Simulation of carrier dependent absorption effects in silicon optical waveguide devices

High-Speed silicon modulators, based on carrier dependent absorption effects, have recently been reported in the literature [1]. For improved performance, these modulators rely on a MOS configuration to control carrier accumulation, rather than on carrier injection from the contacts, to induce an index perturbation for controlling the phase of a propagating signal. Accurate simulation of the carrier distribution is required for the analysis of such a device. This entails the self-consistent solution of the coupled electro-thermal transport equations. An appropriate absorption model is also required in order to couple the carrier distribution to the propagating optical field, via a complex index perturbation. Finally, in order to determine performance, the full optical problem must be solved throughout the device domain. The present work integrates the Box Integral Method of solving the active device transport equations [2] with the Vector Beam Propagation Method (BPM) typically used to analyze passive waveguide structures [3]. A modified Drude Model and Kramers-Kronig relations [4] are used to determine the carrier density dependent absorption and refractive index perturbations. This complex index perturbation is determined as a function of the applied voltage, and used by a simulator based on the BPM to determine the optical performance of an example silicon modulator. Both steady-state and frequency responses are considered. This comprises a general methodology for analyzing realistic semiconductor photonic devices in which the optical propagation is affected by the electro-thermal transport within the device.