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In plasma immersion ion implantation (PIII), ions are extracted from the plasma and implanted in a target subjected to high negative voltage pulses. PIII models assume that the uncovering of enough ions at the moving sheath edge establishes a space-charge-limited ion flow that supplies the ion implant current at the target. The present paper reexamines this assumption in one-dimensional planar geometry by relating the implant current at the target to the Child law current through a delay time function that properly accounts for the transit time of the ion through the sheath. Comparison of the total current calculated both at the target and at the leading edge of the sheath demonstrates that the model provides accurate results as long as the ion time scale is shorter than the characteristic times of the applied voltage waveform.