1. Active Compensation in RF-driven Plasmas by Means of Selected Evolutionary Algorithms : a Comparative Study Ivan Zelinka http://www.ft.utb.cz/people/zelinka Email zelinka@ft.utb.cz Tomas Bata University in Zlin Faculty of Technology Institut of Information Technologies Mostni 5139 Zlin 760 01 Czech Republic

2. Structure of the Lecture I

3. Plasmas Status Quo I Plasmas are radically multiscale in two senses most plasma systems involve electrodynamics coupling across micro-, meso- and macroscale and plasma systems occur over most of the physically possible ranges in space, energy and density scales. The figure here illustrates where many plasma systems occur in terms of typical density and temperature conditions. Plasmas are conductive assemblies of charged particles, neutrals and fields that exhibit collective effects. Further, plasmas carry electrical currents and generate magnetic fields. Plasmas are the most common form of matter, comprising more than 99% of the visible universe.

4. Major topical areas of plasma science and technology Plasma Equilibria, dynamic and staticWave and Beam Interactions in Plasmas Numerical Plasmas and Simulations Plasma SourcesPlasma Theory Plasma-based DevicesPlasma Diagnostics Plasma SheathIndustrial Plasmas Plasmas Status Quo II RevolutionTechnologies IndustrialEngines, Metallurgy ChemicalWaste handling, Catalysts ElectricalTransformers, Switches NuclearReactors, Isotopes ElectronicElectronics, Semiconductors OpticalLighting Sources, Lasers Alan Watts of Environmental Surface Technologies in Atlanta, Georgia has suggested the following grid for organizing industrial plasmas with reference to the major "revolutions" in technology:

5. Plasmas Status Quo III Benefits at Home. High efficiency lighting; manufacturing of semiconductors for home computers, TVs and electronics; flat-panel displays; and surface treatment of synthetic cloth for dye adhesion. Business Applications. Plasma enhanced chemistry; surface cleaning; processing of plastics; gas treatment; spraying of materials; chemical analysis; high- efficiency lighting; semiconductor production for computers, TVs and electronics; and sterilization of medical tools. Plasmas in Transportation. Plasma spraying of surface coatings for temperature and wear resistance, treatment of engine exhaust compounds, and ion thrusters for space flight. Plasma Thrusters for Spacecraft - test of electrostatic ion thruster in large vacuum chamber (NASA) Plasma spraying of high- temperature resistance surface coatings for a diesel engine turbocharger housing

6. Microwave generated plasma around a catalyst for removal of NOx and CO from engine exhausts Modification of Aerodynamic Drag. A flat panel with a layer of one-atmosphere plasma undergoing wind tunnel testing. This technology may lead to improvements in aircraft flight range and landing on short runways. (University of Tennessee) Plasmas Status Quo IV Plasma Lighting. The most prevalent man-made plasmas on our planet are the plasmas in lamps. There are primarily two types of plasma-based light sources, fluorescent lamps and high-intensity arc lamps. Fluorescent lamps find widespread use in homes, industry and commercial settings. Inside every fluorescent lamp there lurks a plasma. It is the plasma that converts electrical power to a form that causes the lamp's phosphor coating to produce the light we see. The phosphor is the white coating on the lamp wall. A fluorescent lamp is shown here with part of the phosphor coating removed to reveal the blue plasma glow inside.

7. New one-atmosphere plasma systems make possible new methods for surface cleaning and sterilization for food, medical, and other applications. Whereas standard heat sterilization is time consuming and irradiation can damage materials, this new plasma technology has been shown to kill bacteria on various surfaces in seconds to minutes. In addition to destroying bacteria, such plasma systems also destroy viruses, fungi and spores. These systems also provide an environmentally benign method for pre-treating surfaces. One-atmosphere plasma systems are now becoming available for various industrial applications. The photo shows laboratory testing of non-thermal amospheric pressure plasmas for the inactivation (or destruction) of microorganisms. Plasmas Status Quo V

8. Products manufactured using plasmas impact our daily lives on: Computer chips and integrated circuits Computer hard drives Electronics Machine tools Medical implants and prosthetics Audio and video tapes Aircraft and automobile engine parts Printing on plastic food containers Energy-efficient window coatings High-efficiency window coatings Safe drinking water Voice and data communications components Anti-scratch and anti-glare coatings eyeglasses and other optics Plasma technologies are important in industries with annual world markets approaching $200 billion: Waste processing Coatings and films Electronics Computer chips and integrated circuits Advanced materials (e.g., ceramics) High-efficiency lighting Impact of Plasmas on Technology

9. Motivation and Aims Use of evolutionary algorithms to deduce fourteen Fourier terms in a radio-frequency (RF) waveform in plasma reactor. Previous experiment: Dyson, A., Bryant, P., Allen, J. E. Multiple harmonic compensation of Langmuir probes in RF discharges, Meas. Sci. Technol. 11(2000), pp 554-559 L Nolle, A Goodyear, A A Hopgood, P D Picton, N StJ Braithwaite, Automated Control of an Actively Compensated Langmuir Probe System Using Simulated Annealing Extension of a previous study as an comparative study SA, DE in: K.V. Price, R.Storn, Lampinen J., DE – Global Optimiser for Scientists and Engineers, Springer-Verlag SA,DE, SOMA in: journal is in searching process Radio frequency inductively-coupled plasma source for plasma processing

10. Langmuir probes are important electrostatic diagnostics for RF-driven gas discharge plasmas. These RF plasmas are inherently non-linear, and many harmonics of the fundamental are generated in the plasma. RF components across the probe sheath distort the measurements made by the probes. To improve the accuracy of the measurements, these RF components must be removed. This has been achieved during this research by active compensation, i.e. by applying an RF signal to the probe tip. Not only amplitude and phase of the applied signal have to match that of the exciting RF, also its waveform has to match that of the harmonics generated in the plasma. The active compensation system uses seven harmonics to generate the required waveform. Therefore, fourteen heavily interacting parameters (seven amplitudes and seven phases) need to be tuned before measurements can be taken. Because of the magnitude of the resulting search space, it is virtually impossible to test all possible solutions within an acceptable time. An automated control system employing EAs has been developed for online tuning of the waveform. This control system has been shown to find better solutions in less time than skilled human operators do. The results are also more reproducible and hence more reliable. Radio-frequency (RF) driven discharge plasmas are widely used in the material processing industry. Plasmas are partially ionized gases, which are not in a thermal equilibrium with their surroundings. They are used, for example, for etching, deposition and surface treatment in the semiconductor industry. In order to achieve best results, i.e. quality, it is essential for users of such plasmas to have tight control over the plasma and hence they need appropriate diagnostic tools. Better diagnostics lead to better control of the plasma and hence to better quality of the products.Introduction

11. Schematics of a RF driven plasma system Problem domain: low temperature plasma systems Radio-frequency driven plasmas RF-powered plasmas by an external power source, usually operating on 13.56 MHz (industrial use) The main application of RF-powered plasmas is to produce a flux of energetic ions, which can be applied continuously to a large area of work piece, e.g. for etching or deposition. 13.56 MHz Langmuir probe

12. Langmuir probes Developed in 1924 by Langmuir, are one of the oldest probes used to obtain information about low-pressure plasma properties. They are metallic electrodes, which are inserted into a plasma. By applying a positive or negative DC potential to the probe, either an ion or an electron current can be drawn from the plasma, returning via a large conducting surface such as the walls of the vacuum vessel or an electrode. This current is used to analyze the plasma properties, e.g. for the determination of the energy of electrons, electron particle density, etc. The region of space-charge (the sheath) that forms around a probe immersed in a plasma has a highly non-linear electrical characteristic. As a result, harmonic components of potential across this layer give rise to serious distortion of the probes signal. In RF-generated plasmas this is a major issue as the excitation process necessarily leads to the space potential in the plasma having RF components. As a consequence of this fact a serious distortion of the probes signal can be observed. It is caused by harmonic components of potential across this layer. In order to achieve accurate measures, this harmonic component has to be eliminated.

13. Problem Complexity and Active Compensation in RF-driven Plasmas and Automated Control System Where: nnumber of points in search space bresolution per channel in bits pnumber of parameters to be optimized Resolution of 12 bits Dimensionality of the search space was 14 (Dyson, A., Bryant, P., Allen, J. E. reported in Multiple harmonic compensation of Langmuir probes in RF discharges, Meas. Sci. Technol. 11(2000), pp 554-559 only 3 harmonics) Search space consisted of n 3.7 x 10 50 search points Mapping out the entire search space would take approximately 10 41 years i.e. 10 32 x longer that our universe exist 240s -> 10 -47 s

14. Before the xwos (xwindow waveform optimization system) control software was developed, the following requirements were identified: The optimization should take place within reasonable time, The search results (fitness) over time should be plotted on-line on screen in order to allow a judgement of the quality of the result, The operator should be able to select values for the EAs parameters, The operator should have the opportunity to set any of the fourteen parameters manually, The operator should have the opportunity to fine-tune the settings found by the automated system, The DC bias (fitness parameter) had to be monitored. The control software was developed in C++ on a 500 MHz Pentium III PC running the Linux 2.2 operating system. The graphical user interface was coded using X-Windows and OSF/Motif. Software Experiment Equipment and Requirements on XWOS System 7 amplitudes7 phases DC Bias History of one evolution of the best and average individual Correlation analysis window

15. Hardware Experiment Equipment All experiments were carried out at the Oxford Research Unit, The Open University, UK. Figure shows the experiment setup. Apart from the control system described above, a digital oscilloscope was used to measure the actual waveforms found by the three optimization algorithms. The control software was running on a PC under the Linux operating system. The algorithms used for this experiments were written in C++ and integrated in the existing Langmuir probe control software. The plasma system used was a standard GEC cell.

16. Optimization Algorithms Used Simulated Annealing (SA) Van Ginneken, L. P. P. P., Otten, R. H. J. M.: The Annealing Algorithm (Kluwer International Series in Engineering and Computer Science,72), Kluwer Academic Publishers, 1989 Differential Evolution (DE) Price K.: An Introduction to Differential Evolution, in New Ideas in Optimization, D. Corne, M. Dorigo and F. Glover, Eds., s. 79–108, McGraw-Hill, London, UK, 1999. Self-Organizing Migrating Algorithm (SOMA) Zelinka Ivan, SOMA – Self Organizing Migrating Algorithm,chapter 7, 33 p. in: B.V. Babu, G. Onwubolu (eds), New Optimization Techniques in Engineering, Springer-Verlag

17. SOMA – Main Idea The main idea on which SOMA is based is competetive-cooperative behavior of the intelligent beings who are together solving given task. Examples can be observed arround the world: Ants Bees Termites Wolves People Gold miners of 19th century Battle strategies … Bacause of used philosophy, terminology used with this algorithm a little bitt differ from standard terminology used with classics EAs. At http://www.ft.utb.cz/people/zelinka/soma/ are available source codes, test functions, and more...

18. SOMA – Terminology and Recommended Parameters Parameter nameRecommended rangeRemark PathLength Controlling parameter Step Controlling parameter PRT Controlling parameter DimGiven by problemNumber of arguments in cost function PopSize Controlling parameter Migrations Stopping parameter MinDiv Stopping parameter If < MinDiv then End

19. SOMA – Principles Parameter definition - Migrations, MinDiv, PopSize, PathLength, Step, PRT, Specimen and Dimension of the problem. Start of SOMA - population generating Run of SOMA precisely (1) (2) (3) (4) (5)

20. SOMA – Principles Leader Individual Step Position given by parameter PathLength PRT=[0,1] PRT=[1,1]

21. Versions: AllToOne AllToOneRandomly AllToAll AllToAllAdaptive SOMA – Basic Versions

22. SOMAs ability to avoid local minimas - during migration loops is created false function - polyhedron and individuals move along to edges of this polyhedron SOMA – Ability to Avoid Local Minimas

23. Handling of boundary constraints Boundary position setting Reset of wrong parameter Spiral movement on N+1 dimensional sphere Random replacement Handling of integer variables Rounding in the population Rounding in the cost function argument input Handling of discrete variables Integer index use Handling of constraints given to the fitness Penalty SOMA – Constraints Handling

24. SOMA – Problem Complexity Objective function - unimodal : multimodal Linear – nonlinear None-fractal type (but because everything in the real world has constrains, fractal type functions can also be optimized) Defined at real, integer or discrete argument spaces Constrained, multiobjective Needle-in-haystack problems NP problems Degree of parameter interactions : low – high, separable – non-separable Type of variables : continuous – discrete / integer / mixed Number of variables : low – high Search space : small – large, finite – infinite, continuous – non-continuous

25. SOMA – Selected Tests I

26. SOMA – Selected Tests II EggHolderStretchedSine

27. 3rd De Jong's function4th De Jong's function Sphere model, 1st De Jong's function Rosenbrock's saddle Rastrigin's functionSchwefel's functionGriewangk's function Stretched V sine wave function (Ackley) Test function (Ackley) Ackley's function Test function - egg holder Rana's function Pathological functionMichalewicz's function Cosine wave function (Masters) SOMA – Tests Functions

28. Chemical reactor optimization and control Chemical reactor structural stability Analytic programming Mechanical engineering examples Fuzzy controller setting Predictive model estimation AntenaInverse Fractal Problem SOMA – Selected Problems

29. Previous Experiments SA had shown better floating potential than human operator SA had shown smaller diversity in floating potential and time For following experiments were parameters set so that used EA showed the best performance as much as possible

30. Experiment Setting – SA, DE Plasma parameters GasArgon Power50 W Pressure100 mTorr Flow rate95 sccm Plasma parameters used for the experiments Parameter settings for the optimization algorithms used in experiments

31. Results I – SA, DE DE SA All data were carefully collected and used to draw a flow of all histories so that average, minimal and maximal values can be easily observed.

32. DE SA Results II – SA, DE Efficiency of used algorithms can be also judge according to correctness and reproducibility of reached results based on statistical point of view

33. DE SA Results III – SA, DE Results were used to restore waveforms observed on osciloscope. Here are depicted average values, minimal and maximal values reached during all experiments.

34. Results VI – SA, DE Results were used to create an algorithm efficiency chart to show efficiency of both algorithms. They shows minimal, maximal and average values reached during the active compensation of RF-driven plasmas.

35. Experiment Setting – SA, DE and SOMA Plasma parameters GasArgon Power50 W Pressure100 mTorr Flow rate95 sccm Plasma parameters used for the experiments Parameter settings for the optimization algorithms used in experiments

36. Results I – SA, DE and SOMA DE SA SOMA All data were carefully collected and used to draw a flow of all histories so that average, minimal and maximal values can be easily observed.

37. Results II – SA, DE and SOMA DE SA SOMA All data were carefully collected and used to draw a flow of all histories so that average, minimal and maximal values can be easily observed.

38. Results III – SA, DE and SOMA DE SA SOMA Results were used to restore waveforms observed on osciloscope. Here are depicted average, minimal and maximal values reached during all experiments.

39. Results III a) – SA, DE and SOMA DE SA SOMA Here are all waveforms in one just for demonstration. Average, minimal and maximal values reached during all experiments cannot be observed here.

40. Results VI – SA, DE and SOMA SA, SOMA, DE Results were used to create four charts: four different view on algorithm efficiency

41. Conclusion Ability to be used: all three algorithms can be used for active compensation in RF-driven plasmas. However, based on results it is clear that SOMA and DE has greater potential for this task. Preciseness and reproducibility: one of the crucial points in science is reproducibility, i.e. the ability to achieve the same results for two identical experiments. In practical applications like this one, a high degree of reproducibility is needed. From figures it is visible, that SOMA and DE has a greater reproducibility than SA. They are is also more precise than SA. Speed: the speed of the optimization process was not determined by the computer power available, but by the time constants of the analogue equipment, e.g. harmonic box. Therefore, all three algorithms have shown similar speed performance in this specific application. Diversity: is tightly connected with preciseness and reproducibility. From this point of view SOMA and DE performed almost three times better than SA. If one remembers that plasmas are highly nonlinear dynamical systems with complicated behavior, then the results produced by SOMA and DE are very sufficient. Algorithms efficiency: from figures it is clearly visible that the best results were obtained by SOMA algorithm, second place took DE and third SA. While results given by SA are significantly the worst one, in the case of SOMA and DE should be mentioned that difference between them was wery small – almost negligible. This small difference shows, that both algorithms are highly usable for dealing with systems kind of blackbox which plasma reactor in fact is. Dynamical position of global extreme: global extreme (thus whole cost function landscape) was not static in time. During above described experiments which took almost 12 hours of noninterrupted works (for 5 days ), plasma in reactor changed its behaviour. This change was linear dependent. Based on experiences with SOMA and DE, it can be stated that both algorithms has follows global extreme (or founded suboptimal solution) position quite well.

42. Acknowledgements This work was partly funded by the Ministry of Education of the Czech Republic, under grant reference MSM 26500014, Grant Agency of the Czech Republic under grand references GACR 102/03/0070 and GACR 102/02/0204. The authors whish to express their thanks to Lars Nolle School of Computing and Technology, The Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, UK A.A. Hopgood N.St.J. Braithwaite Oxford Research Unit, The Open University Alec Goodyear Jafar Al-Kuzee for assistance with the plasma equipment.