Laser diodes are the key components in a wide range of applications such as communications, medicine, and entertainment. Back-of-the-envelope calculation and trial-and-error experimentation have been the dominant methods for design and engineering of laser diodes. As the fabrication technology becomes more sophisticated and the material and geometrical configurations of laser diodes becomes more complex, however, this conventional approach is no longer enough for design optimization and timely engineering to specifications for advanced laser diodes. Hence, computer-aided modeling and simulation, commonplace in microelectronic and microwave design, are expected to play equally important roles in design and engineering of laser diodes, offering significant benefits in insight, efficiency, and cost.
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Ideally, a computer simulation should enable a designer to predict performance of a laser diode for a given set of design parameters, such as material composition, doping, and geometry. Computer-aided-design (CAD) software should also allow users to perform advanced tasks, such as design optimization and parameter extraction. In reality, however, the material and geometric properties of laser diodes are complicated, and underlying physical processes are complex and interrelated.
A configuration typical of a multiple-quantum-well distributed-feedback laser, for example, consists of a transverse cross section made of an undoped multiple-layer active region sandwiched between p- and n-doped cladding layers to provide confinements for both optical field and carriers. A ridge- or a buried-heterojunction structure can be used to achieve the lateral optical and carrier confinements. Along the laser cavity, a combination of corrugated and uncorrugated sections as well as phase-shifted regions provide the optical feedback, in addition to the possible reflections from the facets. There can be a variety of different longitudinal configurations along the laser cavity. For example, there could be multiple electrodes, multiple sections with different grating periods and coupling strengths, phase shifts, and integration with other passive and active devices.
The activity within a diode gets complicated, too. When biased above threshold, electrons and holes are injected through the p and n contacts and recombine in the intrinsic active region to produce photons via stimulated and spontaneous emission processes. The optical fields are confined transversely by the PIN structure perpendicular to, and the ridge/buried heterostructure parallel to, the epitaxial layers. Optical resonance is achieved through optical feedback along the laser cavity, which is normally dominated by a particular lasing mode.
During lasing, nonradiative recombination occurs, which consumes carriers and affects the static and dynamic performance of the laser diode. The injection current will also generate heat in the active region. This, in turn, will affect the radiative and nonradiative recombination and the optical confinement and resonance. Hence, to model and simulate a practical laser diode, the carrier and the optical and thermal processes and their interactions with each other must all be considered self-consistently in the three-dimensional (3-D) structure made of compound, complex semiconductor materials.
Balancing design considerations - For these reasons, rigorous physics-based modeling and simulation of laser diodes in a 3-D configuration is difficult and time-consuming. Moreover, there are many design and model parameters related to optical, carrier, and thermal aspects of a typical laser diode. Therefore, a designer usually concentrates on a small subset of these parameters to gain insight and to balance different design considerations. To cope with the complexity of the model and to meet different design requirements, a hierarchical modeling methodology has been developed and incorporated into a powerful and user-friendly CAD software environment.
The CAD environment consists of three functional blocks-the performance simulators, the design optimizer, and the parameter extractors. For the performance simulators, a graphical user interface allows designers to define transverse and longitudinal configurations of a laser diode by specifying the contacts, the layered structures, the material compositions, the doping levels, and the gratings (if any) for each of the longitudinal sections.
Subsequently, the transverse and lateral properties of the optical field, the carrier transport, and the heat transfer are considered by solving the corresponding governing equations over the two-dimensional (2-D) cross section based on the given structure and material data. The material properties, such as optical gain, refractive index, and radiative and nonradiative recombination rates in the context of bulk and multiple quantum wells, are modeled by using rigorous physics-based models. Hence, model parameters such as the equivalent electric circuit that accounts for the 2-D carrier transport, equivalent thermal circuit for the 2-D heat transfer and model index, and confinement factor for the 2-D optical modal field are extracted. Also extracted are material modal parameters for the optical gain, the optical losses, and the various nonradiative recombination rates (see Fig. 1). These design-dependent modal parameters will not only serve as parameters for the performance simulation in the next stage, but will also allow the user to evaluate a particular design without engaging in a full-scale laser simulation.
Performance simulation
For simulation of laser performance, a self-consistent and experimentally validated one-dimensional model is used. It takes into consideration variation distributions of the carrier, the photon, and temperature along the laser cavity. At this level, users can either accept the calculated modal parameters from the previous level without modification or modify some of these calculated parameters. As soon as the modal parameters are given, users can simulate static, dynamic, and noise characteristics in an efficient and flexible manner. For static analysis, for instance, output powers from both facets, external efficiencies, lasing wavelengths, side-mode suppression ratio, and so on are calculated and displayed as functions of injection current.
Furthermore, lasing spectrum, average carrier, photon, and temperature distributions along the laser cavity at different bias and heat-sink temperatures are also calculated and plotted. In a similar fashion, dynamic characteristics such as small-signal AM and FM modulation, intermodulation response, higher-order harmonic responses, and noise characteristics such as intensity and phase noises can be calculated and displayed. For large-signal dynamic simulation, on the other hand, a more-efficient zero-dimensional model can be used, in addition to the one-dimensional model, based on either standing-wave or traveling-wave formalism.
Parameter extraction
While the performance of a laser diode can be readily measured and characterized, much less is known about the geometrical and material parameters of a fabricated device. Lack of knowledge for some of the key design parameters can seriously hinder the ability to diagnose derivations due to uncertainties in device fabrication and consequently prevent further improvement in both design and fabrication. To overcome this difficulty, computer-aided parameter extraction can prove useful. Such parameter-extraction software is based on a local/global optimization routine, which is used to minimize the errors between the measured and the simulated spectra of the laser as well as other characteristics (see Fig. 2).
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Design optimization is an integral part of the CAD environment for laser diodes. In general, using local and global numerical-optimization algorithms in combination with simulation models, one can carry out design optimization.
REFERENCES
- X. Li, A. D. Sadovnikov, W.-P. Huang, and T. Makino, IEEE J. Quantum Electron. 34(9), 1545 (1998).
- X. Li and W.-P. Huang, IEEE J. Quantum Electron. 32(10), 1848 (1996).
- D. Sadovnikov, X. Li, and W.-P. Huang, IEEE J. Quantum Electron. 32(10), 1856 (1996).
WEI-PING HUANG is president of Apollo Photonics Inc., 5-145 Columbia Street West, Waterloo, Ontario, Canada N3L 3L2, and professor of electrical and computer engineering at McMaster University, Hamilton, Canada L8S 4L7. XUN * is a research assistant professor of electrical and computer engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.