HANDBOOK OF VACUUM
SCIENCE AND TECHNOLOGY
HANDBOOK OF VACUUM SCIENCE AND TECHNOLOGY
Edited by Dorothy M. Hoffman
{deceased) Bawa Singh
David M. Sarnoff Research Center Princeton, New Jersey
John H. Thomas, III 3M Research Laboratories
St. Paul, Minnesota
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Library of Congress Cataloging-in-Publication Data Hoffman, Dorothy M.
Handbook of vacuum science and technology / Dorothy M. Hoffman, Bawa Singh, John H. Thomas, III.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-12-352065-4 ISBN-10: 0-12-352065-7 (alk. paper).
I. Vacuum technology—Handbooks, manuals, etc. I. Singh, Bawa.
II. Thomas, John H.
TJ940.H59 1997 97-26269 621.5'5—dc21 CIP ISBN-13: 978-0-12-352065-4
ISBN-10: 0-12-352065-7
Printed in the United States of America 05 06 07 08 09 IC 9 8 7 6 5 4 3
A Short Foreword
H. F. Dylla
When Dorothy Hoffman asked a contingent of her many colleagues in the vac- uum science and technology community to contribute chapters to a new Handbook of Vacuum Science and Technology, we could not have known that this handbook would become Dorothy's last contribution to the field. Dorothy's untimely death in December of 1996 deprived our world—the international vacuum science and technology community—and the world of music—Dorothy was a concert pianist with the Philadelphia Academy of Music — with a passionate voice for both the science and the arts. Dorothy was among the founding members, and the first woman president, of the American Vacuum Society, incorporated in 1953 to strengthen the coupling of advances in vacuum technology to the burgeoning fields of science (particle and plasma physics, materials, science, space science) and engineering (solid state electronics, thin film optics, materials processing) that require care- fully controlled vacuum environments. When Dorothy retired in 1990 from her po- sition as head of the Thin Film Laboratory at the David Samofif Research Center in Princeton, New Jersey, she had helped ensure the growth and maturity of thin film technology—an endeavor essential to the manufacture of microelectronics and high-performance optics. Dorothy continued to contribute after she retired by volunteering her talents and the benefits of her experience to the American Vacuum Society. As part of the Society's 40th anniversary in 1993, Dorothy conceived the project that resulted in this handbook. Thanks to the efforts of two of Dorothy's colleagues from Sarnoff Laboratory, Bawa Singh and John Thomas, who guided the final editing, our conmiunity now has a new compendium of the underlying science, the technology for producing and controlling vacuum, and the numerous applications that require vacuum. Those fortunate to know Dorothy and those who will share her work in reading this handbook have much to thank her for.
H. F. Dylla Past President, American Vacuum Society Jefferson Laboratory
Newport News, VA
Dorothy M. Hoffman A History and Dedication
We wish to dedicate this book to our friend and co-worker Dorothy Hoffman.
Dorothy passed away December 13, 1996. This book represents the culmination of a lifetime of work and dedication to the area of thin-film development.
Dorothy graduated from Rensselaer Polytechnic Institute and in 1949 received a M.S. degree from Bucknell University. She then joined the International Resis- tor Corp. in Philadelphia and worked on thin films. Her first paper in thin-film technology was presented at the AVS National Symposium in 1954 and was one of the first papers on this topic. That same year she joined the AVS and continued as a very active member until her death. Over the years she served the Society as Secretary, as a member of the Long Range Planning Committee, a Trustee and as Thin Film Committee Chair (before divisions existed). In 1974, she became the first woman to serve as President of the AVS. In later years, she served as an ad- visor to the Thin Film Division and the Board of Directors. She was made an hon- orary member in 1981. Dorothy was one of the founders of the Thin Film Divi- sion and was a founding member of the Delaware Valley Chapter, serving as secretary, vice-chair and chair. All this . . . and more during her 42 years in the area of thin films.
vii
After working at IRC for 10 years, Dorothy joined RCA Laboratories in 1962.
When RCA was sold to GE, she stayed on at the labs, then a subsidiary of SRI In- ternational, through her retirement in 1990. During her RCA years, she was head of the Thin Film Laboratory. Her technical activities included design and applica- tion of thin films to passive optical devices, integrated circuits, thin-film circuits, video disks, and many other common and uncommon applications. When she re- tired, she couldn't stay inactive. So she started her own consulting firm where she continued her work in the area of thin films. During this time, she was heavily in- volved in editing and writing the Handbook of Vacuum Technology. She wanted to finish this project before she was 70—this was sadly not to be.
In addition to her professional society activities, Dorothy was an active member of the Engineers' Club of Philadelphia, Director of and Representative to Engi- neering and Technical Societies. She was a long-time member and past president of the Society of Women Engineers and an active member of the local chapter.
In addition to her professional activities, she was a gifted concert pianist and performed at the Academy of Music in Philadelphia. She was a gardener, wildlife lover—an all-around special person. She was married to Earl Hoffman, who died October 1996, and lived in Titusville, New Jersey.
Dorothy brought a passionate devotion to every one of the many things that she did, and she will be deeply missed by all her friends and colleagues.
John H. Thomas, III
Contents
Preface xvii List of Contributors xxi
Part 1 Fundamentals of Vacuum Teclinology
and Surface Physics I 1.1 Vacuum Nomenclature and Definitions 3
1.1.1 Basic Definition 3 1.1.2 Pressure Regions of Vacuum 3
1.2 Gas Properties 8 1.2.1 Description of Vacuum as a Low-Pressure Gas 8
1.2.2 Characteristics of a Gas—Basic Definitions 8
1.2.3 Gas Laws 9 1.3 Molecular Processes and Kinetic Theory 11
1.3.1 General Description 11 1.3.2 Molecular Motion 12 1.3.3 Kinetic Theory Derivation of the Gas Laws 14
1.3.4 Pressure 15 1.3.5 Molecular Mean Free Path 17
1.3.6 Number of Impacts with the Chamber Wall 19
1.3.7 Time to Form a Monolayer 20 1.3.8 Thermal Transpiration 20 1.3.9 Coefficient of Thermal Conductivity 21
1.3.10 Coefficient of Diffusion 21 1.4 Throughput, Pumping Speed, Evacuation Rate, Outgassing Rate,
and Leak Rate 22 1.5 Gas Flow 25
1.5.1 Nature of Gas Flow 25 1.5.2 Turbulent Flow 27
IX
1.5.3 Viscous, Streamline, or Laminar Flow 28
1.5.4 Molecular Flow 29 1.5.5 Flow Relationships 29
1.6 Conductance 32 1.6.1 Conductance 32
1.6.2 Conductances in Parallel 33 1.6.3 Conductances in Series 33
1.7 Flow Calculations 35 1.7.1 Equations for Viscous Flow 35
1.7.2 Equations for Molecular Flow 37 1.7.3 Knudsen's Formulation 37 1.7.4 Clausing Factors 38 1.8 Surface Physics and Its Relation to Vacuum Science 40
1.8.1 Physical Adsorption or "Adsorption" 40
1.8.2 Chemisorption 42 1.8.3 Sticking Coefficient 43 1.8.4 Surface Area 44 1.8.5 Surface Adsorption Isotherms 45
1.8.6 Capillary Action 47 1.8.7 Condensation 48 1.8.8 Desorption Phenomena 49
1.8.9 Thermal Desorption 50 1.8.10 Photoactivation 52 1.8.11 Ultrasonic Desorption 53 1.8.12 Electron- and Ion-Stimulated Desorption 53
1.8.13 Gas Release from Surfaces 54
References 55 Part 2 Creation of Vacuum 57
2.1 Technology of Vacuum Pumps — An Overview 59 2.1.1 Vacuum Pump Function Basics 59 2.1.2 Gas Transport: Throughput 61 2.1.3 Performance Parameters 62
2.1.4 Pumping Speed 64 2.1.5 Pumpdown Time 65 2.1.6 Ultimate Pressure 69 2.1.7 Forevacuum and High-Vacuum Pumping 71
2.1.8 Pump System Relationships 73 2.1.9 Crossover from Rough to High-Vacuum Pumps 78
2.1.10 Pumping System Design 79
References 83
Table of Contents xi
2.2 Diaphragm Pumps 84 2.2.1 Introduction: Basics and Operating Principle 84
2.2.2 State-of-the-Art Design and Manufacturing 87
2.2.3 Performance and Technical Data 91 2.2.4 Modular Concept for Specific Application Setups:
Standalone Operation 92 2.2.5 Diaphragm Pumps as Backing and Auxiliary Pumps
in Vacuum Systems 93
References 96 2.3 Vacuum Blowers 97
2.3.1 Introduction 97 2.3.2 Equipment Description 97
2.3.3 Blower Operating Principle 100 2.3.4 Blower Pumping Efficiency 101 2.3.5 Blower Pumping Speed Calculations 103
2.3.6 Power Requirements 104 2.3.7 Temperature Considerations 106 2.3.8 Flow and Compression Ratio Control Mechanisms . . . . 108
2.3.9 Liquid-Sealed Blowers 112 2.3.10 Selected System Arrangements 112 2.4 Vacuum Jet Pumps (Diffusion Pumps) 116
2.4.1 Basic Pumping Mechanism 117
2.4.2 Pumping Speed 122 2.4.3 Throughput 127 2.4.4 Tolerable Forepressure 128
2.4.5 Ultimate Pressure 132 2.4.6 Backstreaming 137 2.4.7 Other Performance Aspects 144
References 148 2.5 Cryogenic Pumps 149
2.5.1 Introduction 149 2.5.2 Cryopump Basics 156 2.5.3 Advanced Control Systems 167
2.5.4 Cryopump Process Applications 173 2.5.5 Cryogenic Pumps Specifically for Water Vapor 177
2.5.6 Comparison of Cryopumps to Other Types of Pumps... 179
2.5.7 Future Developments 181
References 181 2.6 Turbomolecular Pumps 183
2.6.1 Turbomolecular Pumps (TMP) 183
2.6.2 Molecular Drag Pumps (MDP) 195
2.6.3 Combination of Pumps (TMP + MDP) 197
2.6.4 Evaluation of Combinations of Backing Pumps
and TMPs, Etc 200 2.6.5 The Use of TMP in Applications: Specific Effects
and Demands 208 2.6.6 Avoiding Operational Mistakes 211
References 212 2.7 Pumps for Ultra-High Vacuum Applications 214
2.7.1 System Design for Ultra-High Vacuum 215 2.7.2 The Selection of Pumps for Ultra-High Vacuum
Applications 216 2.7.3 Sputter-Ion Pumps 220 2.7.4 Getter Pumps 242
References 252 Part 3 Vacuum Measurements 255
3.1 The Measurement of Low Pressures 257
3.1.1 Overview 258 3.1.2 Direct Reading Gauges 260
3.1.3 Indirect Reading Gauges 265 3.1.4 Calibration of Vacuum Gauges 286
References 288 3.2 Mass Analysis and Partial Pressure Measurements 290
3.2.1 Overview and Applications 290
3.2.2 Inlet Systems 300 3.2.3 Ion Generation and Ion Sources 303
3.2.4 Ion Separation Analyzers 308 3.2.5 Detection of Ions 323
References 326 3.3 Practical Aspects of Vacuum System Mass Spectrometers 335
3.3.1 Historical Insight 335 3.3.2 Expected Gases in a Vacuum System 336
3.3.3 The Ion Generation Process 340 3.3.4 Techniques for Analysis 351 3.3.5 Calibration of Vacuum System Mass Spectrometers 364
3.3.6 Some Applications 370
References 374 3.4 Mass Flow Measurement and Control 376
3.4.1 General Principles of Mass Flow Measurement 376 3.4.2 Overview of Thermal Mass Flow Controller Technology 378
3.4.3 Performance Characteristics 382
3.4.4 Troubleshooting 386
References 387
Table of Contents xiii
Part 4 Systems Design and Components 389 4.1 Selection Considerations for Vacuum Valves 391
4.1.1 Introduction 391 4.1.2 Valves for Shutoff 391 4.1.3 Valves forControl 397 4.1.4 Valve Construction 398 4.1.5 Specialty Valves 404 4.1.6 Installation Considerations for Vacuum Valves 407
References 408 4.2 Flange and Component Systems 409
4.2.1 Introduction 409 4.2.2 Selecting a Flange System 410
4.2.3 Conunon Flange Systems 410 4.2.4 Components with Flanges Attached 425
Trademarks 430 References 432 4.3 Magnetic-Fluid-Sealed Rotary Motion Feedthroughs 433
4.3.1 Basic Sealing Principle 433 4.3.2 Application Factors 434 4.3.3 Impact of Feedthrough on Process 436
4.3.4 Impact of Process on Feedthrough 437
4.3.5 Materials Considerations 438 4.3.6 Application Examples 440 4.3.7 Comparison to Other Types of Feedthroughs 442
4.4 Viewports 444 4.4.1 Materials 444 4.4.2 Mounting Systems and Precautions 445
4.5 Construction Materials 446 4.5.1 Properties Defining Material Performance 446
4.5.2 Vacuum Chamber Materials 451 4.5.3 Special-Purpose Materials 455
References 462 4.6 Demountable Seals for Flanges and Valves 463
4.6.1 Sealing Overview: Polymer and Metal Seals 463 4.6.2 The Elastomeric and Nonelastomeric Polymers Used
in Vacuum Sealing 464 4.6.3 Metal Seals 474
References 482 4.7 Outgassing of Materials 484
4.7.1 Relationships Among System Pressure, Pumping Speed,
and Outgassing 484
4.7.2 Initial Pumpdown from Atmospheric Pressure 494 4.7.3 Pressure Vs. Time During Outgassing 495 4.7.4 The Outgassing Rate of Elastomers and Plastics 497
4.7.5 The Outgassing Rate of Metals and Ceramics 501 4.7.6 The Outgassing Rate of Preconditioned Vacuum
Systems After Short Exposure to the Atmosphere 504 4.7.7 Methods of Decreasing the Outgassing Rate 506 4.7.8 Measurement of the Outgassing Rate of Materials 507
References 508 4.8 Aluminum-Based Vacuum Systems 509
4.8.1 Outgassing 509 4.8.2 Demountable Seals 512 4.8.3 Cleaning and Surface Finishing 518
4.8.4 Mechanical Considerations 520 4.8.5 Thermal Conductivity and Emissivity 536
4.8.6 Corrosion 538 4.8.7 Welding Aluminum for Vacuum Applications 541
References 548 4.9 Preparation and Cleaning of Vacuum Surfaces 553
4.9.1 Surface Modification 554 4.9.2 External Cleaning 567 4.9.3 Assembly, Handling, and Storage 587
4.9.4 In Situ Cleaning 591 4.9.5 Documentation 599 4.9.6 Conclusion 601 Trade Names 601 References 601 Part 5 Vacuum Applications 607
5.1 High-Vacuum-Based Processes: Sputtering 609 5.1.1 Sputtering and Deposition 611 5.1.2 Sputter Deposition Technologies 612
5.1.3 Magnetron Applications 624 5.1.4 Future Directions in Sputtering 626
References 627 5.2 Plasma Etching 628
5.2.1 Introduction 628 5.2.2 Review of Plasma Concepts Applicable to Etching
Reactors 628 5.2.3 Basic Plasma Etching Requirements 633
5.2.4 Plasma Diagnostics 641
5.2.5 Basic Plasma Etch Reactors 643
Table of Contents xv
5.2.6 Advanced Plasma Etch Reactors 649
5.2.7 New Trends 665
References 667 5.3 Ion Beam Technology 672
5.3.1 Introduction 672 5.3.2 Ion Beam Etching 678 5.3.3 Ion Beam Sputter Deposition 683
5.3.4 lon-Beam-Assisted Deposition 687 5.3.5 Ion Beam Direct Deposition 689
5.3.6 Conclusion 690
References 691 5.4 Pulsed Laser Deposition 694
5.4.1 Introduction 694 5.4.2 Pulsed Laser Deposition System 695
5.4.3 The Ablation Mechanism 698 5.4.4 Advantages and Limitations 700
5.4.5 Materials Survey 705 5.4.6 Future Outlook 708
References 708 5.5 Plasma-Enhanced Chemical Vapor Deposition 711
5.5.1 Introduction 711 5.5.2 Equipment and Other Practical Considerations 717
5.5.3 Process Scaleup 723 5.5.4 Conclusion 727
References 728 5.6 Conmion Analytical Methods for Surface and Thin Film 731
5.6.1 Introduction 731 5.6.2 The Electron Spectroscopies 732
5.6.3 Methods Based on Ion Bombardment 745 5.6.4 UHV Generation and System Considerations for
Surface Analysis 755
References 757
Part 6 Large-Scale Vacuum-Based Processes 759
6.1 RoU-to-RoU Vacuum Coating 761 6.1.1 Overview of RoU-to-Roll Vacuum Coating 761
6.1.2 Typical Products 764 6.1.3 Materials and Deposition Processes Conmionly Used
in RoU-to-RoU Coating 765 6.1.4 Vacuum Systems for Roll-to-RoU Coating Applications. 775
6.1.5 Substrates (Webs) 779
6.1.6 Process Control 783
6.1.7 Specific Problems Exhibited by Coatings 784
References 787 6.2 The Development of Ultra-High-Vacuum Technology for Particle
Accelerators and Magnetic Fusion Devices 789
6.2.1 Introduction 789 6.2.2 Storage Rings and the Need for UHV 790
6.2.3 UHV for Early Storage Rings 793 6.2.4 Storage Ring Vacuum Vessel and Pumping System
Developments 796 6.2.5 Cold-Bore Machines 798 6.2.6 Superconducting RF Accelerators 800
6.2.7 The Next-Generation Big Accelerator? 801 6.2.8 The Magnetic Fusion Road Map 801 6.2.9 The Early History of Magnetic Fusion 803 6.2.10 Model C: The First UHV Fusion Device 804 6.2.11 The Russian Revolution in Fusion: Tokamaks 805 6.2.12 Plasma Impurities and Vacuum Technology 806 6.2.13 Toward the Breakeven Demonstrations 808
6.2.14 The Next Step in Fusion 810
Acknowledgments 810
References 812
Preface
The Handbook of Vacuum Technology was conceived in 1994 as an addition to Academic Press's Methods of Experimental Physics, Vol. 14: Vacuum Physics and Technology, edited by G. L. Weissler and R. W. Carlson (1979). It was de- cided that rather than add to the series Methods of Experimental Physics, a new book should be produced. This handbook covers areas of vacuum technology not covered in detail in Volume 14 or those where the technology has changed signifi- cantly. A significant number of world-known authors have written chapters for this handbook, where the chapters do somewhat overlap with the original Meth- ods of Experimental Physics, Volume 14, to provide continuity. Readers are re- ferred to Methods of Experimental Physics, Volume 14, for chapters covering concepts such as basic vacuum equations, molecular transport, details on weld- ing, soldering, glass systems (generally not employed in modern vacuum technol- ogy), protective devices, and many other significant older technology bases. We emphasize the importance of Volume 14 of the Methods of Experimental Physics as a basis for this introduction to vacuum technology.
This book has five parts: (1) an introduction; (2) creation of vacuum (pumps and the technology presently used in their operation and design); (3) vacuum measurements (pressure, partial pressure, gas flow, leak detection, calibration and associated technology); (4) system components and design, including construc- tion materials, valves, flanges, operation and maintenance, and system cleaning and cleanliness and finally; (5) applications of high- and ultra-high-vacuum tech- nology. The information included in this handbook is directed toward the practi- tioner of vacuum technology and includes many references for detailed informa- tion in specific areas of interest.
Part 1 is a brief overview of what Methods of Experimental Physics, Volume 14, presented in detail. It is intended to give the reader details and references to past literature. Readers should see Volume 14 and other cited references for funda- mental information on the basic laws employed in vacuum technology as it is practiced today.
xvii
Vacuum technology has progressed in many different ways since its origin. To- day, as in many other areas, vacuum technology has been driven toward automa- tion of equipment and pumps. System design is automated through powerful CAD programs available from conmiercial suppliers. Although very important, software tends to have a short lifetime and changes rapidly. Consequently, the use of these programs and their application is beyond the scope of this text. Readers who need up-to-date information on this topic should contact suppliers of techni- cal programs or use the Internet facilities that many software houses provide free of charge.
Part 2 includes a user-oriented overview and complete discussion of modern pumps used in the practice of vacuum. The discussions are written by experts in the area of their specific pump technology. Included in this chapter are discus- sions of the following: mechanical pumps (a continuation from Methods of Ex- perimental Physics, Volume 14), diaphragm pumps, blowers, diffusion pumps,
cryogenic pumps, turbomolecular pumps, UHV pumps (sputter ion, sorption, get- ter, including nonevaporable getter pumps). In addition to a description of pump operation, we emphasize maintenance and areas of application. Future trends in vacuum pump design are also presented.
Methods of monitoring vacuum processes have evolved over the past decade.
Part 3 of this handbook addresses this topic in detail. New concepts have changed vacuum pressure measurement apparatus. In addition to covering the older pres- sure measurement devices, this handbook covers in detail the use and mainte- nance of rotating disk and capacitance manometers. The "art" of leak detection and partial pressure analysis has become highly automated. Manufacturers of leak detection equipment have included online data logging, improved sensitivity, and automatic calibration of leak rates into the 10 ~^^ torr-liter/sec range. Partial pressure analysis uses the now standard quadrupole-based mass spectrometer.
Automated instrumentation has interfaces that generally are acceptable to high- speed desktop computers. We present applications of partial pressure analysis and leak detection to provide the novice with a useful procedure for applying these methods to current vacuum systems. Similar features are discussed for mass flow (gas flow) measurements in Part 3.
With the accessibility of high-speed desktop computers, local control and mon- itoring of various parameters encountered in vacuum technology have become an integral part of modern vacuum systems. Using various monitors, dynamic real time process control and automatic logging of process performance are provided.
These new attributes make vacuum production and processing routine, and pro- vide a paper or digital log of the process parameters for later examination.
Part 4 discusses components used in modern vacuum system construction and
system design with the user in mind. With the advent of powerful high-speed
desktop computation available at low cost, many new computational programs
have been developed based on either the classical analog approach to mathemati-
Preface xix
cal solutions or matrix manipulation approaches. These techniques allow rapid system design, preconstruction understanding of actual operation, and methods of automation in construction. Engineering CAD/CAM methods are regularly used in producing vacuum components and systems.
Many components used in earlier vacuum systems have been refined with bet- ter materials. Components tend to be automated through the use of electrical/
pneumatic controls. New system design materials, including aluminum, are cov- ered in detail. Vacuum system operation, maintenance and the problems of clean- liness and contamination are discussed for users. Pump selection and integrated system design conclude this section, oriented to a "systems approach" to design- ing integrated vacuum systems in processing materials.
Part 5 is dedicated to applications of high-vacuum and ultra-high-vacuum in commercial products. The main applications of vacuum have been to deposit and etch thin films of materials used in many areas of modern technology, including the semiconductor industry (silicon wafer fabrication, high-density interconnec- tions, etc.), large-area deposition and web coating, and many other areas. To keep the focus of this volume on vacuum technology, we have limited the number of applications covered. These include sputtering, plasma etching, laser ablation, chemical vapor and plasma enhanced chemical vapor deposition, and surface an- alytical applications of ultra-high-vacuum apparatus.
Ultra-high-vacuum systems have been employed in both ultra-clean film depo- sition and surface analysis. The use of UHV in analytical apparatus follows from the requirements of keeping the surface clean during a typical measurement. This is true in most analytical approaches, because they are oriented toward the inves- tigation of the surface or near surface structure, chemistry and composition. High vacuum is required in applications requiring particle (and photon) mean free paths great enough to be detected by in situ detectors. These techniques include X-ray- or electron-probe-based equipment (for example, x-ray photoelectron spectroscopy and auger electron spectroscopy). These methods are reviewed in some detail, as they are practiced today and include many references to further reading. Unique applications include a section on large-scale vacuum based processes.
This handbook, along with the earlier text Methods of Experimental Physics, Vol. 14, Vacuum Physics and Technology, provides a very complete and up-to- date series on the generation of vacuum, vacuum fixturing, vacuum measure- ments, system maintenance and operation, and vacuum applications as it is ap- plied today. Our orientation has been on the practical use of vacuum technology.
We are sure that as a user of vacuum technology, you will find this handbook
invaluable.
List of Contributors
Numbers in parentheses indicate the pages on which the author's contributions begin.
GARY S. ASH (149), CTI-Cryogenics Division, Helix Technology Corporation, Mansfield, Massachusetts 02048
WILLIAM H . BAYLES, JR.
(257), The Televac Division, The Fredericks Company, Inc., Huntingdon Valley, Pennsylvania 19006
How^ARD M.
BRADY(257), Electron Technology Division, The Fredericks Com- pany, Inc., Huntingdon Valley, Pennsylvania 19006
JEFFREY T. CHEUNG
(694), Rockwell Science Center, Thousand Oaks, California 91360
BENJAMIN B . DAYTON
(484), Consultant, East Flat Rock, North Carolina 28726
EMIL DRUBETSKY
(257), The Televac Division, The Fredericks Company, Inc., Huntingdon Valley, Pennsylvania 19006
H. F. DYLLA (789), Jefferson Laboratory, Newport News, Virginia 23606 and Department of Physics, College of William and Mary, Williamsburg, Virginia 23185
F. J.
ECKLE(84),
V A C U U B R A N DGMBH -h CO, D-97877, Wertheim, Germany
JAMES L . GARNER
(509), SMC Corporation, Turtin, California 92780
RON GOEHNER
(257), Electron Technology Division, The Fredericks Company, Inc., Huntingdon Valley, Pennsylvania 19006
MARSBED HABLANIAN
(59, 116), (Retired) Varian Associates, Wellesley, Massa- chusetts 02181
WALTER HELGELAND
(433), Rigaku/USA, Inc., Danvers, Massachusetts 01923 HiNRicH
HENNING(183), Leybold Vakuum GmbH, D-50968, Cologne, Germany L. D. HiNKLE (376), MKS Instruments, Inc., Andover, Massachusetts 01810
DOROTHY HOFFMAN
(deceased)
FRANK JANSEN
(711), BOC Coating Technology, 4020 Pike Lane, Concord, Cali- fornia 94524
XXI
CHUCK KRAFT (444), Larson Electronic Glass, Redwood City, California 94064
LASZLO
V. LiESZKOVSZKY (290), GE Lighting, Cleveland, Ohio 44112
DONALD M . MATTOX
(553), Management Plus, Inc., Albuquerque, New Mexico 87122
R. A.
OUTLAW(335), Teledyne Brown Engineering: Hastings Instruments, Hamp- ton, Virginia 23669
JANDA K. PANITZ
(446), Sandia National Laboratories, Albuquerque, New Mex- ico 87185
V.
PATEL,Ph.D. (628), Sarnoff Corporation, Princeton, New Jersey 08543
NEIL T. PEACOCK
(391, 409), HPS Division of MKS Instruments, Inc., Boulder, Colorado 80301
R. N.
PEACOCK(463), Vice President for Development (Retired), HPS Division of MKS Instruments, Inc., Boulder, Colorado 80301
MICHAEL
J.
POWERS(672), Commonwealth Scientific Corporation, Alexandria, Virginia 22314
JAY RICHMAN
(97), Consultant, Stokes Vacuum, Inc., King of Prussia, Pennsyl- vania 19406
WILLIAM B . ROBBINS
(761), 3M Corporate Research Laboratories, Thin Film Technology Resources, St. Paul, Minnesota 55144
STEPHEN M . ROSSNAGEL
(609), I.B.M., T. J. Watson Research Center, Yorktown Heights, New York 10598
BAWA SINGH (1), David Sarnoff Research Center, Princeton, New Jersey 08543
JACK H . SINGLETON
(214), Consultant, Monroeville, Pennsylvania 15146
JOHN H . THOMAS,
HI (1, 731),
3 MResearch Laboratories, St. Paul, Minnesota
55144
HANDBOOK OF VACUUM
SCIENCE AND TECHNOLOGY
PARTI
Fundamentals of
Vacuum Technology and
Surface Physics
Bawa Singh
David Sarnoff Research Center
John H.Thomas, III 3M Research Laboratories
1.1 Vacuum Nomenclature and Definitions 3 1.1.1 Basic Definition 3
1.1.2 Pressure Regions of Vacuum 3 1.2 Gas Properties 8
1.2.1 Description of Vacuum as the Characteristics of a Low-Pressure Gas 8
1.2.2 Characteristics of a Gas—Basic Definitions 8 1.2.3 Gas Laws 9
1.3 Molecular Processes and Kinetic Theory 11 1.3.1 General Description 11
1.3.2 Molecular Motion 12
1.3.3 Kinetic Theory Derivation of the Gas Laws 14 1.3.4 Pressure 15
1.3.5 Molecular Mean Free Path 17
1.3.6 Number of Impacts with the Chamber Wall 19
1.3.8 Thermal Transpiration 20
1.3.9 Coefficient of Thermal Conductivity 21 1.3.10 Coefficient of Diffusion 21
1.4 Throughput, Pumping Speed, Evacuation Rate, Outgassing Rate, and Leak Rate 22
1.5 Gas Flow 25
1.5.1 Nature of Gas Flow 25 1.5.2 Turbulent Flow 27
1.5.3 Viscous, Streamline, or Laminar Flow 28 1.5.4 Molecular Flow 29
1.5.5 Flow Relationships 29 1.6 Conductance 32
1.6.1 Conductance 32
1.6.2 Conductances in Parallel 33 1.6.3 Conductances in Series 33 1.7 Flow Calculations 35
1.7.1 Equations for Viscous Flow 35 1.7.2 Equations for Molecular Flow 37 1.7.3 Knudsen's Formulation 37 1.7.4 Clausing Factors 38
1.8 Surface Physics and Its Relation to Vacuum Science 40 1.8.1 Physical Adsorption or "Adsorption" 40 1.8.2 Chemisorption 42
1.8.3 Sticking Coefficient 43 1.8.4 Surface Area 44
1.8.5 Surface Adsorption Isotherms 45 1.8.6 Capillary Action 47
1.8.7 Condensation 48
1.8.8 Desorption Phenomena 49 1.8.9 Thermal Desorption 50 1.8.10 Photoactivation 52 1.8.11 Ultrasonic Desorption 53
1.8.12 Electron- and Ion-Stimulated Desorption 53 1.8.13 Gas Release from Surfaces 54
References 55
CHAPTER 1.1
Vacuum Nomenclature and Definitions
I.U
BASIC DEFINITION
The term vacuum is generally used to denote a volume or region of space in which the pressure is significantly less than 760 torr. In the traditional measure- ment system, normal pressure is expressed in millimeters of a column of mercury, and 760 millimeters of mercury is equal to 1 standard atmosphere. The traditional unit of pressure is the torr, which approximately equals 1 millimeter of mercury.
A perfect or absolute vacuum, which implies a space that is entirely devoid of matter, is practically unrealizable. For practical purposes, however, and in accor- dance with the definition proposed by the American Vacuum Society, the term vacuum is generally used to denote a space filled with a gas at less than atmo- spheric pressure [1].
In the metric, or meter-kilogram-second (MKS), system, the unit of pressure is the pascal. In general, however, the torr still remains one of the most widely used units of pressure. Table 1 lists conversion factors between some of the most gen- erally used vacuum units.
1.1.2
PRESSURE REGIONS OF VACUUM
Measuring a system's pressure is the traditional way to classify the degree of vac- uum. Nowadays, the general term vacuum refers to a region that consists of about
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Table I
Conversion Factors for Pressure Units
Unit Torr Pascal Dyne cm Bar
Atmosphere (standard) 1.333X102 1.333 XIO^ 1.333 X 10"^ 1.3158 X 10"^
1 pascal
(newton m~2) 7.5006 X 10"^
dyne Ibar
1 torr (0°C) 1
^^IICWIUU 111 ) / . .
ldynecm-2 7.5006 X 10"^
1 0.1
10
-- u.i 1 7.5006 X 10^ 1.0 X 10^ 1.0 X 10^
1 atmosphere (standard) 1 pound
1.0 X 10-5 9 8692 X 10-^
9.8692 X 10"^
1.0 X 10^ 0.98692
(standard) 760 1.0133 X 10^ 1.0133X10^ 1.0133 1 1
pound
(force) inch-2 5.1715 X 10' 6.8948 X 10^ 6.8948 X 10^ 6.8948 X lO'^ 6.8047 X lO'^
19 orders of magnitude of pressure below 1 atmosphere. For convenience, this ex- tended pressure range is generally divided into several regions that denote the degree of vacuum. This division of the pressure scale below atmosphere is some- what arbitrary and is a convenient method of denoting the different physical phe- nomena that occur within the pressure ranges specified for each category. Many industrial applications of vacuum can be also be classified using these categories.
Table 2 shows the accepted categories and the corresponding pressure ranges.
This table also lists the type of pump generally used to achieve a specified pres- sure range, as well the typical vacuum gauge used for measurement.
To discuss the different physical phenomena associated with the various vac- uum categories that are indicated in Table 2, it is useful to introduce other con- cepts and properties that characterize the degree of vacuum, such as molecular density, mean free path, and time to form a monolayer. These terms are defined as follows:
Molecular density Mean free path
Time to form a monolayer
Average number of molecules per unit volume.
Average distance a molecule travels in a gas between two successive collisions with other molecules of the gas.
Time required for freshly cleaved surface to be covered by a layer of gas of one molecule thick- ness. This time is given by the ratio between the number of molecules required to form a compact monolayer (about 8 X 10 ^"^ molecules/
cm^) and the molecular incidence rate.
1.1.2 Pressure Regions of Vacuum
Table 2
Applications of Vacuum Techniques
Physical Situation Objective Applications
Low pressure Achieve pressure difference.
Low molecular density Remove active atmospheric constituents.
Remove occluded or dissolved gas.
Large mean free path
Long monolayer formation time
Decrease energy transfer.
Avoid collision.
Clean surfaces.
Holding, lifting, transport pneumatic, cleaners, filtering, forming
Lamps (incandescent, fluorescent, electric discharge tubes), melting, sintering, packaging, encapsulation, leak detection
Drying, dehydration, concentration, freeze-drying, degassing, lyophyliza- tion, impregnation
Thermal insulation, electrical insula- tion, vacuum microbalance, space simulation
Electron tubes, cathode ray tubes, television tubes, photocells, photo- multiplier. X-ray tubes, accelerators, storage rings, mass spectrometers, iso- tope separators, electron microscopes, electron beam welding, heating, coat- ing (evaporation, sputtering), molecu- lar distillation
Fraction, adhesion, emission studies, materials testing for space
Figure 1 shows the relationships among these various quantities as a function of pressure. Using the preceding definitions, it is possible to describe the different physical situations that characterize the different vacuum categories.
1.1.2.1 Low and Medium Vacuum
In the low-vacuum and medium-vacuum range, the number of molecules in a vac-
uum vessel in the gas phase are large compared to those covering the surface of
the vessel. Thus the pumping of the space serves to remove molecules from the
gas phase. This vacuum range extends from atmosphere to about 10 "^ torr. Many
industrial processes that need to outgas or dry materials and components use this
region.
Rg.l.
V/Vp Maxwell-Boltzmann molecular velocity distribution curve.
I dn A ( m \3/2 / ,„v2\
2. v„ lYT
3. V, mean "average
/8kT
7 = J = 1.13v„
\ irm
4. Root mean square Vr^s - J = 1-225 v, 3kr
5. Mean energy e = — kT
1.1.2.2 High Vacuum
The high-vacuum region corresponds to a state where the gas molecules are lo-
cated mainly on the surfaces of the enclosure and the mean free path equals or ex-
ceeds the dimensions of the vacuum vessel. The particles travel in the vacuum
enclosure without colliding with other molecules. Thus, in this vacuum region,
under these conditions, the pumping consists of evacuating or capturing mole-
1.1.2 Pressure Regions of Vacuum 7
cules. The molecules leave the surface and individually reach the pump. This re- gion is extensively used in the preparation and application of vacuum coatings, surface treatment, and modification. This region extends from 10 ~'^ to 10 ~^ torr.
1.1.2.3 Ultra-High Vacuum (UHV)
Under ultra-high-vacuum (UHV) conditions, time to form a monolayer is equal to or longer than the usual time for most laboratory measurements. Thus clean sur- faces can be prepared and their properties determined before an adsorbed gas layer is formed. This vacuum range extends from about 10"^ to 10"^^ torr.
An indication of the extensive application of vacuum technology in many key
industrial processes in a diverse range of industries is illustrated in Table 2, where
common vacuum industrial processes are classified according to the degree of
vacuum used.
Gas Properties
1.2.1
DESCRIPTION OF VACUUM AS THE CHARACTERISTICS OF A LOW-PRESSURE GAS
The behavior and characteristics of gases are fundamental to vacuum systems.
Even at the extremely low pressures typically encountered in vacuum technology, gases essentially still behave as gases. The necessity for creating a vacuum is usu- ally related to the need to reduce the number density of gaseous molecules, or their surface collision rates. Behavior of gases in vacuum systems can be generally dis- cussed in terms of the ideal gas laws; and some aspects of overall behavior of vac- uum systems can be described by the static and dynamic properties of gases. The be- havior of gases at low pressure and various aspects of gas flow are considered next.
1.2.2
CHARACTERISTICS OF A GAS—BASIC DEFINITIONS
A low-pressure sample of gas can be completely described if at least three of the four quantities that relate to it are known. These quantities are its pressure, vol- ume, temperature, and the amount of gas in the sample.
Pressure: Pressure is defined as the force per unit area that a gas exerts on the walls of its container. In the MKS system of units, pressure is expressed as newton per square meter, or newton/m^ or newton m~^. The MKS unit is the pascal, where 1 torr = 1 3 3 pascal and 1 pascal = 7.5 torr.
Volume: The volume is simply a measure of the space a gas takes up; it is usu- ally set by the dimensions of the enclosure. The MKS unit of volume is the m-^
but liters are extensively employed to refer to pumping rates, gas flow measure-
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1.2.3 Gas Laws 9
ments, etc. The pumping speed of mechanical pumps is often expressed in cfm (cubic feet per minute).
Temperature: The temperature of a gas at pressure below 1 torr is determined mainly by the temperature of the surfaces with which the gas comes in contact.
Typically the gas is at room temperature. In deriving the equations that describe the behavior of gases, the unit of temperature is K or Kelvin.
Amount of gas: The amount or mass of gas in a given sample is measured in molar gram units or moles.
Gram molecule or mole: Defined as that quantity of gas (or any substance) having a mass equal to its molecular weight in grams. A gram molecule contains 6 X 10^-^ molecules. One mole of any gas at 0°C and a pressure of 760 torr, occupies 22.4 liters of volume. The mass of 1 mole of gas is exactly equivalent to its molecular weight in grams.
Gram molecular volume: The volume occupied by a gram molecule of gas is a universal constant; it is found experimentally to be 22.414 liters at 760 torr and 0°C. As 1 mole of any gas, at a temperature of 0°C and a pressure of 760 torr occupies a volume of 22.4 liters, it is possible from this relationship to calculate the molecular density of any volume of gas if its temperature and pressure are known. For example, 1 cubic centimeter of air at 760 torr and 0°C contains 2.7 X 10 ^^ molecules; whereas at a pressure of 1 torr and a temperature of 0°C,
1 cubic centimeter of air contains 3.54 X 10 ^^ molecules.
1.2.3
GAS LAWS
The gas laws (Boyle's, Charles's, Gay-Lussac's) lead to relationships of the bulk physical quantities of the gas, such as pressure, volume, temperature, and the amount of gas to one another. These relationships describe the behavior of a given quantity of an "ideal" gas; an ideal gas is one where the volume of all the mole- cules is negligible compared to the volume of the gas, and the energy of attraction between the molecules is negligible compared to their mean thermal energy. This means that the sample of gas is dilute and is at a temperature that is not low enough to condense it. Gases that are ideal at room temperature include O2, Ne, Ar, CO, H2, N2, and NO. A summary of the relationships that result from apph- cations of the gas laws to an ideal gas is provided here:
Boyle's law: States that the product of pressure and volume, pW, is constant for a given mass of gas at constant temperature.
Charles's law: States that WIT is constant for a given mass of gas at a constant pressure, where 1/is the gas volume and T = the absolute temperature.
Avogadro's law: States that equal volumes of gas at any gas at the same tem-
perature and pressure contain the same number of molecules. From this law can be obtained an important relationship between the number of moles in a sample and the pressure the gas exerts.
General gas law: The general gas law relates all four quantities needed to describe the state of a gas. The general law states that
PV=nRT (1) for a given mass of gas, where R = universal gas constant (constant of propor-
tionality) with a value of 62.4 torr-liter/mole°K, and n is the number of moles in volume V.
This law is known as the "ideal" gas law, because it is exactly true for ideal gases; most gases at reduced pressures behave as ideal gases.
Dalton's law of partial pressures: The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the individual components.
Partial pressure: The partial pressure exerted by any one component of a mixture of gases is the pressure exerted by that component if it occupied that volume alone.
Avogadro's law: Equal volumes of all ideal gases measured at the same tem- perature and pressure contain the same number of molecules.
Avogadro's number: The number of molecules in a gram molecule of gas or any substance is a universal constant and is 6.023 X 10^-^.
Loschmidt's number: The number of molecules per cm"^ of gas at 760 torr and 0°C is a universal constant equal to 2.637 X 10 ^^.
For 1 mole at standard temperature and pressure (STP), P = 760 torr = 1,013,250 dynes/cm^, V = 22.414 liters, and T = 273.2°K, whence R = 8.31 X 10^ ergs per gram molecule or in thermal units R/J = 1.99 cal per °K (J = mechan- ical equivalent of heat = 4.182 joules cal ^). In more tangible terms, therefore, 1.99 cal will raise the temperature of 1 mole of any ideal gas 1°K. Alternatively, hav- ing raised the temperature of 1 mole of any ideal gas by 1°K, the increase in en- ergy of the gas amounts to 8.31 joules.
1.2.3.1 Nonideal Gases
Examples of some common nonideal gases are ammonia, ethane, benzene, CO2,
mercury vapor, NOSob, SO, and SO2. The gas laws for any gas have to account
for behavior of a gas at low temperature. Below a certain temperature, called the
critical temperature, TQ, the gas begins to condense. Below this critical tempera-
ture, there is a vapor pressure of gas over the liquid condensate, called the vapor
pressure. If the gas is condensed (V is decreased), the pressure will not change,
but more gas will condense into the liquid phase. As the temperature is lowered,
fewer molecules are present over the liquid and the vapor pressure is lower.
CHAPTER 1.3
Molecular Processes and Kinetic Theory
1.3.1
GENERAL DESCRIPTION
The gas laws describe the bulk behavior of gases but provide no insight as to why gases should behave in this fashion. Kinetic theory is an attempt to explain the be- havior of gases in terms of the behavior of the individual molecules that make up the gas. The results of kinetic theory are in close agreement with the gas laws.
The theory is based on the following assumptions:
1. A gas is composed of a large number of molecules. All the molecules of a given chemical substance are exactly alike.
2. The molecules are separated by distances that are large in comparison with their own dimensions.
3. The molecules are in constant state of random and chaotic motion. This mo- tion is related to the temperature of the gas.
4. The molecules exert no force on each other or on the walls of their container except when they collide. The volume occupied by the molecules is negli- gible compared with the volume occupied by the gas.
5. The molecules behave as perfect elastic spheres.
These assumptions are clearly idealized, and no known gas behaves exactly in accordance with this set of assumptions. However, the theory based on these as- sumptions explains the behavior of real gases in very satisfactory manner.
The theory describes the motion of molecules that are in constant motion. The molecules are free to wander throughout any space available to them. The temper-
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11
ature of a gas is a measure of the kinetic energy of the particles. The pressure on the walls of a vessel containing a gas is caused by the impact of the gas mole- cules. If some of the gas is removed, the remaining molecules expand to fill the entire volume but as there are fewer impacts with the walls, the gas pressure drops.
Some additional aspects of gas behavior, important to understanding certain char- acteristics of vacuum, can be calculated from the mathematical expressions de- veloped from kinetic theory. Some of these mathematical relationships, derived from kinetic theory, are presented next; these relationships indicate the depen- dence of physical properties and processes on molecular quantities.
1.3.2
MOLECULAR MOTION
Kinetic theory postulates that gas molecules are in constant motion and that their velocities are temperature dependent. The distribution of velocities is given by the Maxwell-Boltzmann distribution, which states,
/ I \ 2
I dn ^l m \
(2) where m is the molecular velocity, k is the Boltzmann constant, and v the velocity.
This expression provides a statistical distribution of molecular velocities and states that if there are n molecules in the volume, there will be dn molecules hav- ing speeds of v and v + dv. Figure 2 shows a number of quantitative relationships that can be derived from the Maxwell-Boltzmann distribution:
• The most probable velocity:
"^ (3) m
where m is the molecular mass, k is the Boltzmann constant, and T the ab- solute temperature.
The average velocity:
= 1.13v,^ (4) irm
• The root mean square velocity Vf, 3kT
= 1.22v„3x (5)
m
L3.2 Molecular Motion 13 Fig. 2.
o TUrtwlent o Lanainar o Molecular
viscous X < 7
0 0tupbulent ( / ? e = - ^ > 2200) Reynolds
laminap (/?e<1200)
(t)=Gf
(t).d
± . I molcculan X » d
Types of flow through cylinder tubes.
• At high pressures, the mean free path is much smaller than the diameter of the tube (A <
0.0\5d). In this region, viscosity of gas plays an important role and the flow is called viscous.
• Viscous flow is divided into two regions: turbulent flow and laminar flow.
• Mean energy of a molecule:
2 (6)
The mean velocity is used in calculations of gas flow, and the rms velocity is used
when discussing kinetic energy.
1.3.3
KINETIC THEORY DERIVATION OF THE GAS LAWS 1.3.3.1 Boyle's Law
Let S be the gas density, thus
mn = S
where m is the molecular mass and n is molecular volume density. Hence, the pressure is given by
P = -8 = ~mnv^ (7) 3 3
Thus
PV=^V (8) mv^
where m is the total mass of the gas. This relationship shows that at constant tem- perature, the pressure varies directly with density or conversely with volume, which is Boyle's law.
1.3.3.2 Charles and the Ideal Gas Law
(9)
(10) 3
That is, the pressure is equal to two-thirds of the total kinetic energy per unit volume. From the expression for v^^, we have
V ^ = — (11)
m
Thus
P = n k r (12) The average energy
and therefore
of molecule is given by F
P =
~ ~ ~ 2 ~
2nE^^
1.3.4 Pressure 15
where n is the number of molecules per unit volume. Substituting for n = N/V we get
P = ^ (13)
or— = Nk (14)
PVT which is the ideal gas law.
Consider equal volumes of any two different gases at same values of P and T.
Since P and V are same for each gas, and ^ are the same at the same tempera- ture, it follows that n must be the same for each gas. Thus we have "equal vol- umes of all gases at any given values of temperature and pressure contain equal number of molecules." This is, of course, Avogadro's hypothesis, which was stated around 1811. Introducing Avogadro's number, N/^ = 6.023 X 10^^/mole as
Np, = M/m and n = NA/V^ (15) where m is the molar mass and V^ is the molar volume.
PV^ = AT^Rr (16) or
PV^ = RT (17) where R is the universal gas constant, and T is temperature in °Kelvin.
1.3.4 PRESSURE
The following is a simplified derivation of the pressure exerted by a gas on the walls of its container as a result of molecular impacts. Since the molecular im- pacts are perfectly elastic, energy and momentum are conserved and each mole- cule is thrown back from the wall with the same speed as its incident speed.
Consider a molecule of mass m that approaches the enclosure wall with a ve- locity V and rebounds with the same velocity, thus
Change in momentum = 2mv
If n molecules strike a unit area of the wall in unit time, with average velocity v, then
Total impulse exerted on unit area of wall in unit time = 2mnv Pressure = rate of change of momentum per unit area Thus
P = 2mnv (18)
To estimate P, we need to calculate v, the frequency of molecular impact of the unit area of the enclosure surface.
Let n = number of molecules in cube of unit volume. Each molecule can move in six possible directions. The velocity of each molecule is v. On average, ^ of the molecules will move toward each face of the cube. Thus, for a gas with volume density n.
Thus
(n/6)v molecules will cross a unit area in unit time
nv
~6
(19) Hence
P = 2mvn = 2mv • —
6 (20)
Thus
-{mnv-)
Pressure = P 1
•NmiCy (21)
where P
N-
pressure in MKS units (newton m~^) number of molecules per unit volume m = mass of molecule (g)
^ = mean square velocity {cm^ls~^) (C)
The average value of the kinetic energy of translation of molecules (jmC^) is
a direct measure of the absolute temperature of a gas, and therefore the average
kinetic energy of molecules of all gases is the same at the same temperature.
1.3.5 Molecular Mean Free Path 17
1.3.5
MOLECULAR MEAN FREE PATH
The average distance a molecule moves before colliding with another (collisions with chamber walls being excluded) is called the mean free path (mfp) and is given by
1 1 kT
A — Vl i^nd,^) y/lTTdiP (22)
where d^ = molecular diameter (~ 10 "^ cm) n = number of molecules per unit volume Example:
At 760 torr, mfp for air at 20°C = 6.4 X 10 "^ cm At 10 "^ torr, mfp for air at 20°C = 49 m
Derivation: Consider a molecule of diameter d^, velocity v, moving in a gas of density n. The molecule moves distance vdt in time dt so the molecule will collide if there is another molecule of the same diameter within the volume:
8V=7rdo^vdt (23) Since n = molecules/cm^, the volume associated with 1 molecule is l/n/cm^.
Thus when 8v becomes equal to l/n, a collision has occurred:
^ = TTdo^VT, ( 2 4 )
where r^ is the average time between collisions.
The mean free path = distance traveled:
A = VT, = - ^ (25) If we take into account the molecular velocity distribution, we get a more cor-
rect relation:
A = r-^ ^ (26) v27rndQ
Hence the mjp differs for various gases and is inversely proportional to the
pressure. The mean free path must not be confused with the average distance be-
An Overview of Important Points for Different Pressure Ranges
Pressure Range (torr) Mean Free Numbera of Type of
Type of Path a molecules Type of Pressure
lo2 1 ~ O O - ~ 1 0 - ~ lo-* 1 0 - l ~ Vacuum (cm) per cm' Pump Gauge
Rough or -10-5 - 10-1 -1019 - 1015 Mechanical oil-sealed, Liquid-filled U-tube
forevacuum steam ejector, or manometer, mem-
sorption pumps brane compression
f---)
(spiral) gauge Intermediate - 10' - 1 0 ' ~ - l o 1 ' Oil-ejector or oil- Thermocouple or
-
or booster booster pumps alphatron gaugesvacuum
High 1 cm to larger - 10" Oil or Hg Ordinary ionization
P
vacuum than vacuum diffusion pumps gaugevessel
Ultra-high Much larger Less than 10 l o Ion, Ti-getter, cryo-, Bayard-Alpert-type
-
vacuum than vacuum or rotary Roots-type ion gaugevessel Pumps
~~ ~ ~~~ ~
Note: Saturated water vapor pressures: at liquid N2 (- 190°C). less than
+30"C, about 10-30 torr. Saturated Hg vapor pressures, at liquid N2 or dry ice temperature, less than tom. Saturated C 0 2 vapor.
'From simple kinetic theory.
torr; at dry ice temperature (-78°C). about torr; between
+
10 and torr; at or near room temperature, about lo-'1.3.6 Number of Impacts With the Chamber Wall 19
tween molecules, which remains very small even at high vacuum, whereas the mean free path becomes very long due to the small size of molecules and the re- sulting unlikelihood of a collision occurring.
i.3.6
NUMBER OF IMPACTS WITH THE CHAMBER WALL
The impact frequency is a quantity of considerable interest in vacuum technology is the number of molecules that strike a surface in unit time. From kinetic theory, it can be shown that rate of bombardment of each unit surface area is
r = ii-.i(2SY° (27,
4 2 V TTm I The volume density is given by
9.656 X 10 >«^ (28) T
and
thus
T
Ml= 1.45 X lO'*! j - ) (29)
r = 3.5 X 10^2 PI{MT) ^'^ molecules-Vcm-2 (30) where F is in torr
M is in g n s i n ° K
P is pressure in torr M is molecular weight
At a pressure of 760 torr and 20°C, for nitrogen molecules there are 2.93 X 10^^
impacts s-Vcm"-^. At a pressure of 10"^ torr and 20°C, for nitrogen molecules
there are 3.87 X 10^"^ impacts s" Vcm"'^.
1.3.7
TIME TO FORM A MONOLAYER
The number of molecular impacts per second is a difficult quantity to compre- hend. It can be expressed in a more useful way as the time required for the surface to become covered by a single layer of molecules, as for instance in surface physics studies where a clean surface is prepared under high vacuum.
At a pressure of 760 torr and 20°C, the time to form a monolayer of nitrogen molecules is 3 X 10 ~^ seconds. At a pressure of 10"^ torr and 20°C, the time to form a monolayer of nitrogen molecules is about 2000 seconds. These values have been calculated assuming an accommodation coefficient of 1, that is, assum- ing that an incident molecule sticks on first impact.
1.3.8
THERMAL TRANSPIRATION
For two chambers maintained at T^ and T2 °K and separated by a porous partition, equilibrium chamber pressures are established such that
Thermal transpiration is a process that occurs at all pressures, the porous parti- tion being necessary to ensure that at one part of the system the mean free path of the gas is large compared with system dimensions, in this case the dimensions of the pores of the porous material. In high-vacuum systems, this condition exists without the presence of the porous partition, and thermal transpiration requires that the pressure (Pi) registered by a gauge at room temperature (T^) be corrected to ob- tain the pressure (P2) existing at points maintained at a different temperature (72).
Coefficient of viscosity: If 77 = coefficient of viscosity, then
77 oc Anv (32) where m m = mass of molecule (g)
V = arithmetic average molecular velocity = 14,55 l(r/M)^^^ cm s - i Hence
It is surprising that the 77 is independent of pressure. This is verified by experi- ment at normal pressures where molecular collisions are frequent, that is, where
1.3.10 Coefficient of Diffusion 21
the assumption of the kinetic theory holds good. At low pressures, less than 10"^
torr, when the mean free path is 5 cm or more the molecules can travel directly from a moving surface to the walls of the vacuum chamber. Thus the momentum exchange between a moving surface and the walls or the drag on the moving sur- face depends on the number of molecules present (the pressure), and viscosity gauges are constructed to measure pressures below 10"-^ torr.
1.3.9
COEFFICIENT OF THERMAL CONDUCTIVITY
Thermal conductivity is the transfer of thermal energy, whereas viscosity is the transfer of mechanical energy through a gas. Kinetic theory gives an expression for the coefficient of thermal conductivity Cj similar to that for viscosity. In fact,
Cj = vC, (33) where Cy = the specific heat of the gas at constant volume and is constant over
wide ranges of pressures and temperature. With the same reasoning as applied to viscosity, it is possible to construct a thermal conductivity gauge to measure be- low 10"^ torr. Because of their simple construction, versatile control, and detec- tion circuit techniques, thermal conductivity gauges are widely used to measure pressures below 10 torn
1.3.10
COEFFICIENT OF DIFFUSION
The rate at which molecules of gas 1 diffuse into the molecules of gas 2 is given by the following formula:
^ = D ^ (34) where D = coefficient of diffusion {cm^s~^) of gas 1 through gas 2 and depends
on the concentrating gradient dp^/dx. It can be shown that T^'^ V ( l / M i + I/M2)
7 (di + d^f
D = constant X -^ \^ . ^ — (^^^
By putting M1 = M2 = 28, d^ = d2 = 3.75 X 10"^ cm, a factor for the self-
diffusion for nitrogen is obtained.
Throughput, Pumping Speed, Evacuation Rate,
Outgassing Rate, and Leaic Rate
The process of evacuation is in effect the removal of mass from the vacuum vessel: Thus the rate of mass removal (the mass flow) determines the rate at which pressure falls. The relationship between the throughput, Q, and the corre- sponding volumetric flow, 5, are related to the gas pressure as follows:
If the vessel initially contains A^ molecules of mass m/, the rate of change of the total mass m is given by
dm
~dt Substituting for A^ from the equation
dm
~di~
_ ^<
[Nm,) dt
of state {PV =dt\
miPV\
kT ) In practice, the type of gas and the temperature stant during the evacuation, so that
dm
~dt^
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. ' " '
kT
d{PV) dt
(36) NkT),
(37) can be considered to be con-
(38)
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