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Token Bus Lan Performance : Modeling And Simulation, Ramesh Kurnool May 1990

Token Bus Lan Performance : Modeling And Simulation, Ramesh Kurnool

Theses

A simulation model based on CSIM, a process oriented simulated language, to analyze the performance of the Token Bus protocol is developed. Performance measures such as throughput, average delay and maximum delay per packet are presented. System performance is analyzed for different loads, number of stations, network lengths, different physical and logical distribution of the stations with packet length as a parameter. Previous studies were based on the delay-throughput analysis with no discussion on the effect of variation of the logical and physical distribution of the stations on the performance of the model which is done in the present thesis. …


Performance Evaluation And Comparison Of Ordinary, Adaptive And Exhaustive Service In The Token Ring Network, Darshakkumar J. Patel May 1990

Performance Evaluation And Comparison Of Ordinary, Adaptive And Exhaustive Service In The Token Ring Network, Darshakkumar J. Patel

Theses

In the token ring network different types of services gives different delay characteristics. Results to date have shown that in asymmetric traffic, exhaustive service gives more delay to lightly loaded stations where ordinary service wastes time in circulating the token after each transmission. In general, there is a need for more efficient service, which is compromised between ordinary and exhaustive service.

Ordinary and exhaustive service are analyzed in this thesis, and a new service, adaptive service, is proposed. By using timer and counter, adaptive service dynamically changes token holding time at the station. Different types of delay characteristics are derived …


Ellipsometric Analysis Of Computer Disk Structures, Ping He, Bhola N. De, Laing-Yao Chen, Yong Zhao, John A. Woollam, Mark Miller, Edward Simpson May 1990

Ellipsometric Analysis Of Computer Disk Structures, Ping He, Bhola N. De, Laing-Yao Chen, Yong Zhao, John A. Woollam, Mark Miller, Edward Simpson

Department of Electrical and Computer Engineering: Faculty Publications

Abstract: We have used variable angle spectroscopic ellipsometry (VASE) to analyze the materials surfaces and interfaces in multilayer sputtered media computer disks. Specifically, the system C/CoNiCr/Cr/NiP/Al has been investigated for layer thicknesses, interfacial and surface roughness, and radial and circumferential uniformity. By first characterizing the Cr/NiP/Al then CoNiCr/Cr/NiP/Al structures, we were able to fully characterize the complete disk structure. The interface width between the carbon layer and CoNiCr magnetic layer was determined to be approximately 260 Å. This is reasonable considering typical surface roughness present on magnetic disks, and that the carbon “fills” in this surface roughness. VASE is a …


The Parallel Implementation Of The Waveform Relaxation Method For The Simulation Of Structure-Preserved Power Systems, Marija D. Ilić, Mariesa Crow May 1990

The Parallel Implementation Of The Waveform Relaxation Method For The Simulation Of Structure-Preserved Power Systems, Marija D. Ilić, Mariesa Crow

Electrical and Computer Engineering Faculty Research & Creative Works

Several results pertaining to the partitioning of the waveform relaxation (WR) algorithm for dynamic simulation are presented. The WR algorithm is extended to a structure-preserving power system model in which the loads are retained. This results in a system of differential/algebraic equations (DAEs). Power systems are shown to exhibit several dynamic characteristics which make them suitable for simulation by the WR method. A heuristic method for determining a fault-dependent partitioning of the power system for parallel implementation is given.


Spontaneous Coherent Pulsations In Standing-Wave Laser Oscillators: Simplified Models, Lee W. Casperson, Manuela Fe Tarroja Apr 1990

Spontaneous Coherent Pulsations In Standing-Wave Laser Oscillators: Simplified Models, Lee W. Casperson, Manuela Fe Tarroja

Electrical and Computer Engineering Faculty Publications and Presentations

A series of simplifications and approximations is introduced into a recently described model for spontaneous pulsations in standing-wave laser oscillators. To the extent that these simplifications are valid they can lead to significant reductions in computation time and sometimes also to a better understanding of the relative importance of various physical effects. Of special interest is the number of spatial harmonics required to represent adequately the effects of longitudinal spatial hole burning. Other approximations investigated include neglect of spectral cross relaxation, neglect of multiple-energy-level equations, neglect of electric-field derivatives, and neglect of polarization derivatives. In addition, a detailed discussion is …


Analysis And Development Of A Switched Capacitor Power Supply, John Richard Hackworth Apr 1990

Analysis And Development Of A Switched Capacitor Power Supply, John Richard Hackworth

Electrical & Computer Engineering Theses & Dissertations

The combination of a switched capacitor network and switching power supply techniques can result in a transformer less regulated DC power supply that is small, relatively simple, and efficient. In addition, the output of such a system could be operated over a wide range of common mode voltages. Multiple switched capacitor supplies could be stacked to achieve voltage multiplication.

Although the output of a system of this type is a continuous function, the internal operation must be analyzed in finite time elements. This numerical analysis will be shown in both a mathematical approach and a computer model.


Hydrogenation Effects On Trap Related Conduction In Diamond, Linwood Cleveland Watkins Iii Apr 1990

Hydrogenation Effects On Trap Related Conduction In Diamond, Linwood Cleveland Watkins Iii

Electrical & Computer Engineering Theses & Dissertations

In this research work, the results of an experimental investigation on the electrical conduction mechanism in type Ιa and Ilb diamonds are presented. These results are compared with those of previous theoretical studies. The basic physical properties of diamond are discussed. Details of ohmic contact formation on diamond are presented.

The current-voltage characteristics revealed the presence of traps located below the Fermi level. The unfilled trap density was determined. The deep traps were further studied using spectroscopic photoconductivity measurements and the trap energy levels were determined.

The effects of hydrogenation on trap related conduction were studied subsequently. Hydrogenation was carried …


Pulsed Laser Annealing Of Gaas Implanted With Se And Si, Andrzej Rys, Yanan Shieh, Alvin Compann, Huade Yao, Ajit Bhat Apr 1990

Pulsed Laser Annealing Of Gaas Implanted With Se And Si, Andrzej Rys, Yanan Shieh, Alvin Compann, Huade Yao, Ajit Bhat

Department of Electrical and Computer Engineering: Faculty Publications

Carrier activation and mobility were studied by Raman spectroscopy and the Hall effect in pulsed laser annealed samples of GaAs implanted with doses of Si and Se from 2.2. x 1012 to 6.0 x 1014 cm-2. The samples were annealed using a pulsed XeCl excimer laser ( = 308 nm) and a pulsed dye laser (=728 nm) with energy densities from 0.06 to 0.9 J/cm2 and pulse durations of about 10 ns. Very high carrier concentrations of 3 x 1019 and 1.5 x 1019 cm-3 were obtained for the best n-type GaAs …


Experimental Studies Of Bulk Optically Controlled Gaas Switches Utilizing Fast Infrared Quenching, Michael S. Mazzola Apr 1990

Experimental Studies Of Bulk Optically Controlled Gaas Switches Utilizing Fast Infrared Quenching, Michael S. Mazzola

Electrical & Computer Engineering Theses & Dissertations

This dissertation describes some of the properties of copper-compensated, silicon-doped GaAs (Cu:Si:GaAs) with the purpose of demonstrating the feasibility of the Bulk Optically Controlled Switch (BOSS) concept. The BOSS concept involves the excitation of electrons or holes from selected deep centers in the band gap of a bulk Cu:Si:GaAs photoconductor. The conductivity of the Cu:Si:GaAs crystal can be increased or decreased on command by irradiating the crystal with laser light of different wavelengths in the infrared. Photoconductivities as large as 1 (Ω cm)-1 were measured to persist for microseconds after illumination by a 7 ns laser pulse with wavelength …


Effects Of Bandwidth‐Limiting Tuning Elements In Synchronously Pumped Mode‐Locked Lasers, Bahram Zandi, Lee W. Casperson, Duncan Leo Macfarlane Mar 1990

Effects Of Bandwidth‐Limiting Tuning Elements In Synchronously Pumped Mode‐Locked Lasers, Bahram Zandi, Lee W. Casperson, Duncan Leo Macfarlane

Electrical and Computer Engineering Faculty Publications and Presentations

A description of bandwidth‐limiting tuning filters is introduced into a semiclassical model for synchronously pumped mode‐locked dye lasers. The finite phase memory of the molecular wave functions is included as are the isotropic molecular distribution and the finite vibrational relaxation times. The new set of equations has been solved numerically using the best available values for the various parameters. The results have been compared with experimental data obtained using a rhodamine 6G dye laser, which is synchronously pumped using an acousto‐optically mode‐locked argon laser. Tuning element effects have been studied using two‐ and three‐plate birefringent filters and a tuning wedge, …


Pulse-Train Instabilities Of A Synchronously Pumped Mode-Locked Dye Laser: Experimental Phase Plots, Duncan Leo Macfarlane, Lee W. Casperson Mar 1990

Pulse-Train Instabilities Of A Synchronously Pumped Mode-Locked Dye Laser: Experimental Phase Plots, Duncan Leo Macfarlane, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

We present experimental phase plots of the pulse-train instability that occurs in synchronously pumped mode-locked dye lasers. From these plots we infer that the instability is of a quasi-periodic, nonlinear dynamical nature. Further, we note that the information lost in this two-dimensional representation is precisely the periodic-versus-erratic character and therefore is of considerable importance.


An Indirect Sensing Technique For Closed-Loop Diesel Fuel Quantity Control, Carl A. Maccarley, Walter D. Clark, Keay T. Nakae Feb 1990

An Indirect Sensing Technique For Closed-Loop Diesel Fuel Quantity Control, Carl A. Maccarley, Walter D. Clark, Keay T. Nakae

Electrical Engineering

Despite significant advances in electronic control technology applied to diesel engines, commercially available injection systems for automotive diesel engines remain limited by the open-loop mapping of the injection pump. An initial calibration is relied upon to translate a fuel delivery command to an actual fuel quantity. In practice, however, these two variables may be substantially different due to the effects of mechanical wear, repair, and the wide range of operating conditions. Possible ramifications of this discrepancy are excessive exhaust smoke due to overfueling, increased fuel consumption, degraded driveability, and poor idle characteristics. The major obstacle to closing the fuel control …


Processing Of One-Fiber Interferometric Fiber-Optic Sensor Signals, A. Tino Alavie, Barry Grossman, Michael Thursby Feb 1990

Processing Of One-Fiber Interferometric Fiber-Optic Sensor Signals, A. Tino Alavie, Barry Grossman, Michael Thursby

Electrical Engineering and Computer Science Faculty Publications

Recent research conducted in the Fiber -Optic Sensor Systems Laboratory at Florida Institute of Technology in fiber -optic strain sensors for use in smart structures has concentrated primarily on one -fiber interferometers. Sensors using this technique are of particular interest because they are rugged and provide reasonable strain sensitivities, typically a thousand times that of microbend sensors, while requiring only a single optical fiber. As in two -fiber interferometers, some method must be used to convert the sensor signal output to an absolute strain value. One technique is to provide active phase tracking to keep the sensor signal output at …


Fiber-Optic Sensor And Smart Structures Research At Florida Institute Of Technology, Barry Grossman, Tino Alavie, Fred Ham, Jorge Franke, Michael Thursby Feb 1990

Fiber-Optic Sensor And Smart Structures Research At Florida Institute Of Technology, Barry Grossman, Tino Alavie, Fred Ham, Jorge Franke, Michael Thursby

Electrical Engineering and Computer Science Faculty Publications

This paper discusses the fundamental issues being investigated by Florida Institute of Technology (F.I.T.) to implement the technology of smart structural systems for DoD, NASA, and commercial applications. Embedded sensors and actuators controlled by processors can provide a modification of the mechanical characteristics of composite structures to produce smart structures1-3. Recent advances in material science have spurred the development and use of composite materials in a wide range of applications from rotocraft blades and advanced tactical fighter aircraft to undersea and aerospace structures. Along with the advantages of an increased strength-to-weight ratio, the use of these materials has raised a …


The Magnetotransport Analysis Of Hemt Structures At Low Fields, Naghmeh Nouri Jan 1990

The Magnetotransport Analysis Of Hemt Structures At Low Fields, Naghmeh Nouri

Theses

On the basis of a study on numerous HEMT structures, a simple and useful technique was established for the characterization of 2DEG layers. This technique utilizes the magnetic field-dependence of the resistivity and Hall coefficient of the HEMT structure, to determine the values of the sheet density and mobility of 2DEG in the presence of other parallel conductive layers. This method of analysis was compared with previously used techniques such as Shubnikov-de Haas and the etch removal of the parallel conductive layers. Through this comparison and several measurements it was found that this procedure gives reproducible values for the 2DEG …


Adaptive Fir Digital Filter Design And Simulation In The Noise Reduction System, Jack Jiabing Pang Jan 1990

Adaptive Fir Digital Filter Design And Simulation In The Noise Reduction System, Jack Jiabing Pang

Theses

The adaptive FIR digital filter is designed to suppress the noise in the tape recording and audio communication systems. The cutoff frequency of the digital FIR filters can be varied adaptively depending on the energy level of the input signal. In audio communication, especially, in tape recording systems, the noise obviously gets much bigger, when the frequency band of the system increases. The noise reduction system makes use of a phenomenon called masking, where the big signal-to-noise ratio makes human ears not sensitive to the noise. In a constant interval time, the system detects the signal level and compares the …


Formation And Characterization Of Thin Superconducting Y-Ba-Cu-O Films, Gyusuk Kim Jan 1990

Formation And Characterization Of Thin Superconducting Y-Ba-Cu-O Films, Gyusuk Kim

Theses

Thin Y-Ba-Cu-O superconducting films were fabricated reproducibly on MgO (100) substrates by two different processes ; (1) deposition at a low substrate temperature fiom a single sintered YBa2Cu3.3Ox target using RF diode reactive sputtering followed by a post-annealing at around 830 ° C ; (2) deposition at the crystallization temperature under oxidizing atmosphere. The superconducting properties of films deposited by process (1) and (2) were studied. The variation of film composition and thickness as a function of distance from the target gas pressure and distance between target and substrate was studied. The Dependence of the …


Simulation And Design Of Field Emission Diode, Yun Yuan Jan 1990

Simulation And Design Of Field Emission Diode, Yun Yuan

Theses

A new generation of microelectronic devices utilizing vacuum field emission cathodes becomes surging interest in recent years. This paper concentrates on the study of the field emission diode — a basic vacuum microelectronic device. The field emission efficiency, current spatial distribution and time dispersion of conical tips and wedges of various geometrical shapes are compared and calculated by analytical methods and computer simulations. Two field emitter heating effects, namely the Joule heating and Nottingham effect, are discussed theoretically. All the simulation results in this paper are performed on 386 based personal computer. The limiting memory space of PC induced simulation …


Sputter Deposition And Characterization Of High Tc Superconducting Thin Films, Vipulkumar Patel Jan 1990

Sputter Deposition And Characterization Of High Tc Superconducting Thin Films, Vipulkumar Patel

Theses

Preparation of thin superconducting films by direct RF sputter deposition on Si, MgO, SrTiO3 and quartz substrates and silver and Sl3N4 buffer layers (deposited on silicon substrates) was studied. To study resistance versus temperature characteristics of thin films and bulk materials, a computerized measurement system was developed. 1-1.5 pm thick YBaCuO films deposited on Si3N4/Si were found to be insulating with room temperature resistance higher than 236KΩ, while films with Ag as a buffer and/or a passivating layer exhibited metallic behavior with room temperature resistances lower than 700mΩ. The area directly under the 2.25 inches …


Self-Mode-Locking Of A Semiconductor Laser Using Positive Feedback, Dennis J. Derickson, R. J. Helkey, A. Mar, P. A. Morton, J. E. Bowers Jan 1990

Self-Mode-Locking Of A Semiconductor Laser Using Positive Feedback, Dennis J. Derickson, R. J. Helkey, A. Mar, P. A. Morton, J. E. Bowers

Electrical Engineering

A new mode-locking technique, self-mode-locking, is described which uses the detected optical pulses from the mode-locked laser as the active driving source. This technique forms narrow-width mode-locked optical pulses at low repetition rates without the use of a microwave synthesizer


The Extraction Of The Equivalent Circuit Parameters Of Surface Acoustic Wave Resonators, Brent H. Horine Jan 1990

The Extraction Of The Equivalent Circuit Parameters Of Surface Acoustic Wave Resonators, Brent H. Horine

Retrospective Theses and Dissertations

The application of the Electronic Industries Association suggested standard, EIA-512 [1], has been successfully applied to quartz crystal resonators for extraction of the equivalent circuit model parameters. This technique has been shown to be very successful in the operation range to several hundred megahertz. This same technique is proposed to be applied to many differing types of resonators through the full spectrum of frequencies. This thesis will discuss measurement and testing of Surface Acoustic Wave (Saw) resonators at the higher frequencies. The packaging configuration in conjunction with SAW devices can lead to significant parasitic effects. In order to successfully extract …


A Model Of Dc Glow Discharges With Abnormal Cathode Fall, Karl H. Schoenbach, Hao Chen, G. Schaefer Jan 1990

A Model Of Dc Glow Discharges With Abnormal Cathode Fall, Karl H. Schoenbach, Hao Chen, G. Schaefer

Bioelectrics Publications

A model for an abnormal glow discharge, including a self‐consistent analysis of the cathode fall, was developed. It combines microscopic particle simulation by means of Monte Carlo methods with a fluid model of the gas discharge. The model allows calculations of the steady‐state electrical field distribution, the charged‐particle densities, and the current densities along the axis of the discharge. The model was used to simulate a glow discharge in 80% He and 20% SF6 at a pressure of 8 Torr with a current density of 1 A/cm2. The computed discharge voltage agrees well with measured values. The …


Design Of Robust Controllers For Gas Turbine Engines, David E. Moellenhoff, Vittal S. Rao, Charles A. Skarvan Jan 1990

Design Of Robust Controllers For Gas Turbine Engines, David E. Moellenhoff, Vittal S. Rao, Charles A. Skarvan

Electrical and Computer Engineering Faculty Research & Creative Works

This paper describes robust controller design methodologies for gas turbine engines. A linear state variable model for the engine is derived using partial derivatives. The Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) and the Parameter Robust Linear Quadratic Gaussian (PRLQG) robust controller design methodologies have been used to design a controller for gas turbine engines. A new method is proposed by combining the features of LQG/LTR and PRLQG methods and yields good robustness properties with respect to both unstructured uncertainties in the frequency domain and structured parameter variations in the time domain. The new procedure is illustrated with the …


Boundary Element-Image Method Approach To Seismic Modeling, Richard E. Dubroff Jan 1990

Boundary Element-Image Method Approach To Seismic Modeling, Richard E. Dubroff

Electrical and Computer Engineering Faculty Research & Creative Works

The Boundary Element-Image Method is Proposed as a Method for Generating Synthetic Seismograms in a System of Piecewise Homogeneous Layers. the Present Approach Uses the Boundary Conditions Explicitly in Order to Develop a System of Integral Equations. Although This Method Can Be Formulated in a General Way, Specific Computational Advantages Occur When the Basis and Testing Functions Are Chosen as Harmonically Related Complex Sinusoids. -From Authors


The Parallel Implementation Of The Waveform Relaxation Method For Transient Stability Simulations, Marija D. Ilić, Mariesa Crow Jan 1990

The Parallel Implementation Of The Waveform Relaxation Method For Transient Stability Simulations, Marija D. Ilić, Mariesa Crow

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, the authors extend the results of their earlier paper on waveform relamtion (WR), which is a parallel algorithm for transient stability analysis. The WR algorithm is extended to a structure-preserving power system model in which the loads are retained. This results in a system of differential/ algebraic equations (DAEs). Power systems exhibit several unique dynamic properties which may be exploited in an advantageous manner by the WR algorithm. This leads to a greater computational efficiency than most other direct methods of simulation. This paper presents several theoretical results as well as computational results on parallel implementation.


Principles And Clinical Applications Of Magnetic Resonance, Rao P. Gullapalli, Teresa T. Evans, Roger M. Hawk Jan 1990

Principles And Clinical Applications Of Magnetic Resonance, Rao P. Gullapalli, Teresa T. Evans, Roger M. Hawk

Journal of the Arkansas Academy of Science

A review is presented which covers the basic theory of nuclear magnetic resonance (NMR) with regard to angular momentum, magnetic moments, and the classical mechanical description of the NMR experiment. Longitudinal (T,) and Transverse (T2) relaxation times are defined as well as the basic pulse sequences used for their measurement. In particular, the 180°-t-90° and the Hahn Spin Echo pulse sequences are described in detail. Basic Magnetic Resonance Imaging (MRI) theory is discussed with regard to slice selection, frequency encoding, and phase encoding to define the imaged volume element. The equations defining the amount of Tt , T2 , and …


Transistor-Based Measurements Of Electron Injection Currents In P-Type Gaas Doped 1018–1020 Cm-3, M. E. Klausmeier-Brown, M. R. Melloch, Mark S. Lundstrom Jan 1990

Transistor-Based Measurements Of Electron Injection Currents In P-Type Gaas Doped 1018–1020 Cm-3, M. E. Klausmeier-Brown, M. R. Melloch, Mark S. Lundstrom

Department of Electrical and Computer Engineering Faculty Publications

Measurements of electron currents injected into p+‐GaAs are presented for molecular beam epitaxially grown material doped from 2×1018 to 8×1019 cm−3 with Be. The collector current versus base‐emitter voltage characteristics of n‐p+‐n GaAs homojunction bipolar transistors are analyzed, and the results are interpreted in terms of the quantity (n0Dn), where n0 is the equilibrium minority‐carrier concentration and Dn is the minority‐carrier diffusion coefficient. The results are consistent with earlier measurements of (n0Dn) made using metalorganic chemical vapor deposited p+‐n GaAs solar …


High‐Efficiency Al0.22ga0.78as Solar Cells Grown By Molecular Beam Epitaxy, Michael R. Melloch, S. P. Tobin, C. Bajgar, A. Keshavarzi, T. B. Stellwag, G. B. Lush, Mark S. Lundstrom, K. Emery Jan 1990

High‐Efficiency Al0.22ga0.78as Solar Cells Grown By Molecular Beam Epitaxy, Michael R. Melloch, S. P. Tobin, C. Bajgar, A. Keshavarzi, T. B. Stellwag, G. B. Lush, Mark S. Lundstrom, K. Emery

Department of Electrical and Computer Engineering Faculty Publications

The quality of pn junction photodetectors made of Al0.2Ga0.8As has been investigated as a first step in the optimization of tandem solar cells. We have obtained 1 sun AM1.5 efficiencies of 16.1% for 0.25 cm2 Al0.22Ga0.78As solar cellsfabricated from molecular beam epitaxy (MBE) material. This efficiency is 3.2 percentage points higher than the previously best reported efficiency of 12.9% for an Al0.2Ga0.8As solar cell fabricated from MBE material.


Surface Passivation Effects Of As2s3 Glass On Self‐Aligned Algaas/Gaas Heterojunction Bipolar Transistors, H. L. Chuang, M. S. Carpenter, Michael R. Melloch, Mark S. Lundstrom, E. Yablonovitch, T. J. Gmitter Jan 1990

Surface Passivation Effects Of As2s3 Glass On Self‐Aligned Algaas/Gaas Heterojunction Bipolar Transistors, H. L. Chuang, M. S. Carpenter, Michael R. Melloch, Mark S. Lundstrom, E. Yablonovitch, T. J. Gmitter

Department of Electrical and Computer Engineering Faculty Publications

A recently developed As2S3 chemical treatment was used to passivate the perimeters of self‐aligned heterojunction bipolar transistors (HBTs). The As2S3chemical treatment significantly lowered the base current resulting in a two order of magnitude reduction in the collector current density at which dc current gain was observed (β=1). No degradation with time has been observed in the electrical characteristics of the chemically treated HBTs. This absence of degradation is attributed to the impermeability to oxygen of the As2S3 glass which coats the perimeter of the HBT after chemical treatment.


Orientation-Dependent Perimeter Recombination In Gaas Diodes, T. B. Stellwag, Michael R. Melloch, Mark S. Lundstrom, M. S. Carpenter, R. F. Pierret Jan 1990

Orientation-Dependent Perimeter Recombination In Gaas Diodes, T. B. Stellwag, Michael R. Melloch, Mark S. Lundstrom, M. S. Carpenter, R. F. Pierret

Department of Electrical and Computer Engineering Faculty Publications

Perimeter recombination currents affect the performance of GaAs-based devices such as solar cells, heterojunction bipolar transistors, and injection lasers. We report that the n SEf 2 perimeter recombination current has a strong orientation dependence. More than a factor of five variation in the surface recombination current at mesa-etched edges has been observed. These results suggest that with proper device design, perimeter recombination currents could be substantially reduced.