The project underlying this article involved a tiered structure of tool, process, and product sensing capabilities coupled with comprehensive data integration and a structured data analysis regimen to create a single view of etcher, plasma, and product interactions. The study was conducted at Infineon (Dresden, Germany) and relied on data visualization software developed by Curvaceous Software (Gerrards Cross, Bucks, UK). Process parameters were measured using a Hercules in situ plasma-monitoring system from ASI Advanced Semiconductor Instruments (Berlin, Germany).

Trace data can easily be acquired for a wide spectrum of tool variables in modern etching equipment at intervals of a second or less. To be useful for process characterization, however, these data must be reduced (compressed) to figures of merit that concisely describe tool parameter behavior over a given process or, more typically, process step of interest. Compressing the data is essentially a feature-extraction problem in which the time-series pattern of parameter behavior must be synopsized into a set of measures reflecting salient features. Although there are a number of mechanisms to accomplish that procedure, engineers at Infineon use statistical key numbers—minimum, maximum, mean, and standard deviation—calculated to synthesize and represent the behavior of each process parameter across the breadth of a process step or, occasionally, a full-unit process itself.

Science—in this case, plasma physics—is never far from the surface when devising a means to link tool, process, and product behavior while implicitly incorporating the chamber and incoming-wafer condition into the bargain. Establishing that link requires physical knowledge of what happens in the tool and what can be measured at test. The research required to derive such measurements, while exacting and time-consuming, enables engineers to monitor a very small number of complex, information-rich plasma parameters in proxy for a large number of tool variables (measurable and otherwise) as well as product results.

Stable values for physically based plasma parameters, after being reduced to key numbers in order to match the data basis of both tool and product measurements, imply stable tool behavior, chamber condition, incoming-wafer characteristics, and, consequently, product results. Conversely, problems discovered through plasma monitoring at the level of complex process parameters (or, in a simpler case, end-point time) drive the investigation of tool parameter behavior, chamber condition, and incoming-wafer characteristics. Further, product issues evident at test but not discovered by complex-parameter monitoring lead to investigation of other, less carefully characterized, processes.

Once effective metrics—or at least what are expected to be effective metrics in the rough-and-tumble press of a manufacturing environment—have been isolated, they must be confirmed with the data analysis and modeling glue that holds the scheme together. This is an important (albeit frequently underestimated) effort, since an empirical understanding must be gained of plasma measurements as a function of tool, chamber, and wafer condition, and wafer test results must be predicted from an analysis of plasma measurements. Furthermore, data analysis requires the application of standard and not-so-standard analytical methods on "dirty" industrial data.

When data analysis is complete, engineers have real-time data compressed by key numbers, condensed into physically meaningful plasma measurements, and linked by robust, credible mathematical models to wafer-level results. This compression delivers the benefit of deriving a small number of information-rich complex process parameters that represent the large number of raw signals available continuously from an etch chamber.

By any standard, describing process behavior with simple statistics alone (e.g., correlations) is insufficient. To be effective, a description of process behavior requires the development and evaluation of empirical process models that can, at minimum, consider highly correlated inputs, uncover contrary interactions between multiple inputs, find main effects from a large variety of inputs and numerically quantify their influence, then derive a global optimum for the modeled process. In the case study conducted at Infineon, based on the three-pronged strategy of data compression, physical analysis, and data mining, the engineers focused on the objectives, techniques, and work flow diagrammed in Figure 1, then concluded by developing a control strategy derived from that work.

Figure 1: Data-mining work flow used at Infineon.

Because variations under normal manufacturing conditions are random and unlike the deliberate, cleanly structured variations that occur in an experimental design, the nature of manufacturing data adds an additional layer of complexity to the modeling problem. That complexity effectively forces engineers to resort to data-mining techniques and "fish for p-values" within truly disheveled industrial data. Data mining itself implies the use of passive but highly sophisticated methods for exploring, selecting, and modeling relationships in large bodies of data to find and quantify previously unknown patterns. At Infineon, however, data mining has also come to mean the very specific work flow capsulized by Figure 1, which was applied with a data source of more than 15,000 wafers covering a broad spectrum of tool parameters as well as electron density and collision rate plasma parameters. Main and overetch steps, engaging Cl, HCl, NF₃ chemistries and HBr, and He/O₂ chemistries, respectively, were characterized for gate-conductor etch running in a TCP reactor from Lawn Research (Fremont, CA).

To measure electron density and collision rate, Infineon engineers used the Hercules plasma monitoring system, which utilizes self-excited electron plasma resonance spectroscopy (SEERS) to combine nonintrusive plasma current measurements taken inside the process chamber with physically based plasma models to evaluate key plasma characteristics. This accounts for sheath nonlinearity at the RF electrode, which itself provides harmonics with modulated width and high-frequency oscillations in the bulk plasma. By employing a general gas-discharge model, SEERS delivers volume and reciprocally averaged values of electron collision rate, electron density, and bulk power dissipated within the plasma body. Physically, a hydrodynamic approach is taken for the plasma body, with an inert mass of the electrons treated as an inductance and collisions with neutral particles (including power dissipation in the expanding sheath) as a resistance. Taking into account capacitive space charge sheath behavior, the plasma can be regarded as a damped circuit oscillation with nonlinear sheath capacitance exciting the plasma by causing damped oscillations close to the geometric resonance frequency and well below the plasma (Langmuir) frequency. For asymmetrical discharges and sinusoidal RF voltage, a current is known to be the sum of a sawtooth-shaped component plus the damped oscillation, while RF peak voltage of the substrate is measured using a capacitive voltage divider.

From the perspective of semiconductor process and equipment engineering, the Hercules SEERS instrument performs real-time measurement of electron density and collision rate, bulk power, sheath width, and peak-to-peak voltage. Electron density is sensitive to gas concentrations and process-generated polymer particles and thus correlates strongly with RF power and chamber pressure, while collision rate is sensitive to changes in chemistry, chamber conditions, prior wafer processing, and arcing phenomena. Taken together, electron density and collision rate are sensitive to most disturbances that occur in process chambers and, in addition to their fingerprinting application, serve as an excellent, real-time indicator for process, tooling, or incoming-wafer issues.

After performing model derivation and evaluation, the engineers were able to distill the relevant tool parameters from a large body of inputs and then calculate the impact of each tool parameter on both plasma parameters. Figure 2 shows the correlations between plasma and tool parameters for gate-conductor main etch.

Figure 2: Correlation between plasma parameters and tool parameters for gate-conductor contact main etch.

In order to better grasp these correlations, the engineers used Curvaceous Software's Visual Explorer software package, which relies on parallel coordinate analysis (known as Nehring plots at Infineon) to provide high-dimensionality visualization of many parameters simultaneously on one screen. Figure 3, a multidimensional view of the correlation between tool and plasma parameters, indicates that a high matchbox load capacitance monitor value, low RF timer value, and low throttle-valve position value led to a high electron collision rate. Figure 4, another multidimensional view, shows that a high-bias matchbox load/tune capacitance monitor value correlated with a high chamber pressure, low electron collision rate, and high gate-conductor stack width.

Figure 3: Multidimensional view derived from parallel coordinate analysis showing that a high matchbox load capacitance monitor value, a low RF timer value, and a low throttle-valve position value led to a high electron collision rate.

Figure 4: Multidimensional view indicating that a high-bias matchbox load/tune capacitance monitor value correlated with a high chamber pressure, low electron collision rate, and high gate-conductor stack width rate.

Since this analysis was performed on highly noisy industrial data, where the process equipment fed back on and adjusted out random variations, it is not surprising that tool-parameter drifts occurred. Model goodness-of-fit coefficients of 67% for the electron collision rate and 51% for the electron density rate substantiated the patterns generated by parallel coordinate analysis. These results were reasonable, given that they were based on data with a very small variation interval.

This analysis shows that variations in plasma parameters can be explained by variations in tool parameters and that viable complex process parameters "compressed by physics" are suitable for daily process monitoring. The results of this analysis are consistent with previous findings derived from comparable process chambers.^1,2

From the perspective of product engineers (the people who tune the line) and process engineers (those who make the line work), it is of more than casual interest to uncover correlations between plasma parameters and electrical test data or yields. Fortuitously, data-mining software and other standard, commercially available statistical tools are suitable for such calculations, particularly after the relationship between plasma parameters and electrical test results has been scouted out using multidimensional methods. Such methods keep data analysis from degenerating into a blindman's buff game of mindless numerical modeling.

Given the different product populations and process phenomena involved in semiconductor manufacturing, it is advisable to treat different product families (e.g., logic versus DRAM devices) and different process steps or even substeps (e.g., gate-conductor main etch versus overetch) separately, although doing so is labor intensive and, consequently, economically unpopular. Performing separate analytical steps unveils the details of how different process steps behave toward different product populations while preventing key conclusions from escaping attention.

In this case study, for example, no correlation was found between electron collision rate and gate-conductor contact width when DRAM products alone were being fabricated, but when logic products were processed through gate-conductor overetch, a reasonably good correlation did surface. Figures 5a and 5b highlight these findings. However, if DRAM and logic data sources had been lumped together, the correlation shown in Figure 5b quite probably would have gone undetected.

Further analysis investigated the behavior of gate-conductor contact width when logic as well as DRAM products were processed in the etch chamber. The trend charts in Figure 6 illustrate that after the chamber had been dedicated to processing logic products only and then was used again to process both DRAM and logic products, the electron collision rate (Figure 6a) and gate-conductor contact width (Figure 6b) became unstable. Since instability also was noted before chamber dedication, it is evident that the correlation was neither a smoking gun nor a chance numerical relationship, but a genuine process interaction driven by mixing logic and memory wafers in a single chamber.

Preventing just such a potentially costly problem is the purpose of advanced process control. With plasma monitors in place as part of an overall control strategy, serious gate-conductor contact width problems rooted at gate-conductor etch should preannounce themselves in a very striking electron collision rate response.

Although the correlation in Figure 6 was recorded when the gate-conductor contact width for a mix of DRAM and logic products was unstable and occasionally running outside specification limits, equally strong and usable correlations were recorded when that parameter for logic products alone was stable and running within specification limits (as in Figure 5b). In contrast, no correlation was found between electron collision rate and gate-conductor contact width for a stable DRAM process alone, as the DRAM process window is large and gate-conductor etch runs well when memory products are being fabricated.

The correlation between process and product parameters can be used simplistically in the form of a conventional monitoring spec, as illustrated in Figure 7, which shows the relationship between electron collision rate and gate-conductor contact width (Figure 7a) and electron collision rate over time (Figure 7b).

In contrast to a multidimensional visualization approach, this simplistic monitoring spec divides a parameter range somewhat arbitrarily into good and bad regions, where bad regions represent scrap. In order to prevent fault detection components of advanced process control from degenerating into an exercise in sorting wafers, one further step must be taken: the creation of a statistical process control mechanism for failure prevention on manufacturing lines accustomed to operating within fixed limits.

In that mechanism, depicted in Figure 8, control limits represent the borders of a random deviation interval beyond which process problems may be mathematically expected to lie and action must be taken to prevent failures. By definition, these control limits fall within the range of product-oriented specification limits, where variation does not imply scrap but requires engineering action to deal with a budding disaster before it gets out of hand.

Figure 8: Statistical process control mechanism for failure prevention showing control limits of a random deviation interval beyond which process problems may be mathematically expected to lie.

Figure 9: Extended Shewhart charts for gate-conductor overetch on logic parts showing the control limits for two plasma parameters: electron collision rate and electron density.

For production at Infineon with gate-conductor overetch on logic parts, an extended Shewhart chart was generated to deal with the unstable mean of the electron collision rate shown in Figure 8. Figure 9 shows extended Shewhart charts with control limits for two plasma parameters: electron collision rate and electron density.

Like many worthwhile objectives in engineering, advanced process control and, in particular, fault detection behave as step functions. While subcritical investments produce negligible results, assembling a cohesive project can yield handsome rewards. The project described in this article began by isolating instrumentation delivering key process physics metrics; it proceeded to compress and integrate tool, process physics, and product data, and, finally, created credible models linking all three data sources.

A second level of compression—"by physics"—was obtained through extensive data analysis and modeling. That process started by employing multidimensional visualization technology to view multiple parameters simultaneously so that tool, process, and product insights, as well as interrelationships, could be uncovered. Those interrelationships were then viewed under the mathematical microscope of data-mining technology to produce usable numerical models that mapped tool parameters to plasma parameters and plasma parameters to product test results.

Because the process under investigation was plasma driven, the instrumentation used to track plasma behavior measured electron density and collision rate. Raw-data compression was accomplished by reducing real-time data for individual etch steps from tool sensors and plasma instrumentation to statistical key numbers.

The one-two punch of surveying large bodies of data via parallel coordinate analysis (Nehring) plots and then drilling down to derive numerical relationships enabled the line engineers to monitor a small number of information-rich plasma parameters while tracking everything of significance to the process—tool behavior, chamber condition, and incoming-wafer characteristics. Moreover, this analytical process made it possible to foretell electrical test results. Hence, complex parameters, tightly linked to both in-line events and test results, were excellent candidates for a minimalistic but entirely sufficient control system whose two meaningful parameters rather than a score of obliquely related real-time signals throughout the process, could be monitored at the close of overetch. This advanced process control system is up and running, providing useful information to process and product engineers.

The authors of this article would like to gratefully acknowledge the assistance of Lars Christoph, Mohammed Radwan, Siegfried Bernhard, and Jörg Bullmann of Infineon Technologies in Dresden, Germany, as well as Thomas Dittkrist, Thomas Werner, Harald Wendel, and Sören Mothes from the University of Technology in Dresden for their contributions to this project. The authors also wish to thank Michael Klick of the Adolph-Slaby-Institut in Berlin for his description of the Hercules plasma monitoring system.