Carrier-induced refractive index change and optical absorption in wurtzite InN and GaN: Fullband approach

Based on the full band electronic structure calculations, first we consider the effect of n-type doping on the optical absorption and the refractive index in wurtzite InN and GaN. We identify quite different dielectric response in either case; while InN shows a significant shift in the absorption edge due to n-type doping, this is masked for GaN due to efficient cancellation of the Burstein-Moss effect by the band gap renormalization. For high doping levels the intraband absorption becomes significant in InN. Furthermore, we observe that the free-carrier plasma contribution to refractive index change becomes more important than both band filling and the band gap renormalization for electron densities above 10$^{19}$~cm$^{-3}$ in GaN, and 10$^{20}$~cm$^{-3}$ in InN. As a result of the two different characteristics mentioned above, the overall change in the refractive index due to n-type doping is much higher in InN compared to GaN, which in the former exceeds 4\% for a doping of 10$^{19}$~cm$^{-3}$ at 1.55~$\mu$m wavelength. Finally, we consider intrinsic InN under strong photoexcitation which introduces equal density of electron and holes thermalized to their respective band edges. The change in the refractive index at 1.55~$\mu$m is observed to be similar to the n-doped case up to a carrier density of 10$^{20}$~cm$^{-3}$. However, in the photoexcited case this is now accompanied by a strong absorption in this wavelength region due to $\Gamma^v_5 \to \Gamma^v_6$ intravalence band transition. Our findings suggest that the alloy composition of In$_x$Ga$_{1-x}$N can be optimized in the indium-rich region so as to benefit from high carrier-induced refractive index change while operating in the transparency region to minimize the losses. These can have direct implications for InN-containing optical phase modulators and lasers.Comment: Revised with an appendix, two additional figures, and more discussions; 10 pages, 14 figures; published versio

Performance of Widely Tunable Multi-Quantum-Well and Bulk Laser Diodes and the Main Limiting Factors

The output power and tuning performance of multi-quantum-well (MQW) and bulk InGaAsP/InP-distributed Bragg reflector (DBR) tunable laser diodes (TLDs) are investigated over a wide wavelength tuning range using physics-based PICS3D and VPI laser simulation tools within the travelling-wave formalism. The key result of our simulations is the discovery of a new effect in TLDs due to intervalence band absorption (IVBA) in passive phase and DBR sections, which limits the wavelength tuning range. The physical mechanism responsible for such a behavior is a collapse of the spectral-mode selectivity by the DBR due to large IVBA losses in the phase or/and DBR sections. We fundamentally demonstrate different roles played by the IVBA in the active and passive sections of a TLD. It is shown that the IVBA in passive sections and the carrier relaxation broadening (CRB) of the Lorentzian lineshape function in the lasers' active and passive sections play a crucial role in TLD tuning operation. The IVBA coefficient k IVBA and the intraband relaxation time τ in are the major limiting factors that define the output power variation and the achievable tuning range of the lasers. Both bulk and MQW lasers with small k IVBA demonstrate a wide wavelength tuning range above 30 nm, while for large k IVBA , the tuning range drops below 10 nm. We show that the output power variation with tuning due to the CRB parameter τ in is qualitatively different in bulk and MQW TLDs. The TLD tuning and power performance is also strongly affected by the shapes of the net gain and the cavity mirror loss spectra and their mutual positioning with respect to the lasing cavity mode during the tuning. The limiting parameters k IVBA and τin as well as gain and mirror loss spectra must be thoroughly evaluated in each TLD structure prior to the device design and optimization in order to achieve the best performance in terms of the wavelength tuning and the output power stability

Polar optical phonon scattering and negative Kromer-Esaki-Tsu differential conductivity in bulk GaN

Cataloged from PDF version of article.GaN is being considered as a viable alternative semiconductor for high-power solid-state electronics. This creates a demand for the characterization of the main scattering channel at high electric fields. The dominant scattering mechanism for carriers reaching high energies under the influence of very high electric fields is the polar optical phonon (POP) emission. To highlight the directional variations, we compute POP emission rates along high-symmetry directions for the zinc-blende and wurtzite crystal phases of GaN. Our treatment relies on the empirical pseudopotential energies and wave functions. The scattering rates are efficiently computed using the Lehmann-Taut Brillouin zone integration technique. For both crystal phases, we also consider the negative differential conductivity possibilities associated with the negative effective mass part of the band structure. (C) 2001 Elsevier Science B.V. All rights reserved

Comparative analysis of zinc-blende and wurtzite GaN for full-band polar optical phonon scattering and negative differential conductivity

Cataloged from PDF version of article.For high-power electronics applications, GaN is a promising semiconductor. Under high electric fields, electrons can reach very high energies where polar optical phonon (POP) emission is the dominant scattering mechanism. So, we undertake a full-band analysis of POP scattering of conduction-band electrons based on an empirical pseudopotential band structure. To uncover the directional variations, we compute POP emission rates along high-symmetry directions for the zinc-blende (ZB) crystal phase of GaN. We also compare the results with those of the wurtzite phase. In general, the POP scattering rates in the zinc-blende phase are lower than the wurtzite phase. Our analysis also reveals appreciable directional dependence, with the Gamma-L direction of ZB GaN being least vulnerable to POP scattering, characterized by a scattering time of 11 fs. For both crystal phases, we consider the negative differential conductivity possibilities driven by the negative effective mass part of the band structure. According to our estimation, for the ZB phase the onset of this effect requires fields above similar to 1 MV/cm. (C) 2000 American Institute of Physics. [S0003-6951(00)02743-1]

On the Distribution of Traffic Volumes in the Internet and its Implication

Getting good statistical models of traffic on network links is a well-known, often-studied problem. A lot of attention has been given to correlation patterns and flow duration. The distribution of the amount of traffic per unit time is an equally important but less studied problem. We study a large number of traffic traces from many different networks including academic, commercial and residential networks using state-of-the-art statistical techniques. We show that the log-normal distribution is a better fit than the Gaussian distribution commonly claimed in the literature. We also investigate a second heavy-tailed distribution (the Weibull) and show that its performance is better than Gaussian but worse than log-normal. We examine anomalous traces which are a poor fit for all distributions tried and show that this is often due to traffic outages or links that hit maximum capacity. We demonstrate the utility of the log-normal distribution in two contexts: predicting the proportion of time traffic will exceed a given level (for service level agreement or link capacity estimation) and predicting 95th percentile pricing. We also show the log-normal distribution is a better predictor than Gaussian or Weibull distributions

Optical injection locking and optical-fiber data transmission by directly modulated wavelength tunable laser transmitters

Enhancement of the small- and large-signal modulation performance of wavelength tunable laser diode (TLD) transmitters under strong optical injection locking (OIL) is investigated numerically in back-to-back and optical-fiber transmission schemes. Our model is based on the spatiotemporal description of laser dynamics as due to the composite cavity design of TLDs, the usual rate equation formalism is not directly applicable. We demonstrate that TLD transmission strongly depends on wavelength tuning, which was investigated over a 21-nm range between 1529 and 1550 nm emission wavelengths. The best performance for both free-running (FR) and OIL TLDs is achieved at shorter wavelengths, 1529 nm for our device. Although in both cases this is due to larger differential material gain at shorter wavelengths, the underlying physics of the effect is completely different. For an FR TLD, it is the resonance oscillation frequency (ROF) that defines the best modulation speed, while for an OIL TLD, the achievable modulation speed depends on the cavity mode shift due to optical injection. Both the ROF and the cavity mode shift increase when the differential gain increases. However, the ROF is the device’s fixed parameter, while the cavity mode shift is defined by the OIL conditions, and thus, it can be optimized. The superior performance of the optical fiber digital data transmission with the OIL TLD is demonstrated at around 20-Gb/s modulation speed for standard fibers. This result is attributed to an enhanced modulation response and suppressed frequency chirping of the OIL TLD, and it is important for practical utilization of TLD transmitters

Carrier-induced refractive index change in InN

Rapid development of InN technology demands comprehensive assessment of the electronic and optoelectronic potential of this material. In this theoretical work the effect of free electrons on the optical properties of the wurtzite phase of InN is investigated. The blue shift of the optical absorption edge by the free-carrier band filling is known as the Burstein-Moss effect for which InN offers to be a very suitable candidate as has been recently demonstrated experimentally. Due to well known Kramers-Kronig relations, a change in absorption is accompanied by a change in the index of refraction. Considering n-type InN samples with free electron concentrations ranging from 5x10 17 to 5x1020 cm-3, and employing a nonlocal empirical pseudopotential band structure, it is shown that this leads to a few percent change of the index of refraction. These carrier-induced refractive index changes can be utilized in optical switches, futhermore it needs to be taken into account in the design of InN-based optical devices such as lasers and optical modulators. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA

Comparative analysis of zinc-blende and wurtzite GaN for full-band polar optical phonon scattering and negative differential conductivity

For high-power electronics applications, GaN is a promising semiconductor. Under high electric fields, electrons can reach very high energies where polar optical phonon (POP) emission is the dominant scattering mechanism. So, we undertake a full-hand analysis of POP scattering of conduction-hand electrons based on an empirical pseudopotential band structure. To uncover the directional variations, we compute POP emission rates along high-symmetry directions for the zinc-blende (ZB) crystal phase of GaN. We also compare the results with those of the wurtzite phase. In general, the POP scattering rates in the zinc-blende phase are lower than the wurtzite phase. Our analysis also reveals appreciable directional dependence, with the Γ-L direction of ZB GaN being least vulnerable to POP scattering, characterized by a scattering time of 11 fs. For both crystal phases, we consider the negative differential conductivity possibilities driven by the negative effective mass part of the band structure. According to our estimation, for the ZB phase the onset of this effect requires fields above ∼ 1 MV/cm. © 2000 American Institute of Physics

Electron momentum and energy relaxation rates in GaN and AlN in the high-field transport regime

Momentum and energy relaxation characteristics of electrons in the conduction band of GaN and AlN are investigated using two different theoretical approaches corresponding to two high electric-field regimes, one up to 1-2 MV/ cm values for incoherent dynamics, and the other at even higher fields for coherent dynamics where semiballistic and ballistic processes become important. For the former, ensemble Monte Carlo technique is utilized to evaluate these rates as a function of electron energy up to an electric-field value of 1 MV/cm (2 MV/cm) for GaN (AlN). Momentum and energy relaxation rates within this incoherent transport regime in the presence of all standard scattering mechanisms are computed as well as the average drift velocity as a function of the applied field. Major scattering mechanisms are identified as polar optical phonon (POP) scattering and the optical deformation potential (ODP) scattering. Roughly, up to fields where the steady-state electron velocity attains its peak value, the POP mechanism dominates, whereas at higher fields ODP mechanism takes over. Next, aiming to characterize coherent dynamics, the total out-scattering rate from a quantum state (chosen along a high-symmetry direction) due to these two scattering mechanisms are then computed using a first-principles full-band approach. In the case of POP scattering, momentum relaxation rate differs from the total out-scattering rate from that state; close to the conduction-band minimum, momentum relaxation rate is significantly lower than the scattering rate because of forward-scattering character of the intravalley POP emission., However, close to the zone boundary the difference between these two rates diminishes due to isotropic nature of intervalley scatterings. Finally, a simple estimate for the velocity-field behavior in the coherent transport regime is attempted, displaying a negative differential mobility due to the negative band effective mass along the electric-field direction