Eoin P. O’Reilly

Tight-binding analysis of the electronic structure of dilute bismide alloys of GaP and GaAs

We develop an atomistic, nearest-neighbor sp3s* tight-binding Hamiltonian to investigate the electronic structure of dilute bismide alloys of GaP and GaAs. Using this model we calculate that the incorporation of dilute concentrations of Bi in GaP introduces Bi-related defect states in the band gap, which interact with the host matrix valence band edge via a Bi composition dependent band anti-crossing (BAC) interaction. By extending this analysis to GaBiAs we demonstrate that the observed strong variation of the band gap Eg and spin-orbit-splitting (SO) energy with Bi composition can be well explained in terms of a BAC interaction between the extended states of the GaAs valence band edge and highly localized Bi-related defect states lying in the valence band, with the change in Eg also having a significant contribution from a conventional alloy reduction in the conduction band edge energy. Our calculated values of Eg and SO are in good agreement with experiment throughout the investigated composition range x less than 13%. In particular, our calculations reproduce the experimentally observed crossover to an Eg < SO regime at approximately 10.5% Bi composition in bulk GaBiAs. Recent x-ray spectroscopy measurements have indicated the presence of Bi pairs and clusters even for Bi compositions as low as 2%. We include a systematic study of different Bi nearest-neighbor environments in the alloy to achieve a quantitative understanding of the effect of Bi pairing and clustering on the GaBiAs electronic structure.

Band engineering in dilute nitride and bismide semiconductor lasers

Highly mismatched semiconductor alloys such as GaNAs and GaBiAs have several novel electronic properties, including a rapid reduction in energy gap with increasing x and also, for GaBiAs, a strong increase in spin orbit- splitting energy with increasing Bi composition. We review here the electronic structure of such alloys and their consequences for ideal lasers. We then describe the substantial progress made in the demonstration of actual GaInNAs telecomm lasers. These have characteristics comparable to conventional InP-based devices. This includes a strong Auger contribution to the threshold current. We show, however, that the large spin-orbit-splitting energy in GaBiAs and GaBiNAs could lead to the suppression of the dominant Auger recombination loss mechanism, finally opening the route to e?fficient temperature-stable telecomm and longer wavelength lasers with significantly reduced power consumption.

Carrier-induced refractive index in quantum dot structures due to transitions from discrete quantum dot levels to continuum states

The carrier-induced refractive index in quantum dot (QD) structures due to optical transitions from QD levels to continuum states is considered. It is shown that, for large photon energies, the refractive index change is given asymptotically by the Drude formula. Calculations of the linewidth enhancement factor, α, show that α∼1 due to this contribution to the total refractive index. Furthermore, for highly localized QD states, the absorption coefficient at the photon energies ∼0.8–1.0 eV due to these transitions can be on the order of 103 m−1.

Intrinsic limits on electron mobility in dilute nitride semiconductors

A fundamental connection is established between the composition-dependence of the conduction band edge energy and the n-type carrier scattering cross section in the ultradilute limit for semiconductor alloys, imposing general limits on the carrier mobility in such alloys. From the measured nitrogen composition dependence of the bandgap in GaAs1−xNx, the carrier scattering cross section of substitutional nitrogen defects in GaAs is estimated to be 0.3 nm2. Within an independent scattering approximation, the carrier mobility is then estimated to be ∼1000 cm2/V s for a nitrogen atomic concentration of 1%, comparable to the highest measured mobility in high-quality GaInNAs samples at these N concentrations, but substantially higher than that found in many samples. This gives an intrinsic upper bound on the carrier mobility in these materials.

Theory of improved spectral purity in index patterned Fabry-Pérot lasers

The spectral purity of a ridge waveguide Fabry-Perot laser can be improved by patterning the effective refractive index seen by an optical mode propagating in the cavity. Here we present a transmission matrix calculation to first order in the effective index step from which we derive the threshold condition as a function of cavity mode index. This approach enables us to solve the inverse problem relating the index pattern along the cavity to the threshold gain modulation in wavenumber space. Quasiperiodic index patterns are constructed, which lead to improved spectral purity at a predetermined wavelength.

Theory of the electronic structure of dilute nitride alloys: beyond the band-anti-crossing model

We use an sp3s* tight-binding Hamiltonian to investigate the band-anti-crossing (BAC) model for dilute GaNxAs1−x alloys. The BAC model describes the strong band-gap bowing at low N composition x in terms of an interaction between the conduction band edge (E−) and a higher-lying band of localized nitrogen resonant states (E+). We demonstrate that the E− level can be described very accurately by the BAC model, in which we treat the nitrogen levels explicitly using a linear combination of isolated nitrogen resonant states (LCINS). We also use the LCINS results to identify E+ in the full tight-binding calculations, showing that at low N composition E+ forms a sharp resonance in the conduction band Γ-related density of states, which broadens rapidly at higher N composition when the E+ level rises in energy to become degenerate with the larger L-related density of states. We then turn to the conduction band dispersion, showing that the two-level BAC model must be modified to give a quantitative understanding of the dispersion. We demonstrate that the unexpectedly large electron effective mass values observed in some GaNAs samples are due to hybridization between the conduction band edge and nitrogen states close to the band edge. Finally we show that there is a fundamental connection between the strong composition-dependence of the conduction-band-edge energy and the n-type carrier scattering cross-section in Ga(In)NxAs1−x alloys, imposing general limits on the carrier mobility, comparable to the highest measured mobility in such alloys.

Optical matrix element in InAs/GaAs quantum dots: Dependence on quantum dot parameters

We present a theoretical analysis of the optical matrix element between the electron and hole ground states in InAs∕GaAs quantum dots (QDs) modeled with a truncated pyramidal shape. We use an eight-band k∙p Hamiltonian to calculate the QD electronic structure, including strain and piezoelectric effects. The ground state optical matrix element is very sensitive to variations in both the QD size and shape. For all shapes, the matrix element initially increases with increasing dot height, as the electron and hole wave functions become more localized in k space. Depending on the QD aspect ratio and on the degree of pyramidal truncation, the matrix element then reaches a maximum for some dot shapes at intermediate size beyond which it decreases abruptly in larger dots, where piezoelectric effects lead to a marked reduction in electron-hole overlap.

Complex emission dynamics of type-II GaSb/GaAs quantum dots

Optical properties of the GaSb/GaAs quantum dot system are investigated using a time-resolved photoluminescence technique. In this type-II heterostructure the carriers of different species are spatially separated and, as a consequence, a smooth evolution of both the emission wavelength and decay timescale is observed. A wavelength shift of 170 nm is measured simultaneously with the progressive timescale change from 100 ps to 23 ns. These phenomena are explained by the evolution of the carrier density, which brings a modification to the optical transition probability as well as the shift in the emission toward the higher energies.

Derivation of a 10-band model for dilute nitride semiconductors

AbstractThe band-anti-crossing (BAC) model was originally introduced as a phenomenological method to describe theelectronic structure of GaInNAs. We present here a Greens function model to derive explicitly the BAC model inorderedGa(In)N x As 1 x structures.TheGreensfunctionmodelisbasedonthetight-bindingmethod,whichwehaveusedpreviouslytoconfirmthatNformsaresonantdefectstateabovetheconductionbandedgeinGaAs.Byintro-ducingtheGreensfunctionmodelwederiveexplicitlythattheresonancebecomesdelocalisedandspreadoverseveralenergystatesasx increases,butthatthetwo-levelBACmodelstillgivesanexcellentdescriptionoftheconductionbandedgeinorderedsupercells.Wethenextendthemodeltoshowthattheconventional8-bandk pHamiltonianmustbemodifiedtoincludetwoextraspin-degeneratestates,givinga10-bandmodelforGa(In)N x As 1 x heterostructures. 2002ElsevierScienceLtd.Allrightsreserved. Keywords:GaNAs;k pmethod;Quantumwells;Bandanti-crossing 1.IntroductionWhenasmallfractionofarsenicatomsinGaAsarereplaced by nitrogen the energy gap initially decreasesrapidly,atabout0.1eVper%ofNforx < 0:03[1].Thisbehaviour is markedly different to conventional semi-conductors,andisofinterestbothfromafundamentalperspective and also becauseof its significant potentialdeviceapplications.Thereisthereforeconsiderablead-vantagetodevelopingsimplemodelswhichdescribeandpredictthevariationwithNcomposition,x,ofsuchkeyproperties as the energy gap, the Kane interband mo-mentum matrix element and the band edge effectivemassesinGa(In)N

Broadening of Plasmonic Resonance Due to Electron Collisions with Nanoparticle Boundary: а Quantum Mechanical Consideration

We present a quantum mechanical approach to calculate broadening of plasmonic resonances in metallic nanostructures due to collisions of electrons with the surface of the structure. The approach is applicable if the characteristic size of the structure is much larger than the de Broglie electron wavelength in the metal. The approach can be used in studies of plasmonic properties of both single nanoparticles and arrays of nanoparticles. Energy conservation is insured by a self-consistent solution of Maxwells equations and our model for the photon absorption at the metal boundaries. Consequences of the model are illustrated for the case of spheroid nanoparticles, and results are in good agreement with earlier theories. In particular, we show that the boundary-collision broadening of the plasmonic resonance in spheroid nanoparticles can depend strongly on the polarization of the impinging light.