# Simulation-Based Analysis on Operational Control of Batch Processors in Wafer Fabrication
## 1 Introduction  
In wafer fabrication facilities, semiconductor chips are made out of silicon wafers, thin and round slices of semiconductor material, by building electrical circuits on wafers layer by layer. Each layer requires a number of different processes, including oxidation, photolithography, etching, diffusion, deposition, ion implantation, etc. Wafers in the wafer fab move through these processes in lots generally consisting of 20-25 individual wafers. In general, a wafer lot goes through 500-700 process steps on more than one hundred machines [1]. Since semiconductor processing equipment is very expensive, it is shared by the jobs during different process steps, leading to reentrant product flow. (In this paper, the jobs refer to wafer lots.) Because of the long sequences of operations and resource sharing caused by reentrant product flow, most wafer fabs suffer from high work-in-process (WIP) inventories and long lead times (often more than one month). Since the cost of building a wafer fab is enormous, often more than ten billion dollars [2], the system capacity cannot be easily expanded. Hence, the wafer fab should be efficiently operated with a given facility capacity. The process equipment in the wafer fabs is often classified into two types: Discrete processors (DPs) and batch processors (BPs). The DPs process wafers one at a time while the BPs process several wafer lots simultaneously as a batch. Diffusion furnace is a typical example of the batch processor where several wafer lots are placed in a reactor, which is then sealed, heated and filled with carrier gas for changes of their electrical and chemical characteristics [3]. The wafer lots arriving at the BP station are formed as a batch before being served by one of the batch processors. After a batch of wafer lots receive a process service, the batch is split into individual wafer lots before they are transferred toa downstream station. Due to process or facility constraints, there is a limitation on the number of wafer lots in a batch that a batch processor can accommodate, which is referred to as batch capacity. Once a processing cycle begins, additional lots cannot join the batch being processed and must wait for a batch processor to become free. Due to the chemical nature of the process, it is often impossible to include the wafer lots with different recipes together in the same batch [4]. The wafer lots with the same recipe can be viewed as a job family. The job families are incompatible in that the jobs of different families cannot be processed together. In wafer fabs with reentrant characteristics, the wafers of the different processing steps need different processing recipes. Hence, even for the same wafer lots, the job family of a wafer lot depends on its current operation step. Figure 1 shows a schematic representation of a BP station with three batch processors whose batch capacity is six. In the figure, two BPs are under operation while one BP is idle because there are no job families with a full load currently waiting in the queue. (Here, a full load operation is assumed.) The processing time at the batch processors is very long compared with discrete processing times. When a BP finishes processing a batch of wafers, it releases multiple wafer lots to its downstream workstations. The bunched flow of wafer lots leads to the formation of high WIP inventories at the downstream stations, and so the manufacturing systems with BPs suffer from high flow variability. The distinct characteristics of batch processors have a significant influence on the overall wafer fab performance. A batch of wafers should be loaded first before they have processing service on a BP. The loading decision at a BP station is made at two instances [5]: (i) When wafer lots arrive at the BP station (a push decision); or (ii) when a batch processor becomes available (a pull decision). If a batch with a full load and a batch processor are both available, the batch is loaded and processed immediately.