Silicon photonics offers great potential for monolithic integrated photonic and electronic components using existing integrated circuit fabrication infrastructure. However, methods to analyze the impact of IC process variations on performance of photonic components remain limited. Statistical models based on either simulations or experiments that quantify the effect of these variations are necessary to achieve high-yield manufacturing. In order to cope with the non-linearity in the S-parameters of photonic device components and circuits, non-linear parameter fitting is often used prior to statistical modeling, e.g., rational polynomial fitting of ring resonator responses. The conventional approach treats the amplitude and phase of the S-parameters separately in the fitting process; however, this can be problematic when the behavior of the S-parameters becomes complicated under the variations, since it neglects the strong correlation between amplitude and phase. We present a novel representation of S-parameters that decomposes the complex-numbered S-parameters into several components each having a simple response that does not require non-linear parameter fitting, and that supports subsequent statistical analysis. We apply the proposed S-parameter decomposition method to Ysplitters with imposed line edge roughness variations. In contrast to the difficulty of the conventional amplitudephase representation, the decomposed representation shows improvement in statistical modeling of variation ensembles, e.g., using principle component analysis. The method can be extended to other photonic components and circuits with other process variations, to help quantify the effect of process variations for statistical analysis, and to help designers predict and optimize photonic component performance and yield.
Silicon photonics offers the ability to fabricate and integrate photonic and electronic components using existing integrated circuit fabrication infrastructure. Recent work seeks to understand the impact of IC process variations on performance of photonic components. In particular, methods for analysis that identify sensitivity of photonic components to process variations are crucial to enable viable design and manufacturing of silicon photonic systems.
We present two different and complementary methods for understanding the impact of geometric process variations on photonics components: ensemble statistical virtual fabrication simulations, and adjoint methods. These are utilized to identify the most sensitive regions of a Y-splitter photonic component to line edge roughness (LER) due to inherent lithography and etch process variations. In the ensemble approach, we simulate multiple instantiations with random LER applied to specific sections of the Y-splitter. This enables localization and quantification of LER impact on transmission, phase imbalance, and excess losses. These evaluations, however, come at the cost of many simulations. In adjoint sensitivity evaluation, only one or two simulations can identify regions most sensitive to LER. While first-order linear sensitivity is extracted, the adjoint has challenges in quantifying mean variation impacts. Both methods reveal that the Y-splitter is most sensitive to LER in the input taper, accounting for over 95% of the imbalance transmission. These two methods can be combined to quantify mean, variance, and sensitivity of photonic device components in the face of statistical variations. Incorporated into future photonic process design kits (PDKs), these analysis methods will help designers predict and optimize photonic component performance and yield.
Silicon photonics is rapidly emerging as a promising technology to enable higher bandwidth, lower energy, and lower latency communication and information processing, and other applications. In silicon photonics, existing CMOS manufacturing infrastructure and techniques are leveraged. However, a key challenge for silicon photonics is the lack of mature models that take into account known CMOS process variations and their effect on photonic component behavior. A key factor for the adoption of silicon photonics into high-yield manufacturing is to extend process design kits (PDKs) to include photonic process variability models that are aware of variations that may occur during the fabrication process.
We study the effect of a well-known random process variation, line edge roughness (LER), present in the lithography and etch process, on the performance of a fundamental component, the Y-branch, through virtual fabrication simulations. Ideally, the Y-branch transmits the input power equally to its two output ports. However, imbalanced transmission between the two output ports is observed when LER is imposed on the Y-branch, depending on the statistical nature (amplitude and correlation length) of the LER. The imbalance can be as low as 1% for small LER amplitudes, and reach up to 15% for large LER amplitudes. In addition, LER increases the excess loss compared to the nominal (smooth) case. Ensemble statistical virtual fabrication and FDTD photonic simulations across a range of LER amplitude and correlation lengths are reported. These results can be captured as worst-case corner models and included in variation-aware photonic compact models.
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