離子植入機台最適氣體類型配置與工件排程

Abstract

本研究探討半導體廠中離子植入機的二個生產規劃問題，離子植入機的主要功能為對晶圓進行離子摻雜的動作，一部典型的離子植入機最多可安裝三種不同的氣體，且設置時間發生在工件使用不同氣體進行加工時，因此當機台安裝的氣體種類越多時，其功能也越多，但相反地機台則需花費更多的時間在測試氣體每年所產生的新配方是否合格，如此才可作為工件加工時所用，故本研究第一個子題即為探討機台最適氣體類型配置決策，在此決策下假設有m部機台和k種氣體，則氣體應該如何配置與配置幾種的情況下，利用混合整數規劃法可使得機台利用率最大化。之後假設機台最適氣體類型配置已知下，探討工件最佳指派加工和工件最佳排序加工決策，我們利用三種巨集演算法，分別為基因演算法(GA)、模擬退火法(SA)和禁忌搜尋法(TS)來求解問題，並執行大量實驗，結果顯示混合整數規劃法(MIP)可在合理時間內求出最佳的氣體類型配置，而基因演算法求解結果均優於其他二種演算法，可求出工件最佳加工順序與工件最佳指派加工組合。

This research examines two production planning problems for ion implanters, which are a type of machines in semiconductor manufacturing. The function of an ion implanter is to inject various chemical ions (also called chemical gases) into the surface of a silicon wafer. Each type of chemical gas is fed to an ion implanter through a distinct gas pipe. A typical ion implanter in practice can be installed at most with three different types of chemical gases, and a setup time is needed while changing gas types. The more number of gas-types is installed on a machine, the more versatile is the machine—yet at the expense of taking more time to qualify (or tune) the machine while introducing new recipes. Such a trade-off characteristic leads to our first research problem—the gas-type allocation problem. That is, suppose there are m ion implanters and k gas types, how many and which gas-types should be installed on each machine in order to maximize the utilization of the ion implanters for a forecasted demand scenario. We develop a mixed integer program (MIP) to solve the gas-type allocation problem. Assuming the gas-type allocation decision has been made, our next effort is to examine a job allocation and sequence problem. That is, suppose there are n jobs and m machines with pre-defined gas-type patterns, how to allocate jobs to machines and how to sequence the jobs allocated to each machine. We develop three meta-heuristic algorithms, genetic algorithm (GA), simulated annealing (SA), and tabu search (TS), to solve the problem. Extensive numerical experiments have been carried out. Results indicate that the MIP model can find the optimal gas-type allocation problem in reasonable CPU time, and the GA outperforms the other two heuristic algorithms in dealing with the job allocation and scheduling problem.