In this paper, the bias-free operational uni-traveling-carrier photodiode (UTC-PD) for terahertz wave generation is designed via physics-based simulation. The physics-based model is established at first and then the reliability of the simulation is demonstrated by comparison to previously reported experimental results. The epitaxial layers of the UTC-PD are analyzed and investigated to improve its bandwidth and output-power simultaneously. By optimizing the spacers and the collector, and using a combination of optimal graded-doping profile and graded-bandgap material for the absorber, the 3-dB bandwidth and the peaked output-power of the UTC-PD are improved by 36.5% and 2.262 dB, respectively. The 3-dB bandwidth of the optimized bias-free operational UTC-PD with mesa diameter of 8, 6, 5, 4 and 3-μm can achieve 106, 137.67, 158.3, 183 and 211 GHz, respectively.