-width fluctuations are absent. For a large well width (approximately >2.5nm), charge-density redistributions are possible, but the electronic and optical properties are basically dominated by the out-of-plane carrier separation originating from the electrostatic built-in field. The situation changes for lower well widths (<2.5nm), where the Coulomb effect can lead to significant charge-density redistributions and, thus, might compensate for a large fraction of the spatial in-plane wave-function separation observed in a single-particle picture. Given that this in-plane separation has been regarded as one of the main drivers behind the green gap problem, our calculations indicate that radiative recombination rates might significantly benefit from a reduced quantum-well-barrier-interface roughness.
Atom probe tomography (APT) has been used to characterize the distribution of In atoms within non-polar a-plane InGaN
quantum wells
(QWs)
grown on a GaN pseudo-substrate produced using epitaxial lateral overgrowth. Application of the focused ion beam microscope enabled APT needles to be prepared from the low defect density regions of the grown sample. A complementary analysis was also undertaken on QWs having comparable In contents grown on polar c-plane sample pseudo-substrates. Both frequency distribution and modified nearest neighbor analyses indicate a statistically non-randomized In distribution in the a-plane QWs, but a random distribution in the c-plane QWs. This work not only provides insights into the structure of non-polar a-plane QWs but also shows that APT is capable of detecting as-grown nanoscale clustering in InGaN and thus validates the reliability of earlier APT analyses of the In distribution in c-plane InGaN
QWs which show no such clustering.
We present an atomistic description of the electronic and optical properties
of N/GaN quantum wells. Our analysis accounts
for fluctuations of well width, local alloy composition, strain and built-in
field fluctuations as well as Coulomb effects. We find a strong hole and much
weaker electron wave function localization in InGaN random alloy quantum wells.
The presented calculations show that while the electron states are mainly
localized by well-width fluctuations, the holes states are already localized by
random alloy fluctuations. These localization effects affect significantly the
quantum well optical properties,leading to strong inhomogeneous broadening of
the lowest interband transition energy. Our results are compared with
experimental literature data.
Photoluminescence and electroluminescence measurements on InGaN/GaN quantum well (QW) structures and light emitting diodes suggest that QWs with gross fluctuations in width (formed when, during growth, the InGaN is exposed unprotected to high temperatures) give higher room temperature quantum efficiencies than continuous QWs. The efficiency does not depend on the growth temperature of the GaN barriers. Temperature-dependent electroluminescence measurements suggest that the higher efficiency results from higher activation energies for defect-related non-radiative recombination in QW samples with gaps. At high currents the maximum quantum efficiency is similar for all samples, indicating the droop term is not dependent on QW morphology.
Localization lengths of the electrons and holes in InGaN/GaN quantum wells have been calculated using numerical solutions of the effective mass Schrödinger equation. We have treated the distribution of indium atoms as random and found that the resultant fluctuations in alloy concentration can localize the carriers. By using a locally varying indium concentration function we have calculated the contribution to the potential energy of the carriers from band gap fluctuations, the deformation potential, and the spontaneous and piezoelectric fields. We have considered the effect of well width fluctuations and found that these contribute to electron localization, but not to hole localization. We also simulate low temperature photoluminescence spectra and find good agreement with experiment.
InGaN quantum wells have been found to be extremely sensitive to exposure to the electron beam in the transmission electron microscope (TEM). High-resolution TEM images acquired immediately after first irradiating a region of quantum well indicates no gross fluctuations of indium content in the InGaN alloy. During only a brief period of irradiation, inhomogeneous strain is introduced in the material due to electron beam damage. This strain is very similar to that expected from genuine nanometer-scale indium composition fluctuations which suggests there is the possibility of falsely detecting indium-rich “clusters” in a homogeneous quantum well.
The emission spectra of CdS1–xSex solid solutions (x ≦ 0.3) at helium temperatures are studied under monochromatic excitation in different regions of the absorption spectrum. In all samples very intense luminescence due to excitons localized by composition fluctuations is observed. High intensity of luminescence and complete absence of free exciton emission indicate a high probability of exciton localization. A model for exciton localization is proposed. It is assumed that only the hole component of the exciton is localized by the potential fluctuations. The electron is bound to this hole by Coulomb attraction. The energy migration between the localized states is discussed. Three different regions can be distinguished in the excitation spectrum of localized excitons. The first region corresponds to the excitation of free excitons which are trapped to localization sites in the process of energy migration. There is no energy migration in the third spectral region and all the emission is caused by directly photo-excited states. In the intermediate region II a limited energy transfer between the localized states takes place via phonon assisted tunneling.
Electro- and photoluminescence spectra of high-brightness light-emitting AlGaN/InGaN/GaN single-quantum-well structures are studied over a broad range of temperatures and pumping levels. Blue shift of the spectral peak position was observed along with an increase of temperature and current. An involvement of band-tail states in the radiative recombination was considered, and a quantitative description of the blue temperature-induced shift was proposed assuming a Gaussian shape of the band tail. © 1997 American Institute of Physics.
We propose a model for the radiative recombination of electron-hole pairs in (Ga,In)N/GaN quantum objects, including huge internal electric fields and strong carrier localization. This model explains why the time decay of the photoluminescence keeps a constant nonexponential shape, while its time scale can be varied over several orders of magnitude. Instead of localized excitons, we consider an electron and a hole independently localized at sharp potential fluctuations, along two parallel sheets, forming a two-dimensional pseudo-donor-acceptor pair.
Exciton localization in InxGa1-xN was studied. At 2 K, the time-integrated photoluminescence (PL) spectrum showed a Stokes shift from the absorption shoulder and broadening at the lower photon energy side. Site-selectively excited PL measurements determined the mobility edge. The exciton relaxation processes were studied by use of time-resolved PL spectroscopy. The PL decay time increased with the decrease of the detection-photon energy, indicating the dynamical features of exciton localization. In addition, we observed localized exciton luminescence turned into stimulated emission just below the mobility edge.
Urbach tails in semiconductors are often associated to effects of compositional disorder. The Urbach tail observed in InGaN alloy quantum wells of solar cells and LEDs by biased photocurrent spectroscopy is shown to be characteristic of the ternary alloy disorder. The broadening of the absorption edge observed for quantum wells emitting from violet to green (indium content ranging from 0% to 28%) corresponds to a typical Urbach energy of 20 meV. A three-dimensional absorption model is developed based on a recent theory of disorder-induced localization which provides the effective potential seen by the localized carriers without having to resort to the solution of the Schrödinger equation in a disordered potential. This model incorporating compositional disorder accounts well for the experimental broadening of the Urbach tail of the absorption edge. For energies below the Urbach tail of the InGaN quantum wells, type-II well-to-barrier transitions are observed and modeled. This contribution to the below-band-gap absorption is particularly efficient in near-ultraviolet emitting quantum wells. When reverse biasing the device, the well-to-barrier below-band-gap absorption exhibits a red-shift, while the Urbach tail corresponding to the absorption within the quantum wells is blue-shifted, due to the partial compensation of the internal piezoelectric fields by the external bias. The good agreement between the measured Urbach tail and its modeling by the localization theory demonstrates the applicability of the latter to compositional disorder effects in nitride semiconductors.
We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum localization which introduces for each type of carrier a spatial function called localization landscape. These landscapes allow us to predict the localization regions of electron and hole quantum states, their corresponding energies, and the local densities of states. We show how the various outputs of these landscapes can be directly implemented into a drift-diffusion model of carrier transport and into the calculation of absorption/emission transitions. This creates a new computational model which accounts for disorder localization effects while also capturing two major effects of quantum mechanics, namely, the reduction of barrier height (tunneling effect) and the raising of energy ground states (quantum confinement effect), without having to solve the Schrödinger equation. Finally, this model is applied to several one-dimensional structures such as single quantum wells, ordered and disordered superlattices, or multiquantum wells, where comparisons with exact Schrödinger calculations demonstrate the excellent accuracy of the approximation provided by the landscape theory.
We present a detailed theoretical analysis of the electronic structure of c-plane InGaN/GaN quantum wells with indium contents varying between 10\% and 25\%. The electronic structure of the quantum wells is treated by means of an atomistic tight-binding model, accounting for variations in strain and built-in field due to random alloy fluctuations. Our analysis reveals strong localisation effects in the hole states. These effects are found not only in the ground states, but also the excited states. We conclude that localisation effects persist to of order 100~meV into the valence band, for as little as 10\% indium in the quantum well, giving rise to a significant density of localised states. We find, from an examination of the modulus overlap of the wave functions, that the hole states can be divided into three regimes of localisation. Our results also show that localisation effects due to random alloy fluctuations are far less pronounced for electron states. However, the combination of electrostatic built-in field, alloy fluctuations and structural inhomogeneities, such as well-width fluctuations, can nevertheless lead to significant localisation effects in the electron states, especially at higher indium contents. Overall, our results are indicative of individually localised electron and hole states, consistent with the experimentally proposed explanation of time-dependent photoluminescence results in c-plane InGaN/GaN QWs.
The nonlinear optical properties of band tail states in highly excited InGaN/GaN multiple quantum wells have been studied using energy selective optically pumped stimulated emission spectroscopy, nanosecond nondegenerate optical pump-probe spectroscopy, and variable-stripe gain spectroscopy. Energy selective optically pumped spontaneous and stimulated emission studies show "mobility edge" type behavior of the spontaneous and stimulated emission peak positions as the excitation photon energy is tuned across the states responsible for the broadened absorption edge of the InGaN active regions. The relative position of the mobility edge with respect to the absorption edge and the spontaneous and stimulated emission peak positions indicates the emission originates from carriers localized by extremely large potential fluctuations in the InGaN active layers of the MQWs. Nanosecond nondegenerate optical pump-probe spectroscopy of the band edge transitions show strong breaching of band tail states with increasing above-gap optical excitation. The magnitude of the bleaching was found to be significantly affected by the onset of stimulated emission, indicating the carriers responsible for the observed bleaching and stimulated emission share the same recombination channels. Optical gain studies show substantial blueshifts in the gain maximum with increasing above-gap optical excitation. The behavior is attributed to filling of localized states with increasing optical excitation. The spectral range covered by the blueshift further evidences the large magnitude of the potential fluctuations. The experimental results are compared with those obtained from an InGaN layer of comparable indium composition. This work illustrates the dominance of localized state recombination, both spontaneous and stimulated, in the emission spectra of state-of-the-art InGaN MQW structures.
The effects of the threading dislocation (TD) density on the optical properties of a series of comparable InxGa1–xN/ GaN multiple QW structures were studied. The TD density ranged from 2 × 107 cm–2, for a structure grown on a free-standing GaN substrate, to 5 × 109 cm–2 grown on a sapphire substrate. Room temperature internal quantum efficiencies (IQEs) were determined by temperature dependent photoluminescence (PL); no systematic dependence of the IQE on the TD density was found. The excitation power density dependence of the efficiency was investigated, which also showed no systematic dependence on TD density. PL excitation spectroscopy was used to verify that equivalent carrier densities were generated within the QWs of each structure. The lack of systematic dependence of the optical properties on TD density is attributed to the strong carrier localisation in InGaN/GaN QWs. At the highest density of TDs studied, it is estimated that the average defect separation greatly exceeds the in-plane diffusion lengths of electrons and holes; consequently the majority of carriers in the system are isolated from the TDs. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Spatially resolved cathodoluminescence (CL) spectrum mapping revealed a strong exciton localization in InGaN single-quantum-wells (SQWs). Transmission electron micrographs exhibited a well-organized SQW structure having abrupt InGaN/GaN heterointerfaces. However, comparison between atomic force microscopy images for GaN-capped and uncapped SQWs indicated areas of InN-rich material, which are about 20 nm in lateral size. The CL images taken at the higher and lower energy side of the spatially integrated CL peak consisted of emissions from complementary real spaces, and the area was smaller than 60 nm in lateral size.
Dynamical behavior of radiative recombination has been assessed in the In0.20Ga0.80N (2.5 nm)/ In0.05Ga0.95N (6.0 nm) multiple-quantum-well structure by means of transmittance, electroreflectance (ER), photoluminescence excitation (PLE), and time-resolved photoluminescence (TRPL) spectroscopy. The PL at 20 K was mainly composed of two emission bands whose peaks are located at 2.920 eV and 3.155 eV. Although the peak at 3.155 eV was weak under low photoexcitation, it grew superlinearly with increasing excitation intensity. The ER and PLE revealed that the transition at 3.155 eV is due to the excitons at quantized levels between n=1 conduction and n=1 A(Gamma9v) valence bands, while the main PL peak at 2.920 eV is attributed to the excitons localized at the trap centers within the well. The TRPL features were well understood as the effect of localization where photogenerated excitons are transferred from the n=1 band to the localized centers, and then are localized further to the tail state.
We have observed fluorescence line narrowing in the LO-phonon-assisted intrinsic exciton emission of CdSxSe1-x, selectively excited over a range of energies below a critical energy Eem, on the low-energy side of the exciton absorption line. The sharp emission lines disappear rather abruptly as the exciting energy increases through Eem or as the temperature is raised above 10 K. We argue that this sharp line emission arises from excitons localized, on the time scale of the radiative lifetime (about 1 nsec), by alloy fluctuations. Its abrupt disappearance may be evidence for an effective mobility edge. A sideband on each of the sharp LO-phonon-assisted emission lines is also observed. The shape of this sideband can be accounted for by a model of spectral diffusion by acousticphonon-assisted tunneling between localized states.
We have observed oscillations in the low temperature (T<50 K) photoluminescence excitation spectra of an InxGa1−xN∕GaN single quantum well at photon energies above the GaN band gap. We attribute the features in the spectra to excitation of electrons at multiples of the LO phonon energy above the GaN conduction band edge. The rapid cooling of these electrons to the GaN conduction band edge and their subsequent capture leads to a shift, and hence the oscillations, in the photoluminescence spectrum. We interpret the shift in the spectrum as being due to a modification of the occupation of the distribution of localization centers.
We use time-resolved spectroscopy of the LO-phonon sidebands to study the in-plane localization of carriers and excitons in undoped GaAs/AlxGa1-xAs multiple quantum wells at low temperatures. We find three distinct populations contributing to the radiative recombination (excluding shallow background impurities): (a) weakly localized excitons, their localization dimension being larger than the exciton Bohr radius, (b) tightly localized excitons, (c) separately localized electrons and holes that decay radiatively on a microsecond time scale.
In this paper we report detailed low temperature (6 K) photoluminescence excitation spectra of GaAs/AlGaAs multiple quantum well structures while monitoring the intensity of the recombination due to n = 1 electron/heavy hole 1S and 2S excitons. The excitation spectra over the region of interest of the 1S exciton recombination, apart from some previously observed exciton absorption peaks, are flat. Whereas, the excitation spectra of the 2S exciton recombination exhibit some previously unreported decreases in the luminescence intensity. We ascribe these dips to a reduction in the effective 2S exciton temperature and thus the 2S exciton luminescence intensity. The reduction in the 2S exciton temperature at the particular excitation photon energies of the dips is caused by the selective creation of excitons in the continuum and the subsequent emission of one or two LO phonons resulting in 1S excitons with K ∼ 0.
We have studied the low-temperature (T = 6 K) optical properties of a series of InGaN/GaN single-quantum-well structures with varying indium fractions. With increasing indium fraction the peak emission moves to lower energy and the strength of the exciton–longitudinal-optical (LO)-phonon coupling increases. The Huang–Rhys factor extracted from the Fabry–Pérot interference-free photoluminescence spectra has been compared with the results of a model calculation, yielding a value of approximately 2 nm for the in-plane localization length scale of carriers. We have found reasonable agreement between this length scale and the in-plane extent of well-width fluctuations observed in scanning transmission electron microscopy high-angle annular dark-field images. High-resolution transmission electron microscopy images taken with a short exposure time and a low electron flux have not revealed any evidence of gross indium fluctuations within our InGaN quantum wells. These images could not, however, rule out the possible existence of small-scale indium fluctuations, of the order of a few at. %.
This study addresses the ongoing debate concerning the distribution of indium in InxGa1−xN quantum wells (QWs) using a combination of atom probe tomography (APT) and transmission electron microscopy (TEM). APT analysis of InxGa1−xN QWs, which had been exposed to the electron beam in a TEM, revealed an inhomogeneous indium distribution which was not observed in a control sample which had not been exposed to the electron beam. These data validate the effectiveness of APT in detecting subtle compositional inhomogeneities in the nitrides.
The optical properties of InGaN/GaN quantum well structures, with indium fractions of 0.15 and 0.25, have been studied under resonant excitation conditions. The low-temperature (T = 6 K) photoluminescence spectra revealed a broad recombination peak that the authors have attributed to the acoustic-phonon assisted emission from a distribution of localized states, excited via an acoustic-phonon assisted absorption process. Comparing these results with theoretical calculations, where the authors consider the deformation potential coupling of the separately localized electron/hole pairs to an effectively continuous distribution of acoustic phonons, gives a value of approximately 2.5 Å for the in-plane localization length scale.
A mobility edge is defined as the energy separating localised and non-localised states in the conduction or valence bands of a non-crystalline material, or the impurity band of a doped semiconductor. This review is limited to three-dimensional systems, since in one or two dimensions a mobility edge in this sense does not exist, because all states are localised. The author distinguishes between the properties of electrons in the conduction bands of non-crystalline semiconductors, notably hydrogenated amorphous silicon (a-Si-H), and those in a degenerate electron gas, such as that in amorphous Si-Nb alloys or impurity bands in doped crystalline semiconductors. In the former the use of a one-electron model is legitimate, but a consideration of the interaction with phonons is essential; even at the absolute zero of temperature this leads to a broadening of the mobility edge. The main purpose here is to review recent work on the effects of this interaction on the pre-exponential factor sigma 0 in the conductivity expressed as sigma = sigma 0exp(-(Ec-EF)/kBT) and the pre-exponential factor in the drift mobility. In the final section he also gives a brief review of some of the recent work on the effects of the electron-electron interaction in metallic systems and also spin-orbit scattering.
We report measurements of photoluminescence, photoluminescence excitation spectroscopy and photoluminescence time decay on three MOVPE-grown InGaN/GaN multiple quantum well structures with 13% In in the wells and well widths Lz = 1.25, 2.5 and 5.0 nm. The PL spectra are dominated by single emission peaks, together with phonon sidebands spaced by a GaN LO phonon energy (92 meV). The peak energies are red-shifted with respect to energies calculated for exciton recombination in square quantum wells and the wide well sample also shows a significant Stokes shift between emission and absorption. Recombination lifetimes measured at 6 K are energy dependent, increasing as the photon energy is scanned downwards through the emission line. They also depend strongly on well width. On the low energy side of the 5 nm well emission line we measure lifetimes as long as 100 ns. Raising the temperature from 6 to 300 K results in a strong reduction of emission intensity for all samples and reduction of the lifetimes, though by a much smaller factor. The peak positions shift slightly to lower energy but by far less than the shift in the band edge. We consider three different theoretical models in an attempt to interpret this data, an exponential tail state model, a model of localization due to In/Ga segregation within the wells and the quantum confined Stark effect model. The QCSE model appears able to explain most of the data reasonably well, though there is evidence to suggest that, in addition, some degree of localization occurs.
The three-dimensional atom probe has been used to characterize green- and blue-emitting In x Ga 1-x N / Ga N multiple quantum well structures with subnanometer resolution over a 100 nm field of view. The distribution of indium in In x Ga 1-x N samples with different compositions is analyzed. No evidence is found wherein the indium distribution deviates from that of a random alloy, which appears to preclude indium clustering as the cause of the reported carrier localization in these structures. The upper interface of each quantum well layer is shown to be rougher and more diffuse than the lower interface, and the existence of monolayer steps in the upper interfaces is revealed. These steps could effectively localize carriers at room temperature. Indium is shown to be present in the GaN barrier layers despite the absence of indium precursor flux during barrier layer growth. A strong evidence is produced to support a mechanism for the presence of indium in these layers, namely, that a layer of indium forms on the surface of the growing In x Ga 1-x N quantum well, and this layer then acts as a source of indium during GaN barrier layer growth.
Optically pumped stimulated emission (SE) from InGaN/GaN multiple quantum wells (MQWs) grown by metalorganic chemical vapor deposition has been systematically studied as a function of excitation photon energy (Eexc) to further understand the origin of SE in these structures. Optically pumped SE was observed for excitation photon energies well below that of the absorption edge of the MQWs, indicating the states responsible for the soft absorption edge in these structures can efficiently couple carriers with the gain region. ``Mobility edge''-type behavior in the SE peak was observed as Eexc was varied. The effective mobility edge measured in these SE experiments lies ~110 meV above the main spontaneous emission peak and ~62 meV above the SE peak. Tuning the excitation energy below the mobility edge was found to be accompanied by a drastic increase in the SE threshold due to a decrease in the effective absorption cross section. The experimental results indicate that the SE peak observed here has the same microscopic origin as the spontaneous emission peak, i.e., radiative recombination of localized states.