I. Introduction
Ease of fabrication, fine optical confinement and low cost have made silicon-based photonic integrated circuits (SiPICs) the preferred choice in the field of data communication and chip-to-chip interconnects, as SiPICs encompass the limitation of speed and power consumption in electric integrated circuits [1]–[2]. High-speed and efficient modulators play vital roles in realizing fast and practical data transmission systems [3]. As in mature SiPIC modules, the carrier-depletion Mach-Zehnder modulator (MZM) based on the plasma dispersion effect has been mainly harnessed and the electro-optic (EO) bandwidth has been extended to over 40 GHz [4]. However, for compact on-chip applications with massive integration and low power consumption, as the future datacom requires, the microring modulator (MRM) is considered a more promising option. The holistic optimization of the carrier-depletion modulator requires to have optical insertion loss, RC bandwidth and modulation efficiency of the phase shifter taken into consideration, together with the velocity match, impedance match and microwave loss of the electrode [5]. As the doping profiles of the modulator significantly affect the loss, efficiency and loaded junction impedance, the junction design is crucial for high-performance data transmission. Aforetime progress of doping profile optimization has been made on either solely the cross-section or solely the propagation direction of the modulator waveguide [6]–[8]. Generating complex 3D doping profiles steps up as a clear contender for more designs targeting efficient and broad-band modulation structures.