A cluster tool is typical single wafer processing equipment which consists of wafer processing chambers and a wafer handling robot. Cluster tools are prevalently being used in modern wafer fabrication facilities as they provide better wafer quality as compared to batch processors. As wafer circuit widths continually shrink down, wafer fabrication processes have become highly complicated and sophisticated, and hence stringent quality control is required in operating wafer processing equipment. Consequently, wafer fabrication facilities increasingly use a new cluster tool operation strategy that periodically cleanses process chambers to remove chemical residuals formed within the chambers. Such cleaning strategy increases the scheduling complexity of determining a robot task sequence that achieves the maximum tool throughput. Conventional scheduling strategies suggested by previous studies, which are developed for operating cluster tools without chamber cleaning, provide extremely poor tool throughput when chamber cleaning exists. Chamber cleaning also significantly impacts the wafer delays within chambers which are critical to the wafer quality. Therefore, this thesis examines scheduling problems for cluster tools with chamber cleaning. We found an interesting insight that a partial loading strategy, which does not load wafers at all parallel chambers, can reduce the tool cycle time significantly. From these, we found novel scheduling strategies for single- and dual-armed cluster tools that load wafers only at an appropriate number of parallel chambers. Then, the partial loading strategy is further extended so as to be applied for general tool schedules. We propose that such partial wafer loading method also decreases the wafer delays within chambers, that is, partial loading of parallel chambers improves the tool throughput as well as the wafer quality. At the end, we introduce an improved Petri net modeling framework for describing the tool behavior of cluster tools with general chamber cleaning cycles. This thesis reports various mathematical properties and experimental results that verify the efficiency of the proposed scheduling methods and modeling frameworks.