As the design of integrated circuits has become increasingly complicated and dense, serious wafer quality problems are observed in modern wafer fabrication facilities. Therefore, in cluster tools of leading fabs process chambers are periodically cleaned in order to eliminate residual chemicals and impurities that can damage the wafer quality. A chamber cleaning operation is mainly applied to tools in which a wafer delay has a crucial impact on the wafer quality, and hence the need of wafer delay control becomes more significant when chamber cleaning is considered. Thus, we first examine how wafer delays can be specified for cluster tools with chamber cleaning operations. We confirm that wafer delays are substantially increased when chambers are periodically cleaned, and we show that such increased wafer delays cannot be eliminated or reduced using the existing scheduling methods. In such a case, we prove that a partial loading strategy can minimise both the tool cycle time and the wafer delays by controlling the number of wafers being loaded into parallel chambers. We also present how wafer delays under the partial loading strategy can be further reduced by introducing a timing control method that regulates the start times of robot tasks.