提昇晶圓允收測試資料異常速移偵測之研究

行政院國家科學委員會補助專題研究計畫成果報告

行政院國家科學委員會補助專題研究計畫成果報告

行政院國家科學委員會補助專題研究計畫成果報告

行政院國家科學委員會補助專題研究計畫成果報告

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提昇晶圓允收測試資料異常速移偵測之研究

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The Enhanced Abnormal Shift Detection of Wafer Acceptance Test Data

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計畫類別：個別型計畫

計畫編號：NSC－89－2213－E－002－125

執行期間：89 年 8 月 1 日至 90 年 7 月 31 日

計畫主持人：郭瑞祥

共同主持人：張時中

本成果報告包括以下應繳交之附件：

□赴國外出差或研習心得報告一份

□赴大陸地區出差或研習心得報告一份

□出席國際學術會議心得報告及發表之論文各一份

□國際合作研究計畫國外研究報告書一份

執行單位：台灣大學工商管理學系

中 華 民 國

90 年 8 月 1 日

行政院國家科學委員會專題研究

行政院國家科學委員會專題研究

行政院國家科學委員會專題研究

行政院國家科學委員會專題研究計畫成果報告

計畫成果報告

計畫成果報告

計畫成果報告

提昇晶圓允收測試資料異常速移偵測之研究

The Enhanced Abnormal Shift Detection of Wafer Acceptance Test Data

計畫編號：NSC 89-2213-E-002-125

執行期限：89/08/01 ~ 90/07/31

主持人：郭瑞祥 台灣大學工商管理學系

共同主持人: 張時中 暨南大學電機工程學系

摘要

晶圓允收測試資料係指晶圓在完成所有製

造程序後，測試結構所量測的電性測試參數。

此類參數的分析能夠快速的評估整體製程狀

態，並提供了製程異常狀態的警訊以及產品元

件的電性特性。然而由於晶圓允收測試資料是

在生產線末端量測而得，他們具有多機台及時

序錯亂的雙重效應，因此通常不容易直接偵測

出其異常趨勢。為了提昇異常趨勢的偵測速

度，我們利用到生產線上某部機台的製程有速

移時，晶圓允收測試資料的平均值及變異數都

會增加之特性，同時監看晶圓允收資料的平均

值、變異數及製程能力指標，因此發展了一套

結合

Shehwart 管制圖，指數加權移動平均圖

(Exponentially Weighted Moving Average)與指

數 加 權 移 動

Cpk 圖 的 晶 圓 允 收 監 看 系

統:SHEWMAC。經由模擬分析與晶圓廠資料實

證分析，驗證本研究之

SHEWMAC 法較傳統的

Shewhart-EWMA 法更能快速偵測製程異常速

移。

關鍵詞：

關鍵詞：

關鍵詞：

關鍵詞：晶圓允收測試資料，統計製程管制，

指數加權移動估測法

Abstract

Under the effects of multiple-stream and

sequence-disorder, process change caused by one

machine at an in-line step may result in changes

in both the mean and variance of end-of-line

wafer acceptance test (WAT) data sequence. To

speed up trend detection of WAT data without

resorting to an intensive computing power, an

end-of-line SHEWMAC scheme is proposed,

which combines a Shewhart, an exponentially

weighted moving average (EWMA), and an

exponentially weighted moving Cpk (EWMC)

charts for jointly monitoring the mean and

variance of wafer lot average sequence from WAT

data. In view of the wide ranges of process

conditions and low volume of each product in a

foundry fab, a data normalization technique is

adopted to aggregate data of similar products and

a new design method is developed to generate a

robust set of scheme parameters. Simulation

and field data validation show that SHEWMAC is

superior to the combined Shewhart-EWMA

scheme in shift detection speed and is

complementary to the in-line SPC.

Keywords: Wafer Acceptance Test, Statistical

Process Control, Exponentially Weighted Moving

Average

I. INTRODUCTION

Statistical Process Control (SPC) techniques have

been widely adopted in semiconductor fabrication for the purpose of in-line process monitoring and control. Nevertheless, from the viewpoint of process integration, statistical stability at the in-line level does not guarantee the stability of the whole IC fabrication process. Quality control techniques such as acceptance sampling test, trend/control chart, and variance decomposition have therefore been applied and/or extended by fabs [1]-[3] to the monitoring and control of end-of-line wafer acceptance (WAT) data.

WAT data provides the integral statistics about process stability and product performance. It has the salient features of sequence disorder (SD) and multiple

streams (MS) due to operation dispatching as compared

with in-line data of individual machines and/or fabrication steps. In presence of the two features, a change caused by one machine at an in-line step may result in changes in both the mean and variance of a WAT data sequence. A current industrial practice groups WAT data over a period of time (window) and monitors mean, variance or process capability index (Cpk) of data groups respectively. In specific, a control chart of Cpk may serve to detect combined changes in mean and variance, and a window size of one week is taken for grouping so that trend patterns can be extracted under the salient features of WAT data sequence.

In many of the aforementioned WAT monitoring schemes, the control limits and window size are determined empirically because in-line SPC techniques do not apply directly. As a result, window size and control limits thus selected have led to slow process fault detection or frequent false alarms. There have been a lack of solid foundation for the design and analysis of WAT SPC schemes, especially for a fab where product types, process characteristics, and the intensities of SD and MS effects vary widely and frequently.

In [4], the authors proposed a framework of end-of-line quality control (Figure 1) and focused on the end-of-line SPC module. A SHEWMA scheme was developed and implemented in a foundry fab. It is a methodology for generating robust design parameters for the simultaneous application of Shewhart and EWMA control charts to WAT data. Filed data validation shows that the incorporation of SHEWMA control charts complements the existing end-of-line data monitoring/analysis system and in-line SPC schemes for process integration. It indeed improves the false alarm rate, detection speed and diagnosis efficiency from the current practice without resorting to an intensive computing power as the approach taken by [3].

By exploiting the advantages of both SHEWMA and Cpk review schemes, a new and integrated WAT SPC scheme, SHEWMAC, is developed in this research for jointly monitoring mean and variance of wafer lot average sequence from WAT data. The proposed SHEWMAC

scheme consists of a Shewhart, an EWMA, and an exponentially weighted moving Cpk (EWMC) control charts. Figure 2 illustrates the potential advantage of SHEWMAC over SHEWMA. The shaded areas in the mean-versus-variance plots are the respective in-control regions of SHEWMA and SHEWMAC derived by our analysis under approximately the same false alarm rate. It is obvious that when both process mean and variance change together, the monitored statistics are more likely to fall outside the in-control region of SHEWMAC. Namely, SHEWMAC is more sensitive in detecting a combined mean and variance change at a given false alarm rate. Compared with the currently used simple Cpk scheme for batch review, the SHEWMAC scheme has the advantage of easier scheme parameter design and rolling review.

The remainders of this report will first characterize the SD and MS features of WAT data. A SHEWMAC system is then designed for industrial applications. Finally, by using simulation and fab data, the effectiveness of SHEWMAC scheme is validated.

II. SEQUENCE-DISORDER & MULTIPLE-STREAM Figure 3 demonstrates the generation process of a

WAT data sequence. Let {Xi} be a random sequence

representing wafer lot averages of a WAT measurement item, where i is the lot output sequence index at the WAT step. In general, affected by different product flows and dispatching polices, the cycle time from a process step p to the end-of-line WAT step varies among lots. As a result, the lot with a sequence label n at step p very likely has a different lot sequence label i at the WAT step. This is defined as the sequence-disorder effect. Note that the processing of a lot may require more than 300 steps and each step may be processed by any one of a machine group. Define a stream as a sequence of machines that a lot goes through during its fabrication process. There are many possible streams in a fab and the resultant WAT measurements among different streams vary due to machine-to-machine variation. This is defined as the

multiple-stream effect.

A triplet of process conditions (R, M, S) are defined to characterize these two salient features of WAT data, where

- R is the SD range from the monitored step p to WAT

step (defined in Figure 3),

- M is the total number of machines in the monitored

step p, and

- S is the potential magnitude of a shift (in standard

deviation unit).

For example, when (R, M, S)=(15, 2, 1.5), the changes in both mean and variance of WAT data in end-of-line lot

sequence, {X_i}, in contrast with those in in-line lot

sequence from the abnormal machine m is demonstrated in Figure 4. It can be seen that an in-line shift on machine m ramps and then levels off in the WAT data sequence, where the magnitude of leveling off part is reduced and the variance increases as compared with the original in-line shift. It is clear that to enhance the WAT shift detection

speed, the end-of-line SPC scheme should have the capability to simultaneously detect changes in both mean

and variance of {X_i}.

III. SHEWMAC SYSTEM

Figure 5 depicts the schematic diagram of SHEWMAC tool implementation. There are three function modules: Input Data Normalization, Control Charting, and Robust Parameter Generation. In a foundry fab, daily generation of WAT data of each product type may be statistically “rare”. To increase the sample size, WAT data inputs are first normalized so that data of different products belonging to the same processing technology can be aggregated to reach a scale of statistical significance. A normalized data sequence can then be monitored lot-by-lot by the Control Charting module based on the scheme parameters from the Robust Parameter Generation module. The Robust Parameter Generation module takes the requirement of false alarm rate and the possible range of

process conditions Ω≡{(R, M, S)} as inputs. It evaluates

the scheme performance and generates a robust set of SHEWMAC parameters over a wide range of process conditions. The outputs of the SHEWMAC scheme include a Shewhart, an EWMA, and an EWMC control charts of the normalized WAT lot average sequence, and a warning signal when a data point is out of control.

Data Normalization

The objective here is to use the historical WAT lot average sequence to establish the baseline behavior, and later normalize the real time WAT lot average sequence based on this baseline. The baseline behavior consists of

the long-term mean (µˆ_{) and variance ( ˆ}2

X

σ ) of {X_i}. This

paper assumes that {Xi} follows a normal distribution. In

specific, a moving range estimator [5] is adopted to

estimate the variance σˆ_X≈0.887MR , where

∑ = = 0 1 0 / ) (I i i I MR MR ,MRi≡|Xi+1−Xi|,i=1,2,...,I0 , and I0 is the

number of samples. This estimator is unbiased, is robust with respect to shifts in the process mean, and can model the machine-to-machine variation among lots well. Given

µˆ _{and ˆ}2

X

σ , the normalized metric Zi≡(Xi−µˆ)/σˆ_X will be

approximately normally distributed and can be used as the common metric for all products.

Control Charting

In the Control Charting module, the Shewhart chart tests if the average of a lot is normal; the EWMA chart tests if there is any small WAT shift; and the EWMC chart tests if the slight changes in mean and variance result in a significant changes in Cpk. Warning messages from these three charts provide information about the occurrence and the extent of a process shift. If only the EWMA or EWMC chart detects an abnormal trend, there could be a small process shift. When there is a large trend in the EWMA and EWMC charts and a data point out of Shehwart control limits at the same time, a large process shift may

have occurred.

Let the monitored statistics be {Z_i} in the Shewhart

chart. The EWMA sequence is then generated by 1 ) 1 ( − ₋ + = i i i Z A A λ λ 0 1 0W- Z- (1- ) A i i q iq iq λ + ∑ = − = , i=1,2,…, (1) where q q i

W− =λ(1−λ) , 0<λ≤1, and the initial value A0 is

usually set as zero. To get the Cpk values in EWMC chart,

the variance is first estimated by 2

i i i B A V = − , where 1 2 _{(1 )} − − + = i i i Z B B λ λ 0 1 0 2 - Z (1- ) B W i i q q i q i + λ ∑ = − = − , i=1,2,…, (2)

is an exponentially weighted moving estimator of mean

square and B0 is usually set as 1. Given Ai and Bi,

the EWMC sequence is then generated by

(

)

i MinUSL A A LSL V

C = − − , (3)

where USL and LSL are the upper and lower specification limits respectively.

In summary, SHEWMAC scheme parameters consists

of quadruplet (c, λ, h, k), where c is the Shewhart control

limit gain, λ is the EWMA weighting factor, h is the

EWMA control limit gain, and k is the EWMC control limit

gain. Once the SHEWMAC parameters (c, λ, h, k) are

available, control limits of Shewhart chart, EWMA chart,

and EWMC chart are then set as ±c, ±h λ/(2−λ), and k

respectively.

It is clear that Ai and Bi is a moving average and a

moving mean square of {Zi,Zi−1,...,Z1} respectively with

exponentially decreasing weighting coefficients, i.e., they tend to emphasize on utilizing the most recently collected data. To pop out the underlying trend in SD and MS data,

a large window size (a small weighting factor λ) is needed.

However, if the weighting factor λ is too small, the EWMA

and EWMC will not be sensitive to process change and the detection speed will be slow. The other three parameters c,

h, and k should also be designed in accordance with the

choice of λ to maximize the detection speed and maintain a

desirable false alarm rate. Robust Parameter Generation

Figure 6 depicts the design procedures in the Robust Parameter Generation, which are based on the concept of run length. The run length is a random variable characterizing the number of observations that an SPC scheme takes to generate an out-of-control signal after the occurrence of a process change. In view of the fact that in

Eq. (1), each EWMA value Ai is an interpolation of its

former value Ai−1 and the present normalized lot average

i

Z , the average run length of an EWMA chart is usually

characterized as a discrete state Markov chain [6]. Similar to this approach, the Robust Parameter Generation module

models the SHEWMAC as a two-variable, Ai and Bi,

Markov chain. The robust design of SHEWMAC has two folds: to maximize average run length ARL0 for a normal

process and to minimize average run length ARL1 after a process becomes abnormal. In practice, exact process

conditions (R,M,S) cannot be known a priori. For the

feasibility of implementation, the optimal parameters for

each process condition in Ω is first calculated. Then a

robust design of parameters is chosen so that the SHEWMAC scheme results in a satisfactory performance

over possible conditions in Ω.

IV. VALIDATION Simulation

As the proposed SHEWMAC is a simultaneous application of Shewhart, EWMA, and EWMC schemes, it therefore combines all the advantageous features of the three. Figure 7 demonstrates the simulation result that EWMC is good at median shift (1.5~2.5 sigma) detection, EWMA is superior in small shift (<1.5 sigma) detection and Shewhart is suitable for large shift (over 3 sigma) detection. Whichever the shift condition is, the detection speed of SHEWMAC equals the fastest of the three.

Field Data Application

A 0.26 µm logic device is selected with a focus on

monitoring WAT item of Rs_N+, which represents the sheet resistance of N+ structure. In this case, the SHEWMAC

parameters are chosen as (c, λ, h, k)=(3.25, 0.11, 2.90, 0.65)

and the corresponding SHEWMAC control charts are demonstrated in Figures 8(a) and 8(b). The SHEWMAC generates seven warning messages, one from the Shewhart

chart at the 65th _{lot, three from the EWMA chart at the 27}th_,

37th_{, and 64}th _{lots, and the other three from the EWMC chart}

at the 27th_{, 37}th_{, and 55}th _{lots respectively.}

Through the data trace back and stratification functions of engineering data analysis (EDA) systm, it is found that N+ drain/source implant step is the root cause. Figure 8(c) demonstrates the Shewhart chart of Rs_N+ in the lot sequence and processing machines at the faulty step. It is obvious that M1 had a significant machine offset from

the 29th _{to 36}th _{lots in its in-line lot sequence as compared to}

the other machines. Also, a process shift occurred at M4 starting from the 62th lot in its in-line lot sequence. In this case, it is validated that EWMA and EWMC charts are supperior to the Shewhart chart in detecting the samll machine offset of M1. Also, since the EWMC chart reflects the changes in both mean and variance, it enhances the shift detection of M4 by 10 lots as compared to the EWMA chart.

The in-line SPC at the N+ drain/source implant step monitors the sheet resistance taken from the test wafer every 12 hours. It did not detect the two shifts in this case. There may be two reasons. First, the in-line measurements may be less sensitive to the process change as compared to the WAT measurements taken from product wafer. Second, the sampling rate in in-line level is much less than that of WAT. SHEWMAC is thus complementary to the in-line SPC for process integration.

V. CONCLUSIONS

In this research, an end-of-line SPC scheme, SHEWMAC, is proposed to monitor the simultaneous changes in mean and variance of WAT lot average sequence. Simulation and field data validation show that SHEWMAC is superior to the combined Shewhart-EWMA scheme in shift detection speed and is complementary to the in-line SPC.

REFERENCES

[1] D. K. Michelson, “Statistically Calculating Reject Limits at Parametric Test,” Proc. IEEE/CPMT Int'l Electronics

Manufacturing Technology Symposium, pp. 172-177, 1997.

[2] F. N.H. Montijn-Dorgelo and H. J. ter Host, “Expert System for Test Structure Data Interpretation,” IEEE Proc. on

Microelectronic Test Structures, pp. 172-177, 1997.

[3] J. Pak, R. Kittler and P. Wen, “Advanced Methods for Analysis of Lot-to-Lot Yield Variation,” Proc. Int'l Symposium on

Semiconductor Manufacturing, pp. E17-E20, 1997.

[4] C.M. Fan, R.S. Guo and S.C. Chang, “An Integrated Fault Detection Scheme for Wafer Acceptance Test Data,” Proc. Int'l

Symposium on Semiconductor Manufacturing, pp. 440-443,

1998.

[5] E. Yashchin, “Monitoring variance components,” Technometrics, vol. 36, no. 4, pp. 379-393, 1994.

[6] M.S. Saccucci and J.M. Lucas, “Average run lengths for exponentially weighted moving average control schemes using the Markov chain approach,” Journal of Quality Technology, vol. 22, no. 2, pp. 154-162, 1990.

WAT data Root causes Acceptance sampling test End-of-line SPC First-cut diagnosis In-depth

diagnosis and stratificationData trace back

Figure 1: Sequential detection and diagnosis approach for end-of-line quality control

SHEWMA SHEWMAC

Figure 2: In-control regions of SHEWMA and SHEWMAC

15 Y Y16 Y17 Y18 Y19 Y20 20 X 19 X 18 X 17 X 16 X 15 X 1 20= D 4 19= D 2 18=− D 1 17= D 2 16=− D 2 15=− D Machine 1 In-line machine at step p In-line data sequence End-of-line data sequence } ,..., 1 |, max{|D i I R≡ _i = Machine M

Figure 3: Generation process of end-of-line WAT data

W A T d a t a s e q u e n c e -0 .5 0 0 .5 1 1 .5 2 1 4 7 1 0 13 16 19 22 25 2 8 3 1 3 4 3 7 4 0 43 46 49 M ean 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1 4 7 10 13 1 6 19 2 2 25 28 3 1 34 3 7 40 4 3 46 49 Lo t No . Va ri an ce M a c h i n e m d a t a s e q u e n c e M a c h i n e m d a t a s e q u e n c e W A T d a t a s e q u e n c e

Figure 4: The changes in mean and variance of {Xi}

Real time WAT lot average sequence Baseline model estimation Out-of-control warning messages, Shewhart, EWMA & EWMC charts Historical

WAT lot average sequence

False alarm rate requirement & process conditions Robust Parameter Generation Data Normalization Large shift detection Shewhart chart Small shift detection EWMA chart Cpk change detection EWMC chart Input Data Normalization ARL calculation Optimal design Robust design

Figure 5: Schematic diagram of SHEWMAC tool

α _{Ω={(R,M,S)}}

Optimal Designs for Individual Process Conditions

Feasible parameters calculation

} 1 ) , , , ( 0 | ) , , , {( α λ λ = = Φ c hk ARL c hk

Optimal selection of parameters under R, M, S

) , , , , , , ( 1 *) *, *, *, ( Φ ) , , , ( Min ARL c hkRMS Arg k h c k h c λ λ λ ∈ ≡ ) , , *, *, *, *, ( 1 ) , , ( * 1 RMS ARL c h k RMS ARL ≡ λ Robust Designs

Robustness metric calculation

) , , , , , , ( 1 ) , , , , , , ( 1 ∆ARL cλhkRMS=ARL cλhkRMS −ARL1*(R,M,S) ) , , , , , , ( 1 ) , , , ( ) , , ( S M R k h c ARL Max k h c J S M R λ λ = ∆ Ω ∈
Robust selection of parameters

) , , , ( ) , , , ( ) , , , ( Min Jc hk Arg k h c k h c λ λ λ ∈Φ = ) , , , (cλhk

Figure 6: The design procedure of SHEWMAC scheme

25 45 65 85 105 125 1 1.5 2 2.5 3 Magnitude of Shift ARL EWMA EWMC Shewhart

Figure 7: ARL versus magnitude of shift; R=25 and M=3

-4 -3 -2 -1 0 1 2 3 4 1 6 11 16 21 26 31 36 41 46 51 56 61 66 WAT Lot Sequence: i

No rm al ized Val ues

Normalized Lot Average Normalized EWMA

(a) Combined Shewhart-EWMA chart

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 WAT Lot Sequence: i

Rs_N+

(EWMC)

(b) EWMC chart; USL and LSL are set as±3

68 68.5 69 69.5 70 70.5 71 71.5 72 1 6 11 16 21 26 31 36 41 46 51 56 61 66 In-line Lot Sequence: n

Rs_N + ( L ot M ean) M1 M2 M3 M4

(c) Shewhart chart stratified by processing machines Figure 8: Field data validation for SHEWMAC scheme Mean Variance Mean Variance UCL LCL LCL LCL UCL