Section: TelecommunicationsMajor Research topic
:Statistical methods for analysis, design and characterization of PICs
Advisor: MELLONI ANDREA IVANOAbstract:
In a generic fabrication approach, a standardized process is made accessible to designer together with a process design kits (PDKs). A PDK contains a number of building blocks of which the performance and functional behaviour are accurately known, and layout and functional design rules are established. Designers do not have to be concerned about how to design them; they can just take them from a library and start building a circuit to analyse and optimize it with a circuit simulator. Therefore, the designer can concentrate on a higher abstraction level of circuit design. In practice, a PDK is a piece of software code(s) that contains a large amount of foundry-specific information that can be plugged into a design environment and contains all relevant information to design, simulate and fabricate circuits exploiting a given fabrication technology. Among this information, a PDK offers to the users a library of the building blocks made available by the foundry, incorporating, in particular, a deterministic mathematical macro-model of the behaviour of each device, generally in the form of either a transmission or a scattering matrix. However, during fabrication, different sources of variability are usually present. Perhaps the major cause of uncertainties are the tolerances that unavoidably characterize the fabrication process such as waveguide geometry deviation, gap opening issues, material composition fluctuations, and surface roughness. This means that different fabricated devices, which are designed to be nominally the same, differ from one to another as a result of the manufacturing process. The device response is thus no longer regarded as deterministic but is more suitably interpreted as a stochastic process. To obtain a high-quality design of a photonic circuit (e.g. high yield), it is important to include such uncertainties in PDKs and to isolate the most critical parameters of the circuits and to estimate and reduce the cost of post-fabrication correction of the process variability. The possibility to include information on the effect of uncertainties in each building block and the availability of efficient computational strategies to predict the statistical behaviour of the final circuit are highly desirable.
To address the problem of post-fabrication correction and isolate the most critical parameters of the circuit, advanced statistical methods were studied and applied. More specifically, we focus on the application of two sensitivity analysis techniques, namely Elementary Effect Test and Variance-Based Sensitivity Analysis to investigate the behaviour of a photonic circuit under fabrication uncertainties, with the aim to identify the most critical parameters affecting the circuits’ performance. We demonstrate, for the first time, the possibility to use the results of these methods to reduce the power consumption for the mitigation of statistical variation of circuits’ parameters and increase the yield. To include information on the effect of uncertainties in each building block, we propose a Building-Block-based method (BB-gPC) in which we exploit a generalized polynomial chaos (gPC) expansion approach to realize a completely novel class of device models to be used within photonic PDKs. These stochastic models inherently convey stochastic information, which allows performing statistical analyses without any repeated simulation and enables an unprecedented simulation efficiency compared to classical gPC implementations. The BB models, in the form of transmission or scattering matrices, are circuit independent and can be stored and replace the original deterministic macro-model of the building blocks in the process design kit. The new matrices can hence be combined according to the building blocks connections to derive with a single run of the deterministic circuit simulator the stochastic behaviour of any circuit. The stochastic properties of the BB can reflect for example the foundry technological process and they are embedded in the PDK and should not be recalculated for every circuit. Furthermore, we have also demonstrate the use of statistical method (generalized polynomial chaos) to estimate the statistical properties of a circuit from a reduced number of experimental characterization, saving costly and time consuming measurements whilst achieving good accuracy comparable to those obtained by Monte Carlo which should help testing and tuning in future mass production technological processes.
The second part of the work is devoted to the modelling of the influence of temperature on the behaviour of optical devices and design of innovative circuit able to expand the capabilities of a generic foundry. A method to take into accounts the wavelength, composition and temperature dependencies in the calculation of the refractive index and linear thermo-optic coefficient of In1−xGaxAsyP1−y alloys is presented and experimentally validated. The results provide a deeper understanding of the influence of the temperature on the behaviour of optical waveguides and devices, making possible an accurate and realistic modelling of integrated circuits. Lastly, a novel circuit to obtain optical true time delay has been proposed. The proposed device is based on a Mach– Zehnder interferometer with tuneable couplers can be ideally operated with a single control signal and achieves a bandwidth-delay product consistently larger than ring-based delay lines. The device is successfully used in a transmission system to control the delay of a 10 Gbit/s data stream.