radio frequency (rf) measurement and control project report

Radio Frequency (RF) Measurement and ControlProject Report (TECQ001)

International SEMATECHTechnology Transfer 96063138C-ENG

© 1998 SEMATECH, Inc.

SEMATECH and the SEMATECH logo are registered service marks of SEMATECH, Inc.

Product names and company names used in this publication are for identification purposes only and may be trademarks or servicemarks of their respective companies

Radio Frequency (RF) Measurement and Control Project Report(TECQ001)

Technology Transfer # 96063138C-ENGInternational SEMATECH

September 10, 1998

Abstract: This document is a revision of 96063138B-ENG. It describes the technical achievements of thePlasma Etch Technology Radio Frequency (RF) Power Measurement and Control Project(TECQ001), which spanned two years from mid-1994 to mid-1996. The document details theconception, design, development, and prototyping of an advanced concept RF power deliverysystem, which incorporates new technologies. Background information, detailed circuitry andcomponent designs, and mathematical examinations are included. Additional reduction-to-practiceassembly and circuit tuning information can be obtained by contacting the SEMATECH projectmanager or the SEMATECH Calibration Laboratory. Revision C changes the classification of thedocument from SEMATECH Confidential Restricted to SEMATECH Non-Confidential andincludes a Foreword describing the technical developments for which SEMATECH has appliedfor patents.

Keywords: Equipment Performance, RF Sensors, Plasma Etching, Etching Equipment, ElectricalMeasurement

Authors: Tony Moore (SEMATECH/ORNL); Gil Yetter (SEMATECH); Travis Spratlin (ORNL); CharlieNowlin (ORNL)

Approvals: Gil Yetter, Author/Project ManagerRay Delk, Director, Internal Technical SupportJeanne Cranford, Technical Information Transfer Team Leader

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Technology Transfer #96063138C-ENG International SEMATECH

Table of Contents

1 EXECUTIVE SUMMARY....................................................................................................... 1

2 INTRODUCTION..................................................................................................................... 1 2.1 Logistical Approach.......................................................................................................... 2 2.2 Technical Overview.......................................................................................................... 4 2.3 Vision of the Future .......................................................................................................... 7

3 ANALYTICAL RF POWER METROLOGY .......................................................................... 8 3.1 Analytical RF Sensor Based on First Principles ............................................................... 9

3.1.1 Current Signal Sampling Component of RF Sensor ............................................ 17 3.1.2 Voltage Signal Sampling Component of RF Sensor............................................ 23 3.1.3 Integrated RF Sensor Analysis............................................................................. 31

3.2 Harmonic Filtering.......................................................................................................... 34 3.3 Detector Electronics........................................................................................................ 42

3.3.1 Phase Detector Method ........................................................................................ 43 3.3.2 I-Q Detector Method............................................................................................ 51

4 POWER DELIVERY SYSTEM ............................................................................................. 58 4.1 Saturable Reactor Technology........................................................................................ 59 4.2 No Moving Parts, Fast Matching Network Design......................................................... 63

5 A UNIQUE COMPUTER CONTROL STRATEGY ............................................................. 72 5.1 Architecture and Design Strategy ................................................................................... 72

5.1.1 The Software Story .............................................................................................. 72 5.1.2 Computer Hardware Design................................................................................. 73 5.1.3 Computer Software Design.................................................................................. 73

5.2 Implementation ............................................................................................................... 75 5.2.1 Hardware Implementation.................................................................................... 75 5.2.2 Software Implementation..................................................................................... 75 5.2.3 RF User Interface ................................................................................................. 78 5.2.4 Query Module ...................................................................................................... 83

5.3 Computer System Lessons Learned................................................................................ 84 5.3.1 Use a Real-Time Operating System..................................................................... 85 5.3.2 Use Proven Hardware .......................................................................................... 85 5.3.3 Use a User Interface Builder ................................................................................ 85 5.3.4 Query Interface—Separate Conversations........................................................... 86 5.3.5 Integrate Early and Often..................................................................................... 86

5.4 RF Computer Control System Requirements that Guided the Project ........................... 86

6 OVERALL RF POWER MEASUREMENT AND CONTROL SYSTEM PERFORMANCE ................................................................................................................... 87

7 CONCLUSION ....................................................................................................................... 93

APPENDIX A Derivation of Current Loop Sensor .................................................................. 94 A.1 Basic Theory ................................................................................................................... 94 A.2 Solution for Two Coaxial Conductors ............................................................................ 98 A.3 References..................................................................................................................... 102

APPENDIX B Derivation of Voltage Pickup Probe Sensor................................................... 103

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List of Figures

Figure 1 Evolution of the RF Sensor Prototypes ................................................................... 3

Figure 2 Completely Assembled RF Sensor with a Clear Housing....................................... 5

Figure 3 RF Sensor Components........................................................................................... 9

Figure 4 RF Sensor Components With the Current Loop Inside the Hollow Center RF Power Conductor............................................................................................. 10

Figure 5 Cross Section of RF Sensor to Show Current Pickup Loop and Voltage Pickup Probe Placement........................................................................................ 11

Figure 6 RF Sensor with N-Type Connectors ..................................................................... 12

Figure 7 Sensor Assembly with 1/4-20 Bolt Connections .................................................. 12

Figure 8 Hollow Center Conductor Positioned in Sensor Body.......................................... 13

Figure 9 Voltage Pickup Assembly Positioned in Sensor Body.......................................... 13

Figure 10 Current Pickup Loop and Teflon Insulator Installed in Sensor Body, Penetrating the Hollow Center Conductor ............................................................ 14

Figure 11 Sensor Assembly with Teflon Center Conductor Positioning End Pieces............ 14

Figure 12 Sensor Assembly with Metal End Plates Installed................................................ 15

Figure 13 Sensor Assembly with N-Type Connectors Installed ........................................... 15

Figure 14 Sensor Assembly with Screws Installed ............................................................... 16

Figure 15 Assembled RF Sensor ........................................................................................... 16

Figure 16 Exploded View of RF Sensor................................................................................ 17

Figure 17 Magnetic Flux Space............................................................................................. 18

Figure 18 Magnetic Flux Linked Area .................................................................................. 18

Figure 19 RF Power Magnetic Energy Coupling Area ......................................................... 19

Figure 20 Magnetic Flux Illustration of Fundamental Laws ................................................. 19

Figure 21 Linked Magnetic Flux Geometric Area ................................................................ 20

Figure 22 Network Analyzer Plot of Magnetic Field Signal Coupling Response................. 22

Figure 23 Schematic Representation of Current Pickup Loop .............................................. 22

Figure 24 Schematic Illustration of Voltage Sensor.............................................................. 23

Figure 25 Network Analyzer Plot of Voltage Pickup Symmetry by Superimposing Forward and Reverse Repsonse Data.................................................................... 24

Figure 26 Geometric Relationship for Voltage Sensor Plate................................................. 25

Figure 27 Schematic Illustration of the Realized Voltage Probe/Divider Circuit ................. 25

Figure 28 Schematic Representation of Thevinin Current Perspective................................. 25

Figure 29 Transform to a Voltage with Series Impedance Schematic .................................. 26

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Figure 30 Simplified Voltage Sensor Schematic................................................................... 26

Figure 31 Voltage Probe Design Space ................................................................................. 28

Figure 32 Voltage Probe Radial Geometry Illustration......................................................... 28

Figure 33 Voltage Probe E Field Coupling Illustration......................................................... 29

Figure 34 Network Analyzer Plot of Voltage Pickup Coupling Reponse ............................. 30

Figure 35 Network Analyzer Plot of Current Loop Pickup Symmetry by Plotting of Forward and Reverse Current Responses.............................................................. 32

Figure 36 Network Analyzer Plot of N-Type Barrel Insertion Loss at 13.56 MHz .............. 32

Figure 37 Network Analyzer Plot of RF Sensor Insertion Loss at 13.56 MHz..................... 33

Figure 38 Network Analyzer Plot of an N-Type Barrel VSWR at 13.56 MHz..................... 33

Figure 39 Network Analyzer Plot of RF Sensor VSWR at 13.56 MHz................................ 34

Figure 40 TDR Impedance Plot of an RF Sensor Prototype ................................................. 34

Figure 41 Complete Dual Channel RF Harmonic Filter........................................................ 35

Figure 42 Dual Channel RF Harmonic Filter with Cover Off............................................... 35

Figure 43 Initial Harmonic Filter Design Schematic............................................................. 36

Figure 44 Final Harmonic Filter Design Schematic .............................................................. 37

Figure 45 Network Analyzer Plot of Harmonic Filter Frequency Response ........................ 37

Figure 46 Network Analyzer Plot of Harmonic Filter Bandpass Insertion Loss................... 37

Figure 47 Network Analyzer Plot of Harmonic Filter Phase Shift at 13.56 MHz................. 38

Figure 48 Differential Phase versus Temperature for the Two Filter Channels.................... 39

Figure 49 Network Analyzer Plot of the Input Impedance of the Harmonic Filter............... 40

Figure 50 Network Analyzer Plot of the Output Impedance of the Harmonic Filter ............ 40

Figure 51 Silkscreen Layout of PCB for Dual Filter Assembly............................................ 41

Figure 52 Layout of the Components of the Dual Harmonic Filter Assembly ..................... 41

Figure 53 Schematic of Harmonic Filter ............................................................................... 42

Figure 54 Complete Phase Detector Assembly ..................................................................... 44

Figure 55 Phase Detector with Cover Off ............................................................................. 44

Figure 56 PD4 Phase Detector Linearity Plot........................................................................ 45

Figure 57 PD4 Magnitude Detector Linearity Plot................................................................ 45

Figure 58 Silkscreen Layout of the Top Side of the PD4 Phase Detector PCB .................... 46

Figure 59 Silkscreen Layout of the Bottom Side of the PD4 Phase Detector PCB............... 46

Figure 60 Layout of the Components on the Top Side of the PD4 Phase Detector .............. 47

Figure 61 Layout of the Components on the Bottom Side of the PD4 Phase Detector......... 48

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Figure 62 Schematic of PD4 Phase Magnitude Detector ...................................................... 49

Figure 63 Complete I-Q Detector Assembly......................................................................... 51

Figure 64 I-Q Detector Assembly with Cover Off ................................................................ 52

Figure 65 I-Q Detector Modeled and Measured VARS Data Superimposed........................ 53

Figure 66 I-Q Detector Linearity Performance ..................................................................... 54

Figure 67 Silkscreen Layout of the Top Side of I-Q Detector PCB...................................... 54

Figure 68 Silkscreen Layout of the Bottom Side of I-Q Detector PCB ................................ 55

Figure 69 Layout of Components on the Top Side of I-Q Detector PCB ............................. 55

Figure 70 Layout of Components on the Bottom Side of I-Q Detector PCB........................ 56

Figure 71 Schematic of I-Q Detector..................................................................................... 57

Figure 72 Complete Saturable Reactor.................................................................................. 59

Figure 73 Classical Implementation of Saturable Reactors................................................... 60

Figure 74 Complete Saturable Reactor.................................................................................. 61

Figure 75 Cutaway of Saturable Reactor Showing RF Inductor Coil ................................... 62

Figure 76 Illustration of RF Bucking Wiring Method........................................................... 63

Figure 77 Ampere Turns versus R, Q, and X Data for a Saturable Reactor Design that had Two RF Turns per Core (used on the first matcher prototype) ............... 64

Figure 78 Saturable Reactor Assembly ................................................................................. 64

Figure 79 Interior of the High Speed RF Matching Network Prototype ............................... 65

Figure 80 Matching Network Operating Profile Plot ............................................................ 65

Figure 81 Prototype Matcher Design..................................................................................... 66

Figure 82 RF Match Network Tuning Control Current versus Tuning Range Plot .............. 67

Figure 83 Final Matcher Design ............................................................................................ 67

Figure 84 Match Network Input Transformer Assembly ...................................................... 69

Figure 85 Match Network Output Transformer Assembly.................................................... 69

Figure 86 RF Matcher, Saturable Reactor Current Drive Regulator Schematic ................... 70

Figure 87 Matcher RF Deck Schematic................................................................................. 71

Figure 88 System Block Diagram of Hardware .................................................................... 74

Figure 89 Logical Design ...................................................................................................... 74

Figure 90 Physical Design ..................................................................................................... 75

Figure 91 RF Measurement and Control Design................................................................... 76

Figure 92 RF User Interface Design...................................................................................... 78

Figure 93 Main Panel............................................................................................................. 79

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Figure 94 System Level Control Panel.................................................................................. 80

Figure 95 Operation Mode Panel........................................................................................... 80

Figure 96 Edit Sensor Calibration Panel ............................................................................... 81

Figure 97 Dynamic Display of Sensor/System Data Panel ................................................... 82

Figure 98 Data Archive Panel................................................................................................ 82

Figure 99 Performance Plot of the Complete RF Power Delivery System into a Dynamic Step Change Plasma Simulating Linear Load ....................................... 88

Figure 100 Performance Plot of the Complete RF Power Delivery System Tuning Control Signals (see Figure 99)............................................................................. 89

Figure 101 RF Power Delivery System Block Diagram ......................................................... 89

Figure 102 Expanded Time Scale Performance Plot of the First Event (see Figure 100) Showing the Speed of Tuning and Power Delivery Control Accuracy ........ 90

Figure 103 Expanded Time Scale Plot of the Tuning Control Signals at the First Event (see Figure 102)..................................................................................................... 90

Figure 104 Expanded Time Scale Performance Plot of the Second Event (see Figure 100) Showing the Speed of Tuning and Power Delivery Control Accuracy ........ 92

Figure 105 Expanded Time Scale Plot of the Tuning Control Signals at the Second Event (see Figure 104) .......................................................................................... 92

Figure 106 RF Match Network Efficiency and Load Reactance Plot ..................................... 93

Figure 107 Surface Charge Boundary ..................................................................................... 95

Figure 108 Concentric Coaxial Conductors ............................................................................ 95

Figure 109 Magnetic Pickup Loop Representation ................................................................. 95

List of Tables

Table 1 Parts List for Harmonic Filter ............................................................................... 42

Table 2 Parts List for Phase Detector................................................................................. 50

Table 3 Parts List for I-Q Detector..................................................................................... 58

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Acknowledgements

Funds were made available from the Internal Technical Support (ITS) and Etch Divisions foradditional test equipment and prototyping efforts, which greatly helped the success of theproject. The manpower issue was never really resolved, mostly because talented RF engineersare rare within the semiconductor industry. We utilized a variety of fabrication companies toassist us where possible, borrowed folks from other SEMATECH departments and even had theservices of a retired ORNL employee who loves technical puzzles. The team changed its makeup from time to time, while the core team remained largely the same. Many long nights andweekends were contributed by everyone, because we believed in the objectives at hand. In orderto stay focused, we often could not respond to unexpected management requests such asvariations of project-related gantt charts and rewordings of the initial plan or status reports. Weoften used a hide-out office area located over the SEMATECH clean room between air handlersand often resorted to staying at home to be able to focus on serious design problems. From time-to-time, emails, phone calls, and pagers had to be left in the accumulate mode. Even worse werethe temptations to do many more variations of virtually every component we worked on.Somehow, we somehow managed to resist the majority of our own temptations as well as therequests from observers.

Norm Williams of the Plasma Etch Diagnostics department was the primary technical driver ofthis area of investigation and was responsible for developing the scope of this project. DickAnderson, who previously worked with Norm at SEMATECH, had returned to ORNL where helocated Tony Moore and also provided a strong influence during contract negotiations and theestablishment of the Cooperative Research and Development Agreement (CRADA) under whichthe project was conducted. Tom Shannon, in the SEMATECH Contracts department, providedguidance and many long hours of effort to formalize the final contract and memorandumsbetween SEMATECH, ORNL, Martin Marietta Energy Systems (later to become LockheedMartin Energy Research), DOE Washington, and Sandia National Laboratories.

The core team was lead by Tony Moore of Oak Ridge National Laboratory, the first “assignee”from a national laboratory. He was successfully integrated into our engineering culture while heaccomplished his goals. Tony has the capability of driving right to the crux of a problem, whileshedding all of the superfluous baggage. Tony’s unique technical insight allows him to envisionsolutions and inventions that solve problems and also survive the all too critical peer reviewprocess while withstanding the test of time. He pursued his vision with tenacity while beingconstantly mindful of contract deadlines and the fact that he represented the Instrumentation andControls Division back at ORNL as the first ambassador to SEMATECH. He left a lasting andpositive impression on everyone with whom he interacted—the technical staff of SEMATECH,SEMATECH member companies, and the plasma etch system supplier SEMI/SEMATECHmember companies.

Our thanks to Tony and we wish him well upon his return to the ORNL technical staff in theInstrumentation and Controls division.

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Tony coordinated a shadow team of staff members back at ORNL, keeping them busy workingon many of the technical aspects of the devices that were developed. Dennis Sparks was perhapsthe most valuable member in terms of total time spent on the project. Dennis is also the identifiedco-inventor in the patent process on the analytical RF power sensor with Tony. Charlie Nowlin,Tony’s previous manager who retired from ORNL and attained the distinction of a “ProfessorEmeritus” at ORNL, contributed thoughtful analysis on the mathematical model of the voltagepickup portion of the sensor. Travis Spratlin conducted extensive modeling on the current pickupportion of the sensor. Phil Ryan contributed modeling expertise from another vision of theconcepts. Bill Holmes spent many a day with us in Austin helping us turn circuit diagrams drawnon the back of napkins into printed circuit boards, while training the Cal Lab technicians in howto “do it themselves” in the process. Dan Hoffman and John Caughman contributed towards thetesting of functional prototypes and the initial work on a contingency plan to pursue high-speedactuation of a vacuum variable capacitor design.

During Tony Moore’s assignment at SEMATECH, he was part of the Calibration Laboratorystaff working closely with Gil Yetter, the Section Leader. Gil was instrumental in themanagement of this project from the conception stage—working with Norm Williams—all theway through the end of the project. Gil relieved Tony of all of the management and logisticalfunctions to allow Tony to maintain a constant technical focus in order to stay on schedule. TheCal-Lab technicians (Trace Beck, Craig Lopp, and Tim Folliet) provided Tony with fabricationand test assistance throughout virtually every phase of the project. Cal-Lab part time studentinterns (Scott Bushman and Scott Sparks) assisted Tony with a variety of services ranging fromcustom software needs for bench test purposes to conducting experiments on a plasma reactor atthe University of Texas in Austin.

The project would not have been possible without the direct help of Norm Willliams and theEtch Division directors, Ken Maxwell and John Martin. Ray Delk, director of the ITSdepartment, assisted the project team when possible to keep it on track and to provide additionalresources where needed. It must be stated that, in every aspect, this project was conducted as if itwere part of the Etch department and its staff, even though it resided in the CalibrationLaboratory, which is a support organization. The Plasma Etch FTAB monitored and ranked theproject quarterly.

The computer architecture team was led by Bob Flegal at SEMATECH and by Steve Hicks fromORNL. Kathy Lewis and Abel Mireles of SEMATECH assisted Bob Flegal, while Ganesh Raoassisted Steve Hicks back at ORNL, programming with a duplicate system. Steve visitedSEMATECH often, staying for extended periods, to perform operational tests that complimentedthe routine FTPing of software modules back and forth to SEMATECH from ORNL, workingwith Kathy Lewis. Ganesh worked some very long hours (often late into the nights) as the lasttechnical milestone approached when all the systems’ pieces were being integrated. His driveand dedication, as the final hour of the deadline approached, literally saved us from being late.The initial assistance we received from Charlie MeLear at Motorola was very valuable, eventhough we later abandoned the equipment set on which he specialized.

Members of the SEMATECH Plasma Etch Diagnostics department, Victoria Resta and DaveRasmussen, provided assistance a number times and we thank them very much for doing so.

Paul Miller of Sandia National Laboratories provided technical insight and performed an analysison a prototype RF Sensor. His contributions were very valuable because they helped to monitorour progress from another perspective.

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Karen Blair, the administrative support for the Cal Lab, provided a wide range of services thatstarted with the project proposal all the way to this document. Sandra Strickland providedsignificant assistance in preparing this documentation, working with the team members. MikePendley, who recently joined the SEMATECH Cal Lab as an RF engineer, has assisted greatly inthis document as he transitions into his role of assuming Tony’s project efforts.

Overall, these people contributed more energy towards the completion of the project objectivesthan was ever expected to be required at the onset. A true team commitment to quality andmeticulous scientific rigor was ingrained into the fabric of the team by the technical leadership ofTony Moore. All of the team members agree that the constant developments of demonstratableworking prototypes provided the tangible image needed to “rally around” and also pulled usthrough difficult times as deadlines approached. We could see our progress unfold, which madeus feel like we were a part of something and that it was a part of us.

We exceeded most contract performance specifications, while meeting all contract deadlines, OnTime, On Target, and Together.

_______________________________________________________________

I want to personally thank everyone who worked on this project.

Gil YetterProject Manager/Section Leader

SEMATECH Calibration Laboratory

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Foreword

During the course of this RF technology project conducted at SEMATECH from 1994 to 1996entitled “TECQ001, RF Power Measurement and Control Project,” intellectual property wasdeveloped that resulted in applications for US patents. The following RF components weredeveloped:

− A quantitative RF sensor based on first principles (two patents to issue in Fall,1998)

− A phase stable, temperature compensated harmonic filter

− An accurate phase and magnitude detector

− An accurate In phase Quadrature (IQ) detector

− An electronically variable RF inductor/13.56 Mhz saturable reactor (patent issued:Titled “Self Isolating High Frequency Saturable Reactor,” Dated June 23, 1998)

− A fast matcher topology to demonstrate the saturable reactor

− A high speed dual processor computer architecture to operate the integratedFast/Accurate RF power delivery system

Because of the intellectual property concerns associated with patent applications, theSEMATECH Technology Transfer document was released initially as a SEMATECH RestrictedConfidential document issued by name and serial number. The document was distributed to theSEMATECH Radio Frequency Advisory Group (RFAG) member company staff members, andto the RFAG SEMI/SEMATECH suppliers who had signed a specific intellectual property non-disclosure agreement for the document. Revision C of the document changes the classification toSEMATECH Confidential.

The document covers all aspects of the project, including the technical developments for whichSEMATECH has applied for patents, and others for which SEMATECH has not applied forpatents. Specifically, SEMATECH is pursuing patents on the RF sensor itself, but not on theassociated signal detection or filtering electronics. Similarly, SEMATECH has patented thesaturable reactor, but not the match topology or computer architecture that was developed todemonstrate it.

The RF sensor prototypes are quantitative in nature and were limited in scope to achieve thegoals of the project. It should be noted that the sensor design is scaleable to impedance andsignal coupling ratio requirements. The saturable reactor variable inductor offers a “no movingparts” RF tuning technique at 13.56 Mhz and can also be scaled to accommodate a number ofsystem requirements. The unpatented associated electronics that were developed offer severalsignificant advances in the RF sensor signal phase handling and detection areas. The integratedsystem incorporating the matcher topology, developed to demonstrate the saturable reactortechnology, offers an example of an alternative tuning and power control technique.

SEMATECH can assist you with commercializing either the patented or the unpatented devices.SEMATECH used more than one resource to assist us in fabricating our prototypes and thesesuppliers may, in turn, be able to assist you if needed.

The integrated prototype RF system demonstrated a fast and accurate RF measurement andpower delivery capability into a load with less than 1 watt of variability while being challenged.During demonstrations of the system, the response speeds for tuning/power solutions were on theorder of about 5 to 7 milliseconds. In order to collect realistic performance data, a “linear plasma

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simulating load” was developed as a surrogate to reasonably represent typical load conditions.To provide a tuning speed challenge, the reactive component of the surrogate load was step-changed rapidly between an impedance change from 4 ohms real (–j15 ohms imaginary) to4 ohms real (–j25 ohms imaginary) and back.

These technology advances and others have been developed through a collaborative relationshipwith the RF engineering staff members at Oak Ridge National Laboratory and at SEMATECH toassist and facilitate improvements in the semiconductor supplier base. Currently, Oak Ridge canprovide engineering assistance to suppliers desiring to implement a wide range of RF designenhancements. For instance, one way the Oak Ridge staff can provide assistance is through theRF sub-system testing facility at Oak Ridge, which provides a means of exercising designsagainst realistic challenges. Another way is by extended visits to your facilities by Oak Ridge RFtechnologists to address your RF issues and to assist you in acquiring the resources that meetyour needs.

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1 EXECUTIVE SUMMARY

An advanced concept RF power delivery system was conceived, designed, developed, andreduced to a functional working and demonstrable prototype. The RF power system incorporatestwo unique technologies, now undergoing the patent process. The development of an “analytical”RF power sensor based on first-principle concepts and not on conventional calibration practicesis a significant achievement. The other device is a unique electronically variable RF inductor thatobtains RF-matching network speeds in a few milliseconds. The device is based on a noveladvancement of saturable reactor technology; it too is undergoing the patent process. Theperformance of the completed RF power delivery system achieved RF matching network speedson the order of 5 to 7 ms and held power levels, delivered into a plasma simulating load, towithin less than a watt of RF power variation, while being subjected to a dynamically varyingstep response load change.

As a result of this project, other projects in related RF technologies are now in progress betweenORNL and the Etch division of the SEMATECH Interconnect department. The invention of theanalytical RF sensor has inspired technical staff members at the National Institute of Standardsand Technology (NIST) to request detailed information and the loan of a prototype forinvestigating the possibility for its use as a new national standard. A plan to address a number ofrequests for access to these technological achievements is being developed for review at thePlasma Etch FTAB (at their request) and may be realized as some form of follow-on work to thisproject.

All of the project milestones were on time and specifications were met or exceeded.

Revision B of this document replaced two figures with more descriptive versions and correctedthe “W” symbol (used in two of the tables) to an “Ω” symbol. Revision C changes theclassification of the document from SEMATECH Confidential Restricted to SEMATECHNon-Confidential and includes a Foreword describing the technical developments for whichSEMATECH has applied for patents.

2 INTRODUCTION

This document serves as the complete documentation of the Radio Frequency (RF) PowerMeasurement and Control Project (TECQ-001). The project was conducted in the SEMATECHCalibration Laboratory (in the Internal Technical Support division) in close collaboration withthe Plasma Etch Diagnostics department (in the Interconnect division).

The principal supplier for this project was the Instrumentation and Controls Division of OakRidge National Laboratory (ORNL) in Oak Ridge, Tennessee. A technical staff member wasassigned to SEMATECH for the two-calendar-year duration of the project (mid-1994 throughmid-1996) and was the first-ever national laboratory assignee to SEMATECH. Many othermembers of the technical staff at ORNL interfaced with this project through the on-site assigneeat SEMATECH, which greatly contributed to the project’s successful completion.

This document provides a relatively complete set of engineering-level documentation for allaspects of the project. Detailed blueprints and reduction-to-practice assembly and circuit tuninginformation will be contained in a future document. Periodic progress reports presented to theSEMATECH Radio Frequency Advisory Group and the Plasma Etch Focus Technical AdvisoryBoard (FTAB) received favorable criticism throughout this project; however, this is the first

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formally published documentation. This document includes background information, detailedcircuitry and component designs, thorough mathematical examinations, and graphic illustrationsand photographs.

The initial premise for the negotiations with the technical staff in the Instrumentation andControl Division at ORNL was to advance the state-of-the-art in RF power delivery andmeasurements as applied to semiconductor wafer plasma etchers. It is widely accepted thatORNL is a leader in instrumentation technologies and the reduction to practice applications of awide variety of advanced engineering disciplines. We believed that the chances of success forthis project would be greatly enhanced by leveraging the national laboratory resources. Actualcontract relations and resources were funded under the SEMATECH/Sandia NationalLaboratories Cooperative Research and Development Agreement (CRADA) and were accountedfor like the other projects managed and conducted at Sandia, although Sandia’s involvement wasminimal.

2.1 Logistical Approach

Previous efforts by two team members at SEMATECH (Norm Williams and Jim Spain) yieldedan approach for better understanding the boundaries of quantitative RF metrology as applied toplasma wafer processing. Norm’s work produced two U.S. patents based on a calibrated RFsensor supported by expensive and physically large laboratory grade instruments. The patents areidentified as #5,467,013 dated November 14, 1995 and #5,472,561 dated December 5, 1995;both are entitled Radio Frequency Monitor for Semiconductor Process Control. Although eachpatent has the same title, the earlier patent focuses on the sensor design, while the later patentfocuses on data interpretation correlated to plasma energetics. It was obvious that the technologywould need further development if there was to be any hope that the measurement techniquescould be “realized” in the commercial world. Initial discussion with ORNL focused on thedevelopment of a miniature version of the Hewlett Packard (HP) Vector Voltmeter, commonlyknown as a signal detector or phase and magnitude detector. The physical size of the HPinstrument was considered one of the important issues to resolve. The harmonic filter portion ofthe signal processing equipment was quickly identified as a potential show stopper if the1% accuracy goal was to be achieved. Discussions regarding the RF sensor calibration practicesapplied to prior sensor development work directed team efforts toward developing an inherentlyaccurate RF sensor based on first principles. The team believed that an analytical sensor based onfirst principles should ensure that the 1% accuracy goal be met with certainty. However, the newsensor would also provide a way to minimize conjecture over any data collected from the RFengineers within the semiconductor community. Having arrived at a consolidated plan to developand integrate the various components of an RF metrology system, it was noted that a superiormeasurement instrument will tell the user only how bad things are, so the team pursued anadditional aggressive goal for a high-speed (no moving parts) RF matching network. Thebenefits of using a high-speed RF matching network operating in the millisecond tuning rangethat would be integrated with the proposed highly accurate RF sensor were numerous. Thesebenefits included a highly accurate, high-speed integrated RF power delivery system that wouldhelp to reduce chamber-to-chamber matching issues, process variability from wafer-to-wafer andfrom lot-to-lot, and increase wafer throughput.

Because of the complex and aggressive nature of this project (to develop technologies to solvesignificant problems in the plasma etch wafer processing RF power delivery area), the teampursued parallel engineering designs as contingencies to ensure the success of the project.

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The RF sensor design described in this document is the first-principles approach, while the othercontingency sensor design is similar in construction, but requires calibration. Both sensor designswere successfully realized in working prototypes (Figure 1). The calibrated RF sensor design andits variants are being developed into a patent position by ORNL in the Fusion Energydepartment. Future documentation will describe the other sensor design and also many of thelesser details of the project that are not fully described in this document.

Figure 1 Evolution of the RF Sensor Prototypes

The harmonic filter was deemed to be low risk, thus no alternative was investigated. Theharmonic filter design that evolved met all the expectations of the contract and passed peerreview. This device is not patentable and represents an engineering design optimized for phaserelationship stability between two signal paths, one for the sampled RF current signal and theother for the sampled RF voltage signal.

The development of an RF signal processing device that could meet the laboratory gradeperformance of the HP Vector Voltmeter was challenging and required the development of twodifferent solutions, each of which works very well. The main intent of the engineering effort forthe signal processors was to reduce to practice a highly accurate, physically small and low costalternative to the laboratory instruments, dedicated to the operating frequency range of interest toplasma etch at 13.56 MHz. RF signal processing devices commonly used in the semiconductorindustry are often identified as phase/mag units. The name stands for the measurement of thephase differential between two RF signals and the magnitude of each. The team developed ahighly accurate phase/mag detector circuit that we named PD4, which stands for phase detectorversion 4. The other device we developed was adapted from the communications industry and iscommonly known as an in-phase/quadrature phase detector, from which came the name I-Qdetector. Neither of these circuits was viewed to be patentable technology since each representsrefinements and application specific optimization. It should be noted that the use of an I-Qdetector circuit, which is common in communications applications, is a novel idea in thesemiconductor industry and in precision RF power metrology. Both detector circuits provide DCvoltage output signals that are proportional to RF parameters entered into a computer with an A

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to D interface. The algorithms used to reduce the measured parameters into engineering units fordiagnostic observation or control use are fairly straightforward mathematical implementations.The significant difference between each approach is that the PD4 device has high-volumeproduction parts and should be cheaper to construct. However, it requires more signal strengthand the computer must do more calculations to achieve what the other device, the I-Q detector,does with a more expensive set of components and less computer time to generate the sameengineering data. The team believes that both approaches have merit for use.

The desire to develop a high speed RF matching network, which could operate in the envisionedtime frame, necessitated the pursuit of two approaches because of the risk of failure. Because ofearly successes with a low-power prototype, efforts to develop a fast actuator for a vacuumvariable capacitor were abandoned. The development of the electronically variable inductor wasthe main goal of the RF matching network portion of the project, while the “fast” RF matchingnetwork, designed to meet the objectives of this project, is only one possible designimplementation that could be put to use.

The contract-stretch goal for the development of a low impedance RF generator was achieved,but will be described in a future document. The idea for the low-impedance generator was to beable to incorporate the generator inside the RF match network and completely eliminate the 50 Ωcable environment. This concept seemed too radical for many of our peers in light of traditionalpractices. Although we successfully operated the generator in a low-impedance mode, weconverted it to the 50 Ω output mode so that demonstrations of the entire power delivery systemcould be reviewed as a modular set of items that could be used independently. This proved to bea good decision since some members of the SEMATECH community expressed interest in eitherthe measurement or the matcher portions of the project, but not necessarily the entire integratedsystem.

Patent applications have been prepared for the analytical RF power sensor and the saturablereactor used in the “fast” RF match network. Possible patent positions on some of the supportingelectronics were not investigated.

2.2 Technical Overview

The invention of the analytical RF sensor based on first-principles behavior is a significantbreakthrough, because it provides a metrology capability free from conventional calibrationpractices. Rarely does a measurement technique offer the possibility of being both a nationalstandard and a common component in field use. The sensor is a voltage and current samplingdevice that incorporates a unique current pickup coil that couples 100% of the RF magnetic fluxfield. The initial prototypes have proven very accurate in terms of the laboratory bench test data,as compared to modeled predictions based on current loop area measurements within 0.2 dB at13.56 MHz. The sensor exhibits a wide operational bandwidth from 1 MHz to nearly 1 GHz witha linear 20 dB/decade frequency response. While it is true that the intended frequency domain is13.56 MHz, the broadband response demonstrates the design intended to minimize undesirableparasitic effects. Developing a sensor that exhibits the least perturbation to a given applicationwas perhaps the most challenging technical problem to engineer into the sensor design. Whilethe sensor is certainly invasive because of its fixed physical form, we focused on minimizing thedegree to which it is obtrusive. The sensor has been fabricated for the 50 Ω RF transmission-lineenvironment and exhibits electrical characteristics equivalent to a 3-inch length of common RFpower cable. Time domain reflectometry (TDR) measurements and voltage standing wave ratio

5


(VSWR) datasets support this achievement. It must be stated that the use of a sensor designed for50 Ω impedance in a position prior to the RF matching network is obviously a good choice;however, the use of a 50 Ω sensor in the post-RF matching network location represents acompromise. The sensor can be scaled to other impedance values to better optimize applicationrequirements; however, project time limits did not permit such investigation. For the purpose ofthis project, the overall load effects of the 50 Ω impedance design to the RF match network wereexpected to be < 1–2%. In fact, the completed power delivery system dealt with any installationeffects by controlling delivered power to the plasma-simulating load.

This technological achievement has inspired members of the technical staff at NIST to requestdetailed technical information and the loan of a prototype for studies that might lead to theadoption of the design as a national standard. Mechanical design attributes have beendemonstrated to be robust and commercially viable.

The analytical RF sensor (Figure 2) required the development of some novel electronics signalprocessing circuits that perform to laboratory grade performance. The special RF harmonic filterand the two different RF signal detection devices were designed to provide an integratedapproach that was small in form and tailored to 13.56 MHz plasma etch applications. Twodesigns were pursued as contingencies, resulting in both techniques working quite well. Each RFdetector design, as well as the RF harmonic filter, was fabricated with commercial viability inmind in terms of size, complexity, and cost.

Figure 2 Completely Assembled RF Sensor with a Clear Housing

6


A dual-channel harmonic filter was developed to remove unwanted harmonic energy from theRF signal being measured. The intent of the design was to develop clean sinusoids of thefundamental frequency of interest at 13.56 MHz and preserve the phase relationship between theRF power sampled voltage and current waveforms from the analytical sensor outputs. Prior art inuse optimized other performance attributes such as a high Q passband and neglected phasestability. Thermal effects on harmonic filter performance can cause differential phaserelationship shifts of many degrees of phase angle, resulting in large effects on computed RFpower. This effort to develop an improved filter technique was necessary because of the highdifferential phase angles (85° to 89°) between the current and voltage waveforms that areencountered in post-RF match network locations where small phase changes represent largeeffects in calculated RF power. Also, post-match locations as well as cleanroom service areaambient conditions, present unwanted thermal problems. The dual path RF harmonic filterdeveloped in this project provides good filtering and phase stability over a wide temperaturerange.

The invention of the electronically variable inductor known as a saturable reactor that operates at13.56 MHz has raised the status quo from prior art that was limited to an order of magnitudelower operating frequency at 1.8 and 2.0 MHz in RF matching network applications. The crux ofthe invention is the novel approach to minimize the undesirable electrical coupling between theRF coils and DC control current field coils by a unique winding pattern applied to a pair oftoroidal ferrite cores.

The reason for this unique approach was conceived because either an electronically variablecapacitor or a variable inductor was needed for this application. Electronically variablecapacitors were quickly dismissed because of a variety of shortcomings and parasitic effects (i.e.,harmonics). The desire for an inductor design fueled the search for a method to vary the corematerial permeability of an inductor electronically. Conventional transformer configurationswere undesirable because the primary and secondary winding are normally ratio coupled. Weneeded a transformer-like device in which the control windings are not coupled to the active RFwinding. This desired and unusual mode of required operation caused our device to not operatelike a transformer. The fundamental idea of using a variable magnetic field to control thepermeability of an inductor core material is well known in the municipal AC power utilityindustry in the form of a saturable reactor; however, the operating frequency limitations renderthem unusable above a few hundred hertz. The next closest design solution was developed atApplied Materials using saturable reactor technology that operates at 1.8 to 2.0 MHz with aferrite bar core material.

The solution to our problem came after a series of design attempts that led to a novel combin-ation of two toroidal transformer cores with the RF windings cross wound or interleave woundand folded over onto a single axis for adding the DC control windings. Each set of windingsdecouples or prevents coupling between each opposed winding turn by turn. This is the electricalproperty that prevents interwinding capacitance from spoiling the high frequency response andallows construction of a saturable reactor that operates at 13.56 MHz. Each of the windings isorthogonal to each other. The DC control current windings provide the magnetic field to changethe permeability of the toroid core material independent of the RF power conducting inductivewindings, which only sense the change in permeability and respond with a change in inductance.Temperature effects have been insignificant enough that there was no need to add yet a third setof orthogonal windings to monitor temperature effects and compensate for them. A set of initialstudies was conducted, but not completed because of project time limitations and because the

7


final system design worked well without a temperature compensation circuit. Because the projectcontract goal was to achieve a high-speed RF matching network capability, refinements foraspects such as efficiency and thermal energy losses were not optimized. Unlike other saturablereactor approaches, the thermal losses that result in this saturable reactor design primarilyoriginate in the DC current windings used to shift the permeability and not in the RF inductancecoil windings.

The saturable reactor has been incorporated into a functional RF matching network that wastested at 1000 W and above for extended periods into a plasma simulating linear load of4-j20 Ω. To perform laboratory bench tests of the various components and the complete RFpower delivery system, a special test load was fabricated to simulate the linear portion of aplasma load. The simulator is comprised of non-inductive sintered high-power resistors and avacuum variable capacitor. The addition of a solenoid actuated vacuum switch and a smallceramic capacitor provided a means to shift the load conditions through a reasonably large rangeof reactance, thereby providing a wide set of operating conditions for the RF power deliverysystem to perform against as a stress test. Designs for additional circuitry to supply a mechanismto generate the non-linear aspects of a plasma into the simulator load and concepts to use thesimulator in a calorimetry mode are being pursued.

Tests conducted with load step changes from 4-j24 Ω to 4-j14 Ω, which represents a significantoperating space to stress the match network design, demonstrated a tuning speed on the order of5 to 7 ms. Combined with RF generator power control, the delivered power to the plasmasimulating load was held constant to within ± 1 W of setpoint at both load conditions presentedat each excursion of the step change.

To achieve the integrated system performance that has yielded these RF tuning speeds and stablepower delivery levels, a novel computer architecture approach had to be employed. A dual-processor DOS architecture was developed based on a unique modular interface code strategydeveloped by SEMATECH’s MSD/FI department and implemented by a team of SEMATECHand ORNL computer specialists. The strategy solved the essential problem of determining howto have one processor operating the analog input and output duties based on a control algorithmand not be hampered by overhead duties associated with data handling and user interfaces. Thisstrategy has proven to be robust and is portable to other computer architecture environmentswhere multi-processors and high operating speeds present performance problems.

2.3 Vision of the Future

The successful completion of this project has generated many requests from the SEMATECHand SEMI/SEMATECH engineering community to learn more about this technology by usingbeta site evaluations. Plans to address these requests are being prepared for review in appropriateforums at SEMATECH.

Due in part to the early success of this project, a number of other contracted interactions withORNL have been spawned in the plasma etch RF area with the Fusion Energy division. Thetechnical capabilities within the ORNL Fusion area are very impressive because they provideworldwide RF engineering resources in the design of RF power delivery systems with ranges ashigh as 32,000,000 W of RF power, at the same frequency range as our industry commonly usesin plasma etch systems. The simplest way to highlight the importance of their methodologies isto say that a portion of a percent error at their power levels can destroy a lot of expensiveequipment, not to mention the loss of an experiment. It is believed that the RF engineering

8


infrastructure in the semiconductor industry will benefit from the many interactions that are nowbeginning with this largely untapped national resource.

The SEMATECH Radio Frequency Advisory Group (RFAG) forum has been a significant forcein bringing together many of the fragmented group of RF reseachers within the semiconductorindustry and is beginning to develop a strategic long-range focus. To date the RFAG hasdeveloped ideas for a consumer reports-type of RF component testing laboratory and forstandardized testing procedures. This concept was presented at the SEMATECH Etch FTABmeeting and was ranked highly. As a result, a project at ORNL Fusion is underway to addressthose goals. Future RFAG meetings may serve the industry well as we move toward larger wafersizes that will require significantly different RF power delivery solutions.

3 ANALYTICAL RF POWER METROLOGY

The RF sensor design was guided by several requirements that were developed at SEMATECHand were based on industry experience with existing RF sensors and with sensors developed andtested at SEMATECH. The RF sensor development had three major goals. First, the sensorshould be designed as a metrology standard rather than a calibrated device. Second, the sensordesign must be highly unobtrusive so that the device can be easily incorporated into a variety ofsemiconductor manufacturing tools. Finally, the sensor must provide a sufficiently accurate setof RF electrical parameter measurements that would support feedback control for RF powergenerators as well as provide data for process diagnostics. This data could then be used forminimizing process variations, thus maximizing yield from a delivered RF power standpoint.

For a sensor to have an accuracy that is to be considered a reference standard, it should have itsresponse characteristics defined by first principles. Properties that are calculated from elementalphysical characteristics such as the zero state transition of Cesium, which is used as a timestandard, is a good example of first-principle standards. This is the preferred methodmetrologists seek to use when developing a reference standard. The implication of this approachis non-trivial, and it placed constraints on our sensor’s geometry and construction (Figure 3). Inthe design of RF sensors, the preferred method of measuring the RF current component in an RFpower conductor is to measure the magnetic field that surrounds the conductor. This requires thata coil be inserted in this field and the voltage generated is a function of the current in theconductor. Likewise, to measure the RF voltage present on an RF power conductor, it isnecessary to place a probe on or near the conductor. Typically, these probes take one of twoforms, a resistive or a capacitive probe. A capacitive probe was chosen for this project. Thesechoices require adherence to physical equivalencies and symmetry so that the equations used todefine that sensor can be solved in closed form. Careful consideration of the configuration of thevarious components is also required to ensure that the stray circuit parameters are minimized tothe point that they are negligible, or are incorporated within the design to preclude anyunpredicted responses. The approach taken was to minimize stray RF fields by constructing thevoltage and current pickups using transmission line design practices where possible, so that theimpedance of them is known and controlled. The design approach also allows for the sensingelements to be small and rigidly constrained so that the geometry and hence, the signal response,is stable.

9


3.1 Analytical RF Sensor Based on First Principles

The RF sensor design approach evolved from the need to remove the ambiguity associated withthe coupling of the magnetic field pickup coil that has plagued calibration and accuracydeterminations. It has been recognized that the current signal sampling was the problem to focuson since voltage sampling techniques have been highly evolved since the primary problem wasthe amount of coupling that a coil would have when in proximity to the main power conductor. Itwas thought that finding a way to fix the amount of flux linkage or to link all of it was the properapproach. The idea of sampling from all of the magnetic energy was realized when an airdielectric RF power transmission line section was fabricated with a hollow center conductor thatallowed for the insertion of a single turn pickup coil (Figure 4) from the outer wall of the RFtransmission line section through the air gap and into the middle conductor. The form of thesingle turn coil was fabricated so that the area of the linked magnetic field is a rectangle that canbe easily measured by conventional machinist tools. The coil design is unique in that itincorporates a Faraday shield around the pickup coil to maximize the suppression of capacitivelycoupled signals proprotional to the line voltage, while not disturbing the magnetic inductionassociated with the current flowing through the hollow center conductor.

Figure 3 RF Sensor Components

10


Figure 4 RF Sensor Components With the Current Loop Inside the Hollow Center RFPower Conductor

The pickup coil has been designed to a 50 Ω device and thereby does not require special signalimpedance matching circuitry. The induced 90° shift in the sampled magnetic field iscomplemented by the unique voltage pickup probe (Figure 5) that is also a 50 Ω device. Thenature of the voltage pickup probe shifts the voltage signal by 90° and in combination with thecurrent coil signal shift, the overall sampled signals have the same characteristic relationship asthe main power RF transmission line being sampled. Figure 6 is an illustration of a completesensor. Figure 7 is an illustration revealing the inner components of a sensor with 1/4-20 boltconnection end pieces.

Figure 8 through Figure 15 provide sequential assembly steps for an RF sensor, concluding in anexploded view of all components (Figure 16).

11


Figure 5 Cross Section of RF Sensor to Show Current Pickup Loop and VoltagePickup Probe Placement

12


Figure 6 RF Sensor with N-Type Connectors

Figure 7 Sensor Assembly with 1/4-20 Bolt Connections

13


Figure 8 Hollow Center Conductor Positioned in Sensor Body

Figure 9 Voltage Pickup Assembly Positioned in Sensor Body

14


Figure 10 Current Pickup Loop and Teflon Insulator Installed in Sensor Body,Penetrating the Hollow Center Conductor

Figure 11 Sensor Assembly with Teflon Center Conductor Positioning End Pieces

15


Figure 12 Sensor Assembly with Metal End Plates Installed

Figure 13 Sensor Assembly with N-Type Connectors Installed

16


Figure 14 Sensor Assembly with Screws Installed

Figure 15 Assembled RF Sensor

17


Figure 16 Exploded View of RF Sensor

3.1.1 Current Signal Sampling Component of RF Sensor

For the design criteria of the current sensor portion of the device, a current pickup loop must beof a known size and fundamental in response. Secondary effects of stray capacitance andinductance must be minimized and quantified. This must be done to allow the application of firstprinciples to the design.

Faraday’s law says that th electromotive force (EMF) (voltage) induced in a conducting loop isthe negative of the time derivative of the magnetic flux enclosed by the loop. In theory, it followsthat if one could link all the flux produced along a known length of wire carrying an AC current,then one could know explicitly what the current is by measuring the voltage in the loop. Thisapproach is typically used at low frequencies by employing an iron core to capture the flux androuting it through a sense winding having multiple turns so the flux is linked enough times toprovide a usable voltage. This same approach has also been used in RF current sensors usingferrite toroids; however, core losses and non-linearities, as well as high winding inductance anddistributed capacitance, obfuscates a direct first principle link to the current being sensed. Thepresence of a core also adds inductance to the conductor carrying the current making the sensorobtrusive. The industry has experienced occasional difficulties with some of these toroidalcurrent transformers catching fire because of the losses that occur in the core when exited bylarge RF currents. Departure from the first-principle concept introduces errors that cause eachsensor to require calibration. Previous sensor designs followed traditional design conceptscommonly used in the communications industry. These designs, once calibrated for a specificapplication, were adequate for the measurement of power from a generator to a relatively well-matched load. To that end, these sensors have found some use in this industry to measure thepower from the generator to the RF matching networks. Accurately measuring the power

18


delivered from the match network output to the load using traditional sensors is very difficult(i.e, prior SEMATECH patents).

The question becomes, how can one build a circuit to link all the flux (Figure 17) and remaintrue to the concept of first principles? The answer comes from a judicious application ofAmperes Law, which states that the integral of the magnetic flux density around a closed path isequal to µo times the net current across the area enclosed by the path. This means that in acoaxial transmission line, where the currents on the inner and outer conductors are equal andopposite, the flux is zero outside the outer conductor of the line.

Figure 17 Magnetic Flux Space

In other words, the flux exists only between the inner and outer conductor. Further, if the innerconductor were hollow, then the flux inside the hollow center of the inner conductor would bezero also since all the current flows on the outside surface of the inner conductor.

Therefore, if one could pass a wire loop (Figure 18) through the outer conductor across thedielectric through the inner conductor and back out again, one could link all the flux over aprecisely known area (Figure 19) associated with the current in the coax, and the loop voltagecan be analytically determined from fundamental laws.

Figure 18 Magnetic Flux Linked Area

19


Figure 19 RF Power Magnetic Energy Coupling Area

The derivation of the coupling in S.I. units for such a loop is as follows:

For a long wire carrying a current I, the differential magnetic flux density (dB) at a radius (r)from the wire and distance (S) from a unit of moving charge is derived from Biot-Savart Law(Figure 20):

24 S

dsIddB o ×=

πµ

Figure 20 Magnetic Flux Illustration of Fundamental Laws

20


Recall that the vector cross product is the product of the length of the two vectors times the sine

of the subtended angle in the direction normal to their plane (right hand rule) ( )

2

sin

4 S

dIdB o θ

πµ

= .

B, therefore, would equal the integral of dB along l from l=-∞ to +∞. Evaluation of this integralbecomes much more convenient if the expression is rewritten in terms of r and θ. From the

diagram θsin

rS= and

θtan

r−= differentiating with respect to θ gives θ2sin

rd = substituting

into the above equation and integrating gives

( )θ

θ

θθ

πµ π

dr

rI

Bo

o

2

2

2

sin

sinsin

4∫=

−=∫=

ππθ

πµθθ

πµ

o

o

o

o

r

Id

r

IB cos

4sin

4

So,

r

IB o

πµ2

=

Now to get the flux (Φ) over a square area (Figure 21) of the pickup loop inside the coax whereB is non-zero, namely between the outer surface of the inner conductor and the inner surface ofthe outer conductor, and then we integrate B over a radius of a to b along a length L.

drdlr

IdAB o

L

o

b

an π

µ2

∫∫=∫=Φ

∫

=Φ

b

a

L

o

o

r

drI

πµ2

[ ]π

µ

πµ

2

lnln

2

==Φ a

bIL

rIL o

ba

o

Figure 21 Linked Magnetic Flux Geometric Area

21


Now applying Faraday’s Law

dt

dIa

bL

dt

demf

o

π

µ

2

ln

−

=Φ−=

Now for )cos( tII o ω= , where ω is the radian frequency = ,2 fπ

[ ] )sin(ln)sin(2

ln

tfa

bLt

a

bL

emf oo

oo

ωµωωπ

µΙ=−

Ι

−

=

which in phasor form is

oo La

bfj Ιlnµ .

However, this is not simple to implement. The above analysis ignores the fact that the pickuploop would also be subject to capacitive coupling to the inner conductor, which would corruptthe current signal as soon as the inductance of the pickup loop becomes non-zero. This problemis handled by using a coaxial pickup loop so that the outer conductor of the pickup loop isgrounded to the outer conductor of the power carrying coax at both ends. A small cut in thepickup loop’s shield allows it to act as a Faraday shield, effectively keeping the electric fieldfrom reaching the center conductor of the pickup loop while allowing the magnetic field, whichis only proportional to the current, to be completely linked. The split in the pickup coax’s outerconductor prevents the flow of inductively driven current in the shield so that the magnetic fluxis not excluded from the center conductor of the loop. Experimentally, we determined that thesmall cut in the pickup loop shield must be in the exact center of the loop and both external endsmust be terminated in the loop coax’s characteristic impedance, or the propagation delay of thesensed signal for currents traveling in opposite directions in the power coax will not match,which in turn implies a phase error in the net current signal. This error cannot be tolerated as itresults in a measurement error, which is dependent on the standing wave ratio (SWR) on the lineand would depart from our goal of a design based on first principles (Figure 22). So, the loopshield must be cut in the exact center and the cut should be as narrow as possible, no more that 1mm wide. This also implies that the ends must be well terminated in a 50 Ω resistance and theleads must be kept very short to minimize stray inductance.

The pickup loop circuit (Figure 23) can be described as two sections of terminated coax with aseries voltage source in the middle.

The current probe is assembled using a set of fabrication jigs so that the precise dimensionsrequired for the loop are maintained. Modeling of the current probe electrical performance basedon the mechanical measurements shows < 0.2 dB error from the measured data. Test datacollected from the small set of prototypes that we have had fabricated demonstrated that themechanical design is robust. Signal sampling levels from sensor to sensor matched toapproximately within ± 0.1 dB. Also, routine disassembly and reassembly demonstrated no shifton signal sampling levels.

22


Figure 22 Network Analyzer Plot of Magnetic Field Signal Coupling Response

Figure 23 Schematic Representation of Current Pickup Loop

Taking into account the external loading to terminal voltage, 2

ln oo

T

Ia

bfLj

V

=µ

and finally the

current

−=

a

bfL

VjI

o

To

ln

2

µ.

A detailed analysis of the current loop using Maxwell’s equations is shown in Appendix A.

To make the sensor manufacturable, we cut a slit in the center conductor rather than two smallholes. There was no measurable difference between the slit for the loop and the penetration attwo distinct points. This also allows a Teflon sheath to be fabricated, which encloses the loopand prevents voltage breakdown between the loop shield, which is at ground potential, and thecenter conductor, which may be at a very high potential. This also allows the loop to be mountedon a printed board, allowing very repeatable construction and accurate termination as well asmaking the loop removable and the sensor much easier to assemble and disassemble.

23


The use of carefully configured coupled transmission lines, which is necessary to produce an RFsensor with first-principles coupling, also results in a sensor that is passive, is totally linear,dissipates no power, and is as unobtrusive as an equivalent length of air dielectric coaxialtransmission line would be. Because of the effects of the current pickup loop and the voltagepickup capacitor and their associated mounting structures, the diameter of the center conductornear the pickups was reduced to maintain a constant 50 Ω characteristic impedance.

3.1.2 Voltage Signal Sampling Component of RF Sensor

Sampling the voltage accurately is also difficult. Most resistors and capacitors have parasiticimpedances associated with them, as well as voltage and power limits. Smaller components haveless parasitic impedance, but also have lower power and voltage limitations. Since the currentsensor actually senses the derivative of the current, it is desirable to have a differentiating voltagesensor as well so that phase corrections after the sensor can be avoided (Figure 25). Thisconfiguration also avoids the need for a high impedance amplifier to avoid introducing signalerrors from loading effects.

The voltage sensing arrangement then became a C-R differentiator circuit (Figure 24) where Vs

is the voltage being sensed and

RCj

RCjV

cj

iR

RVV s

st ω

ω

ω+

=+

=1

.

Figure 24 Schematic Illustration of Voltage Sensor

24


Figure 25 Network Analyzer Plot of Voltage Pickup Symmetry by SuperimposingForward and Reverse Repsonse Data

Now, if 1/ωc is much larger than R, then Vt ≈ jωRCVs , which is the same form as the currentsignal and the phase shift is taken care of. The question then becomes how can such a circuit berealized without parasitic elements and the imperfections of manufactured capacitors. Trans-mission lines again come to the rescue with their property of characteristic impedance. Byterminating a transmission line in its characteristic impedance, one is able to present thatimpedance to a source at any distance from the actual load; therefore, parasitic inductance andcapacitance associated with connecting the source to the load is minimized. A parallel plate airdielectric capacitor (Figure 26) is very nearly an ideal capacitor when the plate dimensions aresmall with respect to a wavelength. The plate is then brought into proximity of the centerconductor of the power carrying coax of the sensor assembly and positioned opposite the centerof the current pickup loop.

Getting back to first principles, the details are as follows. The voltage to be sensed Vs is dividedbetween the capacitance from the center conductor to the sensor plate Ci and the capacitancebetween the sensor plate and the outer conductor Co (Figure 27).

25


Figure 26 Geometric Relationship for Voltage Sensor Plate

Note: Since iCj

Rω1<< and even further

oCjω1< we expect R to swamp Co and Vρ to be RCVj isω≈ .

Figure 27 Schematic Illustration of the Realized Voltage Probe/Divider Circuit

It is convenient to determine a Thevinin equivalent (Figure 28) for this source. This

transformation yields a Thevinin current source of

Cij

I

Vs

ω

driving Ci and Co in parallel.

Figure 28 Schematic Representation of Thevinin Current Perspective

26


Transforming this back to a voltage source with series impedance (Figure 29) gives the following

Figure 29 Transform to a Voltage with Series Impedance Schematic

which simplifies to (Figure 30)

Figure 30 Simplified Voltage Sensor Schematic

which we then load with R = to Z0 of the sensor probe coax. The terminal voltage (VT) is then asfollows

( )( )

++

=

++

+=

oi

is

oi

oi

is

T CCRj

RCjV

CCjR

CC

RCV

Vωω

ω11

separating into real and imaginary parts ( )

( )

++

++=

222

22

1 oi

ioiisT

CCR

RCjCCCRVV

ωωω

observing that

( )

+=+

i

oioi C

CCCC 1 and defining a geometry constant

i

og C

CK = ,VT can be written

( )( ) ( )

+++

++

+=

22222222

222

1111

1

gi

i

gi

gisT

KCR

RCj

KCR

KCRVV

ωω

ω

ω

now letting i

o RC

1=ω ,

( )

( ) ( )

+++

++

+

=2

2

22

2

2

2

2

1111

1

go

o

go

o

g

sT

K

j

K

K

VV

ωω

ωω

ωωω

ω

27


( )

( )

( )

( )

( )

++

+

+++

+

+=2

2

22

2

2

2

22

11

1

11

1

1g

o

o

g

go

o

g

g

sT

K

Kj

K

K

K

VV

ωω

ωω

ωωω

ω

( )( )

( )

( )

++

++

++

+=

22

2

22

2

11

1

11

1

1

g

o

g

o

g

og

sT

K

K

j

K

K

VV

ωω

ωω

ωω

( )( ) ( )

( )

++

+

+

++

+=

o

g

g

o

g

og

sT K

K

j

K

K

VV

ωω

ωω

ωω 1

111

1

122

2

[ ][ ] ( )g

o

T

TVT KV

V

+== −−

1tan

Re

Imtan 11

ωω

θ

and

( )( )

( )

( )

+

++

++

=−

g

o

o

g

g

og

s

T

K

K

K

K

V

V

1tansin

1

1

1

1

1

ωω

ωω

ωω

For a coupling factor of -60dB, ωo is 1000 times greater than ω and within 0.1%, VT– ≈ jV5 ωRCi,

and i

Ts RC

jVV

ω−

≈ .

28


Next, we need to get at the capacitance in terms of the physical dimensions (Figure 31). Fields

texts1 give the capacitance per unit length of a cylindrical coaxial capacitor an

a

bn

πε2 where

Figure 31 Voltage Probe Design Space

b is the major radius and a is the minor radius. At first glance, a model of the voltage probewould appear to be two short coaxial capacitors connected in series with a small subtended angle

(Figure 32) α rather than 2π radians. Ci would then be

an

Ci ραε

= and Co would be

ρ

αεb

n

.

Figure 32 Voltage Probe Radial Geometry Illustration

1.1.1 1 Rao, N. Narayana, Basic Electromagnetics with Applications, Prentice Hall 1972, Englewood Cliffs, N.J., pp. 382.

29


This simple model, however, neglects that the pickup plate is very short as compared to thelength of the power-carrying cylinders and that it is held to near ground potential by its loadresistor R = 50 Ω. Under this condition, the electric flux lines from the center conductor haveaccess to the rear side of the pickup plate as well as the side facing the center conductor and theground potential at the outer wall is far away compared to the ground potential at the back side ofthe pickup plate. Under this condition, nearly all the flux lines (Figure 33) originating near theplate terminate on the plate and both sides of the plate contribute to Ci, while Co is very nearlyzero.

Figure 33 Voltage Probe E Field Coupling Illustration

The exact model for Ci becomes almost intractable, but can be approximated as

an

ραε

2 and Kg gets very small.

The voltage probe is assembled on a machinist micrometer threaded rod that allows for a precisemeasurement of the distance from the center conductor. The voltage probe is also based on firstprinciples, although the mathematical reduction for this application will require a numericalapproach and has not been completed at the time of this publication.

To evaluate the accuracy of the model, an HP8753C network analyzer was used to set a sensor’svoltage coupling at -60 dB, or 1 mV/V, so Vs = -j1000 VT when loaded with 50 Ω (Figure 34).

30


Figure 34 Network Analyzer Plot of Voltage Pickup Coupling Reponse

The pickup disc diameter was 6.4 mm and the distance of the plate from the center conductorwas 3.5 turns of a ¼ × 40 screw = 2.2225 mm. The inner radius was 5.675 mm and the outerradius was 19.35 mm, ρ = a + 2.2225 mm = 7.8975 mm. The cylindrical model assumes a squarepickup plate with a bend radius of ρ. If we take this pickup as the square contained within andtangent to a circle of radius 3.22 mm, then the sides of the square will be 2 times the radius

and the area ratio of the circle to the square will be 2

π . The subtended angle 57303.8975.7

22.3 ==α

recalling that i

Ts RC

jVV

ω−= then

2

22

πρ

αεπ

−=

an

fr

jVV T

s

and T

T

s VjfR

anjV

V 47.10752 2

−=

−

=

αεπ

ρ

, the

discrepancy between measured and calculated values is 0.7%, which is close to the error ofmeasurement.

A more elegant derivation to describe the capacitive pick-up probe using steradians is shown inAppendix B.

Time domain reflectometer (TDR) measurement indicated no measurable effect on thecharacteristic impedance of the sensor resulting from the presence of the voltage probe. Thebreakdown voltage, using a dielectric strength of 22 V per mill, is then 1900 V, which may bemarginal for post-match installation in some capacitive discharge etchers. In such cases, a lowercoupling must be accepted, or a larger pickup plate must be used.

The final major consideration is the obtrusiveness of the sensor. A sensor can be inobtrusive onlyif it has the same characteristic impedance as that of the transmission path and it does not changethe length of the path. Typically, in the post-match environment the characteristic impedance ofthe signal path is both unknown and varies along the path because the geometry is changing aswell. Also, it is usually difficult, or impossible, to install a sensor and avoid changing the length

31


of the path. The best compromise is to make the sensor as short as possible and use a known andcontrolled impedance so that the obtrusiveness of the sensor can be quantified. 50 Ω was chosenbecause of the availability of test equipment using this impedance and because in the pre-matcharena, it is possible to make the sensor totally unobtrusive. Since conductors and contact areasare large, the sensor dissipates essentially no power. Several connector configurations were triedin an attempt to eliminate characteristic impedance excursions at the connection point.Compromises had to be made for size, cost, and manufacturability reasons, but the final productis pretty much as good as a double female type N barrel connector to about 500 MHz.

Since the desired accuracy of the sensor exceeds the limits of current measurement techniques ata given frequency, the only way to confirm first-principle behavior with measurement is toobserve how the sensor performs over a very wide range of frequencies since at higherfrequency, small stray impedances produce more obvious effects. For that reason, our testing ofthe sensor has extended to the GHz region to determine just how well the constructed sensorconforms to the model. The extrapolation is that if the behavior follows the model as well as youcan measure it at 10 times the frequency of interest, then it is likely that it is substantially betterthan one can measure at the frequency of interest. Also, phase is the most sensitive indicator ofwhen things start going awry. For this reason, and because phase error is devastating to post-match power measurement accuracy, the series of graphs in Section 6 depict the sensorperformance confirmation measurements taken for the project.

3.1.3 Integrated RF Sensor Analysis

A performance anomaly observed in phase symmetry data, identified at Sandia NationalLaboratory, was investigated. The following explaination serves to articulate the cause of thesmall amount of non-symmetry and provide workable solutions to account for it. Referring toFigure 35, the propagation delay of the voltage and current sensors differ by 135.11 picoseconds.

This implies that the transmission line between the voltage sensor and the detector should be26 mm longer than the line from the current sensor to the detector. Additionally, there is excessphase shift in the current pickup loop contributed by a 1.73 GHz pole formed from the loop self-inductance and the external circuit load resistance. This may be compensated for in either of twooperating conditions: over a wide band of frequencies, by inserting a matching pole in thevoltage signal transmission path or at a fixed frequency of operation, an additional length oftransmission line may be inserted into the voltage signal path. The amount of additionaltransmission line required at 13.56 MHz would be approximately 16 mm. The combined totalphase skew at 13.56 MHz would then be 1.1° corresponding to 42 mm or 1.65” additional linelength in the voltage pickup cable.

To verify the criteria for the RF sensor to be as unobtrusive as possible, several measurementswere made. Careful evaluation was made of the insertion characteristics of the sensor. Theinsertion loss (S21) of the RF sensor was measured in a 50 Ω system. The measured loss wasapproximately the same as a Type N barrel, less than .01 dB at 13.56 MHz (Figure 36 andFigure 37). The VSWR (S11) shown in (Figure 38 and Figure 39) is actually better than a TypeN barrel; however, the difference of both of these measurements is less than the resolution of theHP 8753C Network Analyzer that was used to make these measurements. In addition to theS parameter measurements that were made, impedance was measured with a TDR to show theimpedance with respect to distance within the RF sensor. This plot (shown in Figure 40) showsthat the variation of impedance is about 10 Ω. This is due to the two pickup probes in the

32


RF sensor. This variation could be improved by reshaping the center conductor of the RF sensor;however, the length of the variation is so short (approximately 1°) that little if any improvementwould be made by making the line perfect. For this reason and because of time limitations, noattempt was made to further improve the center conductor geometry.

Figure 35 Network Analyzer Plot of Current Loop Pickup Symmetry by Plotting ofForward and Reverse Current Responses

Figure 36 Network Analyzer Plot of N-Type Barrel Insertion Loss at 13.56 MHz

33


Figure 37 Network Analyzer Plot of RF Sensor Insertion Loss at 13.56 MHz

Figure 38 Network Analyzer Plot of an N-Type Barrel VSWR at 13.56 MHz

34


Figure 39 Network Analyzer Plot of RF Sensor VSWR at 13.56 MHz

Figure 40 TDR Impedance Plot of an RF Sensor Prototype

3.2 Harmonic Filtering

It has long been known that the nonlinear components of the plasma load produce harmonics.Work at Sandia National Labs has demonstrated that these harmonics affect not onlymeasurements but equipment reliability and process repeatability. Several manufacturers andresearchers have grasped the need for harmonic filters in RF power measurement systems forplasma applications; however, fewer have appreciated the subtle, but potentially dominant,measurement errors that filters themselves can introduce if their response characteristics are notsuited for the application. Most commercial RF filters are designed and optimized for a desiredattenuation characteristic. While the phase response is not considered particularly important,Chebychev (a common type of filter design) and other elliptic filter designs place poles and zeros

35


to maximize skirt slope in the transition from passband to stopband at the expense of passbandamplitude ripple and frequency-dependent group delay characteristics (non-linear passbandphase response).

The high Q circuits employed also introduce potentially large phase variation with temperature,and phase versus temperature matching from filter-to-filter is poor. For a measurement systememployed between the matcher and the reactor chamber, the filters can easily become the majorsource of measurement error. In oven tests at the SEMATECH Calibration Lab, the differentialphase variation of two commercial Chebychev filters, held tightly in physical contact, showedthat variations of several degrees of phase could be observed over a 5°C change in ambienttemperature. To illustrate the point, if the plasma load is a typical 4-j20 Ω, the phase angle of thecurrent is 78.69° and the power factor is 0.1961. If a phase error of 0.1° is introduced, the powerfactor can be 0.1944, which implies a measurement error in power of 0.9%. This much error isalmost assured under the most optimum conditions. If filters can introduce several degrees ofdifferential phase over a 5°C temperature range, it is easy to see that they can makemeasurements unrepeatable and subject to large errors. In light of this fact, it was necessary tocarefully design filters (Figure 41 and Figure 42) for this application to minimize differentialphase change with temperature excursions.

Figure 41 Complete Dual Channel RFHarmonic Filter

Figure 42 Dual Channel RF HarmonicFilter with Cover Off

36


The design process began by using a filter synthesis and analysis program to examine thesuitability of a Bessel bandpass arrangement. It soon became clear that although the phaseresponse would be favorable, one could not get sufficient attenuation of the second harmonic nomatter what order of filter was used. After some time was spent looking at Butterworth andvarious elliptic responses, it became obvious that standard polynomial-based filters would neverachieve the desired phase and attenuation characteristics in any topology that could actually bebuilt and tuned. The designers took a step back and the filter requirements were re-examined inthe light of what was known about the signal being filtered and what could actually be built. Itwas observed that since the excitation was of a single frequency, the only frequencies that wouldbe generated by a nonlinear load would be integer multiples of the fundamental 13.56 MHz, andunder some rare, but possible circumstances, subharmonics of 13.56 MHz. The filter response atother frequencies really did not matter much. In the light of this observation, an intuitiveapproach was taken. A filter composed of five parallel resonant tank circuits was conceived. Twoshunt-connected end section traps tuned to 13.56 MHz would form the overall bandpasscharacteristic. The Q of these traps would be fairly low by filter standards so as to make thephase versus frequency and temperature characteristics acceptable.

This arrangement, however, would not nearly have sufficient attenuation for the second and thirdharmonics, nor would it significantly reduce any subharmonics. To accomplish this, three seriestraps were set between the two end sections (Figure 43) tuned to 2f0, f0/2, and 3f0, respectively.Moderate Qs for these sections were chosen, mainly limited by considerations of tuneability andthe Q of available surface mount inductors.

Figure 43 Initial Harmonic Filter Design Schematic

Modeling indicated that the fo/2 trap frequency would have to be raised slightly to get the trans-mission phase shift to zero and at the same time have the maximum transmission amplitude at fo

(13.56 MHz). The modeling program was used to get the input and output impedance scaled to50 Ω by juggling Qs and inductances against available values. A prototype was constructed andits performance measured. The experiment agreed well with modeling, except that the inputimpedance was closer to 35 Ω than 50 Ω. Impedance scaling of components was undertaken andanother prototype was constructed. The impedance increased only half as much as calculated,and the amplitude response was flattened and degraded. It was clear that the circuit boardparasitics were imposing a practical limit on the filter impedance. The values from the originalprototype were then restored and the end section inductors were tapped to effect the necessaryimpedance matching (Figure 44). An acceptable match was achieved and the filter response(Figure 45 and Figure 46) was restored at a 2 dB expense in passband attenuation.

37


Figure 44 Final Harmonic Filter Design Schematic

Figure 45 Network Analyzer Plot of Harmonic Filter Frequency Response

Figure 46 Network Analyzer Plot of Harmonic Filter Bandpass Insertion Loss

38


The next task was to temperature compensate the phase response of the filter. Modelingpredicted and the prototype confirmed that the passband phase was most sensitive to the resonantfrequencies of the two end sections and the 7.2 MHz trap. Two samples of each of the inductorswere oven tested to obtain the temperature coefficient of inductance and Q. Results wereconsistent between runs, but were not in accordance with the manufacturer’s specifiedtemperature coefficients. The 4700 nHy inductor for the 7.2 MHz trap indicated a negativetemperature coefficient. This measurement was repeated several times with several differentinductors before it was believed. The temperature coefficient of the 910 nHy inductor wasirrelevant because tuning of the third harmonic trap did not affect passband phase (Figure 47)and the 1000 nHy inductor for the second harmonic trap had very nearly a zero temperaturecoefficient.

Figure 47 Network Analyzer Plot of Harmonic Filter Phase Shift at 13.56 MHz

Temperature compensation would be required for the end sections and the 7.2 MHz trap. Theend sections were compensated by the standard technique using commercially available negativetemperature coefficient ceramic capacitors to offset the inductor’s positive temperaturecoefficient. The 4700 nHy inductor presented a problem, however, since inductor temperaturecoefficients are “always positive”—no one makes positive temperature coefficient compensatingcapacitors. The necessary compensation was achieved by connecting a 3900 nHy inductor with asmall negative temperature coefficient in series with an 820 nHy inductor with an advantageouspositive temperature coefficient to from a 4720 nHy inductor with a nearly zero temperaturecoefficient.

39


Dual channel filters were then laid out with two signal paths side by side on the same PC board.They were mounted in a metal box to provide electrical shielding and to keep both signal pathsisothermal. The result was a temperature vs. differential phase response (Figure 48) of ±069°over a 30°C temperature range or ± 2.3 millidegrees phase/°C, which is about 500 times smallerthan that of the commercially available Chebychev filters previously in use.

Figure 48 Differential Phase versus Temperature for the Two Filter Channels

These filters, as with any filter, have to be tuned during manufacturing to achieve a satisfactoryresult. A network analyzer is required to tune up and troubleshoot these filters. An experiencedtechnician can perform the task in about an hour. The procedure involves setting the resonantfrequencies of the series traps, then trimming the resonance of the end sections for good inputand output impedance matching (Figure 49 and Figure 50). Final zeroing of the differential phaseresponse at 13.56 MHz is completed by trimming the resonant frequency of the 7.2 MHz trap.This is accomplished by clipping down a twisted wire capacitor (commonly called a “gimmick”by old ham radio operators) until the differential phase transmission agrees within ±10 milli-degrees. Attempting to tune these filters without a network analyzer is possible, but probablyfoolhardy.

40


Figure 49 Network Analyzer Plot of the Input Impedance of the Harmonic Filter

Figure 50 Network Analyzer Plot of the Output Impedance of the Harmonic Filter

41


Figure 51 through Figure 53 provide detailed component level fabrication information.

Note: Single-sided board.

Figure 51 Silkscreen Layout of PCB for Dual Filter Assembly

Figure 52 Layout of the Components of the Dual Harmonic Filter Assembly

42


Figure 53 Schematic of Harmonic Filter

Table 1 Parts List for Harmonic Filter

Item Qty. Reference Part Suggested Source

1 2 C12,C1 68 NPO Surface mount, NPO, ceramic, size 805

2 2 C11,C2 470 NPO Surface mount, NPO, ceramic, size 805

3 2 C10,C3 330 N330 MURATA ERIE GRM40S2H331J50V

4 1 C4 39 NPO Surface mount, NPO, ceramic, size 805

5 1 C5 TBD Surface mount, NPO, ceramic, size 805


7 1 C7 TBD Surface mount, NPO, ceramic, size 805



10 2 J2,J1 SMA (F)

11 2 L8,L1 56 COILCRAFT 1008HS-560TKBC

12 2 L2,L7 100 COILCRAFT 1008HS-101TKBC

13 1 L3 1000 COILCRAFT 1008HS-102TKBB

14 1 L4 3900 COILCRAFT 1008HS-392XKBB

15 1 L5 820 COILCRAFT 1008HS-821TKBB

16 1 L6 910 COILCRAFT 1008HS-911TKBC

Notes: 1. All capacitance in pico-farads.2. All inductance in nano-henries.

3.3 Detector Electronics

Probably the greatest challenge in the development of this system has been designing circuitsthat can accurately transform the RF samples from the sensor to DC signals that represent thosesamples in amplitude and phase. A high-accuracy laboratory method is to use a vector voltmeterto measure the amplitudes and relative phases of the RF power current and voltages. Themeasurements of the power delivered to the load and the load impedance can be computed fromthese signals. Currently, expensive and bulky laboratory instruments are used for thesemeasurements.

43


In addition to the size and cost, these instruments do not lend themselves directly to a controlsystem. If the intent is to build a system that has a closed-loop control, the designer has toconsider not only the accuracy of each of the elements in the control system, but also thefunctionality of each of the elements in the control system. While using laboratory instrumentsfor the detectors seems to be a good idea on the surface, they have several drawbacks. The costand size of these instruments initially may appear to be the major limitation. However, theseinstruments must be initialized and the commands sent to them so that the desired measurementscan be made. In addition, these instruments have a variety of output formats that must be readand then converted into useful data for the control system. Laboratory instruments also tend to bevery slow, often hundreds of milliseconds per measurement. This is not a problem for theirintended use, but does present some concern to the designer of a control system where the loopresponse time required is a few milliseconds.

A second technique is to build an application specific detector to make the required amplitudeand phase measurements. Previous work at ORNL on a fusion energy project suggested twopaths. An ECL phase detector and a real and reactive power (I-Q) detector were prototyped tosee which one was best. Both circuits worked well. The choice depends upon the application. Forinstance, the ECL phase detector works over a fairly wide range of frequencies, but requires a10 mV RMS signal to drive it before the measurements can be relied upon, even though thedetector will lock up on signals less than 1 mV RMS. This design also requires more board spacethan the I-Q detector and is extremely critical in terms of board layout and parasitic oscillationsuppression techniques. The I-Q detector is limited to a single frequency of operation. It is verystable and requires less space than the ECL phase detector. In addition, the dynamic range of theI-Q detector is nearly 10 dB greater than the phase detector. The assembly costs of both unitswere kept low by using off-the-shelf components in the designs. There were no adjusting potsused on either board, but a one-time offset trim using surface mount trim resistors at the time offabrication is required. Both detector circuit techniques measure voltage and current in terms oftheir mean square values. It is left to a computer or other devices to reduce this data into RFpower and related information.

3.3.1 Phase Detector Method

A simplified vector voltmeter (Figure 54 and Figure 55) was needed for this project to replacethe laboratory instruments that have been used in the past. A previous laser interferometryproject had successfully used an Analog Devices AD834 four quadrant multiplier in the phasedetection mode. This detector was used to provide phase measurements in the order of 3 milli-degrees. Although the resolution of this design was very good, the calibration was relative, notabsolute. Another problem was that the design was sensitive to signal amplitude variations, aswell as the phase variations it was intended to measure. While this was not a problem for theintererometry experiment, it was a big problem for this project. The amplitude sensitivity wasjudged too large a risk factor and this approach was abandoned in the conceptual stages.

The design concept that was chosen for this project was to design and build a phase detectorimmune to amplitude changes. A simplified vector voltmeter was developed for this applicationthat will provide DC voltages proportional to the magnitudes of the two signals and the phasedifference between them. The design approach that was chosen for this project was to use aphase detector chip combined with a passive integrator and differential amplifier to build a phase

44


Figure 54 Complete Phase Detector Assembly

Figure 55 Phase Detector with Cover Off

detector that would give a very linear output over the range of ±2 π radians. The implementationof this design went through several iterations before the final design. The phase detector sectionwas designed around a Motorola emitter coupled logic (ECL) phase detector chip. The circuitsamples both the current and voltage pickup outputs from the RF sensor after filtering in the dualchannel harmonic filter. Before the signals are sent to the MCH12140 phase detector chip theyare routed through four MC10H115 buffers that are used as hard limiters. These remove all ofthe amplitude variations in both signals. This technique removes any error caused by amplitudevariations in the phase detector. The phase detector performance is shown in Figure 56.

45


The Analog Devices AD834 was used as the amplitude detector. This signal was then bufferedand scaled by a precision opamp. Final DC offset trim is also made in this stage. The DC voltagethese two outputs represent are the voltage and current outputs from the RF sensor. Theperformance of the magnitude detector portion is shown in figure Figure 57.

The equation for data reduction of the phase detector board are well known

θcosIEPPower RMSRMS •=

θcos R ResistanceRMS

RMS

I

E=

θsin X ReactanceRMS

RMS

I

E−=

Figure 56 PD4 Phase Detector Linearity Plot

Figure 57 PD4 Magnitude Detector Linearity Plot

46



Figure 58 Silkscreen Layout of the Top Side of the PD4 Phase Detector PCB

Figure 59 Silkscreen Layout of the Bottom Side of the PD4 Phase Detector PCB

47


Figure 60 Layout of the Components on the Top Side of the PD4 Phase Detector

48


Figure 61 Layout of the Components on the Bottom Side of the PD4 Phase Detector

49


Figure 62 Schematic of PD4 Phase Magnitude Detector

50


Table 2 Parts List for Phase Detector

Item Qty. Reference Part/Value

1 26 C1,C2,C3,C4,C5,C6,C8,C10,C11,C14,C15,C16,C17,C18,C21,C22,C23,C24, C25,C26,C27,C29,C37,C38,C47,C48

0.001 uf, Surface mount size 805

2 19 C7,C9,C30,C31,C33,C43,C45,C61,C62,C63,C64,C65,C66,C69,C70,C72,C73,C75,C76


3 12 C12,C13,C19,C20,C28,C35,C36,C39,C46,C49,C71,C74

0.01uf, Surface mount size 805

4 2 C32,C34 500 pf, Surface mount size 805

5 6 C55,C56,C57,C58,C59,C60 12 pf, Surface mount size 805

6 2 C67,C68 10 uf Tantalum, 25 V

7 2 J1,J2 SMA (F) Pasternack PE 4118

8 1 J3, J4, J5 Signal Outputs to 9-pin D connector

9 1 JP1 POWER 3-pin header 0.100” spacing

10 4 L1,L2,L3,L6 0.68 uh Molded Choke

11 2 L4,L5 150 uh Molded Choke

12 4 R1,R2,R57,R72 100 Ω, Surface Mount size 1206

13 12 R3,R4,R9,R10,R11,R20,R21,R24,R97,R102,R105,R106

1K Ω, Surface Mount size 1206

14 12 R5,R7,R25,R27,R37,R38,R86,R87,R88,R89,R90,R91

27 Ω, Surface Mount size 1206

15 10 R6,R8,R26,R28,R39,R40,R41,R42,R46,R52

330 Ω, Surface Mount size 1206

16 10 R12,R13,R14,R15,R22,R23,R29,R30,R31,R36

1k Ω, Surface Mount size 1206

17 6 R16,R18,R32,R34,R43,R44 51 Ω, Surface Mount size 1206


19 2 R45,R48 2.2k Ω, Surface Mount size 1206

20 2 R47,R49 10k Ω, Surface Mount size 1206

21 2 R50,R51 57.6k Ω, Surface Mount size 1206

22 6 R53,R54,R55,R59,R74,R92 10 Ω, Surface Mount size 1206

23 2 R58,R73 120 Ω, Surface Mount size 1206

24 4 R93,R94,R98,R99 49.9 Ω, Surface Mount size 1206

25 4 R95,R96,R100,R101 TRIM

26 1 R103 82 Ω, Surface Mount size 1206

27 1 R104 39 Ω, Surface Mount size 1206

28 3 U1,U2,U3 MC10H115, 16 PIN DIP

29 1 U4 MCH12140, SO8

30 2 U5,U7 AD834JR, SO8

31 1 U9 OP470GS, SOL16

32 2 U10,U11 LM7805, TO220

33 1 U12 LM7905, TO220

51


3.3.2 I-Q Detector Method

The other approach was to roll back the clock 60 years or so and measure both real and reactivepower directly, then calculate the load impedance and phase angle as the electric power industryhas done for many years. This approach was never used historically at RF frequency because thenecessary direct measurements could not be made, but again the AD834 precision widebandanalog multiplier made it possible. The I-Q detector (Figure 63 and Figure 64) offers a differentapproach to the problem of measuring power dissipated in reactive loads. An I-Q detectorresolves the signal into two orthogonal components. The comonents are expressed as the inphase value and the phase quadrature value. This technique provides the user with four termswith which to determine the characteristics of the load. The values of E 2 and I 2 as well as the inphase and quadarature phase products of E and I are available. Only three of the four terms arerequired to determine the phase and impedance of the circuit. The user is free to overdeterminethe solution, thus adding to the accuracy of the measurements made by this method. For instance,the solution may be derived by using E2, P, and Q. I2, Q, and P could then be used as a secondsolution. These two solutions are then checked for agreement. The final solution can bedetermined by averaging the two methods. This technique permits accurate and repeatable datato be collected.

For best accuracy, the I-Q board must have the phase response of its quadrature power splitterstrimmed. This operation requires precision 0° and 90° phase signal sources at 0.75 V RMS into50 Ω. A silver mica capacitor is used to adjust the phase so that the indicated real power nulls at90° signal phase. A miniature section of transmission line is used to change the path lengthbetween the real power detector and reactive power detector to null the reactive power at 0°signal phase. The transmission line length is 30.1 mm plus 4 mm for each 0.1° phase correctionrequired.

Figure 63 Complete I-Q Detector Assembly

52


Figure 64 I-Q Detector Assembly with Cover Off

For the I-Q detector board voltage (E), current (I), power (P), and reactive power (Q), (not to beconfused with Q associated with LC circuits) are measured directly. Circuit impedances can bederived from the current and voltage by

,,22RMSRMS I

QX

I

PR ==

and the phase of the current with respect to the voltage is

.tan 1

P

Q−−=θ

When R and X are computed using the familiar formula

Q

VXand

P

VR RMS

PRMS

P

22

==

the answer is for a parallel connection of R and X rather than the customary series values (asgiven by the current-based derivation). Some algebra gives the series equivalent values as

22

2

2

2

QP

QVXand

P

QP

VR RMSRMS

+=

+=

Again, Q is measured reactive power, not the circuit “Q” as RF engineers customarily use theterm.

53


The performance of the I-Q detector is shown in Figure 65 and Figure 66.

Figure 65 I-Q Detector Modeled and Measured VARS Data Superimposed

54


Figure 66 I-Q Detector Linearity Performance

Figure 67 through Figure 71 provides detailed component level fabrication information.

Figure 67 Silkscreen Layout of the Top Side of I-Q Detector PCB

55


Figure 68 Silkscreen Layout of the Bottom Side of I-Q Detector PCB

Figure 69 Layout of Components on the Top Side of I-Q Detector PCB

56


Figure 70 Layout of Components on the Bottom Side of I-Q Detector PCB

57


Figure 71 Schematic of I-Q Detector

58


Table 3 Parts List for I-Q Detector

Item Qty. Reference Part

1 8 C1,C11,C14,C22,C26,C35,C38,C47 0.001 uf, Surface mount size 805

2 32 C2,C4,C6,C7,C9,C10,C12,C15,C16,C18,C19,C21,C23,C24,C27,C28,C30,C31,C33,C34,C36,C39,C40,C42,C43,C45,C46,C48,C50,C51,C52,C53


3 1 C3 4.7 uf, Tantalum 25V

4 8 C5,C8,C17,C20,C29,C32,C41,C44 1000 pf, Surface mount size 805

5 4 C13,C25,C37,C49 C

6 2 J1,J5 SMA (F)

7 4 J2,J3,J4,J6 Signal Outputs to 9-pin D connector

8 4 L1, L2, L3, L4 150 uh Molded Choke



11 12 R3,R4,R10,R11,R12,R19,R20,R26,R27,R30,R40,R41

49.9 Ω, Surface Mount size 1206

12 8 R5,R7,R13,R17,R21,R23,R28,R32 R Ω, Surface Mount size 1206


14 8 R42,R43,R44,R45,R46,R47,R48,R49 TRIM

15 2 T1,T2 PSCQ-2-14

16 4 U1,U3,U5,U7 AD834JR

17 4 U2,U4,U6,U8 OP27GS

18 1 U9 LM7805

19 1 U10 LM7905

4 POWER DELIVERY SYSTEM

A major goal of this project was to construct an RF matcher that was completely electronicallycontrolled, with no moving parts. To accomplish this, one must have a variable reactance that iscontrolled by an external bias current or voltage. There are two well known devices with thisproperty, the varactor diode and the saturable reactor.

The varactor diode is a device that changes its capacitance as a function of the reverse biasacross the junction. (Actually, all P-N junction diodes have this property, but the doping profilesare optimized for this purpose in varactors.) They are widely used in radio and television tunersas well as frequency synthesizers and FM and PM modulators. In principle, they could be used inan RF matcher as well, but there are two significant problems that currently prevent this use. Oneproblem is that available varactors are low-power devices capable of handling only a few tens ofmilliwatts. This could be overcome by using large area power rectifiers, as their doping profilesare similar to varactors. The second problem, however, presents a fatal flaw—the voltage swingcaused by the RF signal is large compared to the DC or capacitance controlling bias on the diode.This means that the capacitance would swing significantly over each RF cycle, forming aparametric capacitor and generating harmonics much in the same way that the plasma sheathdoes in the reactor chamber. This problem does not present itself in the small signal

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communication applications of varactors because the RF voltage is in the millivolt range and thebias excursion caused by the RF waveform is small compared to the imposed DC controlvoltage, so the nonlinearity becomes negligible.

With the voltage-variable capacitor eliminated, we are left with the saturable reactors as ourelectronic tuning element. Since the invention of high-power silicon controlled rectifiers (SCRs),saturable reactors are no longer used in AC power regulation, but in the past they have been themost prominent means of AC power regulation. They have also been used in magnetic amplifiercircuits since somewhere around the turn of the century. These circuits have always beenconsidered low-frequency devices because of the effects of parasitic winding capacitances andcore losses. Nickel zinc ferrite magnetic materials have made RF saturable reactors possible byproviding an acceptable combination of permeability, saturation flux density, Curie temperature,core loss, and soft knee hysteresis loops. They do not, however, help the problem of turn-to-turncapacitance.

4.1 Saturable Reactor Technology

Saturable reactors (Figure 72) work by making use of the fact that magnetic materialspermeability varies with the flux density in the core along a path called the hysteresis loop. Sincepermeability (µ) is a linear term in the inductance of a coil (L = Kµn2), if one can vary thepermeability of the core by controlling its operating point on the hysteresis loop, then one canalso vary its inductance by the same method. One must also ensure that the product of the RFcurrent and the number of turns on the RF winding is small compared to the product of theminimum DC current and the number of turns on the DC or control winding. This will ensurethat the movement of the operating point on the non-linear hysteresis loop as a result of thepresence of the RF current is small and, thus, does not result in significant harmonic generation.The cross-sectional area of the core must be sized so that the flux density and core loss are keptwithin acceptable limits.

Figure 72 Complete Saturable Reactor

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A classical implementation (Figure 73) of a saturable reactor is formed from two matchedtransformers wired so that the control windings are bucking while the AC windings are aiding.

Figure 73 Classical Implementation of Saturable Reactors

In this arrangement, assuming the two transformers are matched, the voltage induced acrosswinding C2 due to the AC signal flowing through L1 is subtracted from voltage induced acrosswinding C1 due to the same AC signal flowing through L2. If the transformers are matched, theAC voltage appearing across the DC supply terminals is zero and no AC current flows throughwindings C1 or C2. The AC and DC windings are therefore decoupled from each other andneither is affected by the other. This describes the low-frequency operation of saturable reactors,but does not take into account the capacitive displacement current that flows between windingsand layers of windings in the control winding.

The distributed capacitance in the control winding results in circulating currents and it resonateswith the winding inductance producing destructive voltages at some frequencies. It also results inresistive losses in the copper windings from the associated circulating currents of the distributedRLC network that the control winding actually comprises. These losses and the associatedimpedances are reflected through transformer action back into the AC winding so that instead ofan inductance in series with a small frequency dependent resistor, it becomes a complex networkof inductive and capacitive components and parasitic resonances. These effects can be detectedin some saturable reactors and magnetic amplifier designs at frequencies as low as 440 Hz. Therehave been winding techniques devised to minimize this parasitic interwinding capacitance, butthe frequency response improvement is only a factor of two or three and comes no where nearextending the range to RF frequencies.

It is possible to extend the frequency response of saturable reactors into the low frequency RFregion by severely reducing the number of turns in the control winding and raising the amplitudeof the control current so that the product of the control current and the number of turns remainsequal. This approach soon results in prohibitive control current and still has a fundamentalfrequency limitation. It rapidly becomes clear that the winding capacitance problem must besolved in a fundamental way if a satisfactory saturable reactor is to be designed for RF use at13.56 MHz and above. Since the mere presence of a control winding inescapably impliesinterwinding capacitance, it becomes clear that the effect of the capacitance must be nullified

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since the capacitance itself is inescapable. The approach taken is the technique of bootstrapping,which has been used to extend the high frequency response of electronic amplifier circuits formany years. Bootstrapping is simply making sure that the same voltage is placed on bothterminals of the capacitor. Since there is then no voltage across the capacitor, there is no currentthrough the capacitor and it becomes undetectable electrically and no longer affects the circuitoperation. The degree to which this can be done successfully is the degree to which the capacitorbecomes negligible. This implies that to bootstrap the winding capacitance of an RF saturablereactor, the RF voltage between adjacent points on the control winding must be the same. Thiscan be accomplished if the winding technique (Figure 74) is modified and the properties of thecores match.

Figure 74 Complete Saturable Reactor

Toroidal cores were chosen because of their physical symmetry, their closed magnetic path, andtheir commercial availability. The windings are configured to ensure that the induced EMF fromthe transformer action of one core is summed with an equal and opposite EMF from the othercore before each turn is completed.

To put it another way, each turn of the control winding passes through the adjacent core before itagain passes through the first core so the sum of the induced voltage around each turn is zeroand, therefore, the RF potential at each point on a given turn is the same as at the corresponding

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point on the turns on either side of it. For this to happen, the RF windings (Figure 75), not thecontrol windings, are wired in a bucking (Figure 76) configuration.

Figure 75 Cutaway of Saturable Reactor Showing RF Inductor Coil

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Figure 76 Illustration of RF Bucking Wiring Method

In the toroidal implementation, the two cores are placed side by side about 1/8” apart and thecontrol winding is wound through both cores as though it were only one thick core. The RFwinding is wound in a “figure 8” with the windings crossing in the gap between the cores. Fortransformer purposes, this results in a bucking configuration and the two windings are decoupledby nearly 60 dB. The reactor frequency limitations are now independent of the windingcapacitances and rest solely on the core losses, which increase with frequency. Using twoAmidon FT240-67 toroidal cores constructed of Fair-Rite material #67 with a one-turn RFwinding and a 150-turn control winding, a variable inductor results whose reactance varies(Figure 77) from j50 Ω to j35 Ω as the control current advances from 1 to 12 amps, while theresistive component of the impedance varies from about 0.5 Ω to 0.375 Ω.

This performance is achieved after the core has been taken to heavy saturation one time (30 ampscontrol current momentarily) to place it on the hysteresis loop. If this heavy saturation step isomitted, the inductance will actually increase rather than decrease with the application of controlcurrent. Kapton and fiberglass tape are used to insulate and protect the windings mechanicallyand corona dope is useful in reinforcing the enamel coating on the control winding layers. This isdone to prevent scrapes of the insulation during winding operations (Figure 78) from developinginto shorted turns later in operation.

4.2 No Moving Parts, Fast Matching Network Design

The final goal of the project was to develop a matcher (Figure 79) that would be very repeatable,reliable, and fast enough to ensure that control of RF power delivery would be immediatelyestablished. To accomplish these objectives, a fundamentally different approach was conceived.The RF measurement system would be used to measure the power delivered to the chamber andthe power level would be controlled.

This being accomplished, a conjugate match would not be necessary, but operation within aspecified SWR (Figure 80) circle would be accepted as is common with today’s VHF andwideband HF communications transmission equipment.

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Figure 77 Ampere Turns versus R, Q, and X Data for a Saturable Reactor Design thathad Two RF Turns per Core (used on the first matcher prototype)

Figure 78 Saturable Reactor Assembly

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Figure 79 Interior of the High Speed RF Matching Network Prototype

Figure 80 Matching Network Operating Profile Plot

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Delivered power is then controlled by adjusting the generator to compensate for transmissionlosses. Available data indicated that the resistive component of the load varied over only a fairlynarrow range, while the reactance varied over a substantially larger range. This implies that ifone could tune out the load reactance, the desired performance could be achieved by using fixedtransformers to match the resistive component of the load to the generator source resistance.Such an approach offers several advantages. The matcher can tune with only one variableelement, which tremendously simplifies the tuning algorithm making it faster and inherentlymore robust. Since the load is capacitive, the reactance can be canceled by an inductor, whichpermits the use of a saturable reactor as the tuning element. The tuner therefore can beelectronically tuned, which enhances speed, and all moving parts are eliminated therebyenhancing reliability. Copper losses in the matcher are diminished because it operates in seriesresonance and large circulating currents, normally associated with tank circuits, are eliminated.Disadvantages of the approach are a somewhat limited tuning space and power dissipation in theferrite used to construct the saturable reactor. In the initial prototype (Figure 81), the saturablereactor RF winding consisted of four turns on two cores. Since the saturable reactor wascapacitively coupled to the load to provide DC isolation, the RF current in the load and thereactor were equal. The tuning reactance window was about 35 Ω wide. At the generator side ofthe saturable reactor, a transmission line transformer with a 1:9 impedance ratio transformed theload resistance to 50 Ω.

Figure 81 Prototype Matcher Design

In this configuration, core loss was substantial as efficiency was RL/RL + RM or between 70 and80%. It required 100 cfm of air carefully directed to achieve thermal stability at 150°C with600 W RF power applied. Thermal equilibrium could be maintained only to about 30 W withoutforced air cooling. Two steps were taken to solve the power dissipation problem. First, the turnswere reduced from two turns per core to one turn per core. Since the inductance was reduced, thenumber of reactors was increased to four (Figure 83) to achieve the required amount of totalinductance. Recall inductance scales as n2. It was hoped that this would produce an equivalentinductance swing and series resistance. The inductance swing was better than predicted, about60 Ω reactance swing as opposed to 35 Ω with the previous model. However, the loss resistancealso increased. The second step used a 3:1 impedance transformer between the load and the fourcascaded saturable reactors to lower the RF current in the saturable reactor. The RF current in thesaturable reactor was reduced by . This reduced core loss and distributed those losses overeight cores instead of only two. With the same 100 cfm, 1000 watts steady state power can behandled comfortably. A 4:1 transformer is then used to raise the input impedance to the 50 Ωrange.

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Recall that the saturable reactor uses up to 12 amps of control current (Figure 82) to achieve theampere turns value required to tune the matcher.

Figure 82 RF Match Network Tuning Control Current versus Tuning Range Plot

A common 50 V supply was used to power both the RF generator and the matcher. The controlwinding resistance is approximately 2 Ω. Power dissipated in the control winding can reach300 watts, which is more than the RF losses at 1000 W operating power. If linear regulation ofthe control current were employed, an additional 300 W of heat would be generated.

Lm

L

RR

R

+=

3

η

( ) jORRmatchatZ mLin ++= 43

Figure 83 Final Matcher Design

A pulse width modulated switching regulator circuit is used to control the current in the saturablereactor control windings to minimize the power dissipation associated with the tuning current.Since the hysteresis loop is nonlinear, the control current to reactor inductance transfer functionis also non-linear. An attempt was made to linearize this function by placing an L-C sensingoscillator coil on the reactor cores to feedback on the oscillator frequency shift. The reactor

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inductance could then be indirectly measured using an F to V converter fed by the sensingoscillator to develop a feedback signal to compare to the matcher control signal. This effortfailed because we were not able to develop enough isolation between the 1 MHz sensingoscillator and the 100 KHz power regulator switching transients to allow the system to functionproperly. We believe that this would be a viable approach with a carefully constructed Faradayshield on the sensing oscillator coil, but time and budget did not permit a second attempt on thisproject.

After hard saturation, the ferrite cores have higher losses below 1 amp of control current, so topreclude thermal runaway, the minimum control current is set at approximately 1 amp regardlessof the demand signal coming from the controller. This resulted in the final tuning range beingnarrowed to between -j13 Ω and -j30 Ω capacitive reactance. The fixed capacitor can be used tomove this 17 Ω reactive tuning window over a fairly wide range of reactances. In closed-loopoperation, the tuner’s response time to a 10 Ω step change in load reactance is in the 5–10 msrange. The control system for the tuner uses a two-step algorithm, which first measures the loadimpedance and uses a lookup table to find the approximate tuning solution, then it switches to aservo loop, which nulls the pre-match reactance. Using this matcher and controller incombination, delivered power is leveled to the setpoint value within 8 ms of the step loadchange.


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Figure 84 Match Network Input Transformer Assembly

Figure 85 Match Network Output Transformer Assembly

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Figure 86 RF Matcher, Saturable Reactor Current Drive Regulator Schematic

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Figure 87 Matcher RF Deck Schematic

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5 A UNIQUE COMPUTER CONTROL STRATEGY

5.1 Architecture and Design Strategy

5.1.1 The Software Story

Software Disclaimer: DO NOT USE THIS CODE FOR PRODUCTION.

The RF Control Project was a hardware project, not a software project. The code produced forthis project is prototype code for demonstration only. For example, saftety interlocks are modest.PRODUCTION USE OF THIS SOFTWARE may result in INJURY OR DEATH

The RF power delivery system can be operated without software. However, we chose to use acomputer system to get accurate diagnostic RF sensor information. Over the course of theproject, the computer requirements changed drastically. The initial assumption was that thecomputer architecture would be easy to assemble with a modest amount of programming. Thelatest revision shows that the architecture is complicated, requires a great deal of programming,and is a serious cause for concern.

To operate the RF power delivery system without using a computer requires the use of analogelectronic circuits. The RF sensor and I-Q signal processing circuits provide signals that areproportional to RF power and reactance. The reactance signal can be used to tune the RFmatching network for zero reactance with RF information from the pre-match RF sensor. The RFpower levels to the load could be held constant by use of a variety of electronic circuittechniques using information from the post-match RF sensor and I-Q signal processor. We didnot develop any circuitry for these types of analog control strategies, but we constantly kept it asa backup plan to meet the project milestone time table in case the computer system failed.

The first attempt at developing a computer system for this project was based on the assistance ofthe Motorola Microcontroller Applications Engineering department. The work focused on the68F333 microcontroller on a development board connected to a custom A to D board fabricatedat SEMATECH.

We abandoned this approach because the combination of processor and algorithms could notprocess the data fast enough to meet the system requirements. The system needed to performexternal data collection, calculate, and output a response at a rate of one measurement set permillisecond. The limitations with the 68F333 approach centered around the need to acquire highresolution 16-bit analog signals and to process that information through a control algorithm afterconversion to engineering values. Other Motorola processors might have worked just fine, butwith time running out on the project, the RF control team chose to obtain help from computer-systems-level people and to defer hardware selection. We were unable to secure microcontrollerassistance from other Motorola product applications groups; therefore, we formed a design teammade up of computer engineering technical staff members from ORNL and SEMATECH.

Steve Hicks and Ganesh Rao from the Instrumentation and Controls Division at ORNL workedclosely with the MSD division at SEMATECH. Steve chose a dual processor approach that freedthe main device controlling processor from servicing interrupts associated with user interface andfile handling functions. Bob Flegal developed a special software architecture to handle the inter-process communications.

The communications or query interface is modeled after Gelernter’s work on Linda at YaleUniversity (see Section 5.2.4). This software architecture is so powerful because it is very

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simple. Each process or “agent” in the system communicates using simple messages made up ofthree parts: conversations, topics, and subtopics. Any agent can read these three-part messages;any agent can write messages. The query interface is described in detail in Section 5.2.4.

The control algorithm that operates the integrated RF power delivery system uses only a modestcontrol strategy based on an interdependent lookup table and a set of PID values. Thepredominant time constant of the entire system is the speed at which the saturable reactor in theRF matching network can electrically tune. Although additional enhancements to the strategyhave been discussed, we must collect data from a plasma etcher test installation before makingany changes.

Three areas that the current software implementation must address before it is ready forproduction are safety, robustness, and performance. This implementation meets the performancegoals, but does not meet robustness and safety criteria. This project was conducted in anengineering environment using laboratory safety practices and operated only under the directcontrol of the lead RF engineer without exception. Safety considerations for the devices and theoperating software need significant improvement before any serious manufacturing can beconsidered. Use of this experimental operating system for any purpose other than laboratoryresearch by talented RF engineers could be very hazardous!

The software shows that the integrated RF power measurement and control system actuallyworks and performs to the expectations of the contract specifications. More development will beneeded on the computer architecture and software before it is commercially viable.

5.1.2 Computer Hardware Design

Figure 88 is the hardware design diagram for the RF Control project. Two sensors are used togather data and provide input data for the matcher control algorithm. The pre-match sensor islocated between the RF power generator and the match box. The post-match sensor is locatedbetween the match box and the plasma chamber.

The sensors gather data, filter them through harmonic filters, and then run the RF signals eitherthrough the phase detect (PD4) or the I-Q detector boards. Finally, the analog data goes throughan A/D conversion board and into the faster processor on the dual processor computer.

The control algorithm on the fast processor uses the sensor data to drive the match network. Thecomputer takes the output from the control algorithm and feeds the digital value through a D/Aconverter back to the RF power generator to modify the power signal.

5.1.3 Computer Software Design

In this diagram (Figure 89), each bubble represents a logical piece of functionality. All of thebubbles can be implemented as one big process or as separate processes.

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Figure 88 System Block Diagram of Hardware

Figure 89 Logical Design

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The software team chose to break the functionality into two separate processes as shown inFigure 90. The time-critical work is handled in one process (RF measurement and control). Thetwo processes communicate via the query interface.

Figure 90 Physical Design

5.2 Implementation

5.2.1 Hardware Implementation

The computer hardware used in this project is a Ziatech with dual processors: a 386/387processor and a Pentium ZT8905 processor. The Ziatech hardware manages shared memory,shared disk, shared display, and shared keyboard for multiple processors. In this configuration,the Pentium processor is dedicated to data acquisition and control. The 386 processor isdedicated to user interface, disk processing, and other tasks. The two processors communicateover shared memory.

We recommend using two processors of equal power (i.e., two Pentium processors), if possible.We did not do this and paid for it in user interface response time. If you do choose unequalprocessors, dedicate the faster processor to the measurement and control module.

5.2.2 Software Implementation

The measurement and control module was developed for the ZT8905 Pentium processor boardand uses the Ziatech DDP library. The C language development environment is Watcom C/C++under Microsoft Windows 3.1. The runtime environment is DOS.

The user interface editor is LabWindows for DOS. LabWindows code cannot be compiled usingthe Watcom C/C++ environment. Therefore, we used the Microsoft C/C++ compiler under DOS.

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5.2.2.1 RF Measurement And Control Module

The RF control algorithm is implemented in an interrupt service routine (ISR) that is executed atevery timer tick interrupt generated by the on-board PC timer. The original timer tick ISR isreplaced and the timer reloaded with a new count to generate the desired sample frequency. Theoriginal ISR can be called to maintain the system time if that is required. The on-board timer isnot extremely precise. The error of the interrupt routine is based on its maximum resolution of0.84 µs and a few counts of error (Figure 91).

Figure 91 RF Measurement and Control Design

A stepper motor control capability was incorporated to adjust the vacuum variable capacitor inthe RF matching network. The purpose of adjusting the capacitor is to align the operating rangeof the matching network around the center of the plasma load reactance range. The stepper motorcontrol feature was not fully developed because a manual adjustment of the capacitor was onlyneeded on rare occasion.

5.2.2.2 Configuration

The measurement and control module depends on the user interface to provide ALLconfiguration variable values. The user interface module sends these values to the measurementand control module through the shared memory interface. Neither system is considered “active”until these initial configuration values have been sent and are properly received oracknowledged.

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The exceptions to this rule are sample frequency, data storage length, and control mode. Themeasurement and control module must know these values to come up at all. It defaults to a3000.0 Hz sample frequency, a 3000 element data storage length, and no control. The controlmode refers to the active control algorithm. The software may use different control algorithmsduring execution. Currently, there is only one control algorithm that may be selected. Therefore,the control mode is either off (0) or on (1). Control must be off at startup because the controlalgorithm depends upon the rest of the configuration values to run.

5.2.2.3 A/D Module

There are two possible methods of acquiring data from the A/D channels: interleaved and non-interleaved. The code for each of these methods is contained in external files and only one can beincluded into the ISR. Currently, the ISR includes the interleaved data acquisition method.

The interleaving of A/D commands speeds input. It is much faster than the non-interleaved codeas data acquisition is performed simultaneously on both boards. The first read from each channelmust be discarded because of crosstalk errors that arose from settling time deficiencies in theanalog multiplexer buffer amplifier on the VerlaLogic A/D boards. These “double reads” arenecessary to get correct data, but they impact the speed of data acquisition.

Interleaved code *WITHOUT* double reads *DID NOT WORK !!!* There was a problemwhere the input channels were shifted (i.e., the data from ADC0 was appearing at ADC1.) Thisproblem mysteriously disappeared after a processor swap. The problem was never solved, butbus mastering may have been the culprit. Luckily, double reads seem to solve this problem.

5.2.2.4 Control Module

The control algorithm is included into the ISR. It calculates the generator and matcher setpoints.It uses a table to make the initial guess for the output voltages to the matcher and generator.Then, the PID control algorithm kicks in to bring the error to zero and correct for any errors inthe table. This is, therefore, a dual algorithm controller.

If the match is good, but the power transfer efficiency is poor, this control algorithm will shutdown power to the plasma (i.e., turn the generator off). The matcher control function is used onlyif the RF voltage is greater than the RF voltage threshold. If the PID algorithm fails to reduce theerror to an acceptable limit after a specified number of trials, the controller switches to thelookup table algorithm.

Note, the software is designed to allow more complicated control algorithms. Because thematcher device is slower than the speed of the computer, this control algorithm is sufficient tocontrol the matcher.

5.2.2.5 Display

The measurement and control module provides an engineering screen that can be used when theRF user interface is not running. It is implemented using simple text-based display commandsand assumes an experienced user.

The engineering screen handles keyboard input and runs whenever the ISR routine is notrunning. It checks the user’s input against a list of recognized commands and performs theknown commands. It also reads the shared memory for updated variables and commands fromthe RF user interface. Note, do not use the engineering screen for command input when the userinterface is running.

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Measurements Module/Archiving

The user may request data archiving from the user interface or the engineering screen by issuingthe “record” command. The RF user interface is the PREFERRED way to request data archiving.

The measurement and control code uses “huge arrays” to hold the data in memory. This ensurescontiguous and complete data collection. These huge arrays can be allocated to save any type ofdata. Once the arrays fill up, the measurement and control module waits for a command to savethe data. If another record command is received before a save command, the module will throwaway the existing data and restart the data archive.

5.2.3 RF User Interface

The user interface was developed using LabWindows for DOS from National Instruments. Theuser interface editor provided in LabWindows generates display files which can be included intoC code (Figure 92).

Figure 92 RF User Interface Design

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5.2.3.1 User Interface Module

The user interface module has three parts: the first_time procedure that is run once at system startup, the each_time procedure that is called repeatedly until the system shuts down, and thelast_time procedure that does any clean up just before the agent returns to DOS.

There are five main user interface panels and two pop-up panels (start and help). Every panel isprocessed the same way. The each_time function displays the panel and calls a processing loop.Each processing loop takes the current_panel as input and returns an index to the next panelselected. NO_SELECTION is returned when the user wishes to exit the entire program(Figure 93).

Figure 93 Main Panel

Each processing loop starts by painting values on the panel and reading data values from theshared memory interface. It then traps events on the panel and processes the events. Every panelexcept main has a return button to exit back to the main panel.

The most important information to take away from this interface is not the way it wasimplemented, but how it OPERATES. These panels constitute the RF team’s best guess at whatmight be needed in a user interface. As with any system, this is not the only way to implementthe user interface. Each panel has some operation that may not be intuitive. Those non-intuitiveoperations will be described in the following sections.

Whenever the user changes a value on the system level control panel (Figure 94), the userinterface IMMEDIATELY sends the change to the measurement and control module (Figure 95).If the user does not like the results of the change, pressing the UNDO button will restore theoriginal value.

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Figure 94 System Level Control Panel

Figure 95 Operation Mode Panel

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The sampling frequency must be greater than or equal to 3000.0 Hz before control is turned on.

The calibration panel (Figure 96) displays values for only one board at a time. While the systemSHOULD read all data values from the measurement and control module, it reads only thosevalues being displayed. This is a speed-up compromise to compensate for the slower speed of the386 processor.

Every item associated with the display graphs is user configurable (Figure 97) (i.e., Y-axis range,value being displayed, title).

The post-process button is independent of the record button (Figure 98). The user may select anyinput file to post process, not just the most recently recorded file. No validation of the input fileis done. If the user supplies the name of a file that is not a valid input file, the system may hang.

Figure 96 Edit Sensor Calibration Panel

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Figure 97 Dynamic Display of Sensor/System Data Panel

Figure 98 Data Archive Panel

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Help Panels

The help text is kept in files named panel.hlp. The same mechanism is used to read all help filesand process the help panel. The help interface is very limited. The users can select next andprevious pages as well as return to the calling panel.

5.2.3.2 System Configuration Module

This routine reads the system configuration parameters from a disk file and stores the appropriatevalues in shared memory using the out() procedure defined in the query module. A defaultstartup configuration file is used, but the user may change the configuration file duringexecution. The configuration information is stored in conversation. topic subtopic format inASCII so that the configuration file can be edited using any standard text editor.

Valid configuration files have the following format:

RF CONTROL CONFIGURATION FILE

/* Comments that may span any number of lines.

Only the display maximum will be read */

SENSORID <a character string, no spaces allowed>

CONFIG const value (int, float, char)

CONFIG const value (int, float, char)

This file also manages an internal array of configuration variables and current values. All accessto the configuration variables is controlled through the routines in this file. Therefore, theconfiguration variable array is LOCAL to this file.

5.2.3.3 Calibration Module

This module defines and manages the data collection structure. This data structure containsnumerical values that are sent to the user interface from the measurement and control modulethrough the shared memory interface. The data structure is accessed through the routines in thisfile. Therefore, the data structure is LOCAL to this file.

5.2.4 Query Module

The query interface is designed to be a simple, powerful way to converse between processors.The implementation is hidden from each side so that it can be implemented using the besttechnology available on a given platform. This implementation uses shared memory. All of themessages are ASCII text to aid in debugging and tracing sessions.

Shared memory is organized into message triples. Each message is a triple consisting of aconversation, a topic, and a subtopic. Agents participate in conversations to communicatesubtopic information along topics. Note that conversations, topics, and subtopics may not containspaces. ("test it") is illegal; ("testit") is just fine.

The query interface is implemented using three procedures: out – add a message, rdp – find amessage, rd – find and remove a message. For example, a measurement and control proceduremight indicate that an error in the user interface module has occurred by posting the messageout("ERROR_PENT", "save", "FileNotFound"). Another procedure might be looking forERROR_PENT messages by invoking rdp("ERROR_PENT","save","xxxxx") which will return

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a subtopic in a message matching the “ERROR_PENT" conversation and the "save” topic. Note:if the topic is the string "*" rd and rdp will return the first topic and subtopic that match theconversation.

This interface is modeled after Gelernter's work on Linda at Yale University. For moreinformation on Linda, refer to it on the web. For example, search for Linda on Yahoo.

5.2.4.1 Conversations Implemented in the RF Control Software

The user interface module sends configuration data to the measurement and control moduleusing the CONFIG conversation. The measurement and control module acknowledges receipt ofthe configuration variables through the UPDATE conversation.

The measurement and control module sends data and status information to the user interface overthe shared memory using the DATA conversation. The values are written to the shared memoryonly if a previous value does not exist. This prevents overwrites of existing data and anypossible conflicts where the user interface is reading while the measurement and controlmodule is writing. If the user interface does not read a particular value, it will never change.

The user interface can also send commands over the shared memory using the COMMANDconversation. The measurement and control module executes the commands and returns the errorcode over the shared memory using the ERROR_PENT conversation.

The known conversations, topics, and subtopics are

CONFIG var-name var-value Written by User Interface

UPDATE var-name var-value Written by Measurement and Control

DATA var-name var-value Written by Measurement and Control

COMMAND command-text arguments (if any) Written by User Interface

ERROR_PENT command-text error-code Written by Measurement and Control

Separating the conversations keeps one process from overwriting another's data. Keeping theselines of communication distinct and clear prevents arguments and other misunderstandings frominterfering with the symbiotic operation of the measurement and control module and the userinterface module.

5.3 Computer System Lessons Learned

This section lists just a few of the lessons learned during the second prototype.While some points may seem self-evident, they were big stumbling blocks for

this team and they are well worth emphasizing.

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5.3.1 Use a Real-Time Operating System

The data acquisition and control loop is currently implemented using the timerInterrupt Service Routine (ISR). The following anomalies were encountered usingthis approach. Do not do this in a production system.

1. The time on the measurement and control module processor no longer functions because thedata acquisition and control ISR replaces the timer ISR.

2. Some activities on the Pentium board interfere with the timer ISR. Unfortunately, there is notenough information about the Ziatech to ascertain whether there is a higher priority interruptthat interrupts the timer ISR or whether the operating system just loses information. Theseerrors occurred when writing to a floppy disk and occasionally when swapping processors.

3. Initially, the data acquisition and control ISR was implemented using subroutines. Thisincreased the frequency of ISR interference and system lockups. Therefore, all of theinterrupt code was changed to inline code, but some function structuring is maintained byusing “include” files.

5.3.2 Use Proven Hardware

The Ziatech system was selected because it provides multiple processors with ashared memory disk and display. These are the problems encountered with thisrelatively new product.

Display - We encountered problems with the display when switching processors. The displaymalfunctions during a processor swap if a complicated user interface panel is showing. Thedisplay can only be cleared up by exiting the measurement and control program and issuing a“cls” command. Obviously, we cannot stop the data collection just to clear the panel display.

Mouse - The processor hangs intermittently when the mouse is moved at the wrong time.

Speed - The speed of the 386 processor is very slow. The Pentium is so much faster that itdominates the shared memory interface.

Memory Sharing - The user interface and measurement and control module cannot run underMicrosoft Windows because it does not work with the shared memory implementation.Therefore, the software environment selections were limited to DOS applications.

5.3.3 Use a User Interface Builder

Use a commercial user interface builder. We selected LabWindows for DOSbecause it was the best combination of price/performance we could find for theDOS operating system. LabWindows for DOS is dated, has limited

functionality, and is restricted to a few basic widgets. Despite these shortcomings, it saved alot of time in developing the interface and is far superior to a “roll-your-own” interfacebuilder approach. LabWindows for DOS is still supported by National Instruments and itlives up to its expectations even if the expectations are modest.

86


5.3.4 Query Interface—Separate Conversations

Separating the query conversations keeps one processor from overwritinganother’s conversation. Keeping these lines of communication distinct and clearprevents arguments and other misunderstandings from interfering with the

symbiotic operation of the measurement and control module and the user interface module.

The measurement and control module writes on the DATA, UPDATE, and ERRORconversations. The user interface writes on the CONFIG and COMMAND conversations.Either side can read any conversation. This one-way mechanism is not protected throughhardware or even software locks. It is up to the programmer to follow the conversationrules—so WATCH OUT!

5.3.5 Integrate Early and Often

Integrate all your code sooner than you think possible and continue to dosystem integrations at frequent intervals. It will save you headaches in the longrun. If you want to see the battle scars and hear detailed war stories, call any of

5.4 RF Computer Control System Requirements that Guided the Project

The following are RF computer control system requirements that guided the project:

• Hardware1. Prefer laptop or notebook for use in wafer fabrication area

2. A/D and the D/A must have enough ports for experimentation

• Software1. During data collection, want selective query on demand

2. No constraints on language/platform

3. Load several detection algorithms

4. Control algorithm is not pinned down. Control algorithm selected/changed fromuser interface within 5–10 minutes

5. Data collection can be directed to floppy disk

• User Interface1. Must refresh data display at a rate of three times a second

2. All screens must have a button to return to the main screen (or previous screen ifmore than one level deep)

3. All screens must have a button for help or information

4. Main screen must contain prototype disclaimer

5. Main screen must allow user to start, pause, and stop control

6. UI must provide a screen for selecting control mode and setting control presetsand thresholds

7. UI must allow user to set the size of data averaging array

87


8. UI must provide a sensor calibration screen where the user can interactivelyadjust all sensor gains and offsets while displaying sensor values as collectedfrom the measurement and control module

9. User must be able to set speed of data collection for passive and active control—If control is active, frequency must be at least 3000 Hz

10. UI must provide an interface for commanding the measurement and controlmodule to archive data—Once data is collected, UI must prompt user for a savefile. Optionally, the user can post-process the data and save to a floppy

11. UI must provide data display in graph/strip chart form—User must be able toselect variable to be displayed and graph display range

12. UI must provide a mechanism for saving and restoring configuration/calibrationconstants

*UI = user interface.

• System1. Measurement portion manufacturing cost must be $5000.00 or less

2. Printout of RF portion of software must be confinable to a modest-sized threering binder

3. RF and match box must work together in a 1–5 ms time frame

4. External data collection at one measurement set per one-third millisecond duringdevelopment

5. During product mode two times per second (time stamp OK)

6. Installed prototype must be safe when installed in fabrication area

7. Measurement and control module code and user interface must come upautomatically when machine is booted

6 OVERALL RF POWER MEASUREMENT AND CONTROL SYSTEMPERFORMANCE

The operational testing of RF power measurement and control system was completed bydelivering a constant power level into a load that simulated a set of rapidly varying plasmaconditions. The plasma simulating load was designed to switch between two different loadvalues separated by 10 Ω reactance. The dynamic load switching was done by an independentlyvaried function generator that operated an electro-mechanical solenoid, which in turn actuated asealed vacuum mechanical switch. The vacuum switch added in a parallel capacitor to theadjustable vacuum capacitor in the plasma simulating load when in the closed conditionsuppying the 10 Ω load reactance step change. The function generator was used to control thevacuum switch at speeds from around 5 to 10 Hz to test the ability of the RF system anddetermine how well it actually operated.

An important point needs to be noted prior to viewing these performance graphs. We haveincorporated a feature commonly used in the communications industry into our control strategy.When the RF system computer senses that the matching network is no longer tuned for a loadcondition, as it initially is when the load gets switched from one condition to another, we reducethe RF power from the generator to about 70 W. We do this to protect components in the RF

88


power delivery path (Figure 101) from excess current and voltage stresses that occur undermismatched conditions. We do not lower the power to zero because we want to keep the plasmagoing and to continue supplying enough power to permit accurate measurements. We added aprotection feature based on matcher efficiency. If matcher efficiency drops below a preset value(i.e., 25%), the RF generator will be turned off. This is done to prevent system operation should ahardware fault occur or a load impedance be encountered that the computer tuning algorithmscannot properly resolve.

The series of data graphs in this section are all from the same data set. The first two graphs(Figure 99 and Figure 100) show one cycle of operation of the power delivery into the load as itstep changes from one condition to another and then back. The data graphs are arranged in pairswith the first showing the primary end result information first, which is the information on therequested power level, post-RF match network power levels, pre-RF match network generatorpower level and the RF generator power control voltage. The second graph contains informationon the signal used to control the RF matching network.

Figure 99 Performance Plot of the Complete RF Power Delivery System into aDynamic Step Change Plasma Simulating Linear Load

89


Figure 100 Performance Plot of the Complete RF Power Delivery System TuningControl Signals (see Figure 99)

Figure 101 RF Power Delivery System Block Diagram

90


The next two sets of data graphs (Figure 102 and Figure 103) are blown up or expanded views ofthe first and second events from the first set of graphs. In the expanded form it is much easier toobserve how well the system actually performs.

Figure 102 Expanded Time Scale Performance Plot of the First Event (see Figure 100)Showing the Speed of Tuning and Power Delivery Control Accuracy

Figure 103 Expanded Time Scale Plot of the Tuning Control Signals at the First Event(see Figure 102)

91


The most signifcant message that is being conveyed in this section is the bottom line answerregarding just how well this system works after the time and resources have been consumed.

As you examine the data graphs, you will see the chain of events that unfolds in approximately7 ms:

1. First observe that the requested power level and the delivered power level are essentially thesame (overlaid on each other) and that the RF generator output power is higher since somegets dissipated in the matching network in the form of heat (note that the generator controlvoltage has been multiplied significantly so that it will appear on the graph with the otherdata).

2. As the load is switched to a different load condition, the RF sensor parametric data revealsthat the tune position of the RF matching network is no longer correct and the computerbegins to retune the matching network.

3. The computer begins to adjust the matching network until it determines that the requiredamount of tune adjustment is outside of the PID control capability and then reverts to alookup table to get back into a course tune.

4. While the computer is conducting this two-step control strategy, the control signal to the RFgenerator is lowered to about 70 W of RF power.

5. As the computer observes the matcher approaching a window of operation in which the PIDalgorithm can again operate, the RF generator power levels are brough back up.

6. Proper tuning position and RF power level control is then established.

On the expanded set of graphs for the first event, note that the events centered around the 0.500to 0.503 second time frame are caused by the mechanical switch bounce of the mechanicallyactuated vacuum relay used to switch the load reactance. The RF system intially was attemptingto compensate for the switch bounce until it settled down. The expanded set of data graphs forthe other event does not show this characteristic because the vacuum relay simply opens.

The response characteristics of the system are slightly different as it moves from one set of loadconditions to another (Figure 104 and Figure 105). This is mainly because the saturable reactorsin the RF matching network are driven first in one direction of inductance adjustment and thenrelaxed when going in the other. The performance level we achieved suggested that a moreelaborate saturable reactor drive scheme was not needed.

92


Figure 104 Expanded Time Scale Performance Plot of the Second Event (see Figure 100)Showing the Speed of Tuning and Power Delivery Control Accuracy

Figure 105 Expanded Time Scale Plot of the Tuning Control Signals at the Second Event(see Figure 104)

93


The final graph (Figure 106) is the overall RF matching network efficiency, which helps tounderstand that we use the control of the RF generator output power to compensate for varyingefficiencies depending on the load.

Figure 106 RF Match Network Efficiency and Load Reactance Plot

7 CONCLUSION

In conclusion, this project has raised the status quo in our industry and will provide many of thetechnical staff members in the SEMATECH community new concepts and perspectives to drawupon.

• The analytical RF power sensor goal was successfully designed

• The associated supporting electronics were successfully developed

• The “fast” no-moving-parts electronic matcher was successful due to the design of a uniquesaturable reactor

• The contract stretch goal for a low-impedance RF power generator was accomplished

• All of these were assembled into a functioning RF power measurement and control system

The engineering principles realized in the first version hand-built prototypes would have meetthe minimum level of achievements required by the contract objectives; however, the pusuit ofmore mature prototypes, thorough engineering analysis, and the integratation and demonstrationa the RF power delivery system were not only logical efforts to pursue, but they also provide atangible and lasting memory for our customers.

The test gear and prototyping capabilities accumulated for this project will have value for yearsto come as new RF technology project ideas are investigated, as well as provide us withimproved diagnostic support for current needs.

94


APPENDIX ADerivation of Current Loop Sensor

A.1 Basic Theory

In electromagnetic problems, the starting point is the ubiquitous Maxwell’s equations.Maxwell”s equations (in MKS units) are

t

DJH

t

BE

B

D

∂∂

∂∂

ρ

+=×∇

−=×∇

=•∇

=•∇

0

Equation 1

where E

is the electric field, D

is the electric displacement, B

is the magnetic induction, H

is

the magnetic intensity, and J

is the current density. Maxwell’s equations alone are not enoughto determine the fields. In addition to Maxwell’s equations there are also relationships betweenE

and D

and between B

and H

called constitutive relations. The constitutive relations must beknown before Maxwell’s equations can be solved. For the case of linear homogeneous media, theconstitutive relations become

EJ

HB

ED

σµε

=

=

=

Equation 2

where ε is the permittivity, µ is the permeability, and σ is the conductivity. For the presenttreatment, only linear homogeneous materials will be considered, which means that ε, µ , and σare constants. Electromagnetic problems are mathematical boundary value problems in which thefields or the derivatives of the fields are specified on the boundaries. There can be abruptchanges in crossing boundaries of different materials. For example, if a copper plate is placed ontop of a glass plate, there will abrupt changes in the conductivity and permittivity across theboundary. Across such boundaries there are a set of boundary conditions that must be satisfiedby the fields to be consistent with Maxwell’s equations [Stratton]. These boundary conditions aresummarized below:

s

s

DDn

EEn

KHHn

BBn

σ=−•

=−×

=−×

=−•

)(ˆ

0)(ˆ

)(ˆ

0)(ˆ

12

12

12

12

95


Equation 3

where n is the unit normal in going from medium1 to medium 2 across the boundary

(Figure 107), sK

is the surface current density along the boundary, and σS is the surface charge

between the boundaries. The subscripts, 1 and 2, on the field quantities indicate the region for thefield.

Figure 107 Surface Charge Boundary

The geometry for the pickup loop consists of two coaxial hollow conducting cylinders withcurrent flowing down the inner conductor and back along the outer conductor (Figure 108).

Figure 108 Concentric Coaxial Conductors

The pickup loop is looped through the outer cylinder into the inner conductor and returned backthrough the inner and outer conductors (Figure 109).

Figure 109 Magnetic Pickup Loop Representation

96


For the present treatment, the geometry of the solid inner conducting cylinder will replace thehollow inner cylinder and the outside radius of the outer conductor will be taken to infinity. Thisis a very good approximation if the thickness of the conducting cylinders is large compared withthe skin depth. The axis of the cylinders will be taken along the z axis. For this geometry,Maxwell’s equation can now be separated into two parts: one part containing the transversecomponents of the derivatives and field components (symbolized by a subscript t) and alongitudinal component (symbolized by a subscript z). (For more detail on the procedureoutlined below the reader is referred to the reference by Jackson.) Following the procedure

outlined in Jackson, the ∇ operator can be written in the form z

azt ∂∂

ˆ+∇=∇ , where ∇ t is the

transverse component of the ∇ operator perpendicular to the z axis and âz is the unit vector alongthe z axis. Similarly the field quantities can be separated into a transverse and a longitudinal

component; for example, zzt EaEE ˆ+=

. Upon substituting these changes into Maxwell’s

equations and assuming a complex exponential time dependence for the fields, Maxwell’sequations become

0

ˆˆ

ˆˆ

ˆ

=+•∇

=+•∇

−=×+×∇

−=×∇

=×+×∇

=×∇

z

BB

z

EE

EjJz

BaaB

EjJB

Bjz

EaaE

aBjE

ztt

ztt

ttt

zzzt

zztt

tt

zzzt

zztt

∂∂

ερ

∂∂

εµωµ∂∂

µεωµ

ω∂∂

ω

Equation 4

The above set of equations look rather formidable, but they can be simplified with some effort.

For EJ

σ= Equations 4 become

z

EaBjEj

z

E

z

BaE

j

jBj

z

B

EjE

BjB

ztzztt

t

ztzztt

t

zz

zz

∂∂ωωµσµεω

∂∂

∂∂

ωωµσµεωωµσµεω

∂∂

ωµσµεω

ωµσµεω

∇+×∇=++

∇+×∇+=++

=++∇

=++∇

ˆ)(

ˆ)(

)(

0)(

0)(

22

2

22

2

2

22

22

97


Equation 5

Since the desired solutions are traveling waves along the z axis, the fields will have a z

dependence of the form e±jkz. This means that kjz

±→∂∂

and 22

2

kz

−→∂∂

, and with these

substitutions, Equations 5 become

)6(ˆ)(

)6(ˆ)(

)(

)6(0)(

)6(0)(

22

222

222

222

dEkjaBjEkj

cBkjaEj

jBkj

bEkjE

aBkjB

ztzztt

ztzztt

zzt

zzt

∇±×∇=−+

∇±×∇+=−+

=−++∇

=−++∇

ωσµωεµωωωµσµεωσµωεµω

σµωεµω

σµωεµω

Equation 6

At first appearance, there seems to be little simplification in the problem, but closer examinationreveals that the original set of equations (Equations 4), which involved solving a set of coupleddifferential equations in terms of the vector components of the fields, has now been reduced tosolving scalar ordinary differential equations. To be more specific, Equations 6a and 6b areordinary differential equations where Ez and Bz are scalars, which will be denoted by φt(ξ,ζ).Thesubscript t (t) indicates that the scalar function is in the plane perpendicular to the z directionwhere ξ and ζ are generalized coordinates; for example Cartesian coordinates (x, y), polarcoordinates (r, θ), etc. The procedure is to solve Equations 6a and 6b forEz(ξ,ζ,z) = Ez(ξ,ζ,z)e

j(±kz-ωt) and Bz(ξ,ζ,z) = Bz(ξ,ζ,z)ej(±kz-ωt). Denoting the solution of either

Ez(ξ,ζ,z) or Bz(ξ,ζ,z) by ψt (ξ,ζ,z) = φ (ξ,ζ)ej(±kz-ωt).

Equation 7

where the plus or minus sign indicates the direction of the traveling wave along the z directionand ),( ζξφt stands for Ez (ξ, ζ) or Bz (ξ, ζ). The function φt (ξ, ζ) depends only on the

coordinates in the plane perpendicular to the z axis. Substituting Equation 7 into Equation 6a or6b gives

ff

ck

kj

ttt

πωλλπ

σµωεµωγ

φγφ

2,,2

0222

22

===

−+=

=+∇

98


Equation 8

where c is the velocity of propagation of the wave, λ is the wavelength, and f is the frequency inthe dielectric material of the coax.

In cylindrical coordinates (see Figure 108) Equation 8 becomes

01

)(1 2

2

2

2=++ t

tt

rrr

rrφγ

θ∂φ∂

∂φ∂

∂∂

Equation 9

We next determine Ez and Bz from Equation 9, with the appropriate boundary conditions, andthen using Equations 6c and 6d determine the transverse components of the fields.

For the interior of a coaxial cable with inner conductor of radius a, outer conductor of radius b,and the region between the conductors filled with a dielectric of permittivity ε, the functionφt (r, θ), which satisfies Equation 9 is

∑ ++∑ +=∞

=

∞

= 00)]sin()cos()[()]sin()cos()[(),(

mmmm

mmmmt mDmCrNmBmArJr θθγθθγθφ

Equation 10

where Am, Bm, Cm, and Dm are constants that are determined by the boundary conditions. Jm(x)and Nm(x) are Bessel functions of the first and second kind, respectively. Equation 10 is a generalsolution for each region(i.e., the two conductors and the dielectric region in between).

A.2 Solution for Two Coaxial Conductors

To find the induced emf in the pickup loop, we must first determine the electric and magneticfields in each of the three regions of the two coaxial conductors with an intervening dielectricbetween the two conductors. Ideally, the problem should be solved for the case of finiteconductivity with boundary conditions, but the finite conductivity case cannot be solved withoutthe aid of a computer. The perfect conductor case, however, does permit an analytical, closedform solution. which provides insight into the nature of the solution, and gives a very goodapproximation to the real case.

In the perfect conductor case, the electric and magnetic fields go to zero inside the conductors.

For good conductors (εωσ

>> 1) the fields are constrained to the skin depth of the conductor. So

to a good approximation, the ideal conductor case should yield good results. For perfectconductors, the boundary conditions are

)11(ˆ

)11(ˆ

)11(0ˆ

)11(0ˆ

dDn

cKHn

bEn

aBn

s

s

σ=•

=×

=×

=•

99


Equation 11

Equation 11a is equivalent to the condition 0ˆ =∇•≡ zz BnBn∂∂

on the surface of the conductor and

Equation 11b is equivalent to the condition Ez = 0 on the surface of the conductor. Because the zcomponents of the electric field and the magnetic induction must satisfy the Equations 6a and 6brespectively., the solutions for Ez and Bz are coupled by the parameter γ. In general, there aresolutions only for certain values of γ. For the present problem with perfect conductors it will beshown below that γ must be zero.

The sensor coax has a common current flowing in the inner and outer conductors. The currentflowing in the z direction is related to the electric field by the equation

∫∫ ∫∫ •=•=S S

dSnEdSnJI ˆˆ

σ

Equation 12

where S is the surface perpendicular to z direction and zan ˆˆ = . Equations 10 and 12 show that

)()(),( 00 rNBrJArEz γγθ +=

Equation 13

because the current I is not zero and because the other terms in Equation 10 do not contribute tothe total current as given by Equation 12. Equations 6c and 6d give the transverse components ofthe fields:

)14(ˆ))()((

)14(ˆ))()((

11

11

barNBrJAkj

E

aarNBrJAj

B

rt

t

γγγ

γγγεµω

θ

+±−=

+−=

Equation 14

where âθ is the unit vector in the θ direction and âγ is the unit vector in the r direction.

To apply the boundary condition to Equation 11c, it is necessary to determine the surface current

sK

. Since it is assumed that the current I is flowing in the inner conductor, and similarly -I is

flowing in the outer conductor, the surface current density is defined as the limit of the productof the current density times the length of the transition region into the conductor [Stratton] (i.e.,the skin depth). In mathematical terms, the surface current density is expressed as

0)lim( →∞→= δδ andJasJKs

Applying this definition to a thin cylindrical shell between r = a and r = a – δ, the current isrelated to the current density by the equation

∫ ∫=−

π

δθ

2

0

a

aJrdrdI

Solving for J in terms of I,

100


)2

(2δδπ −

=a

IJ

Applying the definition for the surface current density gives

a

IKs π2

=

Now applying the boundary condition sKHn

=×ˆ and noting that the normal vector n points

radially outward at the inner conductor boundary and radially inward at the outer conductorboundary and also that the current in the outer conductor flows in the opposite direction of thecurrent in the inner conductor, then the boundary conditions now become

)15(2

))()((

)15(2

))()((

11

11

bb

IbNBbJA

j

aa

IaNBaJA

j

πγγ

γεω

πγγ

γεω

−=+

=+−

Equations 15

Applying the boundary conditions to Equation 11b ( 0),( =θaEz and 0),( =θbEz ) gives thefollowing equations:

)16(0)()(

)16(0)()(

00

00

bbNBbJA

aaNBaJA

=+=+

γγγγ

Equation 16

The task now is to determine the coefficients A and B satisfying Equations 15 and 16. Using theproperty of Bessel functions:

zzNzJzNzJ nnnn π

2)()()()( 11 =− ++

and applying Cramer’s rule to equations 15a and 16a gives the coefficients

)(4

)(4

0

2

0

2

aJj

IB

aNj

IA

γεωγ

γεωγ

=

−=

101


Equations 17

Repeating the above procedure for Equations 15b and 16b gives the same results except a isreplaced by b in Equations 17. To obtain a unique solution for the coefficients A and B forarbitrary a and b, it is necessary that γ → 0. Substituting the coefficients in Equations 15 and 16using the expressions for small arguments of Bessel functions:

)2

(1

)(

2)(

)2

ln(2

)(

1)(

1

1

0

0

xxN

xxJ

xxN

xJ

π

π

−→

→

→

→

the fields inside the dielectric become upon taking the limit as γ → 0

)18(ˆ2

)18(ˆ2

)18(0

)18(0

dar

IkE

car

IB

bE

aB

rt

t

z

z

εωπ

πµ

θ

±=

=

==

Equation 18

where ± sign gives the direction along the plus or minus z axis and the fields are zero inside theconductors.

Equations 18c can now be used to determine the induced emf in the pickup loop. The pickuploop circuit will be assumed to be a rectangular loop. For the ideal case, the electromagneticfields will be confined to the region between the conducting cylinders. The induced emf isdefined as the time rate of change of the magnetic flux, which opposes the original flux. Inmathematical terms this is given by

∫∫ •=Φ

Φ−=

S

dSnB

td

demf

ˆ

where Φ is the total magnetic flux.

The current can be separated into two traveling waves , )(),( )()(0

tzkjtzkj eReItzI ωω −−− += ,

where the first term represents the incident wave and the second term a reflected wave with areflection coefficient R. Substituting for B

from Equation 18c, the induced emf becomes

)]Re)(2

[ )()(0

2

1

tzkjb

a

tzkjz

z

eIr

drdzt

emf ωω

πµ

∂∂ −−− +∫∫−=

102


Equation 19

In the dielectric, since γ = 0 and σ = 0, then εµω=k . Using this relationship and letting

L = z2 – z1 and 2

210

zzz

+= (see Figure 109) and performing the indicated integration in

Equation 19, the induced emf can be written in the final form

)(),(

),()2

sin()ln(1

)(2)(2

0

0

tfz

jtfz

j

total

total

eReItzI

tzIL

a

bjemf

−−−+=

=

λπ

λπ

εµωπε

µ

Equation 20

For the case that the loop length is small with respect to the wavelength, then the approximation

λπεµωεµω LLL

=≈2

)2

sin(

Equation 21

can be used to obtain an approximation for the induced emf in Equation 16

),()ln( 0 tzIa

bLfjemf totalµ=

Equation 22

Equation 18 says that the induced emf is proportional to the frequency for high frequencies.

A.3 References

Jackson, John D., Classical Electrodynamics, John Wiley & Sons, Inc., New York (1962).

Stratton, Julius A., Electromagnetic Theory, McGraw Hill,Inc., New York (1941).

Abramowitz, Milton and Irene A. Stegun (editors), Handbook of Mathematical Functions, DoverPublications, Inc., New York (1970).

103


APPENDIX BDerivation of Voltage Pickup Probe Sensor

Recall the equation in Section 3.1.2.

2ln

22

πρ

αεπ

ν ε

−=

a

lfR

jV

=

[ ]2

22

ln

παεπ

ρ

lfR

ajvt

−

Eq. [B1]

= lfR

ajvt

αεπ

ρ

22

ln

−

The steradian is defined in a fashion similar to the radian except that it is the ratio of an area tothe square of the distance from the origin of the coordinate system to the surface. Of course,strictly speaking, it only applies to surfaces of a sphere but, just as in the case of the radian,usage is frequently stretched a bit. In particular, the solid angle Ω subtended by a cylinder oflength l and radius ρ is

ρπρπρ l

l2

/2 2 ==Ω Eq. [B2]

Therefore, the capacitance between two concentric cylinders per steradian of the outer cylinder is

( )( )al

a

l

c/ln2

/ln

2

ρερ

ρπρπε

=

=Ω Eq. [B3]

where ρ is the radius of the outer cylinder and a is the radius of the inner cylinder.

The solid angle Ωρ subtended by our pickup plate of radius β, which we assume is also at adistance ρ from the center of the coordinate system, is

2

2

ρπβ=Ω p Eq. [B4]

104


Then the capacitance between the inner cylinder and the pickup plate is

=

a

c p ρρ

επβ

ln

2

Eq. [B5]

Then, we add the factor 2 to reflect the “two-sided” nature of Cp and use

( ) ( ) ( ) ( )222

ln

22 επβπ

ρρ

πω Rf

a

jV

CRf

jV

RC

jVV

t

p

t

i

ts

−

=−

=−

= Eq. [B6]

The equation in Section 3.1.2 reduces to Eq. [B6] after some changes of variables. To make thesechanges, we note that the side of the inscribed square is l. Then

2

2β=l Eq. [B7]

and

2

2

ρβ

ρα == l

Eq. [B8]

Pulling this together, we get

ρββ

ρβα

22

2

2

2

2 ==l Eq. [B9]

Finally, we reduce the equation in Section 3.1.2.

2ln

22

πρ

αεπ

−=

a

lfR

jVV t

=

[ ]2

22

ln

παεπ

ρ

lR

ajVt

−

Eq. [B10]

= lfR

ajVt

αεπ

ρ

22

ln

−

= 22 22

ln

βεπ

ρρ

fR

ajVt

−

SEMATECH Technology Transfer2706 Montopolis Drive

Austin, TX 78741

http://www.sematech.orgfax: (512) 356-3081

e-mail: [email protected]

radio frequency (rf) measurement and control project report

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