M. J. Godfrey

Optical and microstructural studies of InGaN/GaN single-quantum-well structures

We have studied the low-temperature (T=6K) 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–Perot interference-free photoluminescence spectra has been compared with the results of a model calculation, yielding a value of approximately 2nm 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 ...

Theory of surface stress and surface reconstruction

Abstract We investigate the stresses that are present, even in equilibrium, at solid surfaces. First-principles calculations of the surface stress tensor for the aluminium, iridium, platinum and gold (111) surfaces are reported, which indicate the presence of a tensile surface stress in each case. We compare our results for aluminium with those for jellium and discuss the origins of the surface stress. We investigate the role that surface stress may play in driving surface reconstructions in which the density of surface atoms is altered from the corresponding value for the terminated bulk structure. A simple model is discussed which illustrates the competition between the various forces involved in such a reconstruction.

Carrier localization mechanisms in InxGa1-xN/GaN quantum wells

Localization lengths of the electrons and holes in InGaN/GaN quantum wells have been calculated using numerical solutions of the effective mass Schrodinger 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.

The consequences of high injected carrier densities on carrier localization and efficiency droop in InGaN/GaN quantum well structures

There is a great deal of interest in the underlying causes of efficiency droop in InGaN/GaN quantum welllight emitting diodes, with several physical mechanisms being put forward to explain the phenomenon. In this paper we report on the observation of a reduction in the localization induced S-shape temperature dependence of the peak photoluminescence energy with increasing excitation power density. This S-shape dependence is a key fingerprint of carrier localization. Over the range of excitation power density where the depth of the S shape is reduced, we also observe a reduction in the integrated photoluminescence intensity per unit excitation power, i.e., efficiency droop. Hence, the onset of efficiency droop occurs at the same carrier density as the onset of carrier delocalization. We correlate these experimental results with the predictions of a theoretical model of the effects of carrier localization due to local variations in the concentration of the randomly distributed In atoms on the optical properties of InGaN/GaN quantum wells. On the basis of this comparison of theory with experiment we attribute the reduction in the S-shape temperature dependence to the saturation of the available localized states. We propose that this saturation of the localized states is a contributory factor to efficiency droop whereby nonlocalized carriers recombine non-radiatively.

The Origin and Possible Implications of Surface Stress on Metals

The origin of surface stress on metals is discussed. Self-consistent pseudo-potential calculations of the surface stress tensor at the aluminium [111] and [110] surfaces are reported. In both cases the stress is tensile, favouring contraction in the plane of the surface. The results for aluminium are compared with those for jellium and a simple interpretation is developed in terms of the smoothing of the electronic wavefunctions at the crystal surface. Some implications of the presence of a surface stress for surface phonon dispersion and for surface instabilities are discussed.

Optical and electrical properties of selectively delta‐doped strained InxGa1−xAs/GaAs quantum wells

We report here an investigation of selectively delta‐doped strained InGaAs/GaAs quantum wells. Electronic structures of the systems were calculated by self‐consistently solving the Schrodinger and Poisson equations and the calculations revealed a systematic variation of the band structure as the delta sheet moved away from the center of the well to the edge and finally to the barrier. The results were found to be in agreement with our photoluminescence (PL) measurements. For center‐doped samples, band‐gap renormalization was found to be strong from the PL data, and our realistic random‐phase approximation calculation for the heavily doped sample is in excellent agreement with the PL data. The radiative lifetimes were measured to be around 450 ps for all the samples, and surprisingly they vary very little from sample to sample although the wave‐function overlap was considerably different for some samples. We also report Shubnikov–de Haas (SdH) measurements on the two barrier doped cases. For the heavily do...

Effects of indium segregation and well-width fluctuations on optical properties of InGaN/GaN quantum wells.

We report the results of calculations for the energies of confined electrons and holes and their wavefunction overlap in In x Ga 1-x N/GaN quantum wells (QWs) with an indium concentration of x = 15% in the well material. It is known that the observed increase in the photoluminescence lifetime with increasing well width can be explained qualitatively by the reduction in overlap of the electron and hole wave functions, which is caused by the piezoelectric field in the strained QW material. We show that the energy dependence of the lifetime measured across the emission line can be explained in a similar way, as the result of ±1-monolayer variations in the QW width. We also calculate the energies and electron-hole wave-function overlap for carriers trapped within indium-rich regions of the QW, taking into account the relaxation of the strain field in and around the indium fluctuation. Our results indicate that well-width fluctuations lead to a stronger energy dependence of the lifetime: the magnitude of the effect is the same order as in experiment, and shows a similar increase with increasing well width.

Temperature dependent optical properties of InGaN/GaN quantum well structures

We have investigated the variation of the photoluminescence intensity and decay time as a function of temperature of a series of InGaN/GaN quantum well structures in which the number of quantum wells was varied. All the samples exhibited a decrease in photoluminescence intensity and decay time with increasing temperature with the rate of decrease being reduced as the number of quantum wells was increased. We have compared these results with a theoretical model which describes the effects of thermally excited carrier escape and recapture. We find reasonable agreement with the results of the model and the experiments for the samples incorporating only a few quantum wells supporting the idea that thermally excited carrier loss is the main non-radiative recombination path.

Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter σ confined to a two-dimensional channel of width 1.95σ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction ϕ(K) that is less than the maximum possible ϕ(max), the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any real divergence of the pressure at ϕ(K). We give arguments that this avoided phase transition is a structural feature, the remnant in our narrow channel system of the hexatic to crystal transition, but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale ξ̃(3) as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around 15σ at ϕ(K), which is larger than the penetration lengths that have been reported for three-dimensional systems. It is argued that the α-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches ϕ(K).

Static and dynamical properties of a hard-disk fluid confined to a narrow channel

The thermodynamic properties of disks moving in a channel sufficiently narrow that they can collide only with their nearest neighbors can be solved exactly by determining the eigenvalues and eigenfunctions of an integral equation. Using it, we have determined the correlation length ξ of this system. We have developed an approximate solution which becomes exact in the high-density limit. It describes the system in terms of defects in the regular zigzag arrangement of disks found in the high-density limit. The correlation length is then effectively the spacing between the defects. The time scales for defect creation and annihilation are determined with the help of transition-state theory, as is the diffusion coefficient of the defects, and these results are found to be in good agreement with molecular dynamics simulations. On compressing the system with the Lubachevsky-Stillinger procedure, jammed states are obtained whose packing fractions ϕJ are a function of the compression rate γ. We find a quantitative explanation of this dependence by making use of the Kibble-Zurek hypothesis. We have also determined the point-to-set length scale ξPS for this system. At a packing fraction ϕ close to its largest value ϕmax, ξPS has a simple power law divergence, ξPS∼1/(1-ϕ/ϕmax), while ξ diverges much faster, ln(ξ)∼1/(1-ϕ/ϕmax).