# ML-Based JIT1 Optimization for Throughput Maximization in Cluster Tool Automation
## 2 Related Work
### Maximizing the Throughput of the Cluster Tool  
Because the number of chambers and robots in the cluster facility is limited and repetitive tasks are performed, depending on the scheduling problem, throughput can be variable, which seems to be simple in a limited environment due to the characteristics of cluster tools. Based on facility variables, throughput has a non-linear relationship, so optimization to perform optimal scheduling is not simple [19; 20; 21; 22]. The throughput of the cluster tool is determined according to the throughput of the number of wafers that have completed the specified process recipe for a unit of time (1 h). Throughput is the most important variable to obtain maximum productivity of cluster tools because the scheduling is changed according to the production plan of the semiconductor fab and the setting value of JIT1. In addition, throughput determines the production system quality, which must satisfy the user's needs [23; 24]. However, it is not easy to predict the sustainable throughput of cluster tools due to the complex scheduling and unexpected real-time problems. To date, extensive research has been conducted on the scheduling and throughput of cluster tools [13; 25; 26]. Various throughput models have been studied according to various cluster facility configurations and under conditions such as sequential or parallel PM process or WAC [1; 27; 21]. However, this model has a limitation in providing the theoretical throughput of a specific cluster facility. In reality, cluster tool modeling may not follow theoretical modeling due to various real-time problems. Therefore, an optimization method using a more practical throughput model is needed [21]. Although this timing-based model is easy to understand, it has a limitation since it cannot effectively consider the theoretical throughput of the cluster facility, that is, the real-time scheduling problem. Therefore, a more realistic Petri net modeling study was conducted [28]. Throughput (WPH--wafer per hour), which indicates the number of wafers produced per unit time of the cluster facility, depends on JIT1 and the number of PMs, recipe time,and WAC time. Collecting the throughput results measured under various parameter conditions is essential to obtain modeling for accurate throughput by understanding the relationship between each variable and throughput. This operation is very time consuming, but using big data, it can be possible in semiconductor fabs. However, this study used different values for the four main parameters, such as the number of PMs, recipe time, WAC time, and process time, while 23 values were used for JIT1. In addition, since the data of the semiconductor fab cannot be used for security reasons, as in Figure 2, the throughput result data by simulation of Lam Research were used. Lam Research is a cluster facility based on the Petri net model. Petri net configuration simultaneously processes the loops of PM, AL, and FOUP [29; 30]. The data of the cluster facility is standardized and stores each robot's controller action execution event. WPH is calculated through wafer movement time, wafer process time, wafer WAC time, and waiting time. After the production of the unit, the lot is finished, and the result is saved as an event. This can be expressed as Equation (1) for the calculation of WPH [30]. Equation for maximum productivity of cluster facilities:  
\[Throughput=\frac{(Number\_of\_Chamber\_\times 3600\ s/\mathrm{h})}{(Process\_Time+WAC\_Time+Waer\_Swap\_Time)} \tag{1}\]  
Here, the wafer swap time is a variable that calculates the process rate from when the wafers starting from the load port are out of load in all chambers until all wafers are returned to the load port. Throughput calculated in this way is immediately saved as event data after the entire lot process is finished. Therefore, it is possible to find direct and indirect influence factors by analyzing variables related to throughput through event data analysis [31].