2018 Theses Doctoral

# 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.

## Files

- Bahadori_columbia_0054D_14785.pdf application/pdf 73.9 MB Download File

- Defense.pptx application/vnd.openxmlformats-officedocument.presentationml.presentation 128 MB Download File

## More About This Work

- Academic Units
- Electrical Engineering
- Thesis Advisors
- Bergman, Keren
- Degree
- Ph.D., Columbia University
- Published Here
- July 1, 2018