Institute of

Cognitive Integrated Sensor Systems

Prof. Dr.-Ing. Andreas König

The ongoing growth in semiconductor industries, predicted and driven by Moore's law, leads to a rapid complexity increase in semiconductor manufacturing processes. The number of manufacturing stations, required processing steps, and related parameters rapidly increase and mandatory process monitoring returns a flood of multi-variate data. Yield requirements demand for tight process control. The monitoring such a complex process, which can be met in similar instances in general in industrial manufacturing, however, requires on-line monitoring and decision making as well as ensuing extraction of nonobvious information and structure in the data. Such a procedure of knowledge discovery and the mentioned on-line decision making serve to control the respective complex process, e.g., for quality assurance purposes, keeping the process in a multivariate window of allowed parameter tolerances. Typical aims in semiconcductor manufacturing are the centering of the process in a so-called process window and the assurance of an optimum yield based on functional and electrical tests. The following figure illustrates the concept of a process window:

Due to the underlying complexity and exponential growth law, a tremendous amount of monitoring data is generated by the manufacturing line. The generated data have to be analyzed with regard to the required process specification or qualification, i.e., whether the process remains in the process window. In simple models, predominantly assumed in available professional software for yield optimization, the process window will be described, e.g., by a multi parameter or multivariate bounding box with thresholds in each parametric dimension. Exceeding the threshold makes overt, that the process is going out of specification for one or several of the involved parameters. This approach neglects multivariate dependencies and higher order correlations of variable groups, as outlined inf the following figure:

More advanced approaches employed Kohonen's SOM for static visualization and analysis of semicondcutor manufacuring data of several companies. In the work regarded in this project, alternative dimensionality reduction and visualization techniques, developed in the context of rapid and transparent intelligent system design, will be investigated with regard to their potential in the analysis of semiconductor manufacturing data and potential improvement of existing methodology and tools for improved yield optimization. The work based on data from a CMOS process and fab of Infineon in Dresden. The follwing figures give a peek in the line: Batched 300mm wafers ready to go into a vertical furnace (picture top, left: open furnace tube on the upper left), automatic transport system loading up a fully automatic wafer storage (Stocker, top right picture), a 300mm wafer at so-called floodlight inspection to check for correct printing of the mask (bottom picture):

The overall line can produce data in the order of 1 TByte per day. Collecting and evaluating all data for even a single lot is a formidable task. The resulting very large multivariate dataset must therefore be analyzed for deviations from allowed parameters or operation ranges, i.e., anomaly or novelty detection, and nonobvious multivariate dependencies of the involved parameters and the structure in the data must be disclosed for improved process control. Here, appropriate methods, e.g., from soft-computing, for on-line observation and off-line interactive analysis employing novelty classification, dimensionality reduction and interactive data visualization techniques can be employed. The wafer processing takes places in a so-called wafer fab or manufacturing line and is often further divided into Front-end-of-Line (FEOL) and Backend-of-Line (BEOL) processing. Simply speaking, the FEOL processing provides the active devices within the silicon, the BEOL processing produces the connections between the devices and the backend processing provides the connections to the outside world as well as protective packaging. To simplify the fab logistics, wafers typically run in lots of 25 wafers. This is illustrated in the following figure:

After fabrication electrical tests (ET) on the wafer level are carried out to assess that all single devices defined by the process are within their specified range. The devices tested are separate from the actual ICs on the wafer, often placed into the space between individual chips that is needed to singularize them later. These test structures are laid out carefully to isolate the layers needed to process them as much as possible from other layers. These tests are also called parametric test as the results are actual measurement values for device parameters, like the threshold voltage or saturation current of some specific transistor. The data employed in the following experiments stems from Electrical Parameters extraction of wafer tests. Two lots of 25 wafers each were split identically into three groups at two process steps to vary the process parameters of these steps and in accordance the electrical parameters of certain devices. The intention of the split was to vary the threshold voltages of both n- and p-type logic transistors about the target voltage for each device. This is also called a performance split, indispensable for dynamic performance characterization, as it results in slow, nominal and fast logic gates for the final product. As a side effect, some parameters related to the threshold voltage (most notably saturation current) plus so-called IO device that is coupled to the logic device will also follow the split. The split is illustrated in the following figure:

From the proprietary software system and company database affiliated to the regarded manufacturing process, a subset of data generated for the processing two wafer lots with five measurement positions for each wafer was extracted as experimental data. A split of three, i.e., a partitioning of each wafer batch into three subgroups for individual processing of each partition was carried out during production. The data was converted by Ecxel to our proprietary QuickCog system. A database of 220 vectors with 205 dimensions is the baseline in the following experiments. It will be denoted by SPLIT in the following. The size of this database is given by the typical wafer batch size of 25 times the five measurement sites per wafer. Complementing the parameter data, class affiliations were generated in two files. A three classes file was generated, regarding split information only
for the complete database. The data labeled by this class file will be denoted by SPLIT3 in the following. Additionally, a six classes file was generated according to lot and split affiliation of each wafer/measurement location. The labeled data will be denoted by SPLIT6 in the following. Additionally, according to the underlying lots the data have been separated in two databases denoted by SPLITTrain3 and SPLITTest3 with three classes each, corresponding to the underlying split of 3 of each lot. Finally, for the novelty classification purposes, a training set was extracted from the first lot and containing data only from one split. This will be denoted by SPLITTrain- OCC in the following. The following figure show a taxonomy of visualization techniques, with those techniques emphasized, that have been employed to the semiconductor data:

The developed preprocessing, dimensionality reduction, and interactive visualization methodology implemented in QuickCog and applied to the regarded problem is illustrated in the following figure:

In the first approach, the complete data base was subject to distance preserving dimensionality reducing mapping from 205 to 2 dimensions. The resulting visualization and observable clustering is given in the following figure:

The achieved clustering is determined by the large number of variables unaffected by the split. This will be illustrated by employing the achieved projection for component planes visualization of four selected variables in the next figure:

As becomes obvious from the visualization, C118/C119 support thesplit for both batches, C071 discriminates batches, not the split, and C063 is insignificant for split/batch discrimination. So the application of automated feature selection (AFS) techniques to eliminate irrelevant and insignificant variables in a superised approach seems to be attractive. Standard AFS technique (Sequential-Backward-Selection) employing a separability criterion qsi reduced the data base to 9 features or parameters, which the following feature space visualization with much clearer clustering:

In future work, more advanced feature selection techniques, employing evolutionary techniques, can be considered for this problem, e.g., to deal with larger and different data sets. In the next step of supervised analysis, classification was applied to the data base after AFS downto 9 significant variables. A basic nearest neighbor technique (Reduced-Nearest-Neighbor, RNN) was employed with the first lot for training and the second for testing. The number of classes goes down from L=6 to L=3, as only the split groups are regarded. The lot affiliation is discarded and actually represented by train or test set affiliation. The results are illustrated in the following figure:

Obviously, classification accuracy of 100% was achieved in generalization. Thus, no other classification techniques, such as RBF, PNN, or SVM, have been regarded here. However, as anomaly or novelty detection is a very important concept in (on-line) process monitoring and deviation detection, related concepts of one-class-classification (OCC) were studied next. A NOVCLASS classifier was developed and applied, that uses hypersphere classifier concepts, similar to the famous RCE model, however, the stored hypersphere centers relate only to known, normal data and the radii are computed from observed deviations in the normal or non-novel data. Thus, as sketched in the following figure for the two-dimensional case, a non-parametric mapping of normal regions in feature space is achieved:

In the classification step, anomal or novel patterns are detected, if they drop in outside of the union of all normal hypersheres. Training in the particular case was carried out based only on 30 references from class 1 of the first lot. In resubstitution, all novel measurements were correctly classified by OCC. In generalization, only 87.2 % were achieved, which is illustrated in the following figures:

The errors occured for normal data, that was classified as anomal or novel. Obviously, the little training data made OCC too sensitive with regard to existing variations in the normal data itself. More extensive training data as well as more sophisticated Rmax computation can be considered as effective remedies. The concept of OCC and novelty detection is applicable also other domain, e.g., visual inspection in industrial manufacturing (see also the ISE NOVAS algorithm). From the investigations, feasibility and saliency of the regarded methods for this application domain could be shown. The need for method and in particular tool improvement and domain-specific specialization was detected. A first version of an improved interactive visualization & analysis tool, derived from the Acoustic Navigator, was established and tried (The support of Michael Eberhardt for this part of the work is gratefully acknowledged here). The following figure shows the view of the new Semiconductor-Navigator tool at work:

Finally, the first sketch of a system architecture for semiconductor manufacturing data analysis and process control for yield optimization has been suggested:

The presented work contributes to the industrial application of advanced softcomputing
methods in the field of semiconductor manufacturing process data analysis. In particular, fast and efficient methods for multivariate data dimensionality reduction including automatic methods for parameter (AFS) or parameter group saliency detection, and interactive visualization have been investigated in this first feasibility study. On-line visualization of the process trajectory in the multivariate space is also feasible by available fast methods for adding new data vectors in an existing mapping. The application of more recent methods, e.g., PSO-based and/or multiobjective AFS, and an integrated working environment will be required and highly beneficial for the regarded task. In particular, OCC or novelty detection is a promising concept for this and other applications. More information can be found in the reference given below.