Cyclic Scheduling Of Multi-cluster Tools With Two Wafer Types

As an efficient automated manufacturing system(11)cluster tools can process single wafer efficiently and accurately(11)which has been widely adopted in semiconductor manufacturing(13)A cluster tool is composed of two loadlocks,a transport module and several process modules.To improve productivity further for advanced semiconductor chip processes,multi-cluster tools have been gradually employed by wafer fabs.A multi-cluster tool consists of multiple cluster tools via buffer modules.Since a cluster tool is extremely expensive,it is necessary to develop an efficient method to schedule and control it such that it can be effectively operated and more profits can be obtained for wafer fabs.In recent years,on account of the diversification of chip products,the increasing wafer size and the reduction of wafer batch size,cluster tools with multiple wafer types have been employed in wafer fabrication.Each wafer type has its specific processing flow and steps,which makes a great difference among the schedules for different wafer types.Therefore,it is challenging to find an effective method to schedule a cluster tool to process multiple types of wafers.Existing research shows that the problem of scheduling a multi-cluster tool is NP-hard.It is very significant in the sense of both theory and practice to obtain an effective way to schedule such a system.This study pays more attention to the steady-state process of multicluster tools that process two wafer types subject to wafer residency time constraints.This work investigates a multi-cluster tool with two setting.One is a single-arm multi-cluster tool and the other is a dual-arm multi-cluster tool.Although a dual-arm robot is more efficient than a single-arm robot,the former is more expensive than the latter.Therefore,it is significant to study both single-arm and dual-arm robotic multi-cluster tools.Compared with two-space buffer modules,the investment of onespace buffer modules is much lower.However,it is more challenging to find a feasible schedule for multi-cluster tools with one-space buffer modules than those with two-space buffer modules.In order to pursue higher profits,multi-cluster tools are equipped with onespace buffer modules.Since buffer modules have one-wafer capacity only,two wafer types are bound to compete for it,which leaves less time and space for multiple robots to collaborate.It is known that after all the process steps are completed,the wafers return to the loadlocks through buffer modules directly in multi-cluster tools with two wafer types.For a given cluster tool,there is no buffer space between the incoming buffer module and the outgoing buffer module.Thus,the interaction between its two adjacent cluster tools is direct.In other words,the coupling interconnection exists not only between two adjacent cluster tools,but also among three adjacent cluster tools.Therefore,the addressed scheduling problem is rather challenging.The following contributions have been made:(1)The scheduling strategy and its corresponding cycle for single-arm and dual-arm robots in multi-cluster tools with two wafer types.Based on the conventional swap and pull strategies,a two-swap strategy and a two-pull strategy for dual-arm and single-arm cluster tools with two wafer types are proposed respectively.Additionally,a one-wafer-per-type robot sequence has been developed for dual-arm and single-arm cluster tools,respectively.(2)The one-wafer-per-type cyclic scheduling of linear dual-arm multi-cluster tools with one-space buffer modules subject to wafer residency time constraints.Firstly,activity time of dual-arm cluster tools is parameterized to give their temporal properties.The necessary and sufficient conditions for one-wafer-per-types cyclic schedule are proposed.Secondly,a simple and effective scheduling algorithm is applied to obtain an optimal cyclic schedule if the multicluster tool system is schedulable.Finally,several examples show the effectiveness of the proposed algorithm.(3)The one-wafer-per-type cyclic scheduling of linear single-arm multi-cluster tools with wafer residency time constraints and one-space buffer modules.Firstly,the activity time of single-arm cluster tools is parameterized to give their temporal properties,and then the necessary and sufficient conditions are presented to check the existence of one-wafer-per-type schedule.Assume that the cycle time is known,polynomial-time algorithms are proposed to obtain a corresponding feasible schedule.If the cycle time reaches the lower bound,the lowerbound cycle schedule can be found.If not,the methods to calculate minimum increment are presented to obtain a non-lower-bound feasible schedule.