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

International SEMATECH Technology Transfer 96063138C-ENG

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 service marks of their respective companies

© 1998 SEMATECH, Inc.

Radio Frequency (RF) Measurement and Control Project Report (TECQ001) Technology Transfer # 96063138C-ENG International SEMATECH

September 10, 1998 Abstract:

This document is a revision of 96063138B-ENG. It describes the technical achievements of the Plasma Etch Technology Radio Frequency (RF) Power Measurement and Control Project (TECQ001), which spanned two years from mid-1994 to mid-1996. The document details the conception, design, development, and prototyping of an advanced concept RF power delivery system, which incorporates new technologies. Background information, detailed circuitry and component designs, and mathematical examinations are included. Additional reduction-to-practice assembly and circuit tuning information can be obtained by contacting the SEMATECH project manager or the SEMATECH Calibration Laboratory. Revision C changes the classification of the document from SEMATECH Confidential Restricted to SEMATECH Non-Confidential and includes a Foreword describing the technical developments for which SEMATECH has applied for patents.

Keywords:

Equipment Performance, RF Sensors, Plasma Etching, Etching Equipment, Electrical Measurement

Authors:

Tony Moore (SEMATECH/ORNL); Gil Yetter (SEMATECH); Travis Spratlin (ORNL); Charlie Nowlin (ORNL)

Approvals:

Gil Yetter, Author/Project Manager Ray Delk, Director, Internal Technical Support Jeanne Cranford, Technical Information Transfer Team Leader

iii Table of Contents 1 2

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

Technology Transfer #96063138C-ENG

International SEMATECH

iv 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

International SEMATECH

Technology Transfer # 96063138C-ENG

v 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

Technology Transfer #96063138C-ENG

International SEMATECH

vi 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

International SEMATECH

Technology Transfer # 96063138C-ENG

vii 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

Technology Transfer #96063138C-ENG

International SEMATECH

viii Acknowledgements Funds were made available from the Internal Technical Support (ITS) and Etch Divisions for additional test equipment and prototyping efforts, which greatly helped the success of the project. The manpower issue was never really resolved, mostly because talented RF engineers are rare within the semiconductor industry. We utilized a variety of fabrication companies to assist us where possible, borrowed folks from other SEMATECH departments and even had the services of a retired ORNL employee who loves technical puzzles. The team changed its make up from time to time, while the core team remained largely the same. Many long nights and weekends were contributed by everyone, because we believed in the objectives at hand. In order to stay focused, we often could not respond to unexpected management requests such as variations of project-related gantt charts and rewordings of the initial plan or status reports. We often used a hide-out office area located over the SEMATECH clean room between air handlers and often resorted to staying at home to be able to focus on serious design problems. From timeto-time, emails, phone calls, and pagers had to be left in the accumulate mode. Even worse were the 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 the requests from observers. Norm Williams of the Plasma Etch Diagnostics department was the primary technical driver of this area of investigation and was responsible for developing the scope of this project. Dick Anderson, who previously worked with Norm at SEMATECH, had returned to ORNL where he located Tony Moore and also provided a strong influence during contract negotiations and the establishment of the Cooperative Research and Development Agreement (CRADA) under which the project was conducted. Tom Shannon, in the SEMATECH Contracts department, provided guidance and many long hours of effort to formalize the final contract and memorandums between SEMATECH, ORNL, Martin Marietta Energy Systems (later to become Lockheed Martin 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 he accomplished his goals. Tony has the capability of driving right to the crux of a problem, while shedding all of the superfluous baggage. Tony’s unique technical insight allows him to envision solutions and inventions that solve problems and also survive the all too critical peer review process while withstanding the test of time. He pursued his vision with tenacity while being constantly mindful of contract deadlines and the fact that he represented the Instrumentation and Controls Division back at ORNL as the first ambassador to SEMATECH. He left a lasting and positive impression on everyone with whom he interacted—the technical staff of SEMATECH, SEMATECH member companies, and the plasma etch system supplier SEMI/SEMATECH member companies. Our thanks to Tony and we wish him well upon his return to the ORNL technical staff in the Instrumentation and Controls division.

International SEMATECH

Technology Transfer # 96063138C-ENG

ix Tony coordinated a shadow team of staff members back at ORNL, keeping them busy working on many of the technical aspects of the devices that were developed. Dennis Sparks was perhaps the most valuable member in terms of total time spent on the project. Dennis is also the identified co-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 “Professor Emeritus” at ORNL, contributed thoughtful analysis on the mathematical model of the voltage pickup portion of the sensor. Travis Spratlin conducted extensive modeling on the current pickup portion of the sensor. Phil Ryan contributed modeling expertise from another vision of the concepts. Bill Holmes spent many a day with us in Austin helping us turn circuit diagrams drawn on the back of napkins into printed circuit boards, while training the Cal Lab technicians in how to “do it themselves” in the process. Dan Hoffman and John Caughman contributed towards the testing of functional prototypes and the initial work on a contingency plan to pursue high-speed actuation of a vacuum variable capacitor design. During Tony Moore’s assignment at SEMATECH, he was part of the Calibration Laboratory staff working closely with Gil Yetter, the Section Leader. Gil was instrumental in the management of this project from the conception stage—working with Norm Williams—all the way through the end of the project. Gil relieved Tony of all of the management and logistical functions to allow Tony to maintain a constant technical focus in order to stay on schedule. The Cal-Lab technicians (Trace Beck, Craig Lopp, and Tim Folliet) provided Tony with fabrication and test assistance throughout virtually every phase of the project. Cal-Lab part time student interns (Scott Bushman and Scott Sparks) assisted Tony with a variety of services ranging from custom software needs for bench test purposes to conducting experiments on a plasma reactor at the University of Texas in Austin. The project would not have been possible without the direct help of Norm Willliams and the Etch Division directors, Ken Maxwell and John Martin. Ray Delk, director of the ITS department, assisted the project team when possible to keep it on track and to provide additional resources where needed. It must be stated that, in every aspect, this project was conducted as if it were part of the Etch department and its staff, even though it resided in the Calibration Laboratory, which is a support organization. The Plasma Etch FTAB monitored and ranked the project quarterly. The computer architecture team was led by Bob Flegal at SEMATECH and by Steve Hicks from ORNL. Kathy Lewis and Abel Mireles of SEMATECH assisted Bob Flegal, while Ganesh Rao assisted Steve Hicks back at ORNL, programming with a duplicate system. Steve visited SEMATECH often, staying for extended periods, to perform operational tests that complimented the routine FTPing of software modules back and forth to SEMATECH from ORNL, working with Kathy Lewis. Ganesh worked some very long hours (often late into the nights) as the last technical milestone approached when all the systems’ pieces were being integrated. His drive and 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, even though we later abandoned the equipment set on which he specialized. Members of the SEMATECH Plasma Etch Diagnostics department, Victoria Resta and Dave Rasmussen, 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 analysis on a prototype RF Sensor. His contributions were very valuable because they helped to monitor our progress from another perspective. Technology Transfer #96063138C-ENG

International SEMATECH

x Karen Blair, the administrative support for the Cal Lab, provided a wide range of services that started with the project proposal all the way to this document. Sandra Strickland provided significant assistance in preparing this documentation, working with the team members. Mike Pendley, who recently joined the SEMATECH Cal Lab as an RF engineer, has assisted greatly in this 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 objectives than was ever expected to be required at the onset. A true team commitment to quality and meticulous scientific rigor was ingrained into the fabric of the team by the technical leadership of Tony Moore. All of the team members agree that the constant developments of demonstratable working prototypes provided the tangible image needed to “rally around” and also pulled us through difficult times as deadlines approached. We could see our progress unfold, which made us 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, On Time, On Target, and Together. _______________________________________________________________ I want to personally thank everyone who worked on this project. Gil Yetter Project Manager/Section Leader SEMATECH Calibration Laboratory

International SEMATECH

Technology Transfer # 96063138C-ENG

xi Foreword During the course of this RF technology project conducted at SEMATECH from 1994 to 1996 entitled “TECQ001, RF Power Measurement and Control Project,” intellectual property was developed that resulted in applications for US patents. The following RF components were developed: − 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 integrated Fast/Accurate RF power delivery system Because of the intellectual property concerns associated with patent applications, the SEMATECH Technology Transfer document was released initially as a SEMATECH Restricted Confidential document issued by name and serial number. The document was distributed to the SEMATECH Radio Frequency Advisory Group (RFAG) member company staff members, and to the RFAG SEMI/SEMATECH suppliers who had signed a specific intellectual property nondisclosure agreement for the document. Revision C of the document changes the classification to SEMATECH Confidential. The document covers all aspects of the project, including the technical developments for which SEMATECH has applied for patents, and others for which SEMATECH has not applied for patents. Specifically, SEMATECH is pursuing patents on the RF sensor itself, but not on the associated signal detection or filtering electronics. Similarly, SEMATECH has patented the saturable reactor, but not the match topology or computer architecture that was developed to demonstrate it. The RF sensor prototypes are quantitative in nature and were limited in scope to achieve the goals of the project. It should be noted that the sensor design is scaleable to impedance and signal coupling ratio requirements. The saturable reactor variable inductor offers a “no moving parts” RF tuning technique at 13.56 Mhz and can also be scaled to accommodate a number of system requirements. The unpatented associated electronics that were developed offer several significant advances in the RF sensor signal phase handling and detection areas. The integrated system incorporating the matcher topology, developed to demonstrate the saturable reactor technology, 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 these suppliers may, in turn, be able to assist you if needed. The integrated prototype RF system demonstrated a fast and accurate RF measurement and power 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 the order of about 5 to 7 milliseconds. In order to collect realistic performance data, a “linear plasma Technology Transfer #96063138C-ENG

International SEMATECH

xii 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 stepchanged rapidly between an impedance change from 4 ohms real (–j15 ohms imaginary) to 4 ohms real (–j25 ohms imaginary) and back. These technology advances and others have been developed through a collaborative relationship with the RF engineering staff members at Oak Ridge National Laboratory and at SEMATECH to assist and facilitate improvements in the semiconductor supplier base. Currently, Oak Ridge can provide engineering assistance to suppliers desiring to implement a wide range of RF design enhancements. For instance, one way the Oak Ridge staff can provide assistance is through the RF sub-system testing facility at Oak Ridge, which provides a means of exercising designs against realistic challenges. Another way is by extended visits to your facilities by Oak Ridge RF technologists to address your RF issues and to assist you in acquiring the resources that meet your needs.

International SEMATECH

Technology Transfer # 96063138C-ENG

1 1

EXECUTIVE SUMMARY

An advanced concept RF power delivery system was conceived, designed, developed, and reduced to a functional working and demonstrable prototype. The RF power system incorporates two 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 practices is a significant achievement. The other device is a unique electronically variable RF inductor that obtains RF-matching network speeds in a few milliseconds. The device is based on a novel advancement of saturable reactor technology; it too is undergoing the patent process. The performance of the completed RF power delivery system achieved RF matching network speeds on the order of 5 to 7 ms and held power levels, delivered into a plasma simulating load, to within less than a watt of RF power variation, while being subjected to a dynamically varying step response load change. As a result of this project, other projects in related RF technologies are now in progress between ORNL and the Etch division of the SEMATECH Interconnect department. The invention of the analytical RF sensor has inspired technical staff members at the National Institute of Standards and Technology (NIST) to request detailed information and the loan of a prototype for investigating the possibility for its use as a new national standard. A plan to address a number of requests for access to these technological achievements is being developed for review at the Plasma Etch FTAB (at their request) and may be realized as some form of follow-on work to this project. 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 corrected the “W” symbol (used in two of the tables) to an “Ω” symbol. Revision C changes the classification of the document from SEMATECH Confidential Restricted to SEMATECH Non-Confidential and includes a Foreword describing the technical developments for which SEMATECH has applied for patents. 2

INTRODUCTION

This document serves as the complete documentation of the Radio Frequency (RF) Power Measurement and Control Project (TECQ-001). The project was conducted in the SEMATECH Calibration Laboratory (in the Internal Technical Support division) in close collaboration with the Plasma Etch Diagnostics department (in the Interconnect division). The principal supplier for this project was the Instrumentation and Controls Division of Oak Ridge National Laboratory (ORNL) in Oak Ridge, Tennessee. A technical staff member was assigned to SEMATECH for the two-calendar-year duration of the project (mid-1994 through mid-1996) and was the first-ever national laboratory assignee to SEMATECH. Many other members of the technical staff at ORNL interfaced with this project through the on-site assignee at SEMATECH, which greatly contributed to the project’s successful completion. This document provides a relatively complete set of engineering-level documentation for all aspects of the project. Detailed blueprints and reduction-to-practice assembly and circuit tuning information will be contained in a future document. Periodic progress reports presented to the SEMATECH Radio Frequency Advisory Group and the Plasma Etch Focus Technical Advisory Board (FTAB) received favorable criticism throughout this project; however, this is the first Technology Transfer #96063138C-ENG

International SEMATECH

2 formally published documentation. This document includes background information, detailed circuitry and component designs, thorough mathematical examinations, and graphic illustrations and photographs. The initial premise for the negotiations with the technical staff in the Instrumentation and Control Division at ORNL was to advance the state-of-the-art in RF power delivery and measurements as applied to semiconductor wafer plasma etchers. It is widely accepted that ORNL is a leader in instrumentation technologies and the reduction to practice applications of a wide variety of advanced engineering disciplines. We believed that the chances of success for this project would be greatly enhanced by leveraging the national laboratory resources. Actual contract relations and resources were funded under the SEMATECH/Sandia National Laboratories Cooperative Research and Development Agreement (CRADA) and were accounted for like the other projects managed and conducted at Sandia, although Sandia’s involvement was minimal. 2.1

Logistical Approach

Previous efforts by two team members at SEMATECH (Norm Williams and Jim Spain) yielded an approach for better understanding the boundaries of quantitative RF metrology as applied to plasma wafer processing. Norm’s work produced two U.S. patents based on a calibrated RF sensor supported by expensive and physically large laboratory grade instruments. The patents are identified 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 each patent has the same title, the earlier patent focuses on the sensor design, while the later patent focuses on data interpretation correlated to plasma energetics. It was obvious that the technology would need further development if there was to be any hope that the measurement techniques could be “realized” in the commercial world. Initial discussion with ORNL focused on the development of a miniature version of the Hewlett Packard (HP) Vector Voltmeter, commonly known as a signal detector or phase and magnitude detector. The physical size of the HP instrument was considered one of the important issues to resolve. The harmonic filter portion of the signal processing equipment was quickly identified as a potential show stopper if the 1% accuracy goal was to be achieved. Discussions regarding the RF sensor calibration practices applied to prior sensor development work directed team efforts toward developing an inherently accurate RF sensor based on first principles. The team believed that an analytical sensor based on first principles should ensure that the 1% accuracy goal be met with certainty. However, the new sensor would also provide a way to minimize conjecture over any data collected from the RF engineers within the semiconductor community. Having arrived at a consolidated plan to develop and integrate the various components of an RF metrology system, it was noted that a superior measurement instrument will tell the user only how bad things are, so the team pursued an additional aggressive goal for a high-speed (no moving parts) RF matching network. The benefits of using a high-speed RF matching network operating in the millisecond tuning range that would be integrated with the proposed highly accurate RF sensor were numerous. These benefits included a highly accurate, high-speed integrated RF power delivery system that would help to reduce chamber-to-chamber matching issues, process variability from wafer-to-wafer and from lot-to-lot, and increase wafer throughput. Because of the complex and aggressive nature of this project (to develop technologies to solve significant problems in the plasma etch wafer processing RF power delivery area), the team pursued parallel engineering designs as contingencies to ensure the success of the project. International SEMATECH

Technology Transfer # 96063138C-ENG

3 The RF sensor design described in this document is the first-principles approach, while the other contingency sensor design is similar in construction, but requires calibration. Both sensor designs were successfully realized in working prototypes (Figure 1). The calibrated RF sensor design and its variants are being developed into a patent position by ORNL in the Fusion Energy department. Future documentation will describe the other sensor design and also many of the lesser 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. The harmonic filter design that evolved met all the expectations of the contract and passed peer review. This device is not patentable and represents an engineering design optimized for phase relationship stability between two signal paths, one for the sampled RF current signal and the other for the sampled RF voltage signal. The development of an RF signal processing device that could meet the laboratory grade performance of the HP Vector Voltmeter was challenging and required the development of two different solutions, each of which works very well. The main intent of the engineering effort for the signal processors was to reduce to practice a highly accurate, physically small and low cost alternative to the laboratory instruments, dedicated to the operating frequency range of interest to plasma etch at 13.56 MHz. RF signal processing devices commonly used in the semiconductor industry are often identified as phase/mag units. The name stands for the measurement of the phase differential between two RF signals and the magnitude of each. The team developed a highly accurate phase/mag detector circuit that we named PD4, which stands for phase detector version 4. The other device we developed was adapted from the communications industry and is commonly known as an in-phase/quadrature phase detector, from which came the name I-Q detector. Neither of these circuits was viewed to be patentable technology since each represents refinements and application specific optimization. It should be noted that the use of an I-Q detector circuit, which is common in communications applications, is a novel idea in the semiconductor industry and in precision RF power metrology. Both detector circuits provide DC voltage output signals that are proportional to RF parameters entered into a computer with an A Technology Transfer #96063138C-ENG

International SEMATECH

4 to D interface. The algorithms used to reduce the measured parameters into engineering units for diagnostic observation or control use are fairly straightforward mathematical implementations. The significant difference between each approach is that the PD4 device has high-volume production parts and should be cheaper to construct. However, it requires more signal strength and 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 same engineering 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 envisioned time frame, necessitated the pursuit of two approaches because of the risk of failure. Because of early successes with a low-power prototype, efforts to develop a fast actuator for a vacuum variable capacitor were abandoned. The development of the electronically variable inductor was the main goal of the RF matching network portion of the project, while the “fast” RF matching network, designed to meet the objectives of this project, is only one possible design implementation 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 be able to incorporate the generator inside the RF match network and completely eliminate the 50 Ω cable environment. This concept seemed too radical for many of our peers in light of traditional practices. Although we successfully operated the generator in a low-impedance mode, we converted it to the 50 Ω output mode so that demonstrations of the entire power delivery system could be reviewed as a modular set of items that could be used independently. This proved to be a good decision since some members of the SEMATECH community expressed interest in either the measurement or the matcher portions of the project, but not necessarily the entire integrated system. Patent applications have been prepared for the analytical RF power sensor and the saturable reactor used in the “fast” RF match network. Possible patent positions on some of the supporting electronics were not investigated. 2.2

Technical Overview

The invention of the analytical RF sensor based on first-principles behavior is a significant breakthrough, because it provides a metrology capability free from conventional calibration practices. Rarely does a measurement technique offer the possibility of being both a national standard and a common component in field use. The sensor is a voltage and current sampling device that incorporates a unique current pickup coil that couples 100% of the RF magnetic flux field. 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 at 13.56 MHz. The sensor exhibits a wide operational bandwidth from 1 MHz to nearly 1 GHz with a linear 20 dB/decade frequency response. While it is true that the intended frequency domain is 13.56 MHz, the broadband response demonstrates the design intended to minimize undesirable parasitic effects. Developing a sensor that exhibits the least perturbation to a given application was perhaps the most challenging technical problem to engineer into the sensor design. While the sensor is certainly invasive because of its fixed physical form, we focused on minimizing the degree to which it is obtrusive. The sensor has been fabricated for the 50 Ω RF transmission-line environment and exhibits electrical characteristics equivalent to a 3-inch length of common RF power cable. Time domain reflectometry (TDR) measurements and voltage standing wave ratio International SEMATECH

Technology Transfer # 96063138C-ENG

5 (VSWR) datasets support this achievement. It must be stated that the use of a sensor designed for 50 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 a compromise. The sensor can be scaled to other impedance values to better optimize application requirements; however, project time limits did not permit such investigation. For the purpose of this project, the overall load effects of the 50 Ω impedance design to the RF match network were expected to be < 1–2%. In fact, the completed power delivery system dealt with any installation effects by controlling delivered power to the plasma-simulating load. This technological achievement has inspired members of the technical staff at NIST to request detailed technical information and the loan of a prototype for studies that might lead to the adoption of the design as a national standard. Mechanical design attributes have been demonstrated to be robust and commercially viable. The analytical RF sensor (Figure 2) required the development of some novel electronics signal processing circuits that perform to laboratory grade performance. The special RF harmonic filter and the two different RF signal detection devices were designed to provide an integrated approach that was small in form and tailored to 13.56 MHz plasma etch applications. Two designs were pursued as contingencies, resulting in both techniques working quite well. Each RF detector design, as well as the RF harmonic filter, was fabricated with commercial viability in mind in terms of size, complexity, and cost.

Figure 2

Completely Assembled RF Sensor with a Clear Housing

Technology Transfer #96063138C-ENG

International SEMATECH

6 A dual-channel harmonic filter was developed to remove unwanted harmonic energy from the RF signal being measured. The intent of the design was to develop clean sinusoids of the fundamental frequency of interest at 13.56 MHz and preserve the phase relationship between the RF power sampled voltage and current waveforms from the analytical sensor outputs. Prior art in use optimized other performance attributes such as a high Q passband and neglected phase stability. Thermal effects on harmonic filter performance can cause differential phase relationship shifts of many degrees of phase angle, resulting in large effects on computed RF power. This effort to develop an improved filter technique was necessary because of the high differential phase angles (85° to 89°) between the current and voltage waveforms that are encountered in post-RF match network locations where small phase changes represent large effects in calculated RF power. Also, post-match locations as well as cleanroom service area ambient conditions, present unwanted thermal problems. The dual path RF harmonic filter developed in this project provides good filtering and phase stability over a wide temperature range. The invention of the electronically variable inductor known as a saturable reactor that operates at 13.56 MHz has raised the status quo from prior art that was limited to an order of magnitude lower operating frequency at 1.8 and 2.0 MHz in RF matching network applications. The crux of the invention is the novel approach to minimize the undesirable electrical coupling between the RF coils and DC control current field coils by a unique winding pattern applied to a pair of toroidal ferrite cores. The reason for this unique approach was conceived because either an electronically variable capacitor or a variable inductor was needed for this application. Electronically variable capacitors 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 core material permeability of an inductor electronically. Conventional transformer configurations were undesirable because the primary and secondary winding are normally ratio coupled. We needed a transformer-like device in which the control windings are not coupled to the active RF winding. This desired and unusual mode of required operation caused our device to not operate like a transformer. The fundamental idea of using a variable magnetic field to control the permeability of an inductor core material is well known in the municipal AC power utility industry in the form of a saturable reactor; however, the operating frequency limitations render them unusable above a few hundred hertz. The next closest design solution was developed at Applied Materials using saturable reactor technology that operates at 1.8 to 2.0 MHz with a ferrite bar core material. The solution to our problem came after a series of design attempts that led to a novel combination of two toroidal transformer cores with the RF windings cross wound or interleave wound and folded over onto a single axis for adding the DC control windings. Each set of windings decouples or prevents coupling between each opposed winding turn by turn. This is the electrical property that prevents interwinding capacitance from spoiling the high frequency response and allows construction of a saturable reactor that operates at 13.56 MHz. Each of the windings is orthogonal to each other. The DC control current windings provide the magnetic field to change the permeability of the toroid core material independent of the RF power conducting inductive windings, 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 set of orthogonal windings to monitor temperature effects and compensate for them. A set of initial studies was conducted, but not completed because of project time limitations and because the International SEMATECH

Technology Transfer # 96063138C-ENG

7 final system design worked well without a temperature compensation circuit. Because the project contract goal was to achieve a high-speed RF matching network capability, refinements for aspects such as efficiency and thermal energy losses were not optimized. Unlike other saturable reactor approaches, the thermal losses that result in this saturable reactor design primarily originate in the DC current windings used to shift the permeability and not in the RF inductance coil windings. The saturable reactor has been incorporated into a functional RF matching network that was tested at 1000 W and above for extended periods into a plasma simulating linear load of 4-j20 Ω. To perform laboratory bench tests of the various components and the complete RF power delivery system, a special test load was fabricated to simulate the linear portion of a plasma load. The simulator is comprised of non-inductive sintered high-power resistors and a vacuum variable capacitor. The addition of a solenoid actuated vacuum switch and a small ceramic capacitor provided a means to shift the load conditions through a reasonably large range of reactance, thereby providing a wide set of operating conditions for the RF power delivery system to perform against as a stress test. Designs for additional circuitry to supply a mechanism to generate the non-linear aspects of a plasma into the simulator load and concepts to use the simulator in a calorimetry mode are being pursued. Tests conducted with load step changes from 4-j24 Ω to 4-j14 Ω, which represents a significant operating space to stress the match network design, demonstrated a tuning speed on the order of 5 to 7 ms. Combined with RF generator power control, the delivered power to the plasma simulating load was held constant to within ± 1 W of setpoint at both load conditions presented at each excursion of the step change. To achieve the integrated system performance that has yielded these RF tuning speeds and stable power delivery levels, a novel computer architecture approach had to be employed. A dualprocessor DOS architecture was developed based on a unique modular interface code strategy developed by SEMATECH’s MSD/FI department and implemented by a team of SEMATECH and ORNL computer specialists. The strategy solved the essential problem of determining how to have one processor operating the analog input and output duties based on a control algorithm and not be hampered by overhead duties associated with data handling and user interfaces. This strategy has proven to be robust and is portable to other computer architecture environments where 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 SEMATECH and SEMI/SEMATECH engineering community to learn more about this technology by using beta site evaluations. Plans to address these requests are being prepared for review in appropriate forums at SEMATECH. Due in part to the early success of this project, a number of other contracted interactions with ORNL have been spawned in the plasma etch RF area with the Fusion Energy division. The technical capabilities within the ORNL Fusion area are very impressive because they provide worldwide RF engineering resources in the design of RF power delivery systems with ranges as high as 32,000,000 W of RF power, at the same frequency range as our industry commonly uses in plasma etch systems. The simplest way to highlight the importance of their methodologies is to say that a portion of a percent error at their power levels can destroy a lot of expensive equipment, not to mention the loss of an experiment. It is believed that the RF engineering Technology Transfer #96063138C-ENG

International SEMATECH

8 infrastructure in the semiconductor industry will benefit from the many interactions that are now beginning with this largely untapped national resource. The SEMATECH Radio Frequency Advisory Group (RFAG) forum has been a significant force in bringing together many of the fragmented group of RF reseachers within the semiconductor industry and is beginning to develop a strategic long-range focus. To date the RFAG has developed ideas for a consumer reports-type of RF component testing laboratory and for standardized testing procedures. This concept was presented at the SEMATECH Etch FTAB meeting and was ranked highly. As a result, a project at ORNL Fusion is underway to address those goals. Future RFAG meetings may serve the industry well as we move toward larger wafer sizes 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 SEMATECH and were based on industry experience with existing RF sensors and with sensors developed and tested at SEMATECH. The RF sensor development had three major goals. First, the sensor should be designed as a metrology standard rather than a calibrated device. Second, the sensor design must be highly unobtrusive so that the device can be easily incorporated into a variety of semiconductor manufacturing tools. Finally, the sensor must provide a sufficiently accurate set of RF electrical parameter measurements that would support feedback control for RF power generators as well as provide data for process diagnostics. This data could then be used for minimizing 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 its response characteristics defined by first principles. Properties that are calculated from elemental physical characteristics such as the zero state transition of Cesium, which is used as a time standard, is a good example of first-principle standards. This is the preferred method metrologists seek to use when developing a reference standard. The implication of this approach is non-trivial, and it placed constraints on our sensor’s geometry and construction (Figure 3). In the design of RF sensors, the preferred method of measuring the RF current component in an RF power conductor is to measure the magnetic field that surrounds the conductor. This requires that a coil be inserted in this field and the voltage generated is a function of the current in the conductor. Likewise, to measure the RF voltage present on an RF power conductor, it is necessary to place a probe on or near the conductor. Typically, these probes take one of two forms, a resistive or a capacitive probe. A capacitive probe was chosen for this project. These choices require adherence to physical equivalencies and symmetry so that the equations used to define that sensor can be solved in closed form. Careful consideration of the configuration of the various components is also required to ensure that the stray circuit parameters are minimized to the point that they are negligible, or are incorporated within the design to preclude any unpredicted responses. The approach taken was to minimize stray RF fields by constructing the voltage and current pickups using transmission line design practices where possible, so that the impedance of them is known and controlled. The design approach also allows for the sensing elements to be small and rigidly constrained so that the geometry and hence, the signal response, is stable.

International SEMATECH

Technology Transfer # 96063138C-ENG

9 3.1

Analytical RF Sensor Based on First Principles

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

Figure 3

Technology Transfer #96063138C-ENG

RF Sensor Components

International SEMATECH

10

Figure 4

RF Sensor Components With the Current Loop Inside the Hollow Center RF Power Conductor

The pickup coil has been designed to a 50 Ω device and thereby does not require special signal impedance matching circuitry. The induced 90° shift in the sampled magnetic field is complemented by the unique voltage pickup probe (Figure 5) that is also a 50 Ω device. The nature of the voltage pickup probe shifts the voltage signal by 90° and in combination with the current coil signal shift, the overall sampled signals have the same characteristic relationship as the main power RF transmission line being sampled. Figure 6 is an illustration of a complete sensor. Figure 7 is an illustration revealing the inner components of a sensor with 1/4-20 bolt connection end pieces. Figure 8 through Figure 15 provide sequential assembly steps for an RF sensor, concluding in an exploded view of all components (Figure 16).

International SEMATECH

Technology Transfer # 96063138C-ENG

11

Figure 5

Cross Section of RF Sensor to Show Current Pickup Loop and Voltage Pickup Probe Placement

Technology Transfer #96063138C-ENG

International SEMATECH

12

Figure 6

Figure 7 International SEMATECH

RF Sensor with N-Type Connectors

Sensor Assembly with 1/4-20 Bolt Connections Technology Transfer # 96063138C-ENG

13

Figure 8

Hollow Center Conductor Positioned in Sensor Body

Figure 9

Voltage Pickup Assembly Positioned in Sensor Body

Technology Transfer #96063138C-ENG

International SEMATECH

14

Figure 10

Figure 11

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

Sensor Assembly with Teflon Center Conductor Positioning End Pieces

International SEMATECH

Technology Transfer # 96063138C-ENG

15

Figure 12

Figure 13

Sensor Assembly with Metal End Plates Installed

Sensor Assembly with N-Type Connectors Installed

Technology Transfer #96063138C-ENG

International SEMATECH

16

Figure 14

Sensor Assembly with Screws Installed

Figure 15

International SEMATECH

Assembled RF Sensor

Technology Transfer # 96063138C-ENG

17

Figure 16 3.1.1

Exploded View of RF Sensor

Current Signal Sampling Component of RF Sensor

For the design criteria of the current sensor portion of the device, a current pickup loop must be of a known size and fundamental in response. Secondary effects of stray capacitance and inductance must be minimized and quantified. This must be done to allow the application of first principles to the design. Faraday’s law says that th electromotive force (EMF) (voltage) induced in a conducting loop is the negative of the time derivative of the magnetic flux enclosed by the loop. In theory, it follows that 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. This approach is typically used at low frequencies by employing an iron core to capture the flux and routing it through a sense winding having multiple turns so the flux is linked enough times to provide a usable voltage. This same approach has also been used in RF current sensors using ferrite toroids; however, core losses and non-linearities, as well as high winding inductance and distributed capacitance, obfuscates a direct first principle link to the current being sensed. The presence of a core also adds inductance to the conductor carrying the current making the sensor obtrusive. The industry has experienced occasional difficulties with some of these toroidal current transformers catching fire because of the losses that occur in the core when exited by large RF currents. Departure from the first-principle concept introduces errors that cause each sensor to require calibration. Previous sensor designs followed traditional design concepts commonly used in the communications industry. These designs, once calibrated for a specific application, were adequate for the measurement of power from a generator to a relatively wellmatched load. To that end, these sensors have found some use in this industry to measure the power from the generator to the RF matching networks. Accurately measuring the power

Technology Transfer #96063138C-ENG

International SEMATECH

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 remain true to the concept of first principles? The answer comes from a judicious application of Amperes Law, which states that the integral of the magnetic flux density around a closed path is equal to µ o times the net current across the area enclosed by the path. This means that in a coaxial transmission line, where the currents on the inner and outer conductors are equal and opposite, 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 inner conductor were hollow, then the flux inside the hollow center of the inner conductor would be zero 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 the dielectric through the inner conductor and back out again, one could link all the flux over a precisely known area (Figure 19) associated with the current in the coax, and the loop voltage can be analytically determined from fundamental laws.

Figure 18 International SEMATECH

Magnetic Flux Linked Area Technology Transfer # 96063138C-ENG

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): dB =

Figure 20

µ o Idl × ds 4π S2

Magnetic Flux Illustration of Fundamental Laws

Technology Transfer #96063138C-ENG

International SEMATECH

20 Recall that the vector cross product is the product of the length of the two vectors times the sine µ I sin (θ )dl of the subtended angle in the direction normal to their plane (right hand rule) dB = o . 4π S2 B, therefore, would equal the integral of dB along l from l=-∞ to +∞. Evaluation of this integral becomes much more convenient if the expression is rewritten in terms of r and θ. From the r −r r and l= differentiating l with respect to θ gives dl = 2 substituting diagram S= sin θ tan θ sin θ into the above equation and integrating gives B=

(sin θ )

µo ∫ 4π o Iπ

r

r sin 2 θ dθ 2

sin 2 θ

B=

π µo I π µo I  ∫ sin θ dθ = − cos θ  4πr o 4πr  o

So, B=

µo I 2πr

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

Φ =∫ Bn dA= ∫ ∫

a o

Φ=

µo I drdl 2πr

µ o I b dr  L  ∫ l  2π a r  o 

b µ o IL ln  µ IL a Φ = o ln r ba = 2π 2π

[

Figure 21 International SEMATECH

]

Linked Magnetic Flux Geometric Area Technology Transfer # 96063138C-ENG

21 Now applying Faraday’s Law b − µ o L ln  −d  a  dI emf = Φ= dt 2π dt

Now for I = I o cos(ωt ) , where ω is the radian frequency = 2πf , b − µ o L ln Ι o  a  [− ω sin(ωt )] = Ι µ L ln b f sin(ωt ) emf = o o 2π a

which in phasor form is b jµ o f ln LΙ o . a

However, this is not simple to implement. The above analysis ignores the fact that the pickup loop would also be subject to capacitive coupling to the inner conductor, which would corrupt the current signal as soon as the inductance of the pickup loop becomes non-zero. This problem is handled by using a coaxial pickup loop so that the outer conductor of the pickup loop is grounded to the outer conductor of the power carrying coax at both ends. A small cut in the pickup loop’s shield allows it to act as a Faraday shield, effectively keeping the electric field from reaching the center conductor of the pickup loop while allowing the magnetic field, which is only proportional to the current, to be completely linked. The split in the pickup coax’s outer conductor prevents the flow of inductively driven current in the shield so that the magnetic flux is not excluded from the center conductor of the loop. Experimentally, we determined that the small cut in the pickup loop shield must be in the exact center of the loop and both external ends must be terminated in the loop coax’s characteristic impedance, or the propagation delay of the sensed 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 it results in a measurement error, which is dependent on the standing wave ratio (SWR) on the line and would depart from our goal of a design based on first principles (Figure 22). So, the loop shield must be cut in the exact center and the cut should be as narrow as possible, no more that 1 mm wide. This also implies that the ends must be well terminated in a 50 Ω resistance and the leads 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 a series voltage source in the middle. The current probe is assembled using a set of fabrication jigs so that the precise dimensions required for the loop are maintained. Modeling of the current probe electrical performance based on the mechanical measurements shows < 0.2 dB error from the measured data. Test data collected from the small set of prototypes that we have had fabricated demonstrated that the mechanical design is robust. Signal sampling levels from sensor to sensor matched to approximately within ± 0.1 dB. Also, routine disassembly and reassembly demonstrated no shift on signal sampling levels.

Technology Transfer #96063138C-ENG

International SEMATECH

22

Figure 22

Network Analyzer Plot of Magnetic Field Signal Coupling Response

Figure 23

Schematic Representation of Current Pickup Loop

b jµ o fL ln  I o  a  and finally the Taking into account the external loading to terminal voltage, VT = 2 − j 2VT current I o = . b µ o fL ln  a

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 small holes. There was no measurable difference between the slit for the loop and the penetration at two distinct points. This also allows a Teflon sheath to be fabricated, which encloses the loop and prevents voltage breakdown between the loop shield, which is at ground potential, and the center conductor, which may be at a very high potential. This also allows the loop to be mounted on a printed board, allowing very repeatable construction and accurate termination as well as making the loop removable and the sensor much easier to assemble and disassemble. International SEMATECH

Technology Transfer # 96063138C-ENG

23 The use of carefully configured coupled transmission lines, which is necessary to produce an RF sensor 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 coaxial transmission line would be. Because of the effects of the current pickup loop and the voltage pickup capacitor and their associated mounting structures, the diameter of the center conductor near 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 parasitic impedances associated with them, as well as voltage and power limits. Smaller components have less parasitic impedance, but also have lower power and voltage limitations. Since the current sensor actually senses the derivative of the current, it is desirable to have a differentiating voltage sensor as well so that phase corrections after the sensor can be avoided (Figure 25). This configuration also avoids the need for a high impedance amplifier to avoid introducing signal errors from loading effects. The voltage sensing arrangement then became a C-R differentiator circuit (Figure 24) where Vs is the voltage being sensed and Vt =

Figure 24

Vs R jωRC =Vs . i 1+ jωRC R+ jωc

Schematic Illustration of Voltage Sensor

Technology Transfer #96063138C-ENG

International SEMATECH

24

Figure 25

Network Analyzer Plot of Voltage Pickup Symmetry by Superimposing Forward and Reverse Repsonse Data

Now, if 1/ωc is much larger than R, then Vt ≈ jωRCVs , which is the same form as the current signal and the phase shift is taken care of. The question then becomes how can such a circuit be realized without parasitic elements and the imperfections of manufactured capacitors. Transmission lines again come to the rescue with their property of characteristic impedance. By terminating a transmission line in its characteristic impedance, one is able to present that impedance to a source at any distance from the actual load; therefore, parasitic inductance and capacitance associated with connecting the source to the load is minimized. A parallel plate air dielectric capacitor (Figure 26) is very nearly an ideal capacitor when the plate dimensions are small with respect to a wavelength. The plate is then brought into proximity of the center conductor of the power carrying coax of the sensor assembly and positioned opposite the center of the current pickup loop. Getting back to first principles, the details are as follows. The voltage to be sensed Vs is divided between the capacitance from the center conductor to the sensor plate Ci and the capacitance between the sensor plate and the outer conductor Co (Figure 27).

International SEMATECH

Technology Transfer # 96063138C-ENG

25

Figure 26

Note: Since R > 1) the fields are constrained to the skin depth of the conductor. So For good conductors ( ωε to a good approximation, the ideal conductor case should yield good results. For perfect conductors, the boundary conditions are r nˆ • B = 0(11a) r nˆ × E = 0(11b) r r nˆ × H = K s (11c) r nˆ • D = σ s (11d )

International SEMATECH

Technology Transfer # 96063138C-ENG

99 Equation 11

∂ B z ≡nˆ•∇Bz =0 on the surface of the conductor and ∂n Equation 11b is equivalent to the condition Ez = 0 on the surface of the conductor. Because the z components of the electric field and the magnetic induction must satisfy the Equations 6a and 6b respectively., the solutions for Ez and Bz are coupled by the parameter γ. In general, there are solutions only for certain values of γ. For the present problem with perfect conductors it will be shown below that γ must be zero. Equation 11a is equivalent to the condition

The sensor coax has a common current flowing in the inner and outer conductors. The current flowing in the z direction is related to the electric field by the equation r r I = ∫∫ J • nˆ dS = ∫∫ σ E • nˆ dS S

S

Equation 12 where S is the surface perpendicular to z direction and nˆ = aˆ z . Equations 10 and 12 show that E z (r ,θ ) = AJ 0 (γ r ) + B N 0 (γ r ) Equation 13 because the current I is not zero and because the other terms in Equation 10 do not contribute to the total current as given by Equation 12. Equations 6c and 6d give the transverse components of the fields: r jω µ ε Bt = − ( AJ1 (γ r ) + B N1 (γ r ))aˆθ (14a ) γ r ± jk Et = − ( AJ1 (γ r ) + B N1 (γ r ))aˆ r (14b) γ 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 r K s . 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 product of 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 K s = lim( J δ ) as J → ∞ and δ → 0 Applying this definition to a thin cylindrical shell between r = a and r = a – δ, the current is related to the current density by the equation 2π

a

0

a −δ

I = ∫ dθ ∫ Jrdr

Solving for J in terms of I,

Technology Transfer #96063138C-ENG

International SEMATECH

100 J=

I

δ 2π δ (a − ) 2

Applying the definition for the surface current density gives Ks =

I 2π a

r r Now applying the boundary condition nˆ × H = K s and noting that the normal vector nˆ points radially outward at the inner conductor boundary and radially inward at the outer conductor boundary and also that the current in the outer conductor flows in the opposite direction of the current in the inner conductor, then the boundary conditions now become I − jω ε ( AJ1 (γ a ) + B N1 (γ a )) = (15a ) 2π a γ jω ε I ( AJ1 (γ b) + B N1 (γ b)) = − (15b) 2π b γ

Equations 15 Applying the boundary conditions to Equation 11b ( E z (a,θ ) = 0 and E z (b,θ ) = 0 ) gives the following equations: AJ 0 (γ a) + B N 0 (γ a) = 0(16a ) AJ 0 (γ b) + B N 0 (γ b) = 0 (16b) Equation 16 The task now is to determine the coefficients A and B satisfying Equations 15 and 16. Using the property of Bessel functions: J n+1 ( z ) N n ( z ) − J n ( z ) N n+1 ( z ) =

2 πz

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

A=

− Iγ 2 N 0 (γ a) 4ω ε j

B=

Iγ 2 J 0 (γ a) 4ω ε j

International SEMATECH

Technology Transfer # 96063138C-ENG

101 Equations 17 Repeating the above procedure for Equations 15b and 16b gives the same results except a is replaced by b in Equations 17. To obtain a unique solution for the coefficients A and B for arbitrary a and b, it is necessary that γ → 0. Substituting the coefficients in Equations 15 and 16 using the expressions for small arguments of Bessel functions: J 0 ( x)→ 1 x 2 N 0 ( x)→ ln( ) π 2 x J 1 ( x) → 2 1 2 N1 ( x) → − ( ) π x the fields inside the dielectric become upon taking the limit as γ → 0 Bz = 0(18a ) E z = 0(18b) r µI Bt = aˆθ (18c) 2π r r ± kI Et = aˆr (18d ) 2π ω ε r

Equation 18 where ± sign gives the direction along the plus or minus z axis and the fields are zero inside the conductors. Equations 18c can now be used to determine the induced emf in the pickup loop. The pickup loop circuit will be assumed to be a rectangular loop. For the ideal case, the electromagnetic fields will be confined to the region between the conducting cylinders. The induced emf is defined as the time rate of change of the magnetic flux, which opposes the original flux. In mathematical terms this is given by

emf = −

dΦ dt

r Φ = ∫∫ B • nˆ dS S

where Φ is the total magnetic flux. The current can be separated into two traveling waves , I ( z , t ) = I 0 (e j ( k z −ω t ) + R e j ( − k z −ω t ) ) , where the first term represents the incident wave and the second term a reflected wave with a r reflection coefficient R. Substituting for B from Equation 18c, the induced emf becomes emf = −

∂ z2 b µ I 0 (e j ( k z −ω t ) ) + Re j ( − k z −ω t ) )] ∫ dz ∫ dr[ ∂ t z1 a 2π r

Technology Transfer #96063138C-ENG

International SEMATECH

102 Equation 19 In the dielectric, since γ = 0 and σ = 0, then k = ω µ ε . Using this relationship and letting z1 + z 2 (see Figure 109) and performing the indicated integration in 2 Equation 19, the induced emf can be written in the final form

L = z2 – z1 and z 0 =

emf = j

ω µε L µ1 b ln( )sin( ) I total ( z 0 , t ) επ a 2

I total ( z , t ) = I 0

z j 2π ( − f t ) λ (e

+ Re

z j 2π ( − − f t ) λ )

Equation 20 For the case that the loop length is small with respect to the wavelength, then the approximation ω µε L ω µ ε L π L sin( )≈ = 2 2 λ Equation 21 can be used to obtain an approximation for the induced emf in Equation 16 b emf = j f µ Lln( ) I total ( z 0 , t ) a

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, Dover Publications, Inc., New York (1970).

International SEMATECH

Technology Transfer # 96063138C-ENG

103 APPENDIX B Derivation of Voltage Pickup Probe Sensor Recall the equation in Section 3.1.2.

ν=

− jVε    2αεl  π  2πfR    ρ  2  ln a    

ρ − jvt ln  a = π 2πfR[2αεl ] 2

Eq. [B1]

ρ − jvt ln  a = 2π 2 fRαεl

The steradian is defined in a fashion similar to the radian except that it is the ratio of an area to the 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 of length l and radius ρ is Ω =2πρl / ρ 2 =

2πl ρ

Eq. [B2]

Therefore, the capacitance between two concentric cylinders per steradian of the outer cylinder is  2πεl   ln ( ρ / a )   = ερ cΩ =  2πl ln ( ρ / a ) ρ

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 a distance ρ from the center of the coordinate system, is

πβ 2 Ωp = 2 ρ

Technology Transfer #96063138C-ENG

Eq. [B4]

International SEMATECH

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

cp =

επβ 2 ρ ρ ln  a

Eq. [B5]

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

− jV

ρ  a  − jVt − jVt   = = Vs = ωRCi (2πf )R 2C p (2πf )R 2επβ 2 tρ ln

(

(

)

)

Eq. [B6]

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

2β 2

Eq. [B7]

and

l 2β α= = ρ ρ 2

Eq. [B8]

2β 2β 2β 2 = ρ 2 2 ρ

Eq. [B9]

Pulling this together, we get

αl =

Finally, we reduce the equation in Section 3.1.2. V=

− jVt    2αεl  π  2πfR    ρ  2  ln a    

ρ − jVt ln  a = π 2πR[2αεl ] 2

Eq. [B10]

ρ − jVt ln  a = 2 2π fRαεl ρ − jVt ρ ln  a = 2 2π fRε 2 β 2 International SEMATECH

Technology Transfer # 96063138C-ENG

SEMATECH Technology Transfer 2706 Montopolis Drive Austin, TX 78741 http://www.sematech.org fax: (512) 356-3081 e-mail: [email protected]