Integrated circuit chips are produced on silicon wafers. Robotic cluster tools are widely used since they provide a recon-figurable and efficient environment for most wafer fabrication processes. Recent advances in new semiconductor materials bring about new functionality for integrated circuits. After a wafer is processed in a processing chamber, the wafer should be removed from there as fast as possible to guarantee its high-quality integ-rated circuits. Meanwhile, maximization of the throughput of ro-botic cluster tools is desired. This work aims to perform post-pro-cessing time-aware scheduling for such tools subject to wafer res-idency time constraints. To do so, closed-form expression al-gorithms are derived to compute robot waiting time accurately upon the analysis of particular events of robot waiting for single-arm cluster tools. Examples are given to show the application and effectiveness of the proposed algorithms.