Design of Experiments Project Report
IEE 572
Design of Experiments
Experimental Design in Simulation of Semiconductor Manufacturing
Dr. Douglas Montgomery
Date: December 13, 2000
Team:
Chanettre Rasmidatta
Ching I Tseng
Aditya Rastogi
Executive Summary
Due to the competitive market today in the semiconductor industry, ABC Co. wants to investigate the factors, which affect the average cycle time and throughput. The objective is to minimize the average cycle time and maximize throughput. Since the model has eight factors and two levels each, we want to identify the factors that have large effect. By doing this, 28-4 fractional factorial design is demonstrated and single replication with 6 runs at the center is also used in this experiment. We have emphasized the use of these designs in screening experiments to quickly and efficiently identify the subset of factors that are active and to provide some information on interaction. Half-Normal plot is used in the ANOVA, residual analysis and model adequacy checking, regression analysis and contour plots to help the engineer to have the better interpretation of the experiment as well to examine the active factors in more details.
The results from the experiment suggest that only two out of eight factors were significant, which are release rate and dispatching rule. The model passed the tests for normality and independence assumptions. In additions, the validity of the model was performed based on the regression models to verify the two responses, average cycle time and throughput. The model was verified using the confirmation run and the error was less than one percent. The predicted values were very close to the actual values and thus supporting the design.
Based on the results, we recommend that SSU dispatching rule should be used at release rate of 19.5K wafers per month is the best combination to yield a higher throughput and lower average cycle time.
TABLE OF CONTENTS
1. Experimental Design in Simulation of Semiconductor Mfg. 4
1.1 Problem Statement
1.2 Description of the Model
2. Choice of Factors Levels and Range 6
3. Selection Response Variable 8
4. Choice of Experimental Design 9
5. Performing the Experiment 10
6. Statistical Analysis of the data 11
6.1 Analysis of Variances (ANOVA)
6.2 Model Adequacy Checking
6.2.1 Normality Assumption
6.2.2 Residual Analysis
6.2.3 Box-Cox Transformation
6.3 Regression Analysis
6.3.1 Average Cycle Time
6.3.2 Throughput
6.4 Interaction Graph of Factors A and G
6.5 Optimal Designs
7. Conclusions 24
7.1 Confirmation Testing
7.2 Recommendations
APPENDIX 27
1. Experimental Design in Simulation of Semiconductor Manufacturing
1.1 Problem Statement
ABC Co. is a leading semiconductor manufacturing company. Lately they have discovered that modeling the semiconductor manufacturing and simulating it for various conditions would save lot of time and resources. The manager of the ABC Co. wants to investigate the factors, which affect the average cycle time and throughput. The objective is to minimize the average cycle time and maximize throughput. The lesser the cycle time, the lesser the work-in-process, which means lesser investment in inventory. The shorter cycle time also provides market responsiveness. With this goal in mind he wants to plan an experiment or sequence of experiments designed to take him in the direction of that goal.
1.2 Description of the Model
The model represents a 300mm DRAM facility with approximately 450 process steps and 398 process tools providing 1709 total tool ports, WIP positions, handlers, etc. that are grouped into 80 tool groups. There are 15 operators in 8 different types and the maximum designed capacity was 20,000 wafers/month. Only one type of DRAM part, which processes through one routing, is released into the system. The flow is a highly re-entrant, i.e. jobs feedback through sequences of the tool-groups many times. A lot of 25 parts is released at a fixed interval depending upon the maximum designed capacity. Twenty-one types of reticles, generic resources, with a capacity of two each, are used. Process tool downtimes for both preventative and unexpected maintenance are incorporated, along with employee lunches and breaks. AutoSched AP, a commercial simulation software package was used to model this system.
This model simulates the manual material handling system and the various assumptions for this system are listed below:
· There is no operator’s traveling time to the front of stocker when an inter-bay movement was requested.
· Gaining access to stockers in a bay is considered as resource contingent.
· Load and unload times are 1 minute each.
· The average operator’s traveling speed is assumed to be 2 miles/hr, which is a reasonably slow walking speed, considering the weight of the AGV (Automate Guide Vehicle).
· To compensate for safety precautions and other human factors in the Fab, travel times used are equal to [distance/speed]*a, where a is equal to 1.5.
2. Choice of Factors Levels and Range
From the previous experiment and experience, the Potential Design Factors and the Nuisance factors can be identified. The potential design factors are number of operators, release rate, dispatching rule, stocker quantity, and number of reticles, of which number of reticle is held-constant factor and the design factors are:
1) For operators, there are 5 factors and two levels each. The operator in this model is responsible for loading and unloading the wafers on the machines and they are also responsible for transportation of wafers within the Fab. Varying the number of operators would possibly affect the performance of the system.
2) Release Rate, i.e. the rate at which the wafers are released into the factory, has two levels. The release rate is measured by the number of wafers scheduled to release into the Fab per month. The release rate affects the machine utilization, specially the batching machine that in turn affects the system performance.
3) The dispatching rule for the bottleneck workstations has two levels. The bottleneck machines were identified from the previous experiments. According to the theory of constraints, the bottleneck machine determines the capacity of the Fab that determines the throughput.
4) Stocker Quantity, which has two levels. In this model the stockers are treated as stations and there is one stocker at each bay. The shortage of stockers can cause blocking which can severely delay the manufacturing processes.
The details of the factors, level and range are given in the table below
Table 1 Design Factors and their Levels
Factor / Levels / RangeOperator
OP_DIFF / 2 / 2 / 4OP_PHOTO / 2 / 2 / 4
OP_ETCH / 2 / 3 / 5
OP_WET / 2 / 2 / 4
OP_MOVE / 2 / 35 / 55
Release Rate / 2 / 18K / 19K
Dispatching Rules / 2 / FIFO / Same Setup
Stockers Qty. / 2 / 2 / 4
The Nuisance Factors are the various distributions for the processing time and the down time, which are uncontrollable or the noise factors. The controllable nuisance factor that can be identified is the random number stream that is to be used for the simulation. We intend to keep the random number stream constant throughout the experiment.
3. Selection Response Variable
The purpose of the study is to determine the time taken for a lot of wafers to be produced. This factor is best represented by the average cycle time and thus the average cycle time happens to be one of our response variables.
Various other parameters are necessary to determine the proper running of the factory, one of which is the throughput. Thus the two-response variables for our project are:
1) Average cycle time and
2) Throughput
Cycle time is defined as total elapsed time from lot creation to lot completion that include process time, move time, queue time, and hold time.
The average output of a production process (machine, workstation, line, and plant) per unit time is defined as the system’s throughput.
These response variables can be obtained from the simulation output report. The simulation would run for a period of time at steady state. The steady state would be determined by a long initial run and the statistics collected during this warm-up period would be eliminated from the simulation output.
4. Choice of Experimental Design
Since the model has eight factors and two levels each, we need to identify the factors that have large effects. To do so, screening experiments will be used at the initial stage of the experiment. We will use the 2k Fractional Factorial Design for this screening experiment. We choose 28-4 Fractional Factorial Design, single replication with 6 runs at the center point as shown in Table 2. We determine the number of runs from the results of the Design Expert software.
The alias for this design is a bit different for factor A. The possible reason for this could be the use of center points and also that the factor A is a categorical factor. The defining relation and the aliases is shown in Appendix 1.
Table 2: Design Matrix
Std / Run / Block / Factor1: DISPATCHING RULE / Factor2: OP_DIFF / Factor3: OP_PHOTO / Factor4: OP_ETCH / Factor5: OP_WET / Factor6: OP_MOVE / Factor7: RELEASE RATE / Factor8: STOCKERS QTY. / R1: AVG. CYCLE TIME / R2: THROUGHPUTHours / Lots
1 / 21 / Block 1 / {-1} / -1 / -1 / -1 / -1 / -1 / -1 / -1
2 / 14 / Block 1 / {1} / -1 / -1 / -1 / -1 / 1 / 1 / 1
3 / 17 / Block 1 / {-1} / 1 / -1 / -1 / 1 / -1 / 1 / 1
4 / 22 / Block 1 / {1} / 1 / -1 / -1 / 1 / 1 / -1 / -1
5 / 3 / Block 1 / {-1} / -1 / 1 / -1 / 1 / 1 / 1 / -1
6 / 12 / Block 1 / {1} / -1 / 1 / -1 / 1 / -1 / -1 / 1
7 / 9 / Block 1 / {-1} / 1 / 1 / -1 / -1 / 1 / -1 / 1
8 / 20 / Block 1 / {1} / 1 / 1 / -1 / -1 / -1 / 1 / -1
9 / 10 / Block 1 / {-1} / -1 / -1 / 1 / 1 / 1 / -1 / 1
10 / 2 / Block 1 / {1} / -1 / -1 / 1 / 1 / -1 / 1 / -1
11 / 8 / Block 1 / {-1} / 1 / -1 / 1 / -1 / 1 / 1 / -1
12 / 13 / Block 1 / {1} / 1 / -1 / 1 / -1 / -1 / -1 / 1
13 / 11 / Block 1 / {-1} / -1 / 1 / 1 / -1 / -1 / 1 / 1
14 / 19 / Block 1 / {1} / -1 / 1 / 1 / -1 / 1 / -1 / -1
15 / 6 / Block 1 / {-1} / 1 / 1 / 1 / 1 / -1 / -1 / -1
16 / 18 / Block 1 / {1} / 1 / 1 / 1 / 1 / 1 / 1 / 1
17 / 16 / Block 1 / {-1} / 0 / 0 / 0 / 0 / 0 / 0 / 0
18 / 1 / Block 1 / {1} / 0 / 0 / 0 / 0 / 0 / 0 / 0
19 / 7 / Block 1 / {-1} / 0 / 0 / 0 / 0 / 0 / 0 / 0
20 / 15 / Block 1 / {1} / 0 / 0 / 0 / 0 / 0 / 0 / 0
21 / 4 / Block 1 / {-1} / 0 / 0 / 0 / 0 / 0 / 0 / 0
22 / 5 / Block 1 / {1} / 0 / 0 / 0 / 0 / 0 / 0 / 0
5. Performing the Experiment
The experiments were performed using the AutoSched AP simulation software package. In the initial stage, one long run was made to determine the warm-up period. The warm-up period is the time taken by the simulation model to reach a steady state, where no statistics is collected. Cycle time was plotted against time (in days) and the period was determined to be 94 days as shown in Figure 1.
Fig.1 Warm-up Period Determination
The run length was determined to be 3 years and only single replication was made at each run due to the limited resources. A single run took about two and half hours on a fast machine (PIII, 800Mhz). Refers to Appendix 2 and see the Result Matrix.
6. Statistical Analysis of the data
Upon completion of the runs, the results were fed to the Design Expert software and the results were analyzed. As mentioned earlier, the design chosen was a resolution IV, 28-4 fraction factorial design. The analysis includes ANOVA, residual analysis and model adequacy checking, regression analysis, and contour plots. These analyses are discussed in detail below.
6.1 Analysis of Variances (ANOVA)
Figure 2 below shows the half-normal plot, which shows the effects of various factors. Based on this graph, where the response variable is average cycle time, the factors that lie along the line are negligible and three factors seem to be significant. The two main effects from this analysis are A and G and a two-factor interaction AG.
Fig.2 Half-Normal Plot of Average Cycle Time
The similar analysis was performed for response variable, throughput, as shown in the Figure 3 below.
Fig.3 Half-Normal Plot of Throughput
Table 3 shows the results of analysis of variance. Based on the response variable, average cycle time, it shows that the factors that we chose are significant and their interaction is significant, and that there is no evidence of second-order curvature in the response.
Table 3 ANOVA for Avg. Cycle Time