A User's Guide to Vacuum Technology
Contents
1. Dd C dt whose solutions we do not describe here contains the term D9 This term has the dimensions of length and is called diffusion length For long times the diffusion front moves through the gas in proportion to Df Values of the diffusion constant for several gases in air are given in Appendix B 2 Examination of 2 31 shows the diffusion coefficient will become infinitely large as the density of molecules goes to zero This does not happen When the pressure becomes low enough so that the mean free path is much larger than the dimensions of the container say the diameter of a pipe gas diffusion is limited by molecules recoiling from walls rather than from collisions with each other At low pressures where A gt gt d the diffusion coefficient is given by D r gt 2 35 where r is the radius of the pipe and v is the thermal velocity This is called the Knudsen diffusion coefficient for a long capillary 10 2 3 4 Thermal Transpiration When a tube or orifice connects two chambers of different temperatures their relative pressures depend on the nature of the gas flow in the connecting tubing The nature of the gas flow in the tubing or orifice is characterized by A d where d is the diameter of the connecting tube or orifice For 4 lt lt d the pressure is everywhere the same in both chambers P P2 The densities in the two chambers are related by 2 3 ELEMENTARY GAS TRANSPORT PHENOMENA 23 Lae2. Pa L s 2x10 P Pa A m7 C QO Pa 2x 1 Pa A m gt 3 11 for air at 22 C when P P lt 0 52 3 3 2 Long Round Tubes A general mathematical treatment of viscous flow results in the Navier Stokes equations which are most complex to solve The simplest and most familiar solution for long straight tubes is the equation due to independently to Poiseuille and Hagen and called the Hagen Poiseuille equation __nd R B P P gt 3 12 2ni 2 F P 3 12 The gas flow for air at room temperature becomes 4 Q Pa m s nes At p P 3 13 Q A 0 0 5 1 0 Fig 3 1 Throughput versus pressure ratio in a circular orifice 3 3 CONTINUUM FLOW 31 This specific solution is valid when four assumptions are met 1 fully developed flow the velocity profile is not position dependent 2 laminar flow 3 zero wall velocity and 4 incompressible gas Assumption 1 holds for long tubes in which the flow lines are fully developed The criterion for fully developed flow was determined by Langhaar 4 who showed that a distance of l 0 0568dR was required before the flow streamlines developed into their parallel steady state profile For air at 22 C this reduces to meters 0 05030 when Q is given in units of Pa m s Assumptions 2 and 3 are satisfied if R lt 1200 and if Kn lt 0 01 The assumption of incompressibility holds true provided that the Mach number U the ratio of gas to sound velocity is lt 0 3 U 40
3. eee Le Se 2 3 dE g kT 12 GAS PROPERTIES sop e re Seen ees woebheond fee ay TE eee Pore wh we ee en pee at res ee eee er Genes Senne S AE O Gener ore Peg ee eee ee ee eee andene t T 1 a r 1 L t i T we dew a veqeee waneone 0 0 5 1 5 2 0 1 0 Relative Energy E kT Fig 2 3 Relative energy distribution of a gas at 25 C From this expression the average energy can be calculated as Eave 37 2 and the most probable energy as Ep k7 2 Notice that neither the energy distribution nor the average energy is a function of the molecular mass Each is only a function of temperature as shown in Fig 2 3 For example all the gases depicted in Fig 2 2 have the same energy distribution because they are all have the same average temperature See Fig 2 3 2 1 3 Mean Free Path The fact molecules are randomly distributed and move with different velocities implies that each travels a different straight line distance known as a free path before suffering a collision As illustrated in Fig 2 4 not all free paths are the same length The average or mean of the free paths A is found from kinetic theory 1 A rae gt 2 4 where d is the molecular diameter in meters and n is the gas density in molecules per cubic meter The mean free path is clearly gas density dependent If the temperature is constant it is also pressure dependent See 2 12
4. Values of n d and T for air at 22 C are 2 1 THE KINETIC PICTURE OF A GAS 15 Table 2 1 Low Pressure Properties of Air Pressure n d T Pa m m m m s 1 01x10 760 Torr 2 48x 107 3 43x10 6 5x10 2 86x 1027 100 75 Torr 2 45x107 3 44x10 6 6x10 2 83x1074 1 7 5 mTorr 2 45x107 1 6x107 6 6x107 2 83x107 10 7 5x10 Torr 2 45x10 7 1 6x10 6 64 2 83x10 9 10 7 5x10 Torr 2 45x10 7 41x10 664 2 83x10 7 107 7 5x10 Torr 2 45x104 3 44x10 6 6x104 2 83x1015 Particle density n average molecular spacing d mean free path A and particle flux on a surface I for T 22 C tabulated in Table 2 1 for pressures ranging from atmospheric to ultrahigh vacuum The pressure dependence of the mean free path is given for several gases in Appendix B 1 2 2 GAS LAWS Kinetic theory as expressed in 2 13 summarizes all the earlier experimentally determined gas laws However we review several of the experimentally verified laws here because they are especially helpful to those with no experience in gas kinetics When using kinetic theory we need to remember that the primary assumption of a gas at rest in thermal equilibrium with its container is not always valid in practical situations For example a pressure gauge close to and facing a high vacuum cryogenic pumping surface will register a lower pressure than when it is close to and facing a warm surface in the same vessel 1 This and other non
5. 2 Pumping Rate 360 19 1 1 Pump Size 360 19 1 2 Aerosol Formation 362 Crossover 365 19 2 1 Oil Backstreaming 366 19 2 2 Overload Criteria 369 Diffusion Pumps 369 Turbomolecular Pumps 371 Cryogenic Pumps 373 Ion Pumps 374 References 375 Problems 376 20 High Vacuum Systems 20 1 Diffusion Pumped Systems 379 Xv 345 359 379 xvi 21 22 23 20 1 1 System Operation 382 20 1 2 Operating Concerns 383 20 2 Turbomolecular Pumped Systems 385 20 2 1 System Operation 388 20 2 2 Operating Concerns 389 20 3 Ion Pumped Systems 391 20 3 1 System Operation 391 20 3 2 Operating Concerns 393 20 4 Cryogenic Pumped Systems 394 20 4 1 System Operation 394 20 4 2 Regeneration 394 20 4 3 Operating Concerns 396 20 5 High Vacuum Chambers 397 20 5 1 Managing Water Vapor References 400 Problems 400 Ultraclean Vacuum Systems 403 21 1 Ultraclean Pumps 405 21 1 1 Turbomolecular Pumps 405 21 1 2 Cryogenic Pumps 406 21 1 3 Sputter Ion TSP and NEG Pumps 406 21 2 Ultraclean Chambers 407 21 2 1 Chamber Materials and Components 407 21 2 2 Chamber Pumping 409 21 2 3 Pressure Measurement 412 References 412 Problems 413 High Flow Systems 415 22 1 Mechanically Pumped Systems 417 22 2 Throttled High Vacuum Systems 419 22 2 1 Process Chambers 419 22 2 2 Turbo Pumped 421 22 2 3 Cryo Pumped 424 References 429 Problems 429 Multichamber Systems 431 23 1 Flexible Substrates 432 23 2 Rigid Substrates 434 23 2 1 Inline Syst
6. 2 Relative velocity distribution of several gases at 25 C The average velocities of several gas and vapor molecules are given in Appendix B 2 The root of the mean square velocity is Vms 3k7 m The rms velocity is the square root of the average or mean of each velocity squared times the number of particles with that velocity For Maxwell Boltzmann statistics the average velocity is always 1 128 times as large as Vp While Vms 1 225v In Fig 2 1 we illustrated the temperature dependence of the velocity distribution As the temperature is increased the peak is broadened and shifted to a higher velocity We may also plot 2 1 for different gases having the same temperature Figure 2 2 illustrates the velocity distribution for H He H20 N2 CO2 and Xe There are two concepts illustrated in Figs 2 1 and 2 2 First the average velocity of a particle is proportional to 7 m An increase in temperature or decrease in mass causes an increase in a particle s velocity and the frequency with which it collides with other particles or nearby walls Second not all the particles in a distribution have the same velocity The Maxwell Boltzmann distribution is quite broad over 5 of the molecules travel at velocities greater than two times the average velocity 2 1 2 Energy Distribution Maxwell and Boltzmann also derived an energy distribution which is based on the same assumptions as the velocity distribution It is dn 2N EY e EMT
7. 6 1 Molar Flow Mass Flow and Throughput 109 6 2 Rotameters and Chokes 112 6 3 Differential Pressure Techniques 114 6 4 Thermal Mass Flow Meter Technique 115 6 4 1 Mass Flow Meter 115 6 4 2 Mass Flow Controller 120 6 4 3 Mass Flow Meter Calibration 120 References 121 Problems 121 7 Pumping Speed 7 1 Pumping Speed 123 7 2 Mechanical Pumps 124 7 3 High Vacuum Pumps 125 7 3 1 Measurement Techniques 125 Pump Dependence 126 Measurement of Water Vapor Pumping Speed 126 Pumping Speed at the Chamber 127 7 3 2 Measurement Error 128 References 130 Problems 130 81 109 123 xii 8 10 Residual Gas Analyzers 133 8 1 Instrument Description 133 8 1 1 Ton Sources 134 Open Ion Sources 135 Closed Ion Sources 136 8 1 2 Mass Filters 139 Magnetic Sector 139 RF Quadrupole 141 Resolving Power 145 8 1 3 Detectors 145 Discrete Dynode Electron Multiplier 147 Continuous Dynode Electron Multiplier 148 8 2 Installation and Operation 150 8 2 1 High Vacuum Operation 150 Mounting 150 Stability 151 8 2 2 Medium and Low Vacuum Sampling 153 Differentially Pumped Sampling 153 Miniature Quadrupoles 156 8 3 RGA Calibration 156 8 4 RGA Selection 158 References 159 Problems 160 Interpretation of RGA Data 161 9 1 Cracking Patterns 161 9 1 1 Dissociative Ionization 161 9 1 2 Isotopes 162 9 1 3 Multiple Ionization 163 9 1 4 Combined Effects 163 9 1 5 Ion Molecule Reactions 165 9 2 Qualitative Analysis 166 9 3 Quantitative Analysis 172 9 3 1
8. Tech 6 175 1957 M Pirani and J Yarwood Principles of Vacuum Engineering Reinhold New York 1961 p 100 10 For example see L M Lund and A S Berman J Appl Phys 37 2489 1966 11 C Neumann Math Phys K 24 49 1872 12 J C Maxwell Philos Trans R Soc London 170 231 1879 13 M C L Siu J Vac Sci Technol 10 368 1973 pw DEAN 24 21 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 GAS PROPERTIES PROBLEMS State the assumptions that form the basis of kinetic theory Consider a 1 cm diameter pipe 10 meters long a Sketch the self diffusion constant of air in this pipe over the pressure range 0 01 Pa to 10 Pa b Knowing that the diffusion front moves as d Dt estimate the time required for air to diffuse to the end of the 10 meter long pipe over the pressure range given in a The diffusion constant for gas 1 in gas 2 Di2 describes how gas a gas of one molecular weight diffuses in the background of a second gas For the case where the diffusing gas 1 is light m lt lt mp and is present in a small concentration n lt lt m derive a simplified relationship for 2 30 This happens during helium leak checking Room temperature N molecules are directed toward a surface 100 cm distant To what pressure must a chamber be evacuated in order that the molecules reach the surface on average without first colliding with another Nz molecule
9. has been calculated as 2 3 ELEMENTARY GAS TRANSPORT PHENOMENA 21 E aAP I T where oe 0 0 _1 qyt Dy 03 G0 8 y DG 2 28 This equation has the same general form as 2 25 for free molecular viscosity A is the free molecular heat conductivity and a 2 a are the accommodation coefficients of the cold surface hot surface and system respectively If molecules can thermally equilibrate with the surface say by making many small collisions on a rough surface will have a value that approaches unity If however the same surface is smooth and the molecule recoils without gaining or losing energy a will approach zero The kinetic picture of heat conductivity is rather like viscosity except that energy transfer determines the thermal conductivity and momentum transfer determines the viscous drag Even so Fig 2 5 can be sketched for the thermal conductivity of a gas between two parallel plates where the vertical axis has dimensions of heat flow In SI A has units of W m K Pa whereas E has units of W m Tables of the accommodation coefficient are given elsewhere 3 7 The accommodation coefficient of a gas is not only dependent on the material but on its cleanliness surface roughness and gas adsorption as well When the heated parallel plate is replaced by a heated fine wire the situation changes In the case of a heated fine wire the upper knee of the curve is not dependent on the ratio of A to pla
10. labels have been added throughout the text Basic SI units for pressure Pa time s and length m will be assumed in all formulas unless noted differently within a formula statement IAM WH ad VACUUM TECHNOLOGY REFERENCES W E K Middleton The History of the Barometer Johns Hopkins Press Baltimore 1964 P A Redhead Vacuum 53 137 1999 T E Madey J Vac Sci Technol A 2 110 1984 M H Hablanian J Vac Sci Technol A 2 118 1984 J H Singleton J Vac Sci Technol A 2 126 1984 P A Redhead J Vac Sci Technol A 2 132 1984 T E Madey and W C Brown Eds History of Vacuum Science and Technology American Institute of Physics New York 1984 P R Johansen J Vac Sci Technol A 8 2798 1990 9 D J Santeler et al Vacuum Technology and Space Simulation NASA SP 105 National Aeronautics and Space Administration Washington DC 1966 p 34 CHAPTER 2 Gas Properties In this chapter we discuss the properties of gases at atmospheric and reduced pressures The properties developed here are based on the kinetic picture of a gas Kinetic theory has its limitations but with it we are able to describe particle motion pressure effusion viscosity diffusion thermal conductivity and thermal transpiration of ideal gases We will use these ideas as the starting point for discussing gas flow gauges pumps and systems 2 1 KINETIC PICTURE OF A GAS The kinetic pi
11. preparing this book they make no representation or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages including but not limited to special incidental consequential or other damages For general information on our other products and services please contact our Customer Care Department within the U S at 877 762 2974 outside the U S at 317 572 3993 or fax 317 572 4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print however may not be available in electronic format Library of Congress Cataloging in Publication Data Library of Congress Cataloging In Publication Data is available 0 471 27052 0 Printed in the United States of America 100987654321 For Jean Carol Paul and Amanda This Page Intentionally Left Blank Preface This book is intended for the vacuum system user the university student technician engineer manager or scientist who wishes a fundamental understanding of modern vacuum technolog
12. this perspective that the previous edition of this book has been revised Important formulas have been denoted with a for emphasis Easy questions have been emphasized with a f Thanks are due to countless researchers who individually and collaboratively have advanced this field by creative solutions to real problems I also thank Dr Bruce Kendall for his insightful comments and thoughtful review J F O Hanlon Tucson Arizona Contents ITS BASIS 1 Vacuum Technology 3 1 1 Units of Measurement 6 References 8 2 Gas Properties 9 2 1 Kinetic Picture of a Gas 9 2 1 1 Velocity Distribution 10 2 1 2 Energy Distribution 11 2 1 3 Mean Free Path 12 2 1 4 Particle Flux 13 2 1 5 Monolayer Formation Time 14 2 1 6 Pressure 14 2 2 Gas Laws 15 2 2 1 Boyle s Law 15 2 2 2 Amonton s Law 16 2 2 3 Charles Law 16 2 2 4 Dalton s Law 16 2 2 5 Avogadro s Law 16 2 2 6 Graham s Law 17 2 3 Elementary Gas Transport Phenomena 18 2 3 1 Viscosity 18 2 3 2 Thermal Conductivity 20 2 3 3 Diffusion 21 2 3 4 Thermal Transpiration 22 References 23 Problems 24 3 Gas Flow 25 3 1 Flow Regimes 25 3 2 Throughput Mass Flow and Conductance 27 3 3 Continuum Flow 28 3 3 1 Orifices 29 3 3 2 Long Round Tubes 30 3 3 3 Short Round Tubes 32 3 4 Molecular Flow 32 3 4 1 Orifices 33 3 4 2 Long Round Tubes 34 3 4 3 Short Round Tubes 34 3 4 4 Other Short Structure Solutions 36 Analytical Solutions 37 Monte Carlo Technique 38 3 4 5 Combining Molec
13. 10 GAS PROPERTIES 2 1 1 Velocity Distribution As the individual molecules move about they collide with elastic collisions Elastic collisions conserve energy whereas the colliding particle s velocity is changed after each collision We stated that all velocities are possible but not with equal probability The distribution of particle velocities calculated by Maxwell and Boltzmann is 3 2 dn _ cas ye my KKT 2 1 wW T T m is the particle mass and T is the Kelvin temperature The relation between the Kelvin scale and the Celsius scale is T K 273 16 T C In 2 1 N is the total number of particles and k is Boltzmann s constant Figure 2 1 illustrates 2 1 for nitrogen molecules air at three temperatures It is a plot of the relative number of molecules between velocity v and v dv We see that there are no molecules with zero or infinite velocity and that the peak or most probable velocity v is a function of the average gas temperature The particle velocity also depends on the molecular mass the peak velocity can be expressed as vp 2k7 m The arithmetic mean or average velocity v is useful when describing particle flow V2 gt 2 2 nm 0 500 1000 1500 2000 Velocity m s Fig 2 1 Relative velocity distribution of air at 0 C 25 C and 400 C 2 1 THE KINETIC PICTURE OF A GAS 11 1 0 Xenon 0 8 S 0 6 2 Z 2 0 4 0 2 0 f 0 500 1000 1500 2000 Velocity m s Fig 2
14. A User s Guide to Vacuum Technology Third Edition This Page Intentionally Left Blank A User s Guide to Vacuum Technology Third Edition This Page Intentionally Left Blank A User s Guide to Vacuum Technology Third Edition John F O Hanlon Professor Emeritus of Electrical and Computer Engineering The University of Arizona WILEY INTERSCIENCE A JOHN WILEY amp SONS INC PUBLICATION Copyright 2003 by John Wiley amp Sons Inc All rights reserved Published by John Wiley amp Sons Inc Hoboken New Jersey Published simultaneously in Canada No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording scanning or otherwise except as permitted under Section 107 or 108 of the 1976 United States Copyright Act without either the prior written permission of the Publisher or authorization through payment of the appropriate per copy fee to the Copyright Clearance Center Inc 222 Rosewood Drive Danvers MA 01923 978 750 8400 fax 978 750 4470 or on the web at www copyright com Requests to the Publisher for permission should be addressed to the Permissions Department John Wiley amp Sons Inc 111 River Street Hoboken NJ 07030 201 748 6011 fax 201 748 6008 e mail permreq wiley com Limit of Liability Disclaimer of Warranty While the publisher and author have used their best efforts in
15. For air at room temperature the mean free path is most easily remembered by one of the following expressions 0 67 _ 0 005 cm P Pa or A cm P Tort gt 2 5 2 1 THE KINETIC PICTURE OF A GAS 13 fq Fig 2 4 Individual molecular paths where has units of cm and P is the pressure in Pascal or Torr respectively Kinetic theory also describes the distributions of free paths N Ne 2 6 M is the number of molecules in the volume and N is the number of molecules that traverse a distance x before suffering a collision Equation 2 6 states that 63 of the collisions occur in a distance 0 lt x lt A whereas about 37 of the collisions occur in range lt x lt 5A Only about 0 6 of the particles travel distances greater than 54 without suffering a collision For the case of two gases a and b the mean free path of a in b is 1 hq 22 2 an n KG d a 2 7 2 1 4 Particle Flux The concept of particle flux is helpful in understanding gas flow pumping and evaporation According to kinetic theory the flux T of an ideal gas striking a unit surface or crossing an imaginary plane of unit area from one side is T particles m s nv 4 gt 2 8 where n is the particle density and v the average velocity On substituting 2 2 we see that 14 GAS PROPERTIES V 2 T ES 2 9 2am The particle flux is directly proportional to the particle density and the square root o
16. Getter 258 14 2 Ion Pumps 256 References 260 Problems 261 Cryogenic Pumps 263 15 1 Pumping Mechanisms 264 15 2 Speed Pressure and Saturation 267 15 3 Refrigeration Techniques 271 15 4 Cryogenic Pump Characteristics 276 15 4 1 Medium Vacuum Sorption Pumps 276 15 4 2 High Vacuum Gas Refrigerator Pumps 279 15 4 3 High Vacuum Liquid Pumps 283 References 284 Problems 286 MATERIALS Materials in Vacuum 289 16 1 Metals 290 16 1 1 Vaporization 290 16 1 2 Permeability 290 16 1 3 Outgassing 291 Dissolved Gas 292 Surface and Near Surface Gas 295 16 1 4 Structural Metals 299 16 2 Glasses and Ceramics 300 16 3 Polymers 306 References 309 Problems 311 Joints Seals and Valves 313 17 1 Permanent Joints 313 17 1 1 Welding 314 17 1 2 Soldering and Brazing 318 17 2 17 3 17 1 3 Joining Glasses and Ceramics 319 Demountable Joints 321 17 2 1 Elastomer Seals 322 17 2 2 Metal Gaskets 328 Valves and Motion Feedthroughs 329 17 3 1 Small Valves 330 17 3 2 Large Valves 332 17 3 3 Special Purpose Valves 335 17 3 4 Motion Feedthroughs 337 References 341 Problems 342 18 Lubrication 18 1 18 2 18 3 Lubrication Processes 345 Rheology 347 18 2 1 Absolute Viscosity 347 18 2 2 Kinematic Viscosity 348 18 2 3 Viscosity Index 348 Lubrication Techniques 349 18 3 1 Liquid Lubrication 349 18 3 2 Grease Lubrication 352 18 3 3 Dry Lubrication 353 References 355 Problems 356 SYSTEMS 19 Rough Vacuum Pumping 19 1 19
17. Isolated Spectra 172 9 3 2 Overlapping Spectra 173 References 177 Problems 178 PRODUCTION Mechanical Pumps 183 10 1 Rotary Vane Pump 183 10 2 Rotary Piston Pump 187 11 12 13 10 3 Lobe Pump 189 10 4 Claw Pump 193 10 5 Scroll Pump 194 10 6 Screw Pump 195 10 7 Diaphragm Pump 196 10 8 Mechanical Pump Operation 198 References 199 Problems 199 Turbomolecular Pumps 11 1 Pumping Mechanism 201 11 2 Speed compression Relations 203 11 2 1Maximum Compression Ratio 203 11 2 2 Maximum Speed 206 11 2 3 General Relation 207 11 3 Ultimate Pressure 209 11 4 Turbomolecular Pump Designs 210 11 5 Turbomolecular Drag Pumps 213 References 214 Problems 215 Diffusion Pumps 12 1 Pumping Mechanism 217 12 2 Speed Throughput Characteristics 219 12 3 Boiler Heating Effects 223 12 4 Backstreaming Baffles and Traps 224 References 227 Problems 228 Pump Fluids 13 1 Fluid Properties 229 13 1 1 Vapor Pressure 229 13 2 2 Other Properties 233 13 2 Pump Fluid Types 234 13 2 1 Mineral Oils 234 13 2 2 Synthetic Fluids 235 Esters 236 Silicones 236 Ethers 237 Fluorochemicals 237 13 3 Fluid Selection 238 13 3 1 Rotary Vane Piston and Lobe Pumps 238 13 3 2 Turbomolecular Pumps 240 xiii 201 217 229 14 15 16 17 13 3 3 Diffusion Pumps 241 13 4 Reclamation 244 References 244 Problems 245 Getter and lon Pumps 247 14 1 Getter Pumps 247 14 1 1 Titanium Sublimation Pumps 248 14 1 2 Nonevaporable
18. NT Units of measurement present problems in many disciplines and vacuum technology is no exception The use of noncoherent vacuum units has been common in the US long after the adoption of System International 1 1 UNITS OF MEASUREMENT 7 300 280 O76 6432101 2 345 Logio Pressure Fig 1 1 Relation between the atmospheric pressure and the geometric altitude Reprinted with permission from The Handbook of Chemistry and Physics 59th ed R C Weast Ed copyright 1978 The Chemical Rubber Publishing Co CRC Press Inc West Palm Beach FL 33409 The meter kilogram second MKS system was first introduced over a half century ago its use became commonplace only after a decade or more of classroom education by instructors committed to change In a similar manner those who teach vacuum technique will lead the way to routine use of SI units Instruments are manufactured for use in a global economy and their readings can be displayed in several formats The advantages of using a coherent unit system are manifold Calculations become straightforward and logical and the chance for error is reduced Incoherent units such as permeation constant the volume of gas at standard temperature and pressure per material thickness per material area per sec pressure difference are cumbersome Additionally these permeation units mask their relation to solubility and diffusion Ultimately SI units will be routinely used To assist with this change dual
19. What is the advantage of low pressure chemical vapor deposition over atmospheric pressure chemical vapor deposition Explain why the viscosity of a gas should increase with increasing particle mass and temperature The viscosity of a liquid decreases with increasing temperature The air surrounding it cools an object that is heated by a constant power source What would happen to its temperature if the surrounding air were replaced a by helium and b by argon What is the heat flow by thermal conduction between two 0 1 m sheets of copper with a temperature difference of 100 C and which are separated by 0 1 cm of CO at pressures of a 10 Pa b 10 Pa and c 100 Pa A 0 5 cm diameter tube interconnects two chambers The left hand chamber is heated to a temperature of 250 C while the right hand chamber remains at room temperature Over what pressure range is the pressure in the two chambers the same Over what pressure range does the transpiration equation apply Sketch a plot of Pho Peoia Versus the pressure of the cold chamber Assume diffuse scattering 2 10In Problem 2 9 nitrogen is replaced by helium Sketch a plot of Phot Pecora Versus the pressure of the cold chamber in the transition region How does this compare to the curve in Problem 2 9 for helium CHAPTER 3 Gas Flow In this chapter we discuss the flow of gas at reduced pressures as it is encountered in a vacuum system Gas flow is complex and the
20. ature of the gas wall interaction Lorentz 15 assumed the walls of a pipe are molecularly rough that is molecules are scattered according to the cosine law diffuse reflection Molecules hit a wall oscillate in potential wells and recoil in a direction that is independent of their arrival angle In diffuse reflection scattered molecules have the greatest probability of recoiling at an angle of 90 from the surface Particles not scattering at 90 have as much likelihood of going forward through the tube as going backward toward the source See Fig 3 3 Clausing 16 solved this problem by calculating the probability that a molecule entering the pipe at one end will escape at the other end after making diffuse collisions with the walls Clausing s solution is in the form of an integral that is difficult to evaluate For simple cases such as round pipes Clausing and others have generated approximate solutions The solution has been tabulated in many standard 3 24
21. be anything from a simple mechanical pump or aspirator for exhausting a vacuum storage container to a complex system such as an underground accelerator with miles of piping that is maintained at ultrahigh vacuum Removal of air at atmospheric pressure is usually done with a displacement pump A displacement pump is one that removes the air from the chamber and expels it to the atmosphere Rotary vane and piston pumps are examples of pumps used to exhaust gases at atmospheric pressure Liquid nitrogen capture pumps or sorption pumps have also been designed for exhausting gases at atmospheric pressure They are used only on small chambers because of their finite gas sorption Rotary vane piston and sorption pumps have low pressure limits in the range 107 10 Pa Pumps that will function in a rarefied atmosphere are required to operate below this pressure range Several displacement and capture pumps can remove air at these low pressures The diffusion pump was the first high vacuum pump It is a displacement pump Its outlet pressure is below atmosphere The turbomolecular pump a system of high speed rotating turbine blades can also pump gas at low pressures The outlet pressures of these two pumps need to be kept in the range 0 5 50 Pa so they must exhaust into a rotary vane or piston backing pump or fore pump If the diffusion or turbomolecular pump exhaust gas flow would otherwise be too great a lobe blower will be placed between
22. below atmospheric 2 2 2 5 Avogadro s Law In 1811 Avogadro observed that pressure and number of molecules were proportional for a given temperature and volume ei Rw ed T V constant 2 19 N N Two terms standard temperature and pressure and mole often cause confusion Standard temperature and pressure STP conditions refer to a 2 2 GAS LAWS 17 gas with a temperature of 0 C at pressure of 1 atmosphere However in Chapter 6 we note that some manufacturers of thermal mass flow controllers assume a temperature of 20 C when calibrating flow meters this is called NTP or normal temperature and pressure In SI Avogadro s number of any gas species is N 6 02252x10 and occupies a molar volume of V 22 4136 m Avogadro s number of molecules is known as a mole In SI the unit of volume is the m and the unit of mass is the kg To avoid confusion with cgs units we will use kg mole For example one kg mole of oxygen contains 6 02252x10 molecules and weighs 32 kg Its density at STP is therefore 32 kg 22 4136 n or 1 45 kg m 2 2 6 Graham s Law In the nineteenth century Graham studied the rate of effusion of gases through very small holes in porous membranes He observed the rate of effusion to be inversely proportional to the square root of the density of the gas provided that the pressure and temperature were held constant Since the density of a gas is proportional to its molecular weight Gra
23. cture of a gas is based on several assumptions i The volume of gas under consideration contains a large number of molecules A cubic meter of gas at a pressure of 10 Pa and a temperature of 22 C contains 2 48x10 molecules whereas at a pressure of 10 Pa a very high vacuum it contains 2 5x10 molecules Indeed any volume and pressure normally used in the laboratory will contain a large number of molecules ii Adjacent molecules are separated by distances that are large compared with their individual diameters If we could stop all molecules instantaneously and place them on the coordinates of a grid the average spacing between them would be about 3 4x10 m at atmospheric pressure 10 Pa The diameter of most molecules is of order 2 6x10 m and their separation distances are 6 15 times their diameter at atmospheric pressures For extremely low pressures say 107 Pa the separation distance is about 3x10 m iii Molecules are in a constant state of motion All directions of motion are equally likely and all velocities are possible although not equally probable iv Molecules exert no force on one another except when they collide If this is true then molecules will be uniformly distributed throughout the volume and travel in straight lines until they collide with a wall or with one another Using these assumptions many interesting properties of ideal gases have been derived Some elementary properties are reviewed here
24. dden out rush of gas from scattering 3 3 CONTINUUM FLOW 29 process debris that may reside on the chamber floor The flow in the throttling orifice is turbulent at high pressures In the high flow limit of the turbulent flow region the velocity of the gas may reach the velocity of sound in the gas Further reduction of the downstream pressure cannot be sensed at the high pressure side so that the flow is choked or limited to a maximum or critical value of flow The value of critical flow depends on the geometry of the element for example orifice short tube or long tube and the shape of the entrance A detailed discussion of critical flow has been given by Shapiro 3 Rather than divide the discussion of continuum flow into viscous turbulent and critical it is easier to discuss the flow in terms of the geometry of the pipe We divide this discussion into orifice flow long tube flow and short tube flow and we give equations for each region 3 3 1 Orifices For tubes of zero length an extremely thin orifice the flow versus pressure is a rather complicated function of the pressure Consider a fixed high pressure say atmospheric pressure on one side of the orifice with a variable pressure on the downstream side As the downstream pressure is reduced the gas flowing through the orifice will increase until it reaches a maximum At this ratio of inlet to outlet pressure the critical pressure ratio the gas is flowing at the speed of sou
25. ems 435 23 2 2 Cluster Systems 440 xvii 23 3 Instrumentation Systems 443 References 444 Probiems 444 24 Leak Detection 447 24 1 Instruments 448 24 1 1 Forward Flow Leak Detector 448 24 1 2 Counter Flow Leak Detector 449 24 2 Performance 450 24 2 1 Sensitivity 450 24 2 2 Response Time 452 24 2 3 Sampling Pressurized Chambers 453 24 3 Leak Hunting Techniques 453 References 457 Problems 457 Symbols 459 APPENDIXES A Units and Constants 463 A l Physical Constants 463 A 2 SI Base Units 463 A 3 Conversion Factors 464 B Gas Properties 466 B 1 Mean Free Paths of Gases as a Function of Pressure 466 B 2 Physical Properties of Gases and Vapors at T 0 C 467 B 3 Cryogenic Properties of Gases 468 B 4 Gas Conductance and Flow Formulas 469 B 5 Vapor Pressure Curves of Common Gases 475 B 6 Appearances of Discharges in Gases and Vapors at Low Pressures 477 C Material Properties 478 C 1 Outgassing Rates of Vacuum Baked Metals 478 C 2 Outgassing Rates of Unbaked Metals 479 C 3 Outgassing Rates of Unbaked Ceramics and Glasses 480 C 4 Outgassing Rates of Elastomers 480 C 5 Permeability of Polymeric Materials 481 C 6 Vapor Pressure Curves of Solid and Liquid Elements 482 C 7 Outgassing Rates of Polymers 485 C 8 Austenitic Stainless Steels 486 xviii D Isotopic Abundances E Cracking Patterns E 1 Cracking Patterns of Pump Fluids 492 E 2 Cracking Patterns of Gases 494 E 3 Cracking Patterns of Common Vapors 495 E 4 Cracking Pa
26. equilibrium situations will be discussed as required 2 2 1 Boyle s Law In 1662 Robert Boyle demonstrated that the volume occupied by a given quantity of gas varied inversely as its pressure when the gas temperature remained the same PV PV N T constant 2 14 This is easily derived from the general law by multiplying both sides by the volume V and noting that N nV 16 GAS PROPERTIES 2 2 2 Amontons Law Amontons discovered the pressure in a confined chamber increased as the temperature increased Amontons law can be expressed as ites N V constant 2 15 T T In 1703 he constructed an air thermometer based on this relationship This later came to be known as the law of Gay Lussac 2 2 3 Charles Law The French chemist Charles found in 1787 that gases expanded and contracted to the same extent under the same changes of temperature provided that no change in pressure occurred Again by the same substitution in 2 13 we obtain uR N P constant 2 16 T T 2 2 4 Dalton s Law Dalton discovered in 1801 that the total pressure of a mixture of gases was equal to the sum of the forces per unit area of each gas taken individually By the same methods for a mixture of gases we can develop the relation P nkT n kT n kT n kT 2 17 which reduces to P PR P P 2 18 pressures and densities respectively Equation 2 18 is called Dalton s law of partial pressures and is valid for pressures
27. f T m 2 1 5 Monolayer Formation Time The time to saturate a surface with one layer of molecules is a function of the molecular arrival rate I an molecular size Assuming each molecule sticks and occupies surface area d the time to form a monolayer is 1 4 t _ 2 10 ig Fa nvd At ambient temperature a monolayer of air d 0 372 nm v 467 m s will form in about 2 5 s at a pressure of 10 Pa The formation time will be longer if the sticking coefficient is less than unity 2 1 6 Pressure The absolute pressure on a surface is defined as the rate at which momentum mv is imparted to a unit surface A molecule incident on a surface at an angle from the normal will impart a total impulse or pressure of 2mv cos Q By integrating over all possible angles in the half plane we find that the pressure is P nmvin 2 11 The total energy of a molecule however is proportional to its temperature 2 B Yas 24T 2 12 2 2 Equations 2 11 and 2 12 may be combined to form the ideal gas law P nkT gt 2 13 If n is expressed in units of m k in joules per kelvin and T in kelvin then P will have units of pascal Pa A pascal is a newton per square meter and the fundamental unit of pressure in System International SI Simply divide the number of pascals by 133 32 to convert to units of Torr or divide by 100 to convert to units of millibars A conversion table is included in Appendix A 3
28. gat eo 3 14 U sound nd PU oina 3 For the special case of air at 22 C we have Q Pa L s lt 9 0x10 d P gt 3 15 This is a value of flow that may be exceeded in many cases and would render the results of the Poiseuille equation incorrect Relationships for viscous flow between long coaxial cylinders and long tubes of elliptical triangular and rectangular cross section have been tabulated by Holland et al 5 Williams et al 6 give the relation for flow in a long rectangular duct for air at 20 C b cm h cm P P Q Pa L s 4 6Y TA A P 8 16 where the duct cross section dimensions b and h and the length are given in cm The function Y h b is obtained from the following table h b Y h b Y h b Y 1 0 0 4217 0 4 0 30 0 05 0 0484 0 8 0 41 0 2 0 175 0 02 0 0197 0 6 0 31 0 1 0 0937 0 01 0 0099 In the limit k lt lt b the air flow reduces to the one dimensional solution of Sasaki and Yasunaga 7 Q Pa L s 46y fom bcm A P p P 617 i cm 2 32 GAS FLOW Again h b and l are given in cm The flow in 3 16 and 3 17 like 3 13 is inversely proportional to viscosity and may be accordingly scaled for other gases These relations for long tubes are of limited use They are of use in components such as mass flow meter tubes controlled leaks and piping that connects chambers with remotely located pumps and gas tanks In most practical cases we connect chambers with as short a duct as pos
29. hams law can be stated as 1 2 PESIO a Mg P T constant 2 20 effusion rate M a Grahams law describes how a helium filled balloon loses its gas more quickly than an air filled balloon Fig 2 5 Dalton s law states that the total pressure is the sum of the partial pressures 18 GAS PROPERTIES 2 3 ELEMENTARY GAS TRANSPORT PHENOMENA In this section approximate views of viscosity thermal conductivity diffusion and thermal transpiration are discussed We state results from kinetic theory without derivation 2 3 1 Viscosity A viscous force is present in a gas when it is undergoing shear Figure 2 5 illustrates two plane surfaces one fixed and the other traveling in the x direction with a uniform velocity The coefficient of absolute viscosity n is defined by the equation F du n 2 21 A n P7 2 21 where F is the force in the x direction 4x is the surface area in the x z plane and du dy is the rate of change of the gas velocity at this position between the two surfaces Because the gas stream velocity increases as the moving plate is approached those molecules crossing the plane A from below 1 in Fig 2 5 will transport less momentum across the plane than will those crossing the same plane from above 2 in Fig 2 5 The result is that molecules crossing from below the plane will on the average reduce the momentum of the molecules from above the plane in the same manner molecules crossing from ab
30. ial or research application In this edition the discussion of gauges pumps and materials has been updated where relevant to reflect changes in practice Spinning rotor gauges are no longer a laboratory curiosity Ultrahigh vacuum gauges though limited in their availability will be a necessity in next generation production deposition systems Ultraclean low dead volume metrology and valves along with superior materials and cleaning techniques have made contamination free manufacturing a reality Ultraclean vacuum once the domain of the researcher is now routinely used for high volume production of semiconductor chips and storage vii viii PREFACE media However methodologies for reaching low pressures in a clean manner have changed significantly No longer are single chamber systems baked for twenty four hours Rather cassette based load unload chambers serve as high volume interfaces between atmosphere and ultraclean process chambers These chambers which can be accessed in serial or random order are only exposed to atmosphere during maintenance Large efficient multichamber medium and highvacuum systems are used in high speed coating of numerous consumer products such as window glass solar cells video tape printer paper eyeglass lenses automobile headlamps plastic films and security devices The gap in knowledge and training between those who manufacture and those who use vacuum equipment continues to widen It is from
31. ion In this region gas molecules collide with each other and with walls A viscous gas is characterized by a Knudsen number of lt 0 01 Knudsen s number Kn is a dimensionless ratio of the mean free path to a characteristic dimension of the system say the diameter of a pipe 25 26 GAS FLOW a Kn gt 3 1 F 3 1 In continuum flow the diameter of the pipe is much greater than the mean free path and the character of the gas flow is determined by gas gas collisions The flow has a maximum velocity in the center of the channel and zero velocity at the wall Continuum flow can be either turbulent or laminar viscous The boundary between turbulent and viscous flow can be expressed in terms of Reynolds dimensionless number R for round pipes Upd q R 3 2 where p is the mass density kg m of the gas of viscosity n flowing with stream velocity U in a pipe of diameter d Reynolds number is used to characterize the relative quantity of gas flow It is a ratio of the shear stress due to turbulence to the shear stress due to viscosity Alternatively it tells something about the forces necessary to drive a gas system in relation to the forces of dissipation due to viscosity Reynolds 1 found two flow situations dynamically similar when this dimensionless number was the same When R gt 2200 the flow was always turbulent and when R lt 1200 the flow was always viscous 2 In the region 1200 lt R lt 2200 the flow
32. ission from The Handbook of Chemistry and Physics 59th ed R C Weast Ed copyright 1978 The Chemical Rubber Publishing Co CRC Press Inc West Palm Beach FL 33409 Carbon dioxide data from Mauna Kea Hawaii 2000 Data since 1955 are available as http stratus mlo hawaii gov Projects GASES co2graph htm 101 323 2 Pa or 760 Torr The partial pressure of water vapor is not given in this table because it constantly changes At 20 C a relative humidity of 50 corresponds to a partial pressure of 1165 Pa 8 75 Torr making it the third largest constituent of air The total pressure changes rapidly with altitude as shown in Fig 1 1 whereas its proportions change slowly but significantly In outer space the atmosphere is mainly H with some He 6 In the pressure region below 10 Pa gases evolving from material surfaces contribute more molecules per second to the total gas load than do the gases originally filling the chamber The correct pump is not the only requirement needed to reach low pressures the materials of construction techniques for joining components surface cleaning techniques and operational procedures are all critically important In the remaining chapters the pumps gauges and materials of construction and operational techniques are described in terms of fundamental gas behavior The focus is on the understanding and operation of vacuum systems for a variety of technological applications 1 1 UNITS OF MEASUREME
33. ition or slip flow range where the pipe is several mean free paths wide the velocity at the wall is not zero as in viscous flow and the reflection is not diffuse as in free molecular flow Now let us define throughput mass flow and conductance and develop some practical gas flow formulas 3 2 THROUGHPUT MASS FLOW AND CONDUCTANCE Throughput is the quantity of gas the volume of gas at a known pressure that passes a plane in a known time d dt PV Q In SI throughput has units of Pa m s Because 1 Pa 1 N m and 1 J 1 N m the units could be expressed as J s or watts 1 Pa m s 1 W Throughput is the energy per unit time crossing a plane The energy in question is not the kinetic and potential energy contained in the gas molecules but rather the energy required to transport the molecules across a plane Expressing gas flow in units of watts is awkward and not used but it helps to explain the concept that throughput is energy flow Throughput is a volumetric dimension volume of gas unit time Throughput cannot be converted to mass flow unless the temperature is specified It is in many ways unfortunate that vacuum technologists have chosen to use a volumetric unit which conveys incomplete information Volumetric flow does not conserve mass Mass flow molar flow or molecular flow are respectively the quantity of substance in units of kg kg moles or molecules that passes a plane in a known time Equation 3 3 describes
34. k note security and laser and inkjet paper have joined this group The background pressure must be reduced to the very high vacuum range for electron microscopy mass spectroscopy crystal growth and x ray and electron beam lithography and storage media production For ease of reading we call the very high vacuum region high vacuum and call the pumps high vacuum pumps Pressures in the ultrahigh vacuum range were formerly the domain of the surface analyst materials researcher or accelerator technologist Critical high volume production applications such as semiconductor devices thin Table 1 1 Vacuum Ranges Pressure Range Degree of Vacuum Pa Low 10 gt P gt 33x10 Medium 3 3x10 gt P gt 107 High 10 gt P gt 10 Very high 104 gt P gt 10 Ultrahigh 107 gt P gt 10 Extreme ultrahigh 10t gt P Source Reprinted with permission from Dictionary for Vacuum Science and Technology M Kaminsky and J M Lafferty Eds American Vacuum Society New York 1980 101323 3 Pa 1 atmosphere VACUUM TECHNOLOGY 5 film media heads and extreme UV lithography systems require ultrahigh vacuum base pressures to improve yield by reducing gaseous impurity contamination Additionally processes carried out in these systems must be free of particle contamination so we call them ultraclean vacuum systems A vacuum system is a combination of pumps valves and pipes which creates a region of low pressure It can
35. l gt 2 36 n T When the orifice diameter is such that gt gt d the flux of gas through the orifice is given by 2 8 gt 2 37 1 2 _M2 8kT 2 Pa nm 2kTram In steady state the net flux between the two chambers must be zero for example T 1 2 l 21 with the result P T 1 2 a i gt 2 38 P D Equations 2 36 and 2 38 can be used to calculate the pressures within furnaces or cryogenic enclosures when the pressure gauge is located outside the enclosure at a different temperature Equation 2 36 is used at high pressure A lt d 10 and 2 38 is used at low pressure A gt 10d Thermal transpiration was discovered by Neumann 11 and studied by Maxwell 12 who predicted the square root dependence given in 2 38 The geometry and reflectivity from walls of the connecting tubing introduce deviations from the theory Siu 13 has studied these effects and has predicted that 2 38 is obtained in short tubes only for specular reflection and in long tubes only for diffuse reflection REFERENCES 1 R W Moore Jr Proc 8th Nat l Vac Symp 1961 1 Pergamon New York 1962 p 426 2 E H Kennard Kinetic Theory of Gases McGraw Hill New York 1938 p 9 Ref 2 pp 135 205 and 291 337 S Dushman Scientific Foundations of Vacuum Technique 2nd ed J M Lafferty Ed Wiley New York 1962 p 35 Langmuir Phys Rev 1 337 1913 Ref 4 p 6 Ref 4 p 68 H von Ubisch Vak
36. low with significant gas expansion at the vacuum side 3 4 MOLECULAR FLOW A gas is called a molecular gas when Kn gt 1 0 This is equivalent to stating that Pd lt 6 6 Pa mm 4 95 Torr mm for air at 22 C In this region the flow is called molecular flow For completeness we could say that R lt 1200 however we cannot define a Reynolds number in the region where viscosity cannot be defined The molecular flow region is theoretically the best understood of any flow type This discussion focuses on orifices infinite tubes finite tubes and other shapes including combinations of components in molecular flow 3 4 MOLECULAR FLOW 33 d 100unm P 10 m f l Px P 105 104 103 10 10 P 44 560 Pa Pressure Pa 100 Distance um Fig 3 2 Pressure profile through a fine leak in a vacuum wall as calculated with Santeler s model This model assumes Poiseuille flow through the tube with a precipitous drop in pressure immediately within the vacuum vessel caused by choked flow at the exit 3 4 1 Orifices If two large vessels are connected by an orifice of area A and the diameter of the orifice is such that Kn gt 1 then the gas flow from one vessel P n to the second vessel P2 m is given by Q vAn m AR P 3 18 and the conductance of the orifice is C pa T4 gt 3 19 which for air at 22 C has the value C m s 116 4 m7 3 20 or C L s 11 6 A cm gt 3 21 From 3 18 we note a
37. n interesting property of the molecular flow regime Gas can flow from vessel 2 to vessel 1 at the same time gas is flowing from vessel 1 to vessel 2 without either of the gases colliding with gas that originated in the other vessel 34 GAS FLOW 3 4 2 Long Round Tubes The diffusion method of Smoluchowski 10 and the momentum transfer method of Knudsen 11 and Loeb 12 were the first used to describe gas flow through very long tubes in the free molecular flow region For circular tubes both derivations yield conductances of n d Can v 3 22 tube 75 v For air at 22 C this becomes 3 Case m s 121 3 23 Conductance relations for long noncircular tubes have been derived 13 3 4 3 Short Round Tubes The flow equation for long tubes 3 22 indicates the conductance becomes infinite as the length tends toward zero whereas in Section 3 4 1 we showed the conductance actually becomes v4 4 Dushman 14 developed a solution to the problem of short tubes by considering the total conductance to be the sum of the reciprocal conductances of an aperture and a section of tube of length 1 1 1 Coral C rube C aperture As l d 0 3 24 reduces to 3 19 and as l d it reduces to 3 22 Although this equation gives the correct solution for the extreme cases it is not correct for the intermediate It can be in error by as much as 12 15 The difficulty in performing calculations for short tubes lies in the n
38. nature of the solution depends on the flow rate and gas properties as well as the geometry and surface properties of the duct We begin by defining the flow regimes and introducing the concepts of throughput mass flow and conductance We describe the gas throughput and conductance for several kinds of flow We show how approximation techniques and probability methods are used to solve complex problems such as flow in ducts containing entrance and exit orifices aperture plates or other irregular shapes 3 1 FLOW REGIMES Gas flow regimes are characterized by the nature of the gas and by the relative quantity of gas flowing in a pipe The nature of the gas is determined by examining Knudsen s number whereas Reynolds number describes the relative flow In the viscous gas region high pressures the flow is called continuum flow The flow can be further described as turbulent or viscous Turbulent flow is chaotic like the flow behind a moving vehicle or the rising smoke some distance from a cigarette Laminar or stream flow occurs when the velocity and surface irregularities are small enough for the gas to flow gently past obstructions in laminar streamlines In the molecular gas region the mean free path is so long in comparison to the pipe size that the flow is entirely determined by gas wall collisions The flow in this region is called molecular flow Between the continuum flow region and the molecular flow region is the transition reg
39. nd in the gas The gas flow through the orifice is given by E 1 2 pcde 2y kT 1 2 P Vy Y P y D y ly 1m P P gt 3 8 forl gt P P 2 2 y 1 0 The factor C accounts for the reduced cross sectional area as the high speed gas stream continues to decrease in diameter after it passes through the orifice This phenomenon is called the vena contracta For thin circular orifices C is 0 85 If the downstream pressure P is further reduced the gas flow will not increase because the gas in the orifice is traveling at the speed of sound and cannot communicate with the high pressure side of the orifice to tell it that the pressure has changed In this region P cannot influence the flow so long as P P lt 2 A 1 The ratio of specific heats is whose values are given in Appendix B 4 The flow is given by o ane 2 2y Y 2 B ABC ne m y y 1 gt 3 9 for P P lt 2 y y 30 GAS FLOW This value is called critical or choked flow See Fig 3 1 This limit is important in describing flow restrictors devices that control gas flow and the rate of pumping or venting in a vacuum system choked flow in air to air load locks and flow through small leaks from atmosphere In any of these relationships the conductance can be found from C Q P P2 For air at 22 C A 1 4 and P P 0 525 the choked flow limit is Q Pa m s 200P AC gt 3 10 for air at 22 C when P P lt 0 52
40. ove the plane will increase the momentum of those molecules below the plane To an observer this viscous force appears to be frictional actually it is not It is merely the result of momentum transfer between the plates by successive molecular collisions Again from kinetic theory the coefficient of viscosity is q E nm 2 22 Moving Surface U 2 u od oe arc ae zZ Fixed Surface Fig 2 6 Origin of the viscous force in a gas 2 3 ELEMENTARY GAS TRANSPORT PHENOMENA 19 When the gas density is measured in units of m the molecular mass in kg the velocity i in m s and the mean free path i in m will have units of N s m or Pa s One Pa s is equal to 10 poise A more rigorous treatment of viscosity 3 yields a result with a slightly different numerical coefficient n 0 499nmvd gt 2 23 Substituting 2 2 and 2 4 into this result yields 0 499 4mkT ee 2 24 From 2 24 we See that kinetic theory predicts that viscosity should increase as mT and decrease as the square of the molecular diameter An interesting result of this simple theory is that viscosity is independent of gas density or pressure This theory however is valid only in a limited pressure range If there were a perfect vacuum between the two plates there would be no viscous force because there would be no mechanism for transferring momentum from one plate to another This understanding leads to the conclusion that 2 24 is valid a
41. rrent divided by a potential drop As with electrical charge flow there are situations transition viscous and choked flow in which the gas conductance is nonlinear that is a function of the pressure in the tube Unlike electrical charge flow there are cases in which the molecular conductance depends not only on the object but also on the nature of adjacent objects and how they allow particles to be diffusely scattered from their surfaces We will explore this last issue in detail when we describe methods for combining conductances in the molecular flow regime 3 3 CONTINUUM FLOW A gas is called a viscous gas when Kn lt 0 01 The flow in a viscous gas can be either turbulent R gt 2200 or viscous R lt 1200 Equation 3 2 can be put in a more useful form by replacing the stream velocity with Q U 3 5 AB 3 5 If we replace the mass density using the ideal gas law 3 2 becomes anm g gt 3 6 nkTr d For air at 22 C this reduces to r 841x10 SOT 3 7 In ordinary vacuum practice turbulent flow occurs infrequently Reynolds number can reach high values in the piping of a large roughing pump during the initial pumping phase For a pipe 250 mm in diameter connected to a 47 L s pump R at atmospheric pressure is 16 000 Turbulent flow will exist whenever the pressure is greater than 1 5x10 Pa 100 Torr In practice roughing lines are often throttled during the initial portion of the roughing cycle to prevent the su
42. s can be evaporated from a pure source without reacting in transit Molecules or atoms can be accelerated to a high 3 4 VACUUM TECHNOLOGY energy and sputter away or be implanted in the bombarded surface Electrons or ions can be scattered from surfaces and be collected The energy changes they undergo on scattering or release from a surface can be used to probe or analyze the surface or underlying layers For convenience the subatmospheric pressure scale has been divided into several ranges Table 1 1 lists these ranges The required vacuum level depends on the application Epitaxial growth of semiconductor films reduced pressure epitaxy and laser etching of metals are two processes that are performed in the low vacuum range Sputtering plasma etching and deposition low pressure chemical vapor deposition ion plating and gas filling of encapsulated heat transfer modules are examples of processes performed in the medium vacuum range Pressures in the high vacuum range are needed for the manufacture of traditional low and high tech devices such as microwave power cathode ray and photomultiplier tubes light bulbs architectural and automotive glazing decorative packaging degassing of metals vapor deposition and ion implantation A number of medium technology applications including medical microwave susceptors electrostatic dissipation films and aseptic packaging use films fabricated in a vacuum environment 8 Retail security ban
43. s long as the distance between the plates is greater than the mean free path for example the gas is viscous For a rarefied gas in which the ratio of the mean free path to plate separation A y gt gt 1 the viscous force can be expressed as 4 mh 2 25 A 4kT B Free Molecular Viscous Drag Shear Pressure F A Pa 0 10 10 10 10 10 10 10 10 Pressure Difference Between Plates Pa Fig 2 7 Viscous shear force between two plates at 22 C 20 GAS PROPERTIES where the term in parentheses is referred to as the free molecular viscosity The free molecular viscosity is directly proportional to the molecular density n P kT available to transfer momentum between the plates It is valid in the region A gt gt y The constant B in 2 25 is related to the slip of molecules on the plate surfaces For most vacuum conditions B 1 Figure 2 6 illustrates the magnitude of the viscous force caused by air at 22 C between two plates moving with a relative velocity of 100 m s for three plate separations Equation 2 24 was used to calculate the asymptotic value of the viscous drag at high pressures and 2 25 was used to calculate the free molecular limit A more complete treatment of the intermediate or viscous slip region is given elsewhere 4 The viscous shear force is independent of the plate spacing as long as the mean free path is larger than the spacing This idea was used by Langmuir 5 to construc
44. sible to reduce unwanted pressure drops and we need to know relationships which are valid for these cases 3 3 3 Short Round Tubes As we noted above the flow in short tubes does not obey the Poiseuille equation The flow may switch from viscous to to critical flow without there being any pressure region in which the Poiseuille equation is valid This problem has been treated in several ways Dushman 8 gives a non linear relation for flow in short round tubes It is valid only for unchoked flow Santeler 9 devised a technique in which he models the short tube as an aperture in series with a short tube of length 7 The problem is formulated by assuming an unknown pressure P between the tube and the aperture This is the pressure that would be measured by a gauge just inside the end of the tube that was pointing upstream Figure 3 2 illustrates an application of this technique calculating the pressure drop and airflow through a 100 pm diameter leak in a 1 cm thick vacuum wall Santeler s model uses 3 13 with P replaced by P The flow through the aperture was modeled using 3 10 with P as its inlet pressure and high vacuum P 0 as its outlet pressure Since the two flows are in series they are equal the solution is P 44 560 Pa The answer can be checked to ensure that the assumption of choked flow in the aperture is valid if not then 3 8 must be used in place of 3 10 This model predicts Poiseuille leak f
45. t a viscosity gauge in which damping was proportional to pressure 2 3 2 Thermal Conductivity Heat conductivity between two infinite parallel plates is explained by kinetic theory in a manner analogous to that used to explain viscosity The diagram in Fig 2 6 could be relabeled to make the top plate stationary at temperature T gt and the lower plate a stationary plate at a temperature T where 7 lt 7 gt Heat conduction can be modeled by noting that the molecules moving across the plane toward the hotter plate carry less energy than those moving across the plane toward the cooler surface The heat flow can be expressed as Haik 2 26 dy where H is the heat flow and K is the heat conductivity The simple theory predicts that the heat conductivity K is expressed by K nc where n is the viscosity and c is the specific heat at constant volume This simple theory is correct only to an order of magnitude A more detailed analysis which accounts for molecular rotational and vibrational energy yields K 1oy 5 ne gt 2 27 where y is the ratio of specific c c When y has the units of Pa s and c has units J kg K then K will have units of W m K At room temperature the heat conductivity and viscosity both increase as mT d For infinite parallel plates K does not depend on pressure as long as the mean free path is smaller than the plate spacing In the low pressure region the heat transfer between parallel plates 6
46. te separation but rather on the ratio of to hot wire diameter 8 9 Both thermocouple and Pirani gauges operate in a region in which the heat conduction from the heated wire is linearly dependent on pressure However the knee in their linear range begins at a mean free path equal to a few multiples of the wire diameter and not at a mean free path related to the wire envelope distance 2 3 3 Diffusion Diffusion is a complex phenomenon This discussion has been simplified by restricting it to the situation in a vessel that contains two gases whose compositions vary slowly throughout the vessel but whose total number density is everywhere the same The coefficient of diffusion D of two gases is defined in terms of their particle fluxes I dn dn hep Pee 2 29 1 ze 2 he 2 29 22 GAS PROPERTIES These fluxes result from the partial pressure gradient of the two gases The result from kinetic theory when corrected for the Maxwellian distribution of velocities and for velocity persistence is 9 Eam 1 1 j a EE _ a m m gt 2 30 3n n F m Xda doz y i l 12 where D is the constant of inter diffusion of the two gases In SI it has units of m s For the case of self diffusion the coefficient is 4 KTV D gt 2 31 u ey If the density n is replaced by P KT it becomes apparent that the diffusion constant is approximately proportional to T and P The diffusion equation dC dt
47. the exhaust of the diffusion or turbomolecular pump and the inlet of the rotary pump to pump gas at an increased speed in this intermediate pressure region Capture pumps can effectively remove gas from a chamber at low pressure They do so by freezing molecules on a wall cryogenic pump chemically reacting with the molecules getter pump or accelerating the molecules to a high velocity and burying them in a metal wall ion pump Capture pumps are more useful as high vacuum pumps than as atmospheric exhaust pumps because the number of molecules to be captured at high vacuum is less than the number removed during initial evacuation from atmosphere Air is the most important gas to understand because it is in every vacuum system It contains at least a dozen constituents whose major constituents are described in Table 1 2 The differing ways in which pumps remove air and gauges measure its pressure can be understood in terms of the partial pressures of its components The concentrations listed in Table 1 2 are those of dry atmospheric air at sea level total pressure 6 VACUUM TECHNOLOGY Table 1 2 Components of Dry Atmospheric Air Content Pressure Constituent vol ppm Pa N2 78 084 0 004 79 117 O 20 946 0 002 21 223 CO 0 037 37 5 Ar 0 934 0 001 946 357 Ne 18 18 0 04 1 842 He 5 24 0 004 0 51 Kr 1 14 0 01 0 116 Xe 0 087 0 001 0 009 H 0 5 0 051 CH 2 0 203 NO 0 5 0 1 0 051 Source Reprinted with perm
48. the relationship between molar flow and throughput Q _ Q N kg mole s 3 3 ees N kT RT oe In a similar fashion mass flow is related to throughput by N kg s MO N kT Throughput can be related to molar or mass flow only if the temperature is constant and known A spatial change in the temperature can alter the throughput without altering the mass flow We discuss applications of mass flow in Chapter 6 flow meters and in Chapter 15 where we describe cryogenically pumped systems The flow of gas in a duct or pipe is dependent on the pressure drop across the object as well as its cross sectional geometry Division of the throughput by the pressure drop across a duct held at constant temperature yields a property known as the conductance of the duct __ 2 Cesp gt 3 4 28 GAS FLOW In SI the unit of throughput is the Pa m s and the unit of conductance or pumping speed is the m s however related throughput units of Pa L s and conductance units of L s are widely used Unless explicitly stated all formulas in this chapter use the cubic meter as the volumetric unit The pressures P and P3 in 3 4 refer to the pressures measured in large volumes connected to each end of the channel or component According to 3 4 conductance is the property of the object between the points at which the two pressures are measured For those whose first introduction to flow was with electricity 3 4 is analogous to an electrical cu
49. tterns of Common Solvents 496 E 5 Cracking Patterns of Semiconductor Dopants 497 F Pump Fluid Properties F 1 Compatibility of Elastomers and Pump Fluids 498 F 2 Vapor Pressures of Mechanical Pump Fluids 499 F 3 Vapor Pressure of Diffusion Pump Fluids 500 F 4 Kinematic Viscosity of Pump Fluids 501 F 5 Kinematic Viscosity Conversion Factors 502 References 503 Index 488 492 498 505 Its Basis An understanding of how vacuum components and systems function begins with an understanding of the behavior of gases at low pressures Chapter 1 discusses the nature of vacuum technology Chapter 2 reviews basic gas properties Chapter 3 describes the flow of gases at reduced pressures and Chapter 4 discusses how gas is evolved from the surfaces of materials Together these chapters form the basis of vacuum technology This Page Intentionally Left Blank CHAPTER 1 Vacuum Technology Torricelli is credited with the conceptual understanding of the vacuum within a mercury column by 1643 It is written that his good friend Viviani actually performed the first experiment perhaps as early as 1644 1 2 His discovery was followed in 1650 by Otto von Guericke s piston vacuum pump Interest in vacuum remained at a low level for more than 200 years when a period of rapid discovery began with McLeod s invention of the compression gauge In 1905 Gaede a prolific inventor designed a rotary pump sealed with mercury The thermal conductivit
50. ular Conductances 39 Parallel Conductances 39 Series Conductances 39 Exit and Entrance Effects 44 Series Calculations 45 3 5 The Transition Region 49 3 6 Models Spanning Several Pressure Regions 50 3 7 Summary of Flow Regimes 51 References 52 Problems 53 Gas Release from Solids 57 4 1 Vaporization 57 4 2 Diffusion 58 4 2 1 Reduction of Outdiffusion by Vacuum Baking 60 4 3 Thermal Desorption 61 4 3 1 Desorption Without Readsorption 62 Zero Order Desorption 62 First Order Desorption 62 Second Order Desorption 63 4 3 2 Desorption from Real Surfaces 65 Outgassing Measurements 65 Outgassing Models 67 Reduction of Outgassing by Baking 68 4 4 Stimulated Desorption 70 4 4 1 Electron Stimulated Desorption 70 44 2 lon Stimulated Desorption 70 4 4 3 Stimulated Chemical Reactions 70 4 4 4 Photodesorption 71 4 5 Permeation 71 4 5 1 Molecular Permeation 71 4 5 2 Dissociative Permeation 73 4 5 3 Permeation and Outgassing Units 73 4 6 Pressure Limits 74 References 77 Problems 77 MEASUREMENT 5 Pressure Gauges 5 1 Direct Reading Gauges 81 5 1 1 Diaphragm and Bourdon Gauges 82 5 1 2 Capacitance Manometers 83 5 2 Indirect Reading Gauges 87 5 2 1 Thermal Conductivity Gauges 87 Pirani Gauge 88 Thermocouple Gauge 91 Stability and Calibration 92 5 2 2 Spinning Rotor Gauge 92 5 2 3 Ionization Gauges 94 Hot Cathode Gauges 94 Hot Cathode Gauge Errors 100 Cold Cathode Gauge 103 Gauge Calibration 104 References 105 Problems 106 6 Flow Meters
51. was viscous or turbulent depending on the geometry of the inlet and outlet and on the nature of the piping irregularities Laminar viscous flow the ordered flow of a gas in streamlines occurs in the region bounded by a Reynolds number lower than 1200 and a Knudsen number less than 0 01 When the mean free path is equal to or greater than the pipe diameter say Kn gt 1 and when R lt 1200 the gas is said to be a molecular gas and the flow is called molecular flow To be precise Reynolds number does not have any meaning for a gas in the free molecular regime because classical viscosity cannot be defined The nature of molecular flow is very different from laminar viscous flow Gas wall collisions predominate and the concept of viscosity is meaningless For most surfaces diffuse reflection at the wall is a good approximation that is each particle arrives sticks rattles around in a surface imperfection and is re emitted in a direction independent of its incident velocity Thus there is a chance that a particle entering a pipe in which A gt gt d will not be transmitted but will be returned to the entrance In molecular flow gas molecules do not collide with one another and gases can flow in opposite directions without interaction In the region 1 gt Kn gt 0 01 the gas is neither viscous nor molecular Flow in the transition region is difficult to treat theoretically In this range 3 1 FLOW REGIMES 27 called the trans
52. y and a user s perspective of modern laboratory and industrial vacuum technology Vacuum technology is largely secondary it forms part of other technologies that are central to analysis research development and manufacturing It is used to provide a process environment Many advances in vacuum technique have resulted from the demands of other technologies although scientists and engineers have studied vacuum for its own sake The average user is process oriented and becomes immersed in vacuum technique only when problems develop with a process or when new equipment purchases become necessary A User s Guide to Vacuum Technology 3rd Edition focuses on the operation understanding and selection of equipment for processes used in semiconductor optics and related technologies It emphasizes subjects not adequately covered elsewhere while avoiding in depth treatments of topics interesting only to the designer or curator Residual gas analysis is an important topic whose treatment differs from the usual explanation of mass filter theory Components such as the turbomolecular and helium gas refrigerator cryogenic pumps are now widely used but not well understood The discussion of gauges pumps and materials is a prelude to the central discussion of systems System designs are grouped according to their function Current designs are either single chamber or multichamber the details of each design are determined by the requirements of an industr
53. y gauge diffusion pump ion gauge and ion pump soon followed along with processes for liquefaction of helium and refinement of organic pumping fluids They formed the basis of a technology that has made possible everything from light bulbs to space simulation The significant discoveries of this early period of vacuum science and technology have been summarized in a series of historical review papers 2 7 A vacuum is a space from which air or other gas has been removed All gas cannot be removed The amount removed depends on the application and is done for many reasons At atmospheric pressure molecules constantly bombard surfaces These molecules can bounce from surfaces attach themselves to surfaces or perhaps chemically react with surfaces Air or other surrounding gas quickly contaminates a cleaned surface A clean surface for example a freshly cleaved crystal will remain clean in an ultrahigh vacuum chamber for long periods of time because the rate of molecular bombardment is low Molecules are crowded closely together at atmospheric pressure and travel in every direction much like people in a crowded plaza It is impossible for a molecule to travel from one wall of a chamber to another without colliding with many molecules By reducing the pressure to a suitably low value a molecule from one wall can travel to another without a collision Many effects become possible if molecules can travel long distances between collisions Metal
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