Waveguide photodetectors (WGPDs) are promising candidates for applications in high-speed optical communications and interconnections. In these high-speed photodetectors, both high bandwidth and high external quantum efficiency can be achieved simultaneously. Mushroom-WGPD is proposed to overcome the trade-off between the capacitance and contact resistance of the photodetector. In this article, a physical model of the mushroom-WGPD is presented including both time and frequency responses of this photodetector and how they depend on the parameters of the photodetector. A SPICE model for mushroom-WGPD including all the parasitics is also presented, showing the dependence of the transfer function of this model on the dimensions and the material parameters of the photodetector. The effects of the parasitics are also studied for different photodetector areas. The characteristics of mushroom-WGPD are studied for two cases, first without an inductor added in series with the load resistance and second, if an inductor is added in series to the load resistor. A significant improvement in performance is achieved in the second case where an inductor is added.