Plasma immersion ion implantation (PIII) has been developed as a low_cost and efficient surface modification technique of irregularly-shaped objects. The effect of six pulse waves with different rise_time patterns on the spatio-temporal evolution of plasma sheath, energy and dose of ion implantation has been simulated by particle-in-cell modeling. Statistical results may be obtained through assuming the Boltzmann distribution of electrons, and solving Poisson and Newton equations for tracing each ion in the plasma sheath. The results show that rise_time pattern has a critical influence on the evolution of plasma sheath. There exists maximum thickness difference of plasma sheath for different waveforms. The acceleration of ions is non_uniform due to the non-uniformity of electrical field strength. The maximum gradient of electrical field appears near the edge of plasma sheath. The results also show that optimization of dose and energy of incident ions may be achieved through modification of rise_time pattern. The numerical simulation of sheath expansion can be effectively used to provide a scientific basis for optimizing the PIII process.