Statistical Analysis of TI GHG Stack Data. Joel Dobson, TI Wednesday, Nov 30, 2011

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1 Statistical Analysis of TI GHG Stack Data Joel Dobson, TI Wednesday, Nov 30, 2011

2 Objectives The objective of this presentation is to provide an in-depth description of the rigorous statistical methods that have been used to evaluate the TI stack emissions and gas usage data. The objective of this statistical analysis has been to extract the maximum amount of information from the data sets, relative to the relation between gas usage and emissions However, this same level of analysis is neither appropriate, or as shown in the following charts, even possible, for all data sets. Pg 2

3 An Outline of this Presentation 1. Review our main point and the former work from July 27th presentation at TI. 2. Show that some GHG bottles have appreciable pressure drop (or weight change) across the day of FTIR testing, while others do not. 3. A review of our data structure and its implications for analysis. 4. A statistical comparison of two stacks emission vs usage correlations in two time frames. (Four simple linear regressions.) 5. Checking for correlation of stack concentration (FTIR signal) vs. a production metric (wafer moves per hour) in the GHG process steps. 6. Our conclusions Pg 3

4 Table of Contents Our main point A brief review from July Bottle pressure graphs vs time Explaining our data structure Comparing stacks and timeframes Check for correlation vs wafer moves Conclusions 4

5 Key Takeaways Comparison of slopes of CF4 FTIR vs CF4 Pressure Deltas shows to be similar in both time frames for both stacks data. We tested our hypothesis that Greenhouse Gas FTIR signals (emissions) track Greenhouse Gas Usage. We can estimate the emission factor by dividing total emissions by total usage, across the same time frame. 5

6 Key Takeaways We showed that some GHG weight scale change are far less than others over a single day. For those, the usage may need to be taken across a longer period of time. Gas usage is a better indicator of emissions within the quarter hours of a day than wafer moves. We obtained wafer moves per time period from the GHG processes only. These time series plots do not align to the FTIR time series plots, regardless of lag applied. 6

7 What s our point? Our point is: We can estimate the emission factor by dividing total emissions by total usage, across the same time frame. We do not need the sophisticated statistical analysis to estimate our emissions factors; we can use a quotient. The point of the emissions regression study was to demonstrate the correlation. 7

8 Our main point Linear regression models prove that: [X = GHG usage] is a good predictor for [Y = GHG emissions.] Let s call this our key relationship The most salient point is that Y tracks X. Variability in X is tracked by variability in Y. Yes, indeed there is much variability! We agree. We can more easily get data for X than for Y. 8

9 Table of Contents Our main point A brief review from July Bottle pressure graphs vs time Explaining our data structure Comparing stacks and timeframes Check for correlation vs wafer moves Conclusions 9

A brief review from our July presentation. We studied Y = Qtr Hr avg of Instantaneous CF4 FTIR reading every 7 minutes as a function of X = Qtr Hr avg of CF4 usage every 5 minutes.

10 A brief review from our July presentation. We studied Y = Qtr Hr avg of Instantaneous CF4 FTIR reading every 7 minutes as a function of X = Qtr Hr avg of CF4 usage every 5 minutes. To align the data, we created quarter-hour averages of X and Y readings. Each point is from one quarter-hour. These readings were not accumulated either on X or on Y. Our latest analysis update repeats these non-accumulated analyses, but adds on the new accumulated analyses. R squared of ~50%. This is from South Stack ( Stack 2 ) of Fab 1 from March. 10

11 An improvement over our earlier analysis When Y = m*x + b then delta(y) = m * delta (X) + C We would expect the value of C to be zero. In our analyses in July, we had permitted C to be other than zero. The statistical analyses confirmed that C was not zero, statistically. We suspect this is because our 5-minute data is more poorly resolved than if we had first accumulated it across the day, and then analyzed. We will talk a lot about this accumulation idea in what follows. Analytically, maybe we should have been doing zero intercept regressions! In other words, maybe we should have locked the point (0,0) for the best fit line and then let the slope vary to best-fit the data. Dobson

12 Table of Contents Our main point A brief review from July Bottle pressure graphs vs time Explaining our data structure Comparing stacks and timeframes Check for correlation vs wafer moves Conclusions 12

13 Trends of GHG pressures Two gases, CF4 and NF3, have appreciable pressure drop across the 24 hour testing period. They are from gas bottles that are inside our building at a controlled temperature. They are much smaller bottles than the type one would store on a truck trailer. Our smaller tanks pressure drops are much more of a % of total pressure, across a single day, than would be the % pressure drop for a larger cylinder. 13

14 CF4 bottle pressure trends March Fab 1 CF4 cylinder Pressures vs Minutes in the Day. August Fab 1 CF4 cylinder Pressures vs Minutes in the Day. Each trellis panel is a separate bottle. 14

15 NF3 pressures March Fab 1 NF3 cylinder Pressures vs Minutes in the Day. August Fab 1 NF3 cylinder Pressures vs Minutes in the Day. Each trellis panel is a separate bottle. 15

16 Other Gases ---- C4F8, August, Fab1 All trends are flat or show only a few steps along the entire path. Each trellis panel is a separate bottle. Quite a contrast when compared to NF3 or CF4. 16

17 Other Gases --- C5F8, August, Fab 1 1 All trends are flat or show only a few steps along the entire path. Quite a contrast when compared to NF3 or CF4. Each trellis panel is a separate bottle. These few might show promise if we divide total emissions by total usage. 17

18 Other Gases ---- CH2F2, August, Fab1 All trends are flat or show only a few steps along the entire path. Quite a contrast when compared to NF3 or CF4. Each trellis panel is a separate bottle. This one has a few steps, though. 18

19 Other Gases ---- CHF3, August, Fab 1 All trends are flat or show only a few steps along the entire path. Each trellis panel is a separate bottle. Quite a contrast when compared to NF3 or CF4. 19

20 Other Gases ---- SF6, August, Fab1 All trends are flat or show only a few steps along the entire path. Quite a contrast when compared to NF3 or CF4. These few might show promise if we divide total emissions by total usage. Each trellis panel is a separate bottle. 20

21 Other Gases? Two gases, CF4 and NF3, have appreciable pressure drop across the 24 hour testing period. The other GHGs we measured did NOT show much weight change across a day. Some only show weight measurement steps a few times a day. The scale may not be able to resolve the weight drop well enough for our data needs. No or low usage gases do not have enough data for statistical analysis. We were NOT able to build good models for their emissions vs usage, using our simple regression approach. 21

22 Table of Contents Our main point A brief review from July Bottle pressure graphs vs time Explaining our data structure Comparing stacks and timeframes Check for correlation vs wafer moves Conclusions 22

23 Explaining our data structure Our regression analysis assumes we have gas usages and gas emissions in the same, aligned time-intervals. We have bottle pressures every 5 minutes. FTIR is irregularly spaced, typically from 6 to 9 minutes. This is neither good nor bad. We must take care when analyzing. We will use an interpolation method. We discussed this in July as well. We had averaged the data in quarter hour intervals. 23

24 Our raw-data time-stamps misalign. Fab Tower start stop Minutes N bottle N Ftir ratio Min/FTIR Fab1 N : : Fab1 S : : Fab1 S : : Fab1 N : : Note the difference in count of bottle readings and count of FTIR readings. What is not shown here, is that the FTIR data occur in irregularly spaced time intervals. This makes analysis harder. Nomenclature: North Stack = Stack 1 and South Stack = Stack 2 Dobson

25 Illustrating the misalignment of time stamps. FTIR intervals vary. The interpolated FTIR value. Pressure intervals do not vary. They are every 5 minutes. 25

26 What is different in our new analysis? First, we have interpolated the FTIR readings into the 5 minute intervals from the pressure readings. Second, we have accumulated both the FTIR and the pressure drop across the day. Because averages are appropriate scaled sums, scaled by 1/N, and because N is the same for Y and X here, our overall regression slope will be very similar to the average value of Y divided by average value of X. This helps explain why a zero-intercept model might be reasonable, and the intercept is not very important if we start-off X and Y both at zero. The July presentation used non-accumulated data. Dobson

27 A simple analogy Suppose we have a 3 foot by 48 foot sidewalk. Suppose it is laid in twelve 3x4 blocks. We could use a 50 tape ruler to measure each of the 12 blocks and their measurement error. We could sum up the 12 lengths and combine the 12 errors by Pythagoras's rule. But, we would do better by pulling out the length of the metal tape rule and making one measurement, incurring only one measurement error. The point of this ----> Accumulated measurements are better. 27

28 Table of Contents Our main point A brief review from July Bottle pressure graphs vs time Explaining our data structure Comparing stacks and timeframes Check for correlation vs wafer moves Conclusions 28

29 We next show time line graphs of the FTIR signals for CF4 and NF3 Two separate stacks: North stack = Stack 1 South stack = Stack 2 Two separate months, March & August Makes 4 time line graphs. 29

Gaps show where the FTIR was not read or where it was not detected( Cal? Spike test?).

30 Timeline Graphs FTIR from Fab 1 March, N Stack, ( Stack 1 ) March, S Stack, ( Stack 2 ) August, N Stack, ( Stack 1 ) August, S Stack, ( Stack 2 ) Blue is NF3 FTIR and Red is CF4 FTIR. Gaps show where the FTIR was not read or where it was not detected( Cal? Spike test?). We interpolated the FTIR readings into 5 minute intervals to align into the pressure drop readings. NF3 FTIR has non-detects in S Stack, esp in August. This will be important later on. Dobson

31 CF4 Simple linear regression fit for: Y = CF4 FTIR accumulated across 24 hours on X = CF4 bottle pressure drop across 24 hours For each of two stacks in each of two months. We will show four best-fitted lines. 31

32 CF4 Accumulated Studies, Fab 1 Why are we using pressure on our X-axis? The data provided was pressure data. We could just as easily calculate the mass of CF4 gas used using the ideal gas law. Our cylinders are inside at controlled temperature. Regardless of the units of usage, the slopes are proportional to emission factors. We can later multiply by an appropriate scaling factor that will put the slopes into more meaningful physical units. As stated earlier, the intercept is not of much concern since we can tare the X and Y readings at time zero. Dobson

33 CF4 Accumulated Studies, Fab 1 This looks like good agreement in the two time frames. Remember that North Stack is sometimes called Stack One and South Stack called Stack 2 in some of our presentations. Dobson

34 Parameter Estimates CF4 studies in fab 1 Term Estimate Std Error t Ratio Prob> t P02.5 P97.5 N Stack, March Intercept <.0001* CF4_AccumPDrop <.0001* R squared count 288 N Stack, August Intercept <.0001* CF4_AccumPDrop <.0001* R squared count 267 S Stack, March Intercept <.0001* CF4_AccumPDrop <.0001* R squared count 289 S Stack, August Intercept CF4_AccumPDrop <.0001* R squared count 212 Slopes differ by 5%. Slopes differ by 12%. Slopes in N stack are both 0.12 while those for S stack are 0.32 and Though the slopes 95% confidence intervals do not overlap, we can choose either the larger one or their average to use when estimating our emissions factor. Though the slopes slightly differ in the 2 timeframes, we find the observed agreement phenomenal, strikingly cogent. 34

35 What s our point? Although the slopes in N stack ( Stack 1 ) are statistically distinguishable in the two time frames, March and August, they appear phenomenally similar based on inspection. We can use the sharper one for our estimate. The same is true for S stack. ( Stack 2 ) Our point is more subtle: We can estimate the emission factor by dividing total emissions by total usage, across the same time frame. We do not need the sophisticated statistical analysis to estimate our emissions factors; we can use a quotient. The point of the FTIR STUDY was to demonstrate the correlation. The time frame used to estimate the emissions factor may need to be chosen based upon pressure gauge or weight scale resolution considerations. 35

36 About those intercepts In 3 of our 4 simple regressions, the intercept is NOT zero, statistically. The intercepts are estimated to be: { -0.7, +0.6, -2.3, and -0.1}. These depend on how we define our time zero. But time zero was chosen arbitrarily. It is really only the slopes we are interested in. Our Y span goes from 0 to 40 for N stack and 0 to 140 for S stack. These intercepts are a small fraction of our Y span. Although the intercepts from 3 of our 4 best fitted lines are statistically distinguishable, these intercepts are overall inconsequential. We could use a zero-intercept regression and force the line through the origin at (0,0). That seems reasonable. 36

37 NF3 For the South Stack ( Stack 2 ) in each of two months: First we start off with the time line plots. Accumulated pressure drops are easy to explain: we just read the gauge over time. Analogously, accumulated FTIR concentration values can be mathematically transformed into total mass emissions over the period of the test by multiplying an appropriate conversion factor. That conversion would multiply the FTIR concentration in ppm/volume by the appropriate time interval and by the stack volume velocity. 37

38 NF3 from Fab1 Stack2 in March This is for the South Stack of Fab 1, which we sometimes call Stack 2. Left and Right Y axis scales will match in this March graph and in the August graph on the next page. 38

39 NF3 from Fab1 Stack2 in August The right most points to not match only because of keeping the uniform scales on last page and on this page. Dobson

40 NF3 Simple linear regression fits for: Y = NF3 FTIR accumulated across 24 hours on X = NF3 bottle pressure drop across 24 hours For the South Stack ( Stack 2 ) in each of two months. We will show two best-fitted lines. 40

41 NF3 FTIR regressions, Stack 2, Fab 1 NF3 FTIR. Blue is August and red is March. The software shaded in the prediction intervals but they may be hard to see so we have attempted to add the extra lines manually, to show them off better. (They are actually hyperbolae but the prediction intervals and std errors are so tight, and our data so uniformly spread, that they almost look like lines in our graphs.) We will explain why the slopes are so different, shortly!!! 41

42 Summary of linear fits (NF3) group Term Estimate Std Error P02.5 P _March Intercept slope RSquare N _August Intercept slope RSquare N 287 The slope 95% confidence intervals do not overlap in the 2 separate time frames. We can conservatively choose the higher one as the slope to scale-up for our emissions factor. The lower slope in August is basically explained by the presence of far more ND (which we had set to zero) readings in August. The fab was running lower level in August. Ideally, we would set the slope during the more stringent time frame when the fab is running near full capacity. 42

43 Conclusions thus far. If the FTIR gauge can resolve the chemical being read, then it can be accumulated over time. Non-Detects can make the analysis more difficult. CF4 FTIR signal works somewhat better than NF3 FTIR does, but both have excellent fits. The slopes for Y = Accumulated FTIR on X = Accumulated Pressure Drop appear to be similar. We can take our emissions factor from the larger of the two slopes. 43

44 Conclusions thus far. We can estimate the emission factor by dividing total emissions by total usage, across the same time frame. This supports our original proposal, that GHG usage can be used to predict GHG emissions. We do not need the sophisticated statistical analysis to estimate our emissions factors; we can use a quotient. And, it doesn t have to be a one-day accumulation. Any representative time period will work. 44

45 Table of Contents Our main point A brief review from July Bottle pressure graphs vs time Explaining our data structure Comparing stacks and timeframes Check for correlation vs wafer moves Conclusions 45

46 Time Series for wafer moves. Per request from EPA in July: We next present time series graphs showing: Wafer moves per quarter hour in the GHG process steps. Average FTIR signal per quarter hour. Silane on next page. CF4 the page after that. C2F6 the page after that. We cannot lag these time series to make them to align. 46

47 Other possibly correlated measurements. Red is wafer moves per quarter hour in the CFC process steps. Blue is the FTIR signal for SiH4. X-axis is the quarter hour. We could find no lags that align these time series. 47

48 Other possibly correlated measurements. Red is wafer moves per quarter hour in the CFC process steps. Blue is the FTIR signal for CF4. X-axis is the quarter hour. We could find no lags that align these time series. 48

49 Other possibly correlated measurements. Red is wafer moves per quarter hour in the CFC process steps. Blue is the FTIR signal for C2F6. X-axis is the quarter hour. We could find no lags that align these time series. 49

50 Time Series for wafer moves. We presented time series graphs showing: Wafer moves per quarter hour in the GHG process steps. Average FTIR signal per quarter hour. We cannot lag these time series to make them to align. Emissions correlate to usage but not to wafer moves. 50

51 Table of Contents Our main point A brief review from July Bottle pressure graphs vs time Explaining our data structure Comparing stacks and timeframes Check for correlation vs wafer moves Conclusions 51

52 Conclusions Comparison of slopes of CF4 FTIR vs CF4 Pressure Deltas shows to be similar in both time frames for both stacks data. We tested our hypothesis that Greenhouse Gas FTIR signals (emissions) track Greenhouse Gas Usage. We can estimate the emission factor by dividing total emissions by total usage, across the same time frame. 52

53 Conclusions We showed that some GHG weight scale change are far less than others over a single day. For those, the usage may need to be taken across a longer period of time. Gas usage is a better indicator of emissions within the quarter hours of a day than wafer moves. We obtained wafer moves per time period from the GHG processes only. These time series plots do not align to the FTIR time series plots, regardless of lag applied. 53

54 What s our point? Our point is: We can estimate the emission factor by dividing total emissions by total usage, across the same time frame. We do not need the sophisticated statistical analysis to estimate our emissions factors; we can use a quotient. The point of the emissions regression study was to demonstrate the correlation. 54

55 Our main point Linear regression models prove that: [X = GHG usage] is a good predictor for [Y = GHG emissions.] Let s call this our key relationship The most salient point is that Y tracks X. Variability in X is tracked by variability in Y. Yes, indeed there is much variability! We agree. We can more easily get data for X than for Y. 55

56 Thank you for your time. 56

Developing a Fluorinated Greenhouse Gas Stack Testing Method using FTIR

Developing a Fluorinated Greenhouse Gas Stack Testing Method using FTIR Tina M. Gilliland, P.E., Texas Instruments (TI) Curtis T. Laush, PhD, IMACC 1 Background TI is interested in identifying an alternative