多批次晶圆切换工时的计算及排序
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摘要
随着晶圆制造趋于多品种、小批量的特点,组合设备运行时需要频繁地切换晶圆批次加工。为了提高组合设备的工作效率,研究单臂组合设备中晶圆批次切换工时的计算及排序问题。首先,基于改进的拉式调度策略,分析了单臂组合设备中连续两批晶圆加工的切换过程,并获得相应切换工时的计算表达式。其次,针对多批次晶圆的切换问题,建立了以最小切换总工时为目标的数学模型,并应用模拟退火算法求解近似最优的排序方案。最后,通过仿真实验验证了该方法的可行性和有效性。
Due to the trends of multi-varieties and smaller batch sizes in wafer manufacturing, cluster tools need to switch from processing one wafer batch to another frequently. To improve the efficiency of cluster tools, the scheduling problem that makespan calculation and ranking of wafer batches switching were addressed. Firstly, the switching process between two consecutive batches were analyzed in single-armed cluster tools based on the modified backward scheduling strategy. Then the corresponding closed-form expressions for makespan were derived. Secondly, a mathematical model for minimizing the total processing time of multiple wafer batches switching process was developed. Based on the mathematical model, an approximate optimal ranking scheme for multiple wafer batches switching were obtained by using simulated annealing. Finally, the simulation results showed the feasibility and validity of the proposed method.
Due to the trends of multi-varieties and smaller batch sizes in wafer manufacturing, cluster tools need to switch from processing one wafer batch to another frequently. To improve the efficiency of cluster tools, the scheduling problem that makespan calculation and ranking of wafer batches switching were addressed. Firstly, the switching process between two consecutive batches were analyzed in single-armed cluster tools based on the modified backward scheduling strategy. Then the corresponding closed-form expressions for makespan were derived. Secondly, a mathematical model for minimizing the total processing time of multiple wafer batches switching process was developed. Based on the mathematical model, an approximate optimal ranking scheme for multiple wafer batches switching were obtained by using simulated annealing. Finally, the simulation results showed the feasibility and validity of the proposed method.
引文
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[2]潘春荣,王际鹏,黎良.具有混合晶圆流的单臂组合设备建模及调度[J].现代制造工程,2017(1):29-34.
[3]闵雁,伍乃骐.半导体晶圆制造中组合设备运行和控制综述[J].工业工程,2012,15(2):1-15.
[4]ZUBEREK W M.Timed Petri nets in modeling and analysis of cluster tools[J].IEEE Transactions on Robotics and Automation,2001,17(5):562-575.
[5]CHAN W K V,YI J,DING S.Optimal scheduling of multicluster tools with constant robot moving times,part I:two-cluster analysis[J].IEEE Transactions on Automation Science and Engineering,2011,8(1):5-16.
[6]WU N Q,ZHOU M C.Colored timed Petri nets for modeling and analysis of cluster tools[J].Asian Journal of Control,2010,12(3):252-266.
[7]潘春荣,伍乃骐.晶圆制造自动化组合设备的调度问题研究[J].计算机集成制造系统,2009,15(3):522-528.
[8]WU N Q,CHU C,CHU F,et al.A Petri net method for schedulability and scheduling problems in single-arm cluster tools with wafer residency time constraints[J].IEEE Transactions on Semiconductor Manufacturing,2008,21(2):224-237.
[9]QIAO Y,Zh OU M C,WU N Q,et al.Scheduling and control of startup process for single-arm cluster tools with residency time constraints[J].IEEE Transactions on Control Systems Technology,2016,99:1-14.
[10]ZHU Q H,ZHOU M C,QIAO Y,et al.Petri net modeling and scheduling of a close-down process for time-constrained singlearm cluster tools[J].IEEE Transactions on Systems Man&Cybernetics Systems,2018,48(3):389-400.
[11]KIM H J,LEE J H,JUNG C,et al.Scheduling cluster tools with ready time constraints for consecutive small lots[J].IEEETransactions on Automation Science and Engineering,2013,10(1):145-159.
[12]LEE J H,KIM H J,LEE T E.Scheduling lot switching operations for cluster tools[J].IEEE Transactions on Semiconductor Manufacturing,2013,26(4):592-601.
[13]张杨,郑泉,陈黎卿,等.基于蚁群算法的吸砂泵装配顺序优化设计[J].机械设计与研究,2015,31(2):109-112.
[14]邱明杰.基于燃油性能数据的一种飞机排班方法研究[J].机械设计与研究,2017,33(6):109-112.
[15]LEE T E,LEE H Y,SHIN Y H.Workload balancing and scheduling of a single-armed cluster tool[C]//Proceedings of the5th Asia Pacific Industrial Engineering and Management Systems Conference,Gold Coast,Australia,2004:1-15.
[16]潘春荣,王际鹏.具有多品种晶圆混合加工的单臂组合设备调度[J].控制理论与应用,2016,33(9):1171-1181.
[17]张德丰.MATLAB R2015b数学建模[M].北京:清华大学出版社,2016.