There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

We present a comprehensive and up-to-date compilation of band parameters for all of the nitrogen-containing III–V semiconductors that have been investigated to date. The two main classes are: (1) “conventional” nitrides (wurtzite and zinc-blende GaN, InN, and AlN, along with their alloys) and (2) “dilute” nitrides (zinc-blende ternaries and quaternaries in which a relatively small fraction of N is added to a host III–V material, e.g., GaAsN and GaInAsN). As in our more general review of III–V semiconductor band parameters [I. Vurgaftman et al., J. Appl. Phys. 89, 5815 (2001)], complete and consistent parameter sets are recommended on the basis of a thorough and critical review of the existing literature. We tabulate the direct and indirect energy gaps, spin-orbit and crystal-field splittings, alloy bowing parameters, electron and hole effective masses, deformation potentials, elastic constants, piezoelectric and spontaneous polarization coefficients, as well as heterostructure band offsets. Temperature an...

Band parameters for nitrogen-containing semiconductors

Light-Emitting Diodes. (Monographs in Electrical and Electronic Engineering.) By A. A. Bergh and P. J. Dean. Pp. viii+591. (Clarendon: Oxford; Oxford University: London, 1976.) £22.

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Light-emitting diodes

An electrically pumped light source on silicon is a key element needed for photonic integrated circuits on silicon. Here we report an electrically pumped AlGaInAs-silicon evanescent laser architecture where the laser cavity is defined solely by the silicon waveguide and needs no critical alignment to the III-V active material during fabrication via wafer bonding. This laser runs continuous-wave (c.w.) with a threshold of 65 mA, a maximum output power of 1.8 mW with a differential quantum efficiency of 12.7 % and a maximum operating temperature of 40 degrees C. This approach allows for 100's of lasers to be fabricated in one bonding step, making it suitable for high volume, low-cost, integration. By varying the silicon waveguide dimensions and the composition of the III-V layer, this architecture can be extended to fabricate other active devices on silicon such as optical amplifiers, modulators and photo-detectors.

Electrically pumped hybrid AlGaInAs-silicon evanescent laser

The efficiency droop in GaInN∕GaN multiple-quantum well (MQW) light-emitting diodes is investigated. Measurements show that the efficiency droop, occurring under high injection conditions, is unrelated to junction temperature. Furthermore, the photoluminescence output as a function of excitation power shows no droop, indicating that the droop is not related to MQW efficiency but rather to the recombination of carriers outside the MQW region. Simulations show that polarization fields in the MQW and electron blocking layer enable the escape of electrons from the MQW region and thus are the physical origin of the droop. It is shown that through the use of proper quaternary AlGaInN compositions, polarization effects are reduced, thereby minimizing droop and improving efficiency.

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Origin of efficiency droop in GaN-based light-emitting diodes

Nitride-based light-emitting diodes (LEDs) suffer from a reduction (droop) of the internal quantum efficiency with increasing injection current. This droop phenomenon is currently the subject of intense research worldwide, as it delays general lighting applications of GaN-based LEDs. Several explanations of the efficiency droop have been proposed in recent years, but none is widely accepted. This feature article provides a snapshot of the present state of droop research, reviews currently discussed droop mechanisms, contextualizes them, and proposes a simple yet unified model for the LED efficiency droop.

Illustration of LED efficiency droop (details in Fig. 13).

Efficiency droop in nitride-based light-emitting diodes

Preface. List of Contributors. Part 1 Material Properties. 1 Introduction (Joachim Piprek). 1.1 A Brief History. 1.2 Unique Material Properties. 1.3 Thermal Parameters. References. 2 Electron Bandstructure Parameters (Igor Vurgaftman and Jerry R. Meyer). 2.1 Introduction. 2.2 Band Structure Models. 2.3 Band Parameters. 2.4 Conclusions. References. 3 Spontaneous and Piezoelectric Polarization: Basic Theory vs. Practical Recipes (Fabio Bernardini). 3.1 Why Spontaneous Polarization in III-V Nitrides? 3.2 Theoretical Prediction of Polarization Properties in AlN, GaN and InN. 3.3 Piezoelectric and Pyroelectric Effects in III-V Nitrides Nanostructures. 3.4 Polarization Properties in Ternary and Quaternary Alloys. 3.5 Orientational Dependence of Polarization. References. 4 Transport Parameters for Electrons and Holes (Enrico Bellotti and Francesco Bertazzi). 4.1 Introduction. 4.2 Numerical Simulation Model. 4.3 Analytical Models for the Transport Parameters. 4.4 GaN Transport Parameters. 4.5 AlN Transport Parameters. 4.6 InN Transport Parameters. 4.7 Conclusions. References. 5 Optical Constants of Bulk Nitrides (Rudiger Goldhahn, Carsten Buchheim, Pascal Schley, Andreas Theo Winzer, and Hans Wenzel). 5.1 Introduction. 5.2 Dielectric Function and Band Structure. 5.3 Experimental Results. 5.4 Modeling of the Dielectric Function. References. 6 Intersubband Absorption in AlGaN/GaN Quantum Wells (Sulakshana Gunna, Francesco Bertazzi, Roberto Paiella, and Enrico Bellotti). 6.1 Introduction. 6.2 Theoretical Model. 6.3 Numerical Implementation. 6.4 Absorption Energy in AlGaN-GaN MQWs. 6.5 Conclusions. References. 7 Interband Transitions in InGaN Quantum Wells (Jorg Hader, Jerome V. Moloney, Angela Thranhardt, and Stephan W. Koch). 7.1 Introduction. 7.2 Theory. 7.3 Theory-Experiment Gain Comparison. 7.4 Absorption/Gain. 7.5 Spontaneous Emission. 7.6 Auger Recombinations. 7.7 Internal Field Effects. 7.8 Summary. References. 8 Electronic and Optical Properties of GaN-based Quantum Wells with (1010) Crystal Orientation (Seoung-Hwan Park and Shun-Lien Chuang). 8.1 Introduction. 8.2 Theory. 8.2.1 Non-Markovian gain model with many-body effects. 8.3 Results and Discussion. 8.4 Summary. References. 9 Carrier Scattering in Quantum-Dot Systems (Frank Jahnke). 9.1 Introduction. 9.2 Scattering Due to Carrier-Carrier Coulomb Interaction. 9.3 Scattering Due to Carrier-Phonon Interaction. 9.4 Summary and Outlook. References. Part 2 Devices. 10 AlGaN/GaN High Electron Mobility Transistors (Tomas Palacios and Umesh K. Mishra). 10.1 Introduction. 10.2 Physics-based Simulations. 10.3 Conclusions. References. 11 Intersubband Optical Switches for Optical Communications (Nobuo Suzuki). 11.1 Introduction. 11.2 Physics of ISBT in Nitride MQWs. 11.3 Calculation of Absorption Spectra. 11.4 FDTD Simulator for GaN/AlGaN ISBT Switches. References. 12 Intersubband Electroabsorption Modulator (Petter Holmstrom). 12.1 Introduction. 12.2 Modulator Structure. 12.3 Model. 12.4 Results. 12.5 Summary. References. 13 Ultraviolet Light-Emitting Diodes (Yen-Kuang Kuo, Sheng-Horng Yen, and Jun-Rong Chen). 13.1 Introduction. 13.2 Device Structure. 13.3 Physical Models and Parameters. 13.4 Comparison Between Simulated and Experimental Results. 13.5 Performance Optimization. 13.6 Conclusion. References. 14 Visible Light-Emitting Diodes (Sergey Yu. Karpov). 14.1 Introduction. 14.2 Simulation Approach and Materials Properties. 14.3 Device Analysis. 14.4 Novel LED Structures. 14.5 Conclusion. References. 15 Simulation of LEDs with Phosphorescent Media for the Generation of White Light (Norbert Linder, Dominik Eisert, Frank Jermann, and Dirk Berben). 15.1 Introduction. 15.2 Requirements for a Conversion LED Model. 15.3 Color Metrics for Conversion LEDs. 15.4 Phosphor Model. 15.5 Simulation Examples. 15.6 Conclusions. References. 16 Fundamental Characteristics of Edge-Emitting Lasers (Gen-ichi Hatakoshi). 16.1 Introduction. 16.2 Basic Equations for the Device Simulation. 16.3 Simulation for Electrical Characteristics and Carrier Overflow Analysis. 16.4 Perpendicular TransverseMode and Beam Quality Analysis. 16.5 Thermal Analysis. 16.6 Conclusions. References. 17 Resonant Internal Transverse-Mode Coupling in InGaN/GaN/AlGaN Lasers (Gennady A. Smolyakov and Marek Osinski). 17.1 Introduction. 17.2 Internal Mode Coupling and the Concept of "Ghost Modes." 17.3 Device Structure and Material Parameters. 17.4 Calculation Technique. 17.5 Results of Calculations. 17.6 Discussion and Conclusions. References. 18 Optical Properties of Edge-Emitting Lasers: Measurement and Simulation (Ulrich T. Schwarz and Bernd Witzigmann). 18.1 Introduction. 18.2 Waveguide Mode Stability. 18.3 Optical Waveguide Loss. 18.4 Mode Gain Analysis. 18.5 Conclusion. References. 19 Electronic Properties of InGaN/GaN Vertical-Cavity Lasers (Joachim Piprek, Zhan-Ming Li, Robert Farrell, Steven P. DenBaars, and Shuji Nakamura). 19.1 Introduction to Vertical-Cavity Lasers. 19.2 GaN-based VCSEL Structure. 19.3 Theoretical Models and Material Parameters. 19.4 Simulation Results and Device Analysis. 19.5 Summary. References. 20 Optical Design of Vertical-Cavity Lasers (Wlodzimierz Nakwaski, Tomasz Czyszanowski, and Robert P. Sarzala). 20.1 Introduction. 20.2 The GaN VCSEL Structure. 20.3 The Scalar Optical Approach. 20.4 The Vectorial Optical Approach. 20.5 The Self-consistent Calculation Algorithm. 20.6 Simulation Results. 20.7 Discussion and Conclusions. References. 21 GaN Nanowire Lasers (Alexey V. Maslov and Cun-Zheng Ning). 21.1 Introduction. 21.2 Nanowire Growth and Characterization. 21.3 Nanowire Laser Principles. 21.4 Anisotropy of Material Gain. 21.5 Guided Modes. 21.6 Modal Gain and Threshold. 21.7 Conclusion. References. Index.

Nitride semiconductor devices : principles and simulation

I. Fundamentals 1. Introduction to Semiconductors 2. Electron Energy Bands 3. Carrier Transport 4. Optical Waves 5. Photon Generation 6. Heat Generation and Dissipation II. Devices 7. Edge-Emitting Laser 8. Vertical- Cavity Lasers 9. Nitride Light Emitters 10. Electroabsorption Modulator 11. Amplification Photodetector

Semiconductor Optoelectronic Devices: Introduction to Physics and Simulation

The authors analyse the performance and device physics of nitride laser diodes that exhibit the highest room-temperature continuous-wave output power The analysis is based on advanced laser simulation The laser model self-consistently combines band structure and free-carrier gain calculations with two-dimensional simulations of wave guiding, carrier transport and heat flux Material parameters used in the model are carefully evaluated Excellent agreement between simulations and measurements is achieved The maximum output power is limited by electron leakage into the p-doped ridge Leakage escalation is caused by strong self-heating, gain reduction and elevated carrier density within the quantum wells Built-in polarisation fields are found to be effectively screened at high-power operation Improved heat-sinking is predicted to allow for a significant increase of the maximum output power

Joachim Piprek

Papers

Origin of efficiency droop in GaN-based light-emitting diodes

Efficiency droop in nitride-based light-emitting diodes

Nitride semiconductor devices : principles and simulation

Semiconductor Optoelectronic Devices: Introduction to Physics and Simulation

Physics of high-power InGaN/GaN lasers