Physical Layer Modeling and Optimization of Silicon Photonic Interconnection Networks

The progressive blooming of silicon photonics technology (SiP) has indicated that optical interconnects may substitute the electrical wires for data movement over short distances in the future. Silicon Photonics platform has been the subject of intensive research for more than a decade now and its prospects continue to emerge as it enjoys the maturity of CMOS manufacturing industry. SiP foundries all over the world and particularly in the US (AIM Photonics) have been developing reliable photonic design kits (PDKs) that include fundamental SiP building blocks such as wavelength selective modulators and tunable filters. Microring resonators (MRR) are hailed as the most compact devices that can perform both modulation and demodulation in a wavelength division multiplexed (WDM) transceiver design. Although the use of WDM can reduce the number of fibers carrying data, it also makes the design of transceivers challenging. It is probably acceptable to achieve compactness at the expense of somewhat higher transceiver cost and power consumption. Nevertheless, these two metrics should remain close to their roadmap values for Datacom applications. An increase of an order of magnitude is clearly not acceptable. For example costs relative to bandwidth for an optical link in a data center interconnect will have to decrease from the current $5/Gbps down to <$1/Gbps. Additionally, the transceiver itself must remain compact. The optical properties of SiP devices are subject to various design considerations, operation conditions, and optimization procedures. In this thesis, the general goal is to develop mathematical models that can accurately describe the thermo-optical and electro-optical behavior of individual SiP devices and then use these models to perform optimization on the parameters of such devices to maximize the capabilities of photonic links or photonic switch fabrics for datacom applications. In Chapter 1, Introduction, we first provide an overview of the current state of the optical transceivers for data centers and datacom applications. Four main categories for optical interfaces (Pluggable transceivers, On-board optics, Co-packaged optics, monolithic integration) are briefly discussed. The structure of a silicon photonic link is also briefly introduced. Then the direction is shifted towards optical switching technologies where various technologies such as free space MEMS, liquid crystal on silicon (LCOS), SOA-based switches, and silicon-based switches are explored. In Chapter 2, Silicon Photonic Waveguides, we present an extensive study of the silicon-on-insulator (SOI) waveguides that are the basic building blocks of all of the SiP devices. The dispersion of Si and SiO2 is modeled with Sellmiere equation for the wavelength range 1500–1600 nm and then is used to calculate the TE and TM modes of a 2D slab waveguide. There are two reasons that 2D waveguides are studied: first, the modes of these waveguides have closed form solutions and the modes of 3D waveguides can be approximated from 2D waveguides based on the effective index method. Second, when the coupling of waveguides is studied and the concept of curvature function of coupling is developed, the coupled modes of 2D waveguides are used to show that this approach has some inherent small error due to the discretization of the nonuniform coupling. This chapter finishes by describing the coefficients of the sensitivity of optical modes of the waveguides to the geometrical and material parameters. Perturbation theory is briefly presented as a way to analytically examine the impact of small perturbations on the effective index of the modes. In Chapter 3, Compact Modeling Approach, the concept of scattering matrix of a multi-port silicon photonic device is presented. The elements of the S-matrix are complex numbers that relate the amplitude and phase relationships of the optical models in the input and output ports. Based on the scattering matrix modeling of silicon photonics devices, two methods of solving photonic circuits are developed: the first one is based on the iteration for linear circuits. The second approach is based on the construction of an equivalent signal flow graph (SFG) for the circuit. We show that the SFG approach is very efficient for circuits involving microring resonator structures. Not only SFG can provide the solution for the transmission, it also provides the signal paths and the closed-form solution based on the Mason’s graph formula. We also show how the SFG method can be utilized to formulate the backscattering effects inside a ring resonator. In Chapter 4, Scalability of Silicon Photonic Switch Fabrics, we develop the models for electro-optic Mach-Zehnder switch elements (2×2). For the electro-optic properties, the empirical Soref’s equations are used to characterize how the loss and index of silicon changes when the charge carrier density is changed. We then use our photonic circuit solver based on the iteration method to find accurate result of light propagation in large-scale switch topologies (e.g. 4×4, and 8×8). The concept of advanced path mapping based on physical layer evaluation of the switch fabric is introduced and used to develop the optimum routing tables for 4×4 and 8×8 Benes switch topologies. In Chapter 5, Design space of Microring Resonators, we introduce the concept of curvature function of coupling to mathematically characterize the coupling coefficient of a ring resonator to a waveguide as a function of the geometrical parameters (ring radius, coupling gap, width and height of waveguides) and the wavelength. Extensive 2D and 3D FDTD simulations are carried out to validate our modeling approach. Experimental demonstrations are also used to not only further validate our modeling of coupling, but also to extract an empirical power-law model for the bending loss of the ring resonators as a function the radius. By combining these models, we for the first time present a full characterization of the design space of microring resonators. Moreover, the value of this discussion will be further apparent when the scalability of a silicon photonic link is studied. We will show that the FSR of the rings determines the optical bandwidth but it also impacts the properties of the ring resonators. In Chapter 6, Thermo-optic Efficiency of Microheaters, we develop analytical models for the thermo-optic properties of SiP waveguides. For the thermo-optic properties, the concept of thermal impulse response is mathematically developed for integrated micro-heaters. The thermal impulse response is a key function that determines the tradeoff between heating efficiency and heating speed (thermal bandwidth), as well as allows us to predict the pulse-width-modulation (PWM) optical response of the heater-waveguide system. One of the motivations behind this study was to find the highest possible efficiency for thermal tuning of microring resonators to use it in the evaluation of the energy consumption of a photonic link. The results indicate 2 nm/mW which is in agreement with the trends that we see in the literature. In Chapter 7, Crosstalk Penalty, we theoretically and experimentally investigate the optical crosstalk effects in microring-based silicon photonic interconnects. Both inter-channel crosstalk and intra-channel crosstalk are investigated and approximate equations are developed for their corresponding power penalties. Inclusion of the inter-channel crosstalk is an important part of our final analysis of a silicon photonic link. In Chapter 8, Scalability of Silicon Photonic Links, we present the analysis of a WDM silicon photonics point-to-point link based on microring modulators and microring wavelength filters. Our approach is based on the power penalty analysis of non-return-to-zero (NRZ) signals and Gaussian noise statistics. All the necessary equations for the optical power penalty calculations are presented for microring modulators and filters. The first part of the analysis is based on various ideal assumptions which lead to a maximum capacity of 2.1 Tb/s for the link. The second part of the analysis is carried out with more realistic assumptions on the photonic elements in the link, culminating in a maximum throughput of 800 Gb/s. We also provide estimations of the energy/bit metric of such links based on the optimized models of electronic circuits in 65 nm CMOS technology

Experimental characterization of CMOS photonic devices

Current electrical interconnects in super-computers and high-performance processors present a bottleneck in terms of bandwidth and power consumption. A migration to the optical domain in order to cope with the connectivity between units (e.g. CPUs and memory) is needed to overcome these issues. Zero-change CMOS photonic devices represent a very attractive solution to the design of optical on-chip links. This approach makes use of up-to-date CMOS process, having enormous benefits regarding integration with state-of-the-art electronics. Designing and characterizing zero-change CMOS photonic devices is key for the future of optical interconnects. This thesis presents the characterization both theoretical and experimental of a Silicon-Germanium ring resonator modulator. It represents the first ever depletion modulator up to the date using SiGe as an active material. Moreover, it shows the best wavelength shift reported so far for zero-change CMOS modulators, enhancing the shift of a pure Silicon device. The demonstration of this device begins a new era of optical modulator designs using silicon-germanium to enhance modulation efficiency, and therefore reduce power consumption.Las interconexiones eléctricas de supercomputadores y de microprocesadores de alto rendimiento representan actualmente un bottleneck en cuanto a ancho de banda y potencia consumida se refiere. Se necesita una migración hacia el dominio óptico, para realizar la conectividad entre las diferentes unidades (por ejemplo CPU y memoria), con tal de superar estas limitaciones. Los dispositivos fabricados con la tecnología zero-change CMOS representan una solución muy atractiva para el diseño de links ópticos dentro de un chip. Esta técnica utiliza procesos CMOS actuales, beneficiándose así enormemente de la fácil integración con dispositivos electrónicos actuales. Diseñar y caracterizar dispositivos trabajando con zero-change CMOS es clave para el futuro de las interconexiones ópticas. Esta tesis presenta la caracterización tanto teórica como experimental de un modulador tipo ring resonator de Silicon-Germanium. Es el primer modulador de depletion utilizando SiGe como un material activo. Además, este dispositivo muestra el desplazamiento en longitud de onda más grande publicado hasta la fecha, comparándolo con otros moduladores zero-change CMOS, mejorando el desplazamiento de dispositivos de puro silicio. La demostración de este dispositivo comienza una nueva era de diseños de moduladores ópticos que utilizaran silicon-germanium para mejorar la eficiencia de modulación, y por lo tanto reducir el consumo de potencia.Les interconnexions elèctriques de super-computadors i microprocessadors de alt rendiment representen actualment un coll d'ampolla en quant a ample de banda i potència consumida. Es necessita una migració cap al domini òptic, per realitzar la connectivitat entre les diferents unitats (per exemple entre la CPU i la memòria), per tal de superar aquests problemes. Els dispositius fabricats sota zero-change CMOS technology representen una solució molt atractiva al disseny de links òptics dins d'un xip. Aquesta tècnica utilitza processos CMOS actuals, tenint enormes beneficis en quant a la integració amb dispositius electrònics actuals. Dissenyar i caracteritzar dispositius treballant amb zero-change CMOS és clau pel futur de les interconnexions òptiques del futur. Aquesta tesi presenta la caracterització tant teòrica com experimental d'un modulador ring resonator de Silicon-Germanium. Representa el primer modulador de depletion usant SiGe con un material actiu. A més a més, aquest dispositiu mostra el desplaçament en longitud d'ona més gran publicat fins ara en qualsevol dispositiu zero-change CMOS, millorant el desplaçament de dispositius de pur silici. La demostració d'aquest dispositiu comença una nova era de dissenys de moduladors òptics que utilitzaran silicon-germanium per millorar l'eficiència de modulació i per tant per reduir el consum de potència

Integrated fast optical modulators

Over the past two decades, the demand for network interconnects, for both communication systems and intra/on-chip data links, increased in terms of capacities and bandwidth. To transmit digital signal over an optical traveling wave, the optical wave should be modulated using the digital electronic signal. An electro-optical modulator is responsible for switching the optical wave to pass or block it depending on the information digital signal. Such modulators are the key components in any optical communication system, since they convert the digital electronic signals to optical signals to travel over the optical fibers for long distances with minor losses. On chip level, copper interconnects are the bottleneck for the next generation technology because of their losses, dispersion, and speed. This has paved the way for replacing them with optical interconnects. Electro-optical modulators are the workhorses of such interconnects. To achieve the goal of replacing electrical interconnects with optical ones, a high level of integration should be accomplished. This can be only achieved by combining both optical and electrical components on the same substrate. Thus, silicon photonics is being a prominent candidate for this technology because of its low cost, and CMOS compatibility. Silicon as active material for optical modulation has a lot of limitations such as weak electro-optic effects and slow response of plasma dispersion effect. This raised the necessity for studying other novel alternative materials such as organic polymers, indium-tin-oxide (ITO), and vanadium dioxide. In this dissertation, novel electro-optical modulators, based on different active materials and different structures, are proposed. The main concern in these designs is the compatibility with the wide spread silicon CMOS technology. These modulators rely on the plasmonic theory to confine light beyond the diffraction limit. We introduce four high performance electro-optical modulators that operates under the telecommunication wavelength (1550 nm). An organic hybrid-plasmonic optical directional coupler is designed and studied. The power-splitting mechanism based on the change of the polymer electro-optical characteristics upon applying an external electric field. A finite element method with a perfect matching layer used to simulate this design. An extinction ratio of 14.34 dB is achieved for 39 μm modulation length. Two hybrid silicon electro-optical modulators are introduced and analyzed. The active material for these designs is Indium-Tin-Oxide. The first is based on tri-coupled waveguides with electrical tuning mechanism that is designed to change both the coupling conditions and introduces additional intrinsic losses. Based on this design, extinction ratio of 6.14dB and insertion losses of 0.06 dB are realized at 21 µm modulator length; as well as, extinction ratio of 11.43 dB and insertion losses of 1.65 dB are realized at 34 µm modulator length. The second device is an electro-absorption modulator, based on dielectric slot waveguide with an ITO plasmonic modulation section. An extinction ratio of 15.49 dB and an insertion loss of 1.01 dB can be achieved for 10 μm long modulation section. Modal and finite difference time domain analysis were performed to verify and simulate both designs. Last but not least, an optical switch based on a hybrid plasmonic-vanadium dioxide waveguide is presented. The power-attenuating mechanism takes the advantage of the phase change properties of vanadium dioxide that exhibits a change in the real and complex refractive indices upon switching from the dielectric phase to the metallic phase. An extinction ratio per unit length of 4.32 dB/μm and insertion loss per unit length of 0.88 dB/μm are realized. Also, Modal and finite difference time domain analysis are taken up to study and optimize this design. The proposed silicon electro-optical modulators can potentially play a key role in the next generation of the on-chip electronic-photonic integrated circuits

Modeling of Silicon Photonic Devices for Optical Interconnect Transceiver Circuit Design

Optical interconnect system efficiency is dependent on the ability to optimize the transceiver circuitry for low-power and high-bandwidth operation, motivating co-simulation environments with compact optical device simulation models. This chapter presents compact Verilog-A silicon carrier-injection and carrier-depletion ring modulator models which accurately capture both nonlinear electrical and optical dynamics. Experimental verification of the carrier-injection ring modulator model is performed both at 8 Gb/s with symmetric drive signals to study the impact of pre-emphasis pulse duration, pulse depth, and dc bias, and at 9 Gb/s with a 65-nm CMOS driver capable of asymmetric pre-emphasis pulse duration. Experimental verification of the carrier-depletion ring modulator model is performed at 25 Gb/s with a 65-nm CMOS driver capable of asymmetric equalization