# ENBIS: European Network for Business and Industrial Statistics

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## ENBIS-18 in Nancy

*2 – 25 September 2018; Ecoles des Mines, Nancy (France)*Abstract submission: 20 December 2017 – 4 June 2018

### Investigation of Multi-Run Independent Component Analysis on Simulated Semiconductor Data

*4 September 2018, 11:40 – 12:00*

#### Abstract

- Submitted by
- Anja Zernig
- Authors
- Anja Zernig (KAI - Kompetenzzentrum Automobil- und Industrieelektronik GmbH)
- Abstract
- In semiconductor industry hundreds of process steps are needed to manufacture safe and reliable devices, commonly known as chips. After the Frontend process, each device on the wafer can be measured. Hence, so-called wafermaps are drawn, where the measurement value of each device is plotted on its corresponding position on the wafer given by x and y coordinates. Some wafermaps show conspicuous features, which are recognized by humans as patterns on the wafer like e.g. a gradient from one side to the other side of the wafer. Some of these patterns are typical signatures of process steps, which become visible in certain measurements. Other appearing patterns indicate fluctuations in the production, which need to be controlled.

Ideally, the pattern of one Frontend process step is directly visible in one wafermap of the measurement data. However, often patterns are distributed over various measurements and hence they are only visible if these measurements are evaluated together. To unhide latent patterns in multivariate semiconductor data, Independent Component Analysis (ICA) is proposed. ICA is applied to a selected set of measurement data. After the ICA transformation a set of sources is given that are maximum independent of each other. To calculate the ICA transformation, the fastICA algorithm invented and implemented by A. Hyvärinen [1] is used. Like for any stochastic optimization procedure, also for the ICA the outcome depends on the starting condition. Since the “best” starting condition cannot be determined, remedy provides a repetition of the algorithm, called multi-run ICA [2].

Multi-run ICA consists of the following calculation steps. The fastICA algorithm is performed several times with different starting conditions. This leads to different source matrices, where in a next step the most reliable sources need to be identified. To this end, the individual matrices are combined to one large matrix. Then, hierarchical clustering is used together with a distance measure and a fixed cluster number, which is equal to the number of sources per run. With this method the best combination of sources can be identified and used for further analysis.

For the evaluation of the multi-run ICA, simulated data of semiconductor wafermaps have been investigated. Since the simulated wafermaps are constructed independent from each other and are linearly mixed, only minor influences of varying starting conditions can be observed. Generally, this cannot be stated for real semiconductor measurement data because real data never exactly follow the ICA model. For this reason, applying multi-run ICA can prevent from being fooled by a suboptimal solution.

[1] A. Hyvärinen, J. Karhunen and E. Oja. Independent Component Analysis. John Wiley & Sons, 2001

[2] J. Himberg and A. Hyvaerinen, "Icasso: software for investigating the reliability of ICA estimates by clustering and visualization," 2003 IEEE XIII Workshop on Neural Networks for Signal Processing, 2003, pp. 259-268.