  Citation: Peng, Y.; Sorin,W.V.; Cheung, S.; Yuan, Y.; Huang, Z.; Fiorentino, M.; Beausoleil, R.G. Small-Signal Analysis of All-Si Microring Resonator Photodiode. Electronics 2022, 11, 183. https:// doi.org/10.3390/electronics11020183 Academic Editor: Dongseok Suh Received: 30 November 2021 Accepted: 5 January 2022 Published: 7 January 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). electronics Article Small-Signal Analysis of All-Si Microring Resonator Photodiode Yiwei Peng, Wayne V. Sorin , Stanley Cheung, Yuan Yuan * , Zhihong Huang, Marco Fiorentino and Raymond G. Beausoleil Hewlett Packard Labs, Hewlett Packard Enterprise, Milpitas, CA 95035, USA; yiwei.peng@hpe.com (Y.P.); wayne.sorin@hpe.com (W.V.S.); stanley.cheung@hpe.com (S.C.); zhihong.huang@hpe.com (Z.H.); marco.fiorentino@hpe.com (M.F.); ray.beausoleil@hpe.com (R.G.B.) * Correspondence: yuan.yuan@hpe.com Abstract: All-silicon microring resonator photodiodes are attractive for silicon photonics integrated circuits due to their compactness, wavelength division multiplexing ability, and the absence of germanium growth. To analyze and evaluate the performance of the microring photodiode, we derived closed-form expression of the response transfer function with both electrical and optical behavior included, using a small-signal analysis. The thermo-optic nonlinearity resulting from optical loss and ohmic heating was simulated and considered in the model. The predicted response achieved close agreement with the experiment results, which provides an intuitive understanding of device performance. We analytically investigated the responsivity–bandwidth product and demonstrated that the performance is superior when the detuning frequency is zero. Keywords: photodiodes; resonators; photothermal effects; silicon; optoelectronics 1. Introduction The silicon photonics platform has been considered the most attractive solution for high-speed network and artificial intelligence applications due to its low cost and high miniaturization [1,2]. Because the cutoff wavelength of bulk Si is only around 1.1 μm, the photodetection at telecommunication wavelengths is usually achieved by the heteroepitax- ial growth of germanium (Ge) or heterogeneous integration of III-V materials [3–6]. Both methods require added material costs and extra process steps. All-Si photodetection based on defect state absorption has been demonstrated to achieve high quantum efficiency and high bandwidth [7,8]. However, the method needs special steps, such as defects implanta- tion, which are not compatible with the standard process in foundries. Si photodetectors (PDs) based on two-photon absorption (TPA) and photon-assisted tunnelling (PAT) can absorb sub-bandgap wavelengths [9]. Applying a high bias voltage across the PN junction, the spatial distance between the conduction and valence band will be shortened due to the strong electric field. The electrons in the valence band can possibly tunnel into the conduction band [10]. However, the mechanisms are weak and PDs suffer from low re- sponsivity. Microring resonator (MRR) PD benefits from optical resonant enhancement effect is a promising solution to improve responsivity [11]. Intel has reported a 112 Gb/s (56 GBaud PAM4) all-Si MRR PD with a responsivity of 0.23 A/W [12]. Thus far, there is not much dynamic analysis work to quantify the performance of the MRR PD. Some steady-state and dynamical discussions on MRR modulators show that the modulation rate and efficiency are limited by the resonator quality factor (Q) [13–18]. For the MRR PDs, Q value limits the rate at which the optical power can be injected in the ring and absorbed, which determines the modulation speed. At the same time, the resonant enhancement effect, and thus the responsivity, are related to the Q value. Bandwidth improvement always comes at the expense of a reduced responsivity and it is important to weigh the tradeoff in design [19]. The performance of MRR PD also Electronics 2022, 11, 183. https://doi.org/10.3390/electronics11020183 https://www.mdpi.com/journal/electronics