Scheduling start-up process for time-constrained single-arm cluster tools

摘要

Due to the trend of using larger wafer diameter and smaller lot size, cluster tools need to switch from processing one lot of wafers to another frequently. It leads to more transient periods in wafer fabrication. Their efficient scheduling and control problems become more and more important. It becomes difficult to solve such problems, especially when wafer residency time constraints must be considered. This work develops a Petri net model to describe the behavior during the start-up transient processes of a single-arm cluster tool. Then, based on the model, for the case that the difference of workloads among the steps is not too large and can be properly balanced, a scheduling algorithm to find an optimal feasible schedule for the start-up process is given. For other cases schedulable at the steady state, a linear programming model is developed to find an optimal feasible schedule for the start-up process.

主权项

1. A computer-implemented method for scheduling a cluster tool, the cluster tool comprising a single-arm robot for wafer handling, a loadlock for wafer cassette loading and unloading, n process modules each for performing a wafer-processing step with a wafer residency time constraint where the ith process module, iε{1, 2, . . . , n}, is used for performing Step i of the n wafer-processing steps for each wafer, and a specialized processor configured to control the robot, the loadlock, and the process modules through execution of the method, the method comprising:
when max≦iU and Ψ1≦iU, i=1, 2, . . . , n, determining, by the specialized processor, values of ω0, ω1, . . . , ωd for each of plural system states Msd, d=0, 1, . . . , n−1, of the cluster tool, where Msi, 1≦i≦n−1 denotes that i instances of a wafer unloading from the robot to any one of the n process modules have occurred since system start-up, and ωj,jε{0, 1, . . . d}, is a robot waiting time used in the state Msd for the robot to wait before unloading a wafer in Step j from the robot to the (j+1)th process module; wherein the determining of ω0, ω1, . . . , ωd for each of the system states Msd, d=0, 1, . . . , n−1, comprises: setting, by the specialized processor, ω0=0 and ω1=a1 for the states Ms0 and Ms1;where:
max=max{iL, iεNn}; Ψ1=2(n+1)μ+(2n+1)α+α0 iU=ai+4α+3μ+δi, iεNn/{1}; iU=a1+3α+α0+3μ+δ1; iL=ai+4α+3μ, iεNn/{1}; iL=a1+3α+α0+3μ; ai, iεNn, is a time that a wafer is processed in the ith process module; δi, is the wafer residency time constraint of Step i, given by a pre-determined longest time for which a wafer in the ith process module is allowed to stay therein after this wafer is processed; α is a time of loading a wafer to or unloading the wafer to the robot in Step i; μ is a time of the robot moving from one wafer-processing step to another; α0 is a time of the robot unloading a wafer from the loadlock and aligning the same; and Nm={1, 2, . . . , m} for a positive integer m.