In this paper, physically-based simulations are carried out to investigate and design broadband and high-output power uni-traveling carrier (UTC) photodiodes. The physical model is first verified by comparison to experimentally measured results. The graded-bandgap structure, which can induce potential gradient, is considered to be used in the absorption layers. It is shown that the electric field in the absorption layer is increased by the gradient, thus the performance of bandwidth and saturation current is improved by 36.6% and 40% respectively for our considered photodiode. Moreover, a modified graded-bandgap structure is proposed to further increase the electric field, and an additional 9.5% improvement in bandwidth is achieved. The final proposed UTC-PD structures will result in 399-GHz bandwidth and 49-mA DC saturation current.