Physics-based time-domain modeling of high-speed VCSELs

The recent pandemic has triggered a social revolution hinged on communication technologies (ICTs), leading to the umpteenth step of digitalizing our existence. In industrialized countries, the digital divide has been almost overcome, providing to almost every citizen high-speed access to the internet. Such huge data transport capacity enabled to move towards a new paradigm, where computation is localized in data centers, performing all the processing behind the services, accessible by the users through low-cost terminals. From the perspective of ICT engineers, this moved the research and development interest from long-haul communications, usually based on high-power lasers or transmitting information through external modulators, to short-range optical links. Targeting high-speed and minimal losses, vertical-cavity surface-emitting lasers (VCSELs) appear as the ideal choice. VCSELs enable very high-speed operation thanks to the reduced active region volume; direct modulation is possible, minimizing additional losses; packaging and coupling with optical fibers are optimal, due to their circular symmetry. The research on VCSELs is therefore a big technological challenge and simulating their dynamics is a fundamental step in this sense. Usually, to optimize the bit rate, the implemented modulation schemes are complex, e.g. Multilevel Pulse Amplitude Modulation (PAM). For this reason, a small-signal analysis may be inadequate. Another potential solution is given by a lumped rate equation model, which unfortunately is an approximation and requires the introduction of many parameters that are not simple to determine starting from the designed physical structure. Furthermore, more and more complicated structures are arising (tunnel junctions, Quantum dots), and their description with a rate equation model may be not suitable. Also, the temperature is an important limiting factor of VCSELs’ bandwidth and a physics-based analysis is necessary to include heating effects. During this work, a time integration scheme is applied to implement a time-domain device-level simulator, starting from a 1D static Electro-Thermal-Optic solver. Efforts are made to identify a time integration method that ensures robustness and efficiency, as the time domain drift-diffusion-optical problem turns out to be numerically complex. The software is tested on an AlGaAs 850 nm structure formed of two p and n Distributed Bragg Reflectors (DBR) and an intrinsic region with 3 Quantum Wells. Then, the solver is validated on the small-signal regime and the steady-state regime, both available from the previously existing solver. While the intrinsic response is taken into account by the model, the extrinsic parasitics, an important limiting factor of the VCSEL response, are included as an external lumped circuit. The time-domain analysis proves to be a very useful tool to understand deeply the transient behaviour and the main bandwidth limitations of the device, arising from combined optical recombinations and carrier transport effects. Finally, the investigated device is tested with a 2 and 4-PAM modulation. Also, noise sources can be extracted to compute the Signal to Noise Ratio (SNR) of the output signal. The conclusion of this work is that a lumped equation model is more suitable for a system-level application, as it is faster and easier to implement, while a physics-based simulator is a necessary tool for device-level optimization and to extract parameters for the lumped model.