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This tutorial paper focuses on the physical origin of thermal droop, i.e., the decrease in the luminescence of light-emitting diodes (LEDs) induced by increasing temperature. III-nitride-based LEDs are becoming a pervasive technology, covering several fields from lighting to displays, from automotive to portable electronics, and from horticulture to sensing. In all these environments, high efficiency is a fundamental requirement, for reducing power consumption and system cost. Over the last decade, a great deal of effort has been put in the analysis of the efficiency droop, the decrease in LED internal quantum efficiency (IQE) induced by high current density. On the other hand, an IQE decrease is observed also for increasing temperature, a phenomenon usually referred to as thermal droop. For commercial LEDs, the IQE decrease related to thermal droop can be comparable to that of efficiency droop: for this reason, understanding thermal droop is a fundamental step for making LEDs capable of operating at high temperature levels. In several fields (including street lighting, automotive, photochemical treatments, projection, entertainment lighting, etc.), compact and high-flux light sources are required: typically, to reduce the size, weight, and cost of the systems, LEDs are mounted in compact arrays, and heat sinks are reduced to a minimum. As a consequence, LEDs can easily reach junction temperatures above 85–100 °C and are rated for junction temperatures up to 150–175 °C (figures from commercially available LED datasheets: Cree XHP70, Osram LUW HWQP, Nichia NVSL219CT, Samsung LH351B, and LedEngin LZP-00CW0R) and this motivates a careful analysis of thermal droop. This paper discusses the possible physical causes of thermal droop. After an introduction on the loss mechanisms in junctions, we will individually focus on the following processes: (i) Shockley–Read–Hall (SRH) recombination and properties of the related defects; (ii) Auger recombination and its temperature dependence, including the discussion of trap-assisted Auger recombination; (iii) impact of carrier transport on the thermal droop, including a discussion on carrier delocalization, escape, and freeze out; (iv) non-SRH defect-related droop mechanisms. In addition, (v) we discuss the processes that contribute to light emission at extremely low current levels and (vi) the thermal droop in deep ultraviolet LEDs, also with reference to the main parasitic emission bands. The results presented within this paper give a tutorial perspective on thermal droop; in addition, they suggest a pathway for the mitigation of this process and for the development of LEDs with stable optical output over a broad temperature range. [ABSTRACT FROM AUTHOR]

An efficient finite-element reduced-order quasi-TEM model for the frequency-dependent characteristics of lossy multiconductor transmission lines is presented. Conductor losses are evaluated as functions of frequency through a magneto-quasi-static model. Numerically generated problem-matched basis functions reduce the problem size and, therefore, the CPU time required by frequency sweeps without appreciable loss of accuracy. The proposed approach is applied to complex coplanar waveguides and to multiconductor interconnects; its results are compared with quasi-analytical techniques and with the full-wave finite-element method. Index Terms--Coplanar waveguides (CPWs), Damascene multilevel interconnects, electrooptic modulators, finite-element method (FEM), magneto-quasi-static problem, micromachined CPWs, model order reduction, multiconductor transmission lines (MTLs), ohmic losses, skin effect.

A theoretical justification is presented of the partial-capacitance (PC) approach, widely exploited in the modeling of coplanar waveguides on finite-thickness and multilayered substrates. The analysis is based on the static spectral-domain approach to the computation of the capacitance of a set of planar conductors embedded into a multilayered substrate. It is shown that the PC method can be derived from approximating the static Green's function of a multilayered dielectric as the sum of partial contributions; such a decomposition can be applied to the Green's function either in parallel (admittance) or series (impedance) form. The resulting (parallel or series) PC approaches are shown to be accurate with substrates having layers of decreasing or increasing permittivity, respectively. Lines backed by magnetic or electric walls are introduced as limiting cases of multilayered structures. Index Terms--Coplanar lines, partial-capacitance (PC) approach, planar transmission lines, spectral-domain static Green's function techniques.

A new class of coaxial broad-band directional couplers for high-power RF testing is presented. These devices overcome the drawbacks of classical stripline and coaxial couplers, and allow simple low-cost mechanical construction. A design technique for the new longitudinally nonuniform transversally nonsymmetricai couplers is described, providing the synthesis of any coupling shape versus frequency. As a first demonstration of the proposed method, a set of broad-band (2-7.5 GHz) low-coupling (-30, -33, -35 dB) nonsymmetrical coaxial directional couplers in air has been designed, built, and characterized, showing very good agreement between predicted and obtained performances. Index Terms--Broad-band couplers, coaxial cables, coaxial couplers, conformal mapping.

We present a detailed simulation study on plasmonic-organic hybrid electro-optic modulators based on coupled symmetric or asymmetric plasmonic slots. An electro-optic polymer is exploited as an active material, and the device is compatible with a silicon photonics platform. The proposed device operates at 1550 nm wavelength, typical of data center or long-haul telecommunication systems. The device performance in terms of area, plasmonic losses, optical bandwidth, intrinsic modulation bandwidth and energy dissipation are comparable to already proposed Mach-Zehnder solutions, but with potentially better extinction ratio, coupling losses due to photonic-plasmonic transitions, and flexibility in exploiting, without any performance penalty, asymmetric slots to shift the ON and OFF states bias. Finally, the bias dependence of the modulation chirp is investigated, comparing through and cross-coupling configurations. [ABSTRACT FROM AUTHOR]

Numerical conformal mapping is exploited as a simple, accurate, and efficient tool for the analysis and design of coaxial waveguides and couplers of complex cross section. An implementation based on the Schwarz-Christoffel Toolbox, a public-domain MATLAB package, is applied to slotted coaxial cables and to symmetrical coaxial couplers, with circular or polygonal inner conductors and external shields. The effect of metallic diaphragms of arbitrary thickness, partially separating the inner conductors, is also easily taken into account. The proposed technique is validated against the results of the finite-element method, showing excellent agreement at a fraction of the computational cost, and is also extended to the case of nonsymmetrical couplers, providing the designer with important additional degrees of freedom. Index Terms--Coaxial cables, coaxial couplers, conformal mapping.

The evaluation of the frequency response of waveguiding structures by means of the full-wave finite-element method requires solving a large generalized eigenvalue problem for each frequency. This paper describes a novel approach, based on the singular-value decomposition, which drastically reduces the order of the eigenvalue problem. By inspection of the singular values, the accuracy level of the procedure may be controlled. The technique is applied to the analysis of open and closed waveguides with arbitrary cross section, lossy conductors, and anisotropic dielectric layers, by means of vector elements of generic order; higher order elements are shown to allow the accurate evaluation of fields inside lossy conductors with fewer unknowns, besides exactly modeling normal field discontinuities at material interfaces. Examples of application of the reduced-order technique are shown concerning both non-TEM and quasi-TEM structures. Index Terms--Finite-element method, higher order vector elements, reduced-order models, singular-value decomposition.

The band structures of InGaN, AIGaN and InAIN were studied.

The atomic potentials of the wurtzite phase of GaN, InN and AIN, were studied.

Herein, an overview on the physics‐based and system‐oriented modeling of organic electro‐optic Mach–Zehnder modulators for optical communication systems is presented. State‐of‐the‐art solutions in electro‐optic organic materials and modulator designs are reviewed, with particular stress on silicon organic hybrid (SOH) and plasmonic organic hybrid (POH) solutions. Then, the physics‐based simulation of concentrated and traveling‐wave modulators is discussed both through 3D optical simulations and a combination of 2D and 3D models, where the modulator is partitioned into convenient subdomains. Neural network behavioral models are finally discussed and case studies are proposed on the physics‐based and system‐level simulation of SOH and POH Mach–Zehnder modulators. [ABSTRACT FROM AUTHOR]

Monte Carlo technique was used to simulate electrical characteristics of single and multiple quantum barrier varactors (QBV). The voltage was modulated at 50 GHz and FFT of the current was applied to also simulate the RF behavior. Results showed that only odd harmonics are generated and the current level of the third harmonic is about ten percent of the injected signal current level. Moreover, it is demonstrated that Monte Carlo simulation is a useful tool to predict nonlinear behavior in QBV.

Closed-form CAD-oriented conformal-mapping approximations are presented for the HF attenuation of two-conductor symmetrical coupled coplanar waveguides (CCPW's). The expressions are compared with the results obtained from a full-wave electromagnetic (EM) simulator and found to yield acceptable agreement. A modified form is also presented according to [1], which partly overcomes the low-frequency limitations of the skin-effect approximation. Index Terms - Attenuation, conformal mapping, coplanar waveguides, couplers, design automation software, skin effect.

Defects can significantly modify the electro-optical characteristics of InGaN light-emitting diodes (LEDs); however, modeling the impact of defects on the electrical characteristics of LEDs is not straightforward. In this paper, we present an extensive investigation and modeling of the impact of defects on the electrical characteristics of InGaN-based LEDs, as a function of the thickness of the quantum well (QW). First, we demonstrate that the density of defects in the active region of III-N LEDs scales with increasing thickness of the InGaN QW. Since device layers with high indium content tend to incorporate more defects, we ascribed this experimental evidence to the increased volume of defects-rich InGaN associated to thicker InGaN layers. Second, we demonstrate that the current–voltage characteristics of the devices are significantly influenced by the presence of defects, especially in the sub turn-on region. Specifically, we show that the electrical characteristics can be effectively modeled in a wide current range (from pA to mA), by considering the existence of trap-assisted tunneling processes. A good correspondence is obtained between the experimental and simulated electrical characteristics (I–V), by using—in the simulation—the actual defect concentrations/activation energies extracted from steady-state photocapacitance, instead of generic fitting parameters. [ABSTRACT FROM AUTHOR]

The ICT scene is dominated by short-range intra-datacenter interconnects and networking, requiring high speed and stable operations at high temperatures. GaAs/AlGaAs vertical-cavity surface-emitting lasers (VCSELs) emitting at 850–980 nm have arisen as the main actors in this framework. Starting from our in-house 3D fully comprehensive VCSEL solver VENUS, in this work we present the possibility of downscaling the dimensionality of the simulation, ending up with a multiphysics 1D solver (D1ANA), which is shown to be capable of reproducing the experimental data very well. D1ANA is then extensively applied to optimize high-temperature operation, by modifying cavity detuning and distributed Bragg's reflector lengths. [ABSTRACT FROM AUTHOR]

We present a multiband envelope-function model for wurtzite nanostructures based on a rigorous numerical procedure to determine operator ordering and band parameters from nonlocal empirical pseudopotential calculations. The proposed approach, implemented within a finite-element scheme, leads to well-posed, numerically stable envelope equations that accurately reproduce full-Brillouinzone subband dispersions of quantum systems. Although demonstrated here for III-nitride nonlocal empirical pseudopotentials, the model provides a general theoretical framework applicable to ab initio electronic structures of wurtzite semiconductors. [ABSTRACT FROM AUTHOR]

In state-of-the-art, large format, HgCdTe-based infrared focal plane arrays the typical pixel size (3–10 μ m ) is of the order of the operating wavelength and much smaller than the carrier diffusion length. This makes inter-pixel crosstalk a limiting factor, especially in planar structures. Employing three-dimensional electromagnetic and electrical simulations we show that, besides reducing the dark current through Auger suppression, majority carrier depletion of the detector absorber is also effective in curtailing the inter-pixel crosstalk due to carrier diffusion. In the case of a 5 μ m -pitch pixel, a proper design of the absorber composition and doping profile allows to reduce inter-pixel crosstalk by more than a factor of two when increasing the reverse bias from - 0.1 to - 0.5 V , keeping the contribution to crosstalk coming from carrier diffusion between 2 and 12% in the mid- and long-wavelength infrared spectrum. [ABSTRACT FROM AUTHOR]

Probing the thermal effects that limit the performance of vertical-cavity surface-emitting lasers (VCSELs) reveals an intricate interplay between carrier transport, recombination mechanisms, thermal conduction, and optical features. An understanding of this interplay requires an accurate yet computationally-efficient multiphysical approach at the microscopic level. We address this task by characterizing oxide-confined multimode 850 nm VCSELs over a wide temperature range, and by simulating them with VENUS, our in-house multiphysics simulator. The agreement with the experimental results in the whole explored temperature range provides physical insight into the mechanisms that determine VCSEL rollover and turn off, and demonstrates the predictive capabilities of the model. A complete set of model parameters determined through this combined experiment-simulation approach is presented. [ABSTRACT FROM AUTHOR]

The properties of vertical-cavity surface-emitting lasers (VCSELs) are investigated by means of a multiphysical Vcsel Electro-opto-thermal NUmerical Simulator (VENUS). VENUS includes a three-dimensional vectorial electromagnetic code, a description of the quantum well optical response, a heat equation solver, and a quantum-corrected drift-diffusion simulator. The proposed suite includes coupling mechanisms often overlooked in VCSEL simulation and allows to reassess the impact of parameters, which can be critically dependent on implementation details inaccessible in commercial codes. The agreement with experimental results holds the promise of the application of this framework to the computer-aided design of innovative VCSEL concepts. [ABSTRACT FROM AUTHOR]

In this paper, analytical computer-aided-design (CAD)-oriented conformal-mapping approximations are presented for the high-frequency attenuation of symmetric and asymmetric coplanar waveguides (ACPW's) with finite-extent lateral ground planes. A discussion is presented on the effect of ground-plane width on the losses, and design criteria are derived. Index Terms - Attenuation, conformal mapping, coplanar waveguides, design automation software.

We present a k·p model for wurtzite semiconductors that allows the accurate approximation of the electronic structure over the entire Brillouin zone. The inclusion of an additional expansion point besides Γ allows significant improvements over standard full-Brillouin-zone approaches while keeping a manageable number of model parameters. We provide complete information about the Hamiltonian matrices of both expansion points and discuss the details of the optimization process used to determine the matrix parameters. As a demonstration of our scheme, we propose an approximation of the electronic structure of wurtzite ZnO, optimized for application to full-band Monte Carlo electron transport simulation. (A MATLAB implementation of the k·p model for ZnO is available from the authors.) [ABSTRACT FROM AUTHOR]

A nonlocal semiempirical pseudopotential calculation of the electronic structure of wurtzite ZnO is proposed. The local and nonlocal components of the atomic effective potentials have been sequentially optimized and an excellent quantitative agreement has been achieved with a wide range of band features (energy gaps at high symmetry points, valence band ordering, in-plane and perpendicular components of the effective masses for electrons and holes at Γ), selected not only from available experimental and ab initio results, but also from new calculations performed with the code developed by the ABINIT project. The valence band description has been further improved through the inclusion of spin-orbit corrections. The complex dielectric function along the main crystallographic directions corresponding to the optimized electronic structure is also presented, along with extensive comparisons of all the computed quantities with the literature data. [ABSTRACT FROM AUTHOR]

Wave-vector-dependent rates of disorder-induced alloy scattering have been computed for wurtzite AlGaN and InGaN to determine the transport properties of III-nitride alloys through full band Monte Carlo simulation. Contrary to previous studies, the empirical selection of a constant alloy scattering potential has been replaced by a more fundamental approach based on detailed information about the electronic structure and the corresponding screened atomic potentials. Band structures and atomic potentials have been determined in the framework of the nonlocal empirical pseudopotential method; good agreement of the fundamental energy gap with available experimental information has been achieved over the entire composition range of the alloys with the inclusion of a disorder contribution in the pseudopotential. The calculated alloy scattering potential is in reasonable agreement with the few indirect measurements available for AlGaN. Calculations of electron steady-state velocity-field curves confirm that alloy scattering has significant effects on the transport properties of AlGaN and InGaN. [ABSTRACT FROM AUTHOR]

In this article we discuss the effect of temperature on the impact ionization coefficients in wide band-gap semiconductors and compare it to that of bulk GaAs. The impact ionization coefficients as a function of temperature are examined for three semiconductors: gallium arsenide, cubic phase silicon carbide, and zinc-blende phase gallium nitride. It is found that the magnitude of the phonon energy is principally responsible for changes in the impact ionization coefficients as a result of temperature change. While the energy band gap of a material does have a temperature dependence that directly affects the impact ionization transition rate, that change is much smaller than the relative change in the magnitude of the phonon-scattering rates in all of the materials studied here. The phonon energies are found to play a vital role in the magnitude of the change in the scattering rates as a function of temperature. Materials with relatively small phonon energies have phonon scattering rates that change considerably with temperature, and therefore have impact ionization coefficients that also change considerably with changes in temperature. Conversely, the phonon scattering rate in materials with a large phonon energy is less affected and thus these materials have impact ionization coefficients that are relatively insensitive to changes in the temperature. [ABSTRACT FROM AUTHOR]

This work presents nonlocal pseudopotential calculations based on realistic, effective atomic potentials of the wurtzite phase of GaN, InN, and AlN. A formulation formulation for the model effective atomic potentials has been introduced. For each of the constitutive atoms in these materials, the form of the effective potentials is optimized through an iterative scheme in which the band structures are recursively calculated and selected features are compared to experimental and/or ab initio results. The optimized forms of the effective atomic potentials are used to calculate the band structures of the binary compounds, GaN, InN, and AlN. The calculated band structures are in excellent overall agreement with the experimental/ab initio values, i.e., the energy gaps at high-symmetry points, valence-band ordering, and effective masses for electrons match to within 3%, with a few values within 5%. The values of the energy separation, effective masses, and nonparabolicity coefficients for several secondary valleys are tabulated as well in order to facilitate analytical Monte Carlo transport simulations. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This work presents detailed information on the band structures of the III-nitride wurtzite ternary alloys, computed through the virtual crystal approximation approach. The key ingredient of this study is the set of realistic atomic effective potentials described in Part I of the present work, dedicated to the constituent binary compounds. The model relies on the linear interpolation of the structural parameters and of the local and nonlocal effective potentials: no further empirical corrections are included. The dependence on the mole fraction is computed for the energy gaps at all the high-symmetry points, the valence-band width, and the electron effective masses in the valleys relevant for carrier-transport simulation. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Highlights • Simulation of HgCdTe infrared detectors with realistic alloy composition profiles essential for their optimization. • Realistic full-wave electromagnetic with compositionally-graded layers is difficult with commercial simulators. • We give practical hints for discretizing the grading into sublayers. • We test several different discretizations. • We assess when the grading may be neglected. Abstract The ability to simulate HgCdTe infrared detectors with realistic alloy composition profiles is essential for their optimization. We give practical guidelines for the realization of combined three-dimensional, realistic full-wave electromagnetic and electrical modeling for the description of detectors with compositionally-graded layers, suitable to most available numerical solvers. Following the known procedure to sample the compositionally-graded layers into a number N of sublayers, we assess the effects of different choices for N , both on calculation accuracy and computational cost. Quantum efficiency spectra calculated with the proposed approach are compared with those determined through two shortcuts: ray tracing, based on classical optics, and full-wave simulation where graded layers are replaced by constant, spatially-averaged optical properties. It is shown that the former is not generally a valid alternative, since it does not address interference effects due to back-reflections, while the latter can lead to incorrect estimates of the detector cutoff wavelength. [ABSTRACT FROM AUTHOR]

The Schwarz-Christoffel toolbox, a free MATLAB package for the computation of conformal maps, is applied to the quasi-static analysis of coplanar waveguides (CPWs) of arbitrary cross section in order to provide computationally efficient and very accurate estimates of their capacitance, inductance, characteristic impedance, and skin-effect attenuation. A few examples of many-sided polygonal waveguides are discussed, and the trapezoidal CPW, important, for example, for electrooptic modulators, is described in full detail, providing general guidelines for the electrode geometry optimization. The technique is validated through a comparison with the results of a full-wave finite-element method, and excellent agreement is demonstrated both in vacuo and with two-layer dielectric substrates. Index Terms--Coplanar waveguides, electrooptic modulation, integrated opto-electronics, skin effect.

A set of thick coplanar waveguides on lithium niobate substrates, with and without a thin Si[O.sub.2] buffer layer, has been experimentally characterized through on-wafer measurements. The effective refractive index and attenuation were extracted from raw (uncalibrated) measurements up to 40Hz through the thru-reflection-line approach. The characteristic impedance was then obtained from the propagation constant, using an accurate estimate of the in-vacuo capacitance derived from a new conformal mapping approach able to exactly account for large electrode thickness. We observed that the attenuation of lines with or without the oxide buffer layer consistently exhibits a different frequency behavior, thus suggesting that dielectric losses can play a significant role in the upper microwave range. This is confirmed by the results from a full quasi-TEM analytical model, including losses and frequency dispersion, which was derived by extending the model in [1]. The measured and simulated data show good agreement both for the propagation characteristics (attenuation and effective permittivity) and for the line impedance. Index Terms--Coplanar waveguides, dielectric losses, electrooptic modulation, integrated optoelectronics, loss measurements, skin effect.

The potential applications of germanium and its alloys in infrared silicon-based photonics have led to a renewed interest in their optical properties. In this letter, we report on the numerical determination of Auger coefficients at T=300K for relaxed and biaxially strained germanium. We use a Green's function based model that takes into account all relevant direct and phononassisted processes and perform calculations up to a strain level corresponding to the transition from indirect to direct energy gap. We have considered excess carrier concentrations ranging from 1016 cm-3 to 5×1019 cm-3. For use in device level simulations, we also provide fitting formulas for the calculated electron and hole Auger coefficients as functions of carrier density. [ABSTRACT FROM AUTHOR]