Scheduling of dual-arm multi-cluster tools considering wafer residency time constraints
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摘要: 组合设备群代表了当前晶圆制造装备发展的新趋势，其调度控制水平直接攸关半导体芯片制造企业的整体经济效益。针对半导体芯片制造中考虑晶圆驻留时间约束的双臂组合设备群，文章提出了一种基于特征转换的调度控制方法。首先，引入一种概念型晶圆制造系统，即特征双臂组合设备，并给出相应的稳态调度方法。其次，采用特征转换方法，将线性/树形结构的双臂组合设备群转换为特征双臂组合设备。随后，根据转换后的特征双臂组合设备重新调整双臂组合设备群的机械手作业序列，并求解可行的稳态调度方案。最后，通过实例验证了所提方法的有效性。Abstract: Multi-cluster tool represents the current trends of wafer fabrication equipment, resulting that its scheduling and control can directly affect the overall economic efficiency of semiconductor chip manufacturers. Considering the wafer residency time constraint in semiconductor chip fabrication, a feature-transformation-based scheduling approach is presented to improve the productivity of dual-arm multi-cluster tools. Firstly, a conceptual wafer fabrication system called the characteristic dual-arm cluster tool is proposed, and its steady-state scheduling method is investigated as well. Secondly, by using a feature transformation approach, a multi-cluster tool with arbitrary topology can be effortlessly reduced into a characteristic dual-arm cluster tool. Thirdly, according to the transformed characteristic dual-arm cluster tool, the individual robot activity sequence is reassigned, and then a feasible steady-state schedule for the multi-cluster tool can be obtained. Finally, illustrative examples are offered to validate the effectiveness of the presented approach.
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Key words:
- semiconductor equipment /
- wafer fabrication /
- cluster tool /
- time constraint /
- scheduling
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算法1: 求解特征双臂组合设备稳态调度 输入：αi, βi, γi, i ∈ $\mathbb{N} $h; θi, i ∈ Ωh; ρ0, ρh+1 输出：ωi1, ωi2, i ∈ $\mathbb{N} $h; ϕd 1. If $ {\bigcap }_{i\in {\mathbb{N}}_{h}}[{\varphi }_{iL},{\varphi }_{iU}] $ ≠ $\varnothing $ then 2. If ϕt ≤φLmax then 3. ϕd ← φLmax; 4. ωi2 ← 0, i ∈ $\mathbb{N} $h; 5. 将非负值φLmax – ϕt 随机分配予ωi1, i ∈ $\mathbb{N} $h; 6. else 7. if ϕt ≤φUmin then 8. ϕd ← ϕt; 9. ωi1 ← 0, i ∈ $\mathbb{N} $h; 10. ωi2 ← 0, i ∈ $\mathbb{N} $h; 11. else 12. 设备不可调度； 13. end if 14. end if 15. else 16. if ϕt ≤φLmax then 17. if ϕt ≤φLmax – $ {\displaystyle\sum }_{i\in {\mathbb{P}}_{d}}({\phi }_{L\mathrm{m}\mathrm{a}\mathrm{x}}-{\phi }_{iU}) $then 18. ϕd ← φLmax; 19. ωi2 ← φLmax – φiU, i ∈ $\mathbb{P} $d; 20. ωi2 ← 0, i ∈ $\mathbb{Q} $d; 21. 将非负值φLmax – ϕt –$ {\displaystyle\sum }_{i\in {\mathbb{P}}_{d}}{\omega }_{i2} $随机分配予ωi1, i ∈ $\mathbb{N} $h; 22. else 23. 设备不可调度； 24. end if 25. else 26. 设备不可调度； 27. end if 28. end if 
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算法2: 求解双臂组合设备群稳态调度 输入：αij, βij, ρci, θci, γci, i ∈ $\mathbb{N} $K, i ∈ $\mathbb{N} $n[i] 输出：ωij1, ωij2, i ∈ $\mathbb{N} $K, j ∈ $\mathbb{N} $n[i]; ϕm 1. h ←$ {\displaystyle\sum }_{i=1}^{K}{n}_{ci} $; 2. {Pk} ← {P10, Pij}; /*沿路径$\mathcal{R} $重置协调工序与设备真空锁工序编号*/ 3. {αi, βi, ρi, θi, γi} ← {αij, βij, ρci, θci, γci}; /*传递加工参数至特征双臂组合设备*/ 4. 调用算法1，若算法1判定可以调度，则求解ϕm, ωi1, ωi2, i ∈ $\mathbb{N} $h；若算法1判定不可调度，则转向 Step 7; 5. ϕm ←ϕd; 6. {ωij1, ωij2} ←{ωi1, ωi2}; /*重复执行step 2-3还原机械手等待时间*/ 7. End.
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