Paper
In this paper, a sinusoidal vertical PN junction phase shifter on a silicon waveguide is designed, and the results demonstrate that modifying the shape of the PN junction significantly increases the area of the depletion region within the standard waveguide width of 500 nm, thereby enhancing the overlap between the depletion region and optical waveguide modes under reverse bias conditions. Furthermore, by adjusting the sinusoidal amplitude ( A ) of the doping contact interface, it is observed that when A =0.065µm, the resulting sinusoidal PN junction most effectively enhances the interaction between carriers and photons, leading to the highest modulation efficiency and the lowest loss. Based on this, further adjustment of the doping concentration distribution in the waveguide was conducted using a doping compensation method. It is observed that setting the doping concentration at 3×10 18 cm −3 in the heavily doped region and at 1×10 18 cm −3 in the lightly doped region enables the phase shifter to achieve high modulation efficiency while maintaining low loss. This is attributed to the highest optical intensity being concentrated in the central region of the waveguide, as well as to the positive correlation between doping concentration and modulation efficiency. The final designed device with a length of 1.5 mm successfully attained a low V π L of 0.58V⋅cm, resulting in high modulation efficiency. By employing traveling wave electrodes and ensuring that the effective refractive index of the radio frequency (RF) matches the optical group index (OGI), circuit-level simulations were conducted. The device exhibited a 3 dB bandwidth of 8.85 GHz and eye diagrams of up to 40 Gbit/s, with a maximum extinction ratio (ER) of 8.27 dB and a bit error rate (BER) of 8.83×10 −6 , which can be widely used in the field of high-speed silicon optical modules.