Vehicle OHT DispatchingPerformance Analysis ofan AMHS in 300mm Semiconductor FABs

ZHOU Bing-hai(周炳海)，ANAR Jean-Marie，ZHENG Wen(郑 雯)

School of Mechanical Engineering，Tongji University，Shanghai 201804，China

Introduction

Semiconductor fabrications are well known for being one of the most complex manufacturing processes［1］.In semiconductor industry，for the semiconductor fabrication plants，automated material handling systems［2］(AMHSs)have been widely used to transport wafer lots.Semiconductor manufacturing process includes a lot of processing steps.Wafer lots repeatedly go through deposit film，pattern film，etch film，wafer testing，and cleaning process.During the manufacturing process，an inter-bay of AMHSs moves wafer lots between stockers，whereas an intra-bay of AMHSs moves wafer lots between stockers and tools，or between tools within the same bay.The material handling cost stands for 20%to 50%of the total manufacturing cost， and material handling in semiconductor fabrication line is critically important.However in the inter-bay and intra-bay，bottlenecks and queuing time still occur due to many causes such as machine unreliability，number of overhead-hoist-transport(OHT)vehicles，queuing time，processing time，loading ratio，and percentage of priority jobs.To avoid such inconveniences that may lead to considerable losses，carefulattention mustbe focused on the OHT dispatching policies.

These policies can be classified into three main categories:single attribute dispatching rules，multi-parameter dispatching rules，and vehicle positioning rules.On the one hand，single attribute dispatching rules［3，4］only include one attribute such as wafer lots priority in process［5］or bottleneck machines［6］.Other common investigated rules［7］are as follows:first in first out(FIFO)，earliestduedate(EDD)，shortestremaining processing time(SRPT)，critical ratio(CR)，and modified nearest job(MNJ)［8］.On the other hand，multi-parameter dispatching rules include several parameters simultaneously or sequentially.Therefore ithasbeen presented two OHT dispatching rules based on the Hungarian algorithm［9，10］:one is a fuzzy logic-based multi-mission oriented dispatching rule［11］，the other is a heuristic preemptive dispatching rule［12］.Vehicle positioning rules consider distance among OHT vehicles［13］，vehicle movements［14，15］， trans-locating assignments［16］，preemptive areas［17］，and so on.A multi-attribute dispatching rule is proposed based on the Hungarian algorithm.It integrates six factors:distance between lots and vehicles，waiting time in queue，number of lots in queue at the departure，number of lots in queue at destination，carts utilization，and lot priority.A peculiarity of the semiconductor manufacturing process is the presence of prioritized wafer lots.These wafer lots can be executed with different operations for experiment or inspection on process conditions，and also they can be born as pilot or risk wafer lots for process characterization or design validation before releasing a new product for production.Such wafer lots are called hot wafer lot(HWL)or super hot wafer lot(SHWL)，and they should be given priority over others.Another peculiarity of the semiconductor manufacturing process is the high cost of the OHT vehicles;consequently they must be dispatched wisely and efficiently.A plant manager aims at reducing the total production cost by minimizing the number of OHT vehicles circulating in the layout，thus the utilization of OHT vehicles must be optimized.In order to consider these two peculiarities，they are integrated into the dispatching rule.However，literatures are seldom reported that those two last parameters have been integrated simultaneously with the other one and used to obtain a balanced efficiency regarding the FAB output factors.

1 Problem Statements

A common AMHS can be described as a combination of three main elements:stockers，tracks，and OHT vehicles.In the presented model，it is considered that OHT vehicles perform direct delivery，which means that the OHT vehicle doesn’t need to stop by a stocker while performing a delivery.While in traditional wafer plant，an OHT vehicle doesn’t perform direct delivery.Since OHT vehicle movements are restricted to specific zones，from its point of departure to its final destination a wafer lot is carried by several OHT vehicles in a traditional wafer fab.Here a wafer fabrication line with 2 stockers and 4 bays is considered.Each bay contains 6 processing stations，thus the fabrication line has a total of 24 workstations.Wafer lots are carried between these stations by OHT vehicles.These OHT vehicles use the single track loop to move between the bays of the system，and consequently the OHTs are not allowed to pass while OHTs are on the same track.However shortcuts are installed to avoid possible bottlenecks on the rail.Note that the OHT vehicles are allowed to move only in a clockwise direction.Since there is only one rail，this measure prevents frontal collision between OHT vehicles.Furthermore，in our model，two types ofmovement are considered:inter-bay movement and intra-bay movement.A movement is considered as an inter-bay transportation when the departure station and the arrival destination station are in the same bay.The inter-bay transport movement means that the OHT vehicle has to go through the central rail to accomplish the transport.Wafers are contained in compartments called front opening unified pods(FOUPs)，which are dropped down or picked up by the OHT vehicle at the processing stations.It is assumed that an OHT vehicle can transport only one wafer lot at a time.

A bay is composed of a workstation，a buffer-in，and a buffer-out.When a process is over，the outgoing wafer lot is stocked in the buffer-out where it requests an OHT vehicle to pick it up.It then stays in the buffer-out until an OHT vehicle responds to its request and comes to pick it up.

Three types of wafer lots are in the wafer processing line and each one follows its own sequence.Moreover，since the proposed model takes into consideration the level of priority of the jobs，each wafer lot is assigned a level of priority from regular wafer lot，HWL or very HWL.Thus，wafer lot 1，wafer lot 2，and wafer lot 3 are considered as very HWLs，HWLs，and regular wafer lots correspondingly.Obviously the number of wafer lots of each category is distributed according to a discrete probability distribution rule.Indeed，regular wafer lots outnumber the very HWLs.A type(1，2 or 3)is assigned to each wafer lot that enters in the wafer production line;however the type of the next wafer lot entering can't be forecast.This allows keeping the stochastic effects which exist in real wafer plants.

After entering in the production line，wafer lots will follow sequences according to their types.As mentioned above，there are some characteristics such as re-entrant processing，variant processing times，and stations shared between wafer lots in a wafer processing line.Thus，three different sequences are set with the specificities.Each wafer lot has a 15-step sequence with variant processing times，so that the process can be considered as non-synchronous.The sequences are defined in Table 1.

Table 1 Wafer lots sequences

The model is built with Arena 9.0 Rockwell Software.Four，five or six OHT vehicles are dedicated to the transport of wafer lots in the layout.OHT vehicles follow a specific module sequence，when they arrive at the dispatch module.Every time an OHT vehicle goes through the dispatch decision module while a Visual Basic(VB)code is launched，and the active OHT vehicle is dispatched according to the outputs of the entire FAB system.The system can be considered as dynamic，since its information is updated when an OHT vehicle becomes idle.This scenario logic is necessarily given that there is no parking for the OHT vehicles.It is assumed that an OHT vehicle can have only two states:idle or busy.An OHT vehicle is considered as idle when it doesn’t answer a request.It is considered busy while it carries a wafer lot to its destination or while it answers a request.

2 Dispatching Rule Presentation

It is assumed that the OHT dispatching issue can be considered as an assignment problem.There are n OHT vehicles that can be assigned to l wafer lots;each assignment involves a transportation cost.Moreover，all wafer lots must be moved，and one OHT vehicle can only be assigned to one wafer lot so that the final cost is minimized.

2.1 Definition of the assignment problem Let

andcijstands for the cost of matching lot j with OHT vehicle i.Minimize

There are several methods to solve this problem above.The presented dispatching modelis based on the Hungarian algorithm，which is also called Munkres algorithm.The Hungarian algorithm solves the assignment problem within time bounded by a polynomial expression of the maximum between n and l.The main advantage of using the Hungarian algorithm is that it allows to consider several parameters simultaneously.However，the Hungarian algorithm is a 5-step algorithm that must be adapted to the dispatching problem.Thus，an original cost parameter is introduced.This cost parameter is designed according to the requirements of the OHT dispatching problem，because it directly impacts the dispatching of the OHT vehicles.

2.2 Hungarian algorithm steps

Let’s consider a cost matrix C whose coefficient Cijis the cost of matching OHT vehicle i with wafer lot j.Since matrix C must be squared，if the number of OHT vehicles is different from the number of requesting wafer lots，dummy wafer lots or dummy OHT vehicles are added to obtain a squared matrix.

Step 1Create a new cost matrix by choosing the minimum cost for each row and subtracting it for each row.

Step 2Create a new cost matrix by choosing the minimum cost in each column and subtracting it in each column.

Step 3Determine the minimum number of lines required on the rows and columns to cover all the zeros.If this number is equal to the number of rows(or columns)，the matrix is reduced，and go toStep 5.If this number is lower than the number of rows(or columns)，go toStep 4.

Step 4Find the minimum value among the cells which are not covered by a line.Subtract this value to all the cells which are not covered.Add this value to the cells located at the intersection of two lines.Return toStep 3.

Step 5Determine the optimum solution.

2.3 Cost parameter design

A multi-attribute dispatching policy is presented with considering sixdifferent outputs ofthe FAB system.To integrate these six outputs，a specific cost coefficient is designed.All these coefficients are updated when an OHT vehicle becomes idle.The queues in the system are scanned to find requesting wafer lots.If a queue is empty，it is assigned a prohibitive coefficient.Therefore，no OHT vehicle can be sent to it.

3 Simulation and Results

To test the efficiency of the proposed dispatching policy，the following usual single attribute dispatching rules can be used as benchmarks to compare with the proposed rule:Shortest Travel Distance(STD)rule，Waiting Time First(WTF)rule，and Preemptive Job First(PJF)rule.

otherwise，the response must be minimized

where Yiminand Yimaxare the lower and the upper limits defined for each output studied，respectively.

Simulationis run by using Arena Rockwell Software and its VB function user，on a 2.8 GHz Intel Core i7 MacBook Pro with 1.5 GB of RAM using Parallel Desktop to run Windows XP. Foreach scenario，the simulation experiments are performed for 77 h with a 5 h warming period.Moreover，the simulation experiments are run according to the assumptions described in the first part.The layout designed to meet these requirements is presented in Fig.1.Since the impact of the six weight parameters is studied，4 096(46)scenarios are run.In this manner，one can assign a weight between 0 and 3 to each parameter.All combinations of parameters are studied.

Fig.1 Wafer FAB layout of Arena Rockwell model

Over 4 000 simulations are run to test the efficiency of the proposed dispatching rule.Since it involves six different outputs，a multi-answer output impact on the FAB system is expected.To analyze the relevance ofthe proposed cost parameter，the evolution of these outputs as a function of the value of the desirability function is studied.Especially the evolution of LT is studied according to the desirability function(Fig.2).Furthermore the evolution of CT is studied(Fig.3).The weight parameters xDand xPare the most important weight parameters according to the sensitive analysis results，since their average mark is equal to or greater than two in the fifty best scenarios(respectively 2.59 and 2.00).However they must be associated with other input parameters to reach their best efficiency.

Since the results with 4 OHT vehicles(Table 2)are quite comparable with other results obtained with 5(Table 3)and 6 OHT vehicles(Table 4)，the discussion is focused on the first results.For the five scenarios，the average WIP is 23.34 wafer lots，which highlights the fact that the FAB runs with a low stock rate.Indeed，there are 24 stations in the layout model and the WIP is 22.13 wafer lots for the best scenario.It means that stock costs are saved，which is highly valuable particularly in wafer industry.This observation is also confirmed by the value of the LT. Indeed，LT is 0.369 for the best scenario.Compared with STD and WTF，it is respectively 65%(from 1.065 h to 0.369 h)and 63%(1.006 h to 0.369 h)decrease.

Concerning the HWL rate，the average arrivals of wafer lots with early due date are 20%in our simulation model，so a 20%HWL ratio is expected at least at the exit system.The best HWL ratio is obviously obtained by the PJF policy，which is logical given that priority wafer lots are preemptive on regular wafer lots. Yet，this high HWL ratio must be put into perspective.The other indicators are not optimized for PJF.However，results indicate that regular wafer lots are not carried by OHT vehicles;only wafer lots with priority 1 or 2 are considered by the rule at the expense of regular wafer lots ranked 3.

The average resource utilization is low from 23.68%(for WTF)to 43.27%(for STD)，but the goal is not to optimize the resource utilization even if it is a crucial point in a wafer FAB(scheduling problem).However the proposed dispatching rule outperforms WTF(+66%from 23.68%to 39.29%)and PJF(+38% from 28.34% to39.29%)concerningthis indicator.But it doesn’t outperform STD.Indeed，processes are often busier because the WIP level is very high(44.68 wafer lots).

The OHT utilization is over than 70% for the scenario proposed，and even reaches 79.84%.It is 65%more than PJF(from 48.26%to 76.99%)and 64%more than WTF(from 48.68%to 76.99%).The STD reaches 87.5%，which is 14%more than scenario#1.

TP and CT are also observed，for the scenarios from 1 to 5.The average TP is 3.5 wafer lots per hour.It is 86%more than PJF and 67%more compared with WTF.However，when there are 6 OHT vehicles，the STD is outperformed by all the scenarios and especially by scenario#5(17%from 3.906 to 4.571).Moreover the lowest CT is made by scenario#1 with 41.629 h CT，thus wafer lots in scenario#1 spend on average less time in the processing line than wafer lots which belong to STD，WTF or PJF.

Table 2 Simulation results(mean and StDev)of 4 OHTs

Table 3 Simulation results(mean and StDev)of 5 OHTs

(Table 3 continued)

Table 4 Simulation results(mean and StDev)of 6 OHTs

4 Conclusions

An AMHS in 300 mm semiconductor manufacturing system is a highly automated system，where OHT vehicles carry wafer lots.However，transport is a non-value added task in the processing line.Thus OHT dispatching logics are trying to achieve a zero waiting time.This goal is made difficultly by the specifications of the wafer fabrication process.The proposed dispatching rule was implemented on a reduced model of wafer FAB processing line with 24 work stations and four，five or six OHT vehicles with a non-synchronous processing line.Six system inputs are integrated into the cost parameter of the Hungarian algorithm to improve the productivity of the system.We particularly focus our attention on OHT vehicles utilization and priority ratio of wafer lots.Thanks to a sensitive analysis and a desirability function，the five best solutions are filtered and compared with the single attribute dispatching rules.A compromise is found among WIP，lead-time，throughput，cycle time，and to a lesser extent process utilization.Moreover hot wafer lot ratio and OHT vehicle utilization are maintained at a high level to keep the efficiency of the FAB system.Thus，for a manager，this dispatching rule can be a helpful support for decision in a wafer plant.

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