High Road to Process Control: Multivariate Methods
Robert H. McCafferty RHM Consulting, Sandy Hook, Conn. -- Semiconductor International, 7/1/2001
| At a Glance |  | ||
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Diffusion of information among many signals is rapidly moving to the fore, with accurate decision making dependent not simply on extracting information from them all taken singly but their interactions as well. Hence, multivariate methods are becoming an order of the day, for purposes of both honing process control and driving fault detection with event recognition.
As process complexity has increased, its engineering has — not surprisingly — turned to the engineer's favorite tool: a computer. Moreover, into these ever faster and more powerful entities we have virtually shoveled numbers from a wealth of new instrumentation — only to draw rotely derived numerical answers about our processes from copious computational output. This has generally worked but, unfortunately, actual understanding of what transpires within a process chamber as well as accuracy have suffered.
Figure 1 plots line-level CMOS data in parallel coordinates (a multi-dimensional data visualization and analysis technology whose basic underpinnings are illustrated by Figure 2) to illustrate the reality of what had escaped purely numerical analysis. By laying data out along parallel — rather than conventionally orthogonal — axes, one can engage however many variables are rationally necessary to describe a process. In this case, yield and speed sort along the two leftmost axes; 14 product engineering variables thought to drive yield and speed are spread to the right. Every line (black or yellow) represents an actual lot-level observation.
| 1. Parallel coordinate plot of CMOS manufacturing data. 1 Note the "black hole" in parameter X15. |
| 2. The parallel coordinate transformation is the first step in applying multi-dimensional data visualization and analysis. |
Adding fuel to this fire are results portrayed by plotting data on parallel coordinates from an ordinary, refinery steam boiler (Fig. 3) and imposing constraints on allowable blow-down flow, stack O2, smoke discharge and steam temperature. One would expect, in something considerably less exotic than semiconductor processing, to encounter more standard (perhaps even uninteresting) results. Hence, disregarding the black holes on Cond, TotAir, WBP, Air1F and Air2F in the top plot, as well as white holes (places where the plant has never operated) on TotAir and WBP (among other variables), we would ordinarily expect all variables to be simply connected in their relationship to process outputs. Consequently, having been trained to operate a process between high and low limits for each independent variable, any process engineer would conventionally place a high limit on the uppermost yellow point of each variable axis, and a low limit on the lowermost yellow point of each axis. He should then expect to find a yellow line connecting values at the upper spec limits and lower spec limits of adjoining axes.
| 3. Refinery steam boiler data presented on parallel coordinates (top). Independent variables include feed water conductivity (Cond), total air flow (TotAir), wind box pressure (WBP), air flow one (Air1F) and air flow two (Air2F). The bottom figure shows a substantially improved process window derived by parallel coordinate methods. |
Doggedly sticking to axioms of conventional process control, however, one can apply the technique of generating upper and lower specification limits to the extremes of an "all good" industrial data set as outlined in yellow by the bottom plot of Figure 3. Here, production meeting specification for all five quality variables — only 12% of total line output — is plotted in yellow while that falling between newly devised parameter specification limits (a "boxing" algorithm was actually used to generate these) appears in blue. Because of black holes (there are at least six in this data set) and non-simply connected behavior, everything between new specification limits (i.e. all the blue observations) amounts to 39% of total production but encompasses all the premium (yellow) line output. By simply operating between these limits, therefore, yield is boosted by a factor of 2.5 — to 120 observations out of 391 or 30.6%. So, cracking the code of how a process behaves in parallel coordinates — where it can be fully visualized — even without rectifying holes and addressing the unexpected connectivity that is apparent among process variables, yields significant economic benefit.
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| 4. A two-dimensional box of a conventional process window (top), and its practical implications (bottom). |
Thinking further through the notion of operating within a process window2 (i.e. strictly between a high and low for all process parameters) one is confronted with the scenario of Figure 4a, where the range of outputs from unit processes P1 and P2 form a box. Since P1 and P2 are almost never independent in their influence on overall process quality measurements, the usable region of output for P1 and P2 taken together generally lies along a main diagonal. This typically yields a
pseudo-elliptical region where viable results for overall quality are found, substantially smaller than the original P1/P2 box with voids (black holes) potentially within.
By tradition, and for professional self-preservation, process engineers have long ago learned to operate within the reduced process window of Figure 4b. This works, but there are disadvantages to this practice. Everything outside the blue area but inside the gray is valid production — that is routinely scrapped or downgraded as off-spec. Further, as overall process complexity increases and one must integrate not simply unit processes P1 and P2, but P1, P2, ... Pn, with n a very large number (as in semiconductors), the actual volume defining the multi-dimensional box of an n-dimensional "process window" becomes vanishingly small. This would correspond to weaving only one tightly constrained path in either yellow (all good) query of Figure 3, and presents a nearly intractable control problem. Finally, the blue box (a conventional "process window") of Figure 4b touches the edge of its gray envelope in at most two places yet, because all processes are run to maximum throughput given other constraints, it is precisely that edge that defines their economic optimum. So, the process window philosophy, an old friend, virtually guarantees suboptimal performance with needless scrap and excruciating control investment when its patterns of behavior are probed in the light of multi-dimensional visualization.
| 5. Multi-dimensional best operating zone (between red lines) for the rescaled CMOS data of Figure 1. Blue lines trace optimal product trajectory, with green arms projecting available process latitude at various measurement gates. |
For simplicity, it is best if holes are eliminated, as was the one in X15 by redesign at a major semiconductor manufacturer. By staying within this zone — which represents how a particular product (design) will manufacture under the given process and tool set for which data was available — it can be guaranteed that a particular lot has a chance at optimum results as defined by the initial (yellow) query. Projecting the BOZ shape as a function of upstream results (which do change the picture in a batch sequential manufacturing scenario such as that of semiconductors) onto parallel coordinate axes then yields available process latitude. This is true for a product lot at each process step as it moves down the manufacturing line, to eventually return economically optimum results at test. This is depicted for a different process by Figure 6. Here, the red outline is a BOZ, green lines trace boundaries of available latitude at each variable axis (process step), and blue points are measurement values for an economically high-performing product's process history — thus yielding a uniquely effective and rewarding form of geometric process control.
Fault detection, event recognition
| 6. Process history for economically high-performing product (unrelated process). |
The case at hand, as with those preceding it, stems from a real manufacturing scenario. In this instance, the topic is sputter cleaning prior to PVD, where incomplete ashing of photoresist can wreak havoc with downstream processing, but effective handling of RGA data deftly detects faults from incoming wafers, process failures or tool problems.3 The objective, of course, is not simply to numerically detect those faults, but to do so in a fashion consistent with process control that readily leads to their classification, diagnosis and elimination. Examining available data from all dataset rows, good and bad, yields the parallel coordinate plot of Figure 7 (top plot), where minimum, maximum, mean and standard deviation are plotted consecutively following observation number (axis P1) for chamber pressure and concentration for each of eight potential chamber contaminant species. Values of minimum chamber pressure, where the pumps could not pull vacuum below 10-5 Torr, have been highlighted by the visual query in yellow, since this obviously represents abnormal processing.
| 7. Post-sputter clean RGA data (top) with pressure issue highlighted in yellow, and the cluster formation after the pressure issue is removed (bottom). |
Shifting our focus to exclude these and all similar observations finally yields the data set — where 15,142 observations out of the original 16,956 that did not show base pressure pumpdown problems have been retained — plotted in Figure 8, which can be used to build a known good BOZ.
Conducting that operation — which essentially establishes a channel down which a high-yielding lot of high-ASP parts must pass in the full line case of Figure 5, or within which an individual tool must operate when exhibiting fault-free production in this instance — creates the red outline of Figure 8 (bottom).
| 8. Known good data used to create the best operating zone (BOZ, top). The bottom figure shows the BOZ (red outline), operating region (green process channel), and measurement points (blue dots) for post-sputter RGA data. |
Conclusions
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| 9. Multi-dimensional signature of a failure and its mechanism. |
Screen captures of Curvaceous Visual Explorer 2.1 for Windows used to illustrate this article were included with permission from Curvaceous Software (Gerrards Cross, UK, www.curvaceous.com).
Robert H. McCafferty operates RHM Consulting as the North American agent for Curvaceous Software Ltd. He began his work in semiconductors at IBM Microelectronics (Burlington, Vt.). From there he consulted for a subsidiary of Bolt, Beranek and Newman (BBN), which became part of Brooks Automation, where he specialized in semiconductors and pattern recognition. He has a B.S. and an M.S. in mechanical engineering, and an M.S. in computer science from the University of Virginia.Phone: 1-203-270-1626
e-mail: bobmccaf@earthlink.net
REFERENCES
- E.W. Bassett, "IBM's IBM Fix," Industrial Computing, Vol. 14, No. 4, 1995, p. 24.
- R.W. Brooks, "Viewing Process Information Multi-Dimensionally for Improved Process Understanding, Operation and Control," Aspenworld Conference, Boston, October 1997.
- R.H. McCafferty, R.W. Brooks, "Multivariate Fault Detection Via Geometric Process Control," Proc. of 2nd Advanced Equipment Control/Advanced Process Control Conference Europe, Dresden, Germany, April 2001.
