We use a 2D drift-diffusion model to study the nonlinear response of a partially depleted absorber (PDA) phododetector. The model includes external loading, incomplete ionization, the Franz-Keldysh effect, and history-dependent impact ionization. It also takes into account heat flow in the device. With all these effects included, we obtain excellent agreement with experiments for the responsivity and for the harmonic power at different modulation frequencies. The role of these different physical effects is elucidated, and we find that both the Franz-Keldysh effect and the load resistance play a key role in generating higher harmonic power at larger reverse biases. Increasing the size of the p-region absorption layers reduces the impact of the Franz-Keldysh effect. Decreasing the effective load resistance also decreases the higher harmonic powers. We also show that the model can suggest design changes that will improve device performance.