The density-matrix theory of semiconductor lasers with relaxation broadening model is finally established by introducing theoretical dipole moment into previously developed treatments. The dipole moment is given theoretically by the k . p method and is calculated for various semiconductor materials. As a result, gain and gain-suppression for a variety of crystals covering wide wavelength region are calculated. It is found that the linear gain is larger for longer wavelength lasers and that the gain-suppression is much larger for longer wavelength lasers, which results in that single-mode operation is more stable in long-wavelength lasers than in shorter-wavelength lasers, in good agreement with the experiments.

Density-matrix theory of semiconductor lasers with relaxation broadening model - Gain and gain-suppression in semiconductor lasers

▪ Abstract Highly strained semiconductors grow epitaxially on mismatched substrates in the Stranski-Krastanow growth mode, wherein islands are formed after a few monolayers of layer-by-layer growth. Elastic relaxation on the facet edges, renormalization of the surface energy of the facets, and interaction between neighboring islands via the substrate are the driving forces for self-organized growth. The dimensions of the defect-free islands are of the order λB, the de Broglie wavelength, and provide three-dimensional quantum confinement of carriers. Self-organized In(Ga)As/GaAs quantum dots, or quantum boxes, are grown by molecular beam expitaxy (MBE) or metal-organic vapor phase epitaxy (MOVPE) on GaAs, InP, and other substrates and are being incorporated in microelectronic and opto-electronic devices. The use of strain to produce self-organized quantum dots has now become a well-accepted approach and is widely used in III–V semiconductors and other material systems. Much progress has been made in the ar...

Quantum dot opto-electronic devices

In this paper, we present the attractive characteristics of low-energy ion-implantation-induced quantum-well intermixing of InP-based heterostructures. We demonstrate that this method can fulfil a list of requirements related to the fabrication of complex optoelectronic devices with a spatial control of the bandgap profile. First, we have fabricated high-quality discrete blueshifted laser diodes to verify the capability of low-energy ion implantation for the controlled modification of bandgap profiles in the absence of thermal shift. Based on this result, intracavity electroabsorption modulators monolithically integrated with laser devices were fabricated, for the first time, using this postgrowth technique. We have also fabricated monolithic six-channel multiple-wavelength laser diode chips using a novel one-step ion implantation masking process. Finally, we also present the results obtained with very low-energy (below 20 keV) ion implantation for the development of one-dimensional and zero-dimensional quantum confined structures.

Low-energy ion-implantation-induced quantum-well intermixing

We have studied the effects of an uniaxial stress on the binding energy of a shallow donor impurity in a parallelepiped-shaped GaAs–(Ga,Al)As quantum dot. In the calculations we have used a variational technique within the effective-mass approximation. The stress was applied in the z direction and the donor impurity was located at various positions along the z axis. Our results show that the donor binding energy increases with increasing stress and for decreasing sizes of the quantum dot. Also, we have found that the binding energy for various values of the donor position along the z axis for constant quantum well box size increases with the proximity of the impurity to the center of the structure. Moreover, we obtain the shallow-donor binding energies as functions of uniaxial stress in the limit in which the quantum dot turns into either a quantum well or a quantum-well wire.

Uniaxial stress dependence of the binding energy of shallow donor impurities in GaAs–(Ga,Al)As quantum dots

We have developed a three-dimensional model for electronic states calculation of interdiffused quantum dots (QDs) with arbitrary shape by solving the BenDaniel-Duke's equation in momentum space domain. The proposed model features several advantages such as automatic solution to the Fick's diffusion equation, a relatively compact and efficient Hamiltonian matrix, and natural representation of a large array of QDs. Without considering the interdiffusion effect, our model yields good agreement with our references of $\mathrm{InAs}∕\mathrm{GaAs}$ QDs ground state energy calculation. We analyze the interdiffusion effect in QDs with various shapes of theoretical and practical interest like spherical, cubical, pyramidal, and lens shaped. We study the effect of QD size and aspect ratio to the blueshift profile due to interdiffusion. We found a similar blueshift profile in these QDs at almost any size that can be well approximated by $\mathrm{sech}(x)$ function. This model will serve as a valuable tool for QD band gap engineering based on the interdiffusion technique.

Electronics states of interdiffused quantum dots

Quantum wires with widths down to 45 nm have been realized by implantation induced intermixing of a surface near GaAs/AlGaAs quantum well. A very steep lateral potential has been achieved together with extreme low damage in the wire regions. As a result the optical transitions in photoluminescence excitation spectroscopy could be observed for all wire widths. With decreasing wire width an increasing Stokes shift has been determined due to the increasing importance of fluctuations in wire dimensions. A weak wire width dependence of transitions near the former two‐dimensional light‐hole level was observed, which is attributed to the predicted reduced energy shift of states near this level.

Photoluminescence excitation spectroscopy on intermixed GaAs/AlGaAs quantum wires

Optical properties of wire and dot structures for photonic applications

Time-resolved investigations on the photoluminescence of GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wires as a function of the wire width and the potential well depth indicate a reduction of the energy relaxation in quasi-one-dimensional (1D) systems. The systematic change of the wire width and potential well depth of the quantum wires with mask widths down to 40 nm were realized by ion-implantation-induced intermixing of quantum wells. Lifetime measurements on the high-energy side of the quantum wire emission yield increased decay times for the smallest wires. This is consistent with our observation of increased carrier temperatures and slowed cooling in the quantum wires with increasing carrier confinement. We explain the reduction of the relaxation with the decreased possibility for the scattering particles to fulfill both energy and momentum relaxation in wires with gradually increasing 1D behavior.

Carrier relaxation in intermixed GaAs/AlxGa1-xAs quantum wires

By implantation induced intermixing we have realized GaAs/AlGaAs quantum dots with diameters down to 70 nm. In low‐temperature photoluminescence an increasing shift to higher energies, up to 7 meV, with decreasing dot diameter is observed. From a simple model we conclude that a very steep lateral potential has been achieved and that the shift is partly due to the radial confinement. All dot structures show a high luminescence intensity and in the time integrated measurements no indication for a strong reduction of the energy relaxation is observed. This could be attributed to the measured carrier capture from the lateral barrier into the dots and by the shape of the radial potential which determines the energy levels in the dots.

GaAs/AlGaAs quantum dots by implantation induced intermixing

Using time-resolved photoluminescence, we have studied the nonradiative recombination of excess charge carriers in oxygen-implanted GaAs/${\mathrm{Al}}_{0.4}$${\mathrm{Ga}}_{0.6}$As single quantum wells. In order to reveal the recombination mechanism, the carrier lifetime is measured as a function of temperature and well width. We observe a decrease of the measured lifetime with increasing implantation dose and the nonradiative part of the recombination rate increases with increasing temperature. We find that the nonradiative recombination is thermally activated and the activation energies increase with decreasing well width. Under the assumption of strongly localized deep impurities we can explain this behavior with multiphonon capture processes and an analysis of the well-width dependence of the activation energies allows for the determination of the coupling strength for electron capture. In agreement with deep-level transient-spectroscopy (DLTS) measurements we determine a deep level 430 meV below the conduction band.

Nonradiative recombination via strongly localized defects in quantum wells.

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