Metodi sperimentali della fisica moderna Luca Gavioli Dipartimento di Matematica e Fisica Università Cattolica del Sacro Cuore Via dei Musei 41, I-25121 Brescia, Italy luca.gavioli@.unicatt.it http://www.dmf.unicatt.it/~gavioli/corsi/MSFM/ www.dmf.unicatt.it/nano 1 OUTLINE • Introduction • Basic concepts of vacuum • Vacuum Hardware (pumps, gauges) • Mass Spectrometry •References • Ferrario: Introduzione alla tecnologia del vuoto: Cap 1-4, 8-11 • Woodruff – Delchar: Modern techniques of surface science (Cambridge University Press) Chap 2,3 • Chambers, Modern Vacuum Physics (Chapman & All) • Published papers 2 Research applications: impact on everyday life GETTERS NEED OF VACUUM TV TUBES LCD BACKLIGHT GAS LIGHTS (NEON, HIGH POWER LAMPS) DEWAR (FOR DRINKS) Getters are stripes of material adsorbing the gas Active material: alkali (Cs, Rb), rare earths (Yb, Lu), Hg Support: Al2O3, Zr Interaction of gas (CO2, O) with getter surface (passivation or oxidation) Role of the surface morphology: surface area/bulk 3 Basic concepts of vacuum •UHV Apparatus •Gas Kinetics •Vacuum concepts •Vacuum Pumps •Vacuum Gauges •Sample Preparation in UHV •Cleaving •Sputtering&Annealing •Fracturing •Scraping •Exposure to gas/vapor •Evaporation/Sublimation 4 Ultra High Vacuum Apparatus 5 Ultra High Vacuum Apparatus 6 Gas kinetics Maxwell-Boltzmann distribution 1D f vx N V m e 2k BT mv x2 2 k BT N = Total number of molecules kB = Boltzmann constant N=nNA = total number of molecules n = Molecular density Maxwell-Boltzmann distribution 3D 2N f v V 3 m e 2k BT mv 2 2 k BT In polar coordinates F v 4f v v 2 2N V 1 2 3 m 2 v e k BT mv 2 2 k BT Mean number of particles per unit volume between v and v+dv 7 Gas kinetics T (°C) Maxwell-Boltzmann distribution 3D F v 2N V 1 2 3 m 2 v e k BT mv 2 2 k BT Molecular speed dFv 2k BT v~ dv m v vrms 8k BT m 3k BT v m 2 Most likely Average Neon @ 300 K mNe = 20 • 1.67 x 10-27 kg Quadratic mean vrms 3 1.381023 300 610 m / s 2 1.671026 8 Gas kinetics Arrival rate R: number of particles landing at a surface per unit area,unit time vdt cos dS volume Mol. per unit volume F v dV dR F v vdV cos R dR F v v cos dV f v dV sin d d v 2dv 2 /2 R d sin cos d F (v) v 2 dv 0 0 0 N R 4V R 2 2 0 N V m e 2k BT mv 2 2 k BT 1 2 V m kT B 3 8kBT m pV NKBT m R p 2mkBT mv 2 2 2kBT v e v 3dv v 8kBT p v p N v V 4 kBT 4 2mkBT 2N 9 Gas kinetics Arrival rate R of atoms at a surface per unit area kB = Boltzmann’s constant (erg/K) T = Temperature (K) R p = Pressure (torr) p 2mkBT m = Molecular mass (g) R 3.5 10 22 p mT molecule s-1 cm2 O2 at p = 760 torr, 293 K R = 2.75 1023 molecules s-1cm2 O2 at p = 1 x 10-6 torr, 293 K R = 3.61 1014 molecules s-1cm2 10 Gas kinetics: why the UHV Residual Gas H2O CO O2 CO2 CH4 Solid Surface N2 1 Monolayer ~ 1014 – 1015 atoms/cm2 Bulk Solid Adsorbed Atoms & Molecules 11 Gas kinetics Mean free path 2r 2r The sphere with 2r is the hard volume The surface of the sphere is the effective section or cross section for impact The number of impacts per unit time is N 2 N f 4r v 4r V V 2 8kBT m 12 Gas kinetics For different molecules A and B rA rB rAB rA rB 2 N f 4rAB V 2 mAmB mA mB 8kBT Mean free path v f v V f N 4 2r 2 kBT 1 2r 2 p is so large that the collisions with walls are dominant with respect to molecular collisions 13 14 Why the UHV O2 at p = 1 x 10-6 torr, 293 K R = 3.61 1014 Sticking probability = 1 1 monolayer of atoms or molecules from the residual gas is adsorbed at the surface in: 1 sec 10 sec 100 sec 1,000 sec 10,000 sec 100,000 sec @ @ @ @ @ @ p= p= p= p= p= p= Utra High Vacuum (UHV): 1 1 1 1 1 1 x 10-6 torr x 10-7 torr x 10-8 torr x 10-9 torr x 10-10 torr x 10-11 torr p = 10-10-10-11 torr 15 Plots of relevant vacuum features vs. pressure 16 Gas flux through a pipe pipe d p = pressure on plane dV = volume change across plane dV/dt= Volumetric flow rate Flux dV Qp dt dN at Q KBT dt [Q] = [p][L]3[t]-1 Nat ; R KB NAV ; M mNAV NAV nRT Nat KBT ; pV Nat KBT n d ( pV ) dN at KBT Q dt dt Volumetric flux: variation of number of molecules through an area (Throughput) 17 Gas flux through a pipe dV Qp dt Qm d dt Mass flux Volumetric flux M = total mass Variation of mass through an area KB M dNat dNat d d (mNat ) mNAV dNat M M KBT Q Qm dt dt NAV dt KB NAV dt RT dt RT M Qm Q RT M mNAV M=mole mass Factors affecting the flux • • • • Magnitude of flow rates Pressure drop at the pipe ends Surface and geometry of pipe Nature of gases 18 Regimes of gas flux through a pipe (Throughput) Flux Qp dV dt For < d viscous For d intermediate For > d molecular d pipe Viscous S = layer contact area dvx /dy = mol speed gradient The mol-mol collisions are dominant Ff S Friction force dv x dy = viscosity laminar turbulent 19 Regimes of gas flux through a pipe Qp dV dt Qm d dt Volumetric flux pipe d mass flux For a pipe with diameter d and section d2/4 Q’ mass flux per unit section Reynolds number d Re Q' Q ' Qm 4Qm area d 2 = viscosity Laminar: Re<1200 turbulent: Re>2200 20 Regimes of gas flux through a pipe Reynolds number d Re Q' Re RT d Q Re M 4 4Qm d d 2 M 4 Q RT d Laminar: Q < 8 103 (T/M)d [Pa m3/s] Turbulent: Q > 1.4 104 (T/M)d [Pa m3/s] 21 Regimes of gas flux through a pipe dV Qp dt For < d viscous For d intermediate For > d molecular Knudsen number = d/ intermediate molecular d Only for intermediate and molecular flux 3 d/ 80 d/ 3 For air at RT kT 1 B 2 2r p kBT 1 2r 2 p 10-2 p d 0.5 p d 10-2 22 Pipe conductance: C Z Pipe impedance: Q p p0 Flux across pipe [C] = [L]3[t]-1 Pressures at pipe ends 1 SI: m3s-1 C cgs: lt s-1 In parallel Q1 C1 P Q2 C 2P Q Q1 Q2 C1 C2 P CT C1 C2 N C Ci i 1 23 In series Q1 C1 P1 Q2 C 2P2 Q1 Q2 QT PT P1 P2 C1 C 2 CT Q1 = Q2 = QT or gas would accumulate QT QT QT PT C1 C 2 CT 1 CT 1 C1 1 1 C2 C N i 1 1 Ci 24 Pipe conductance Viscous and intermediate regime d 4 p1 p2 C L 2 Laminar 5 d C p12 p22 L Turbulent Molecular regime d3 C L Long cylindrical pipe d3 4 C 1 d L 3 For air at 0 C: 11,6 d3/L [lt/s] Elbow pipe The molecules must collide with walls at least once before exiting Equivalent to a longer piper 25 Relevant physical parameters of a pumping system Q= flux through aspiration aperture p = Vessel Pressure V = Vessel Volume p0 S = Volumetric flow rate C Pumping speed S = Q/p0 [S] = [L]3[t]-1 SI: m3s-1 cgs: lt s-1 In the presence of a pipe Q at the pump inlet is the same as Q in pipe Q Sp0 Se p p S Se p0 p 1 1 p p0 p p0 p0 C Q Sp0 S Effective pumping speed S 1 Se 1 1 S Se S 1 Se 1 S 1 C 26 Relevant physical parameters of a pumping system p0 Q= flux through aspiration aperture p = Vessel Pressure V = Vessel Volume C Pumping speed S = Q/p0 1 Se 1 S Se 1 C Effective pumping speed [S] = [L]3[t]-1 SC S C if S = C the Se is halved 27 Relevant physical parameters of a pumping system Q= flux through aspiration aperture p = Vessel Pressure V = Vessel Volume p0 Sources of flux (molecules) Q Q0 Q1 Q1 = True leak rate (leaks from air, wall permeability) Q2 = Virtual leak rate (outgas from materials, walls) Outgas rate for stainless steel after 2 hours pumping: 10-8 mbar Ls-1 cm-2 28 Pump-down equation for a constant volume system dp V pS Q dt Q = Q0 +Q1 S = Pumping speed p = Vessel Pressure V = Vessel Volume Q Q1 Q0 Short time limit True leak rate Only the gas initially present contributes Long time limit Virtual leak rate Other outgassing sources contribute 29 Pump-down equation for a constant volume system dp V pS Q dt Q = Q0 +Q1 S = Pumping speed p = Vessel Pressure V = Vessel Volume Short time limit True leak rate Constant S dp V pS dt Q=0 dp S dt p V t V p0 ln S p Time needed to reduce p by 50 % 0,69 V= 1000 L P0 = 133 Pa S= 20 L/s V S t = 331,6 s p p0e S V t Vol of 1 m3 = 103 L to be pumped down from 1000 mbar to 10 mbar in 10 min = 600 s V p 1000 S ln 0 ln102 7.5L / s t p 600 7.5 L/s = 27 m3/h 30 Pump-down equation for a constant volume system dp V pS Q dt Q = Q0 +Q1 S = Pumping speed p = Vessel Pressure V = Vessel Volume Long time limit Virtual leak rate Other outgassing sources contribute dp/dt = 0 0 pS Q pu Q S Ultimate pressure 31 Example p x2 32 Differential pumping operate adjacent parts of a vacuum system at distinctly different pressures A, B to be maintained at pressures P1 and P2, P1 >> P2 A: gas in with flux QL gas to B with flux q Q1 = flux pumped S1 = Q1/p1 QL/p1 B: gas in with flux q To keep pressure p2 S2 = q/p2 q = C(p1 − p2) C p1 S2 = Cp1/p2 The size of the aperture depends by its function conductance C is determined. 33 Example CVD coatings on panels Antireflective coatings, p-n junction growth for solar panels P1 P0 C P2 C S1 S1 = Cp0/p1 P1 P0 C S2 S2 = Cp1/p2 S3 S3 = Cp2/p1 34 Gas-solid interaction H2O CO CO2 N2 H2 inelastic trapped physical adsorption (shortened to Physisorption): bonding with structure of the molecule unchanged CH4 He elastic Chemisorption: bonding involves electron transfer or sharing between the molecule and atoms of the surface Can be thought of as a chemical reaction O2 35 Gas-solid interaction Physisorption CO Origin: Van der Waals forces H2O CH4 CO2 O2 U z b c r 12 r 6 N2 H2 He Typical q: 6 - 40 kJ/mol = 0,062 - 0,52 eV /molecule The well depth is the energy of adsorption 36 Gas-solid interaction Chemisorption CO Origin: Electron sharing or transfer between molecules and surface atoms H2O CH4 CO2 O2 U z b c r 12 r 6 N2 H2 He Typical q: 40 - 1000 kJ/mol = 0,52 - 10 eV /molecule The well depth is the energy of adsorption 37 Gas-solid interaction How does this affect vacuum? Molecule trapped in the adsorbed state at temp. T potential well of depth q Dilute layer (no interactions with other mol.) How long does it stays? O2 Surface atoms have Evib = h = KBT = KBT/h At RT = 0.025/(6.63 × 10−34 ÷ 1.6 × 10−19) = 6 × 1012 s−1 1013 s−1 = number of attempts per second to overcome the potential barrier and break free of the surface. probability that fluctuations in the energy sharing will result in an energy q e q KBT e q KBT Boltzmann factor probability per second that a molecule will desorb 38 Gas-solid interaction e q KBT probability per second that a molecule will desorb p(t) = probability that it is still adsorbed after elapsed t O2 p(t+dt) = p(t) x (1-dt) probability of not being desorbed after dt dp = p(t+dt) - p(t) = - dt p(t) dp p dt p t e t average time of stay a 1 1 e q KBT 39 Gas-solid interaction average time of stay O2 a a 1013e q KBT 1 1 e q KBT At RT 1013 s−1 Molecule dependance 97 kJ / mol = 1 eV / molecule Temperature dependance Note: Simple model Neglects all other interactions, surface diffusion, adsorption sites so a can change 40 P = 1000 mbar Desorption P = 10-7 mbar pumping Equilibrium Experimental relation q1 qG 1h q1 qG t t t 1h Far from equilibrium till…. Gas flux /area = 0.5 = 1 for metals = 0.5 for elastomers =1 q1 5x10−8 mbar L s−1cm-2 1 mbar L pV Nat KBT Nat 2.46x1019 Outgassing rate 1012 molec s−1cm-2 41 Desorption How important is the molecule/surface interaction energy? H2O Rate of desorption 1 dna na a dt des q a 1013e N2 q KBT dna KT 13 10 e B dt des Simple model calculation idealized UHV system RT, V= 1 L, A = 100 cm2 S = 1 L/s only gas source: initially complete ML of specified binding energy adsorbed at the wall fall of pressure at RT q 42 Outgassing Gas is continuously released, (at relatively small rates) from walls Principally water vapor Limit to attainable vacuum achievable in reasonable times (hours) ∼10−6 mbar Origin of fluxes: Permeation Adsorption Solubility Desorption 43 Gas-solid permeation p1 = 1000 mbar p2 = 1x10-8 mbar H2O CO CO2 CH4 N2 H2 He O2 Residual Gas 44 Gas-solid permeation p1 = 1000 mbar Permeation is a complex process Adsorption p2 = 1x10-9 mbar Residual Gas Dissociation Solution into the solid Diffusion Recombination Desorption 45 Gas-solid permeation p1 = 1000 mbar Permeation process can be quantified trough Phenomenological quantities p2 = 1x10-9 mbar Residual Gas permeability =Q/(p1-p2)A Q=flux trough wall A= unit area [Q] = [p][L]3[t]-1 =[L]3[t]-1[L]-2 m3s-1m-2 ls-1cm-2 46 Gas-solid permeation cm3s-1cm-2 Pa-1 For a given gas A = wall area d = wall thickness Qp K p f p1 f p2 He A d f p p, p depending on diffusion mechanisms Kp = Permeability coefficient p = 13 mbar d = 1 mm m3s-1m-1Pa-1 47 Gas-solid permeation Metal – gas Kp Table of gas permeability Glass He, Ne, O2 p Metals H2, No rare gas Ar, p Polymers All gases p 48 Solubility Is the quantity of substance A that can be dissolved in B at given T and p For a gas Gas quantity dissolved in solid volume unit at standard conditions For undissociated molecular gas (interstitial) c = gas concentration c s p Henry’s law Valid for low concentrations and for glass and plastic materials No formation of alloys 49 Solubility H2 on metals For dissociated gas Interstitial or substitutional c s p Sievert’s law Valid for low concentrations and for metals Note the high solubility of H2 in Ti,Zr 50 Vacuum Pumps Throughput pumps • Pistons • Gears • Turbines • Jet stream Capture pumps • Cold traps • Ionization • Getters Differences: pressure range, speed, gas selectivity 51 Pressure Ranges Spanned by Different Vacuum Pumps More than one pump to HV and UHV 52 What pump to use? Pumping speed S = Q/p p = inlet pressure • Depends on the gas type • S varies with p from V S dp p pu dt V S = [L]3[t]-1 dp pS dt For a pressure range where S does not depend on p, i.e. the pumping speed is constant Sdt V p pu log(p pu ) t dp St V log(p pu ) S V ln 10 Compression ratio: This can be used to measure S or to estimate the time to reach pu pout CR pinlet 53 What pump to use? • Ultimate pressure • Time to reach the u.p. • Residual gas composition • Other (absence of magnetic fields) 54 Rotary Roughing Pump inlet Exhaust valve Oil Rotor blade Eccentric rotor Spring Cylindric body S: 2,5 ÷ 102 m3/h 0.7 ÷ 28 l/s CR: 105 Starting operating pressure: 103 mbar 1 m3/h = 0.28 l/s Pu: 10-2 mbar 55 Dual stage Rotary Roughing Pump inlet Exhaust valve Rotor blade Eccentric rotor Spring Pu: 10-3 ÷ 10-4 mbar Advantages Disadvantages • No saturation • Heavy duty • Low cost (2500 €) • Oil backstreaming • Need traps for oil vapor • Noisy 56 Rotary Roughing Pump: gas ballast CR=105 Op. temp T 70 °C The gas can liquefy inside the rotation chamber Vapor pressure Pump water vapor at 70 °C when P reaches 3.3 104 Pa The vapor liquefies and does not reach P > 1 105 Pa So the exhaust valve does not open The vapor remains inside the pump and is mixed with oil Decrease pump speed, and can damage the rotor by increasing the friction 57 Rotary Roughing Pump: gas ballast Solution: gas ballast NO gas ballast Gas ballast The valve is set to decrease the CR to 10 liquid Ballast valve The vapor does not liquefy 58 Diaphragm Pump Housing Valves Head cover Diaph. clamping disc Diaphragm Diaphragm supp. disc Connecting rod Eccentric bushing CR: 102 103 Starting operating pressure: 103 mbar Pu: ~ 1 mbar 59 Diaphragm Pump Advantages Oil-free No saturation Low cost Disadvantages High ult.pressure (4 mbar) Low pump speed Noisy 60 Root Pump Eight-shaped rotor turning in opposite direction •Clearance between rotors ~ 0.3 mm •No lubricants •CR depends on clearance Advantages Oil-free No saturation High throughput Disadvantages Need prevacuum Medium cost delicate 61 Root Pump S and CR of a root pump depend on the preliminary pump installed ahead patm pp pr root palette Sr Sp The gas flux is the same for both pumps Sr Pr Sp Pp Pp CRr Pr Sr SpCRr Palette: 60 m3/h = 16,8 l/s Sr = 16,8 x 40 = 672 l/s 62 Turbomolecular Pump S: 50 ÷ 5000 l/s CR: 105 109 Starting operating pressure: 10-2 mbar Pu: 10-10 mbar 63 Turbomolecular Pump Principle of operation Molecular regime Low pressure side High pressure side The speed distribution (ellipse) depends on the angle between V and blade The pumping action is provided by the collisions between blades and molecules 64 Turbomolecular Pump Pumping speed: depends on gas type After bake out Residual gas: H2 65 Compression Ratio of a Turbomolecular Pump 66 Turbomolecular Pump Rotor suspension Ball bearings (lubricant required) Magnetic (lubricant absent) Advantages Disadvantages No saturation Clean (magnetic) UHV Any orientation Cost Delicate Quite noisy 70 l/s ~5000 € 250 l/s ~10000 € 2000 l/s ~23000 € 67 Molecular drag pump Turbo disk Threaded stator Safety ball bearing Magnetic bearing Cylindrical Rotor Operating principle: Same as turbo but different geometry Threaded stator No blades but threads Forevacuum flange (outlet) Gas entry Electrical socket Lubricant reservoir 68 Molecular drag pump S: 40 ÷ 100 l/s CR: H2: 102 109 He: 103 104 Starting operating pressure: 1-20 mbar Pu: 10-7 mbar N2: 107 109 They are use in combination with turbo in a single mounting so Higher backing vacuum pressure Use a low CR backing pump (i.e. membrane for clean operation) 69 vapor diffusion pump Fluid is heated and ejected from nozzles at high speed baffle due to the nozzle shape and pressure difference between inside and pump cylinder. Fluid speed up to Mach 3-5 The gas molecules are compressed to the pump base through collisions with oil vapor 70 vapor diffusion pump The pumping speed and the pressure strongly depends on oil type S: 20 ÷ 600 l/s Advantages No saturation Heavy duty Low cost Starting operating pressure: 10-2 mbar Pu: 10-9 mbar Disadvantages gas reaction Liquid vapor tension Contamination Needs water cooling 71 Getter pumps Pumping mechanism - Gas-surface chemical interaction - Chemisorption - Solution of gas inside material Sublimation getters The active material is sublimated by thermal heating Non evaporable getters The active material is constituted by porous medium 72 Sublimation getter pumps Pumping mechanism - Gas-surface chemical interaction - Chemisorption - Solution of gas inside material Sublimation getters Ti or Ti – Mo filaments The material form a thin film on the pump walls that becomes the active layer The molecules are chemisorbed on the film 73 Non evaporable getter pumps Pumping operation Cartridge of porous material (Zr-16%Al) Activated by heating (750 °C) and kept at operating T 300 °C to increase molecule diffusion Problem: saturation of getter material requires cartridge change 74 Pumping speed (l/s) Getter pumps T S A m Adsorption probability area mass S strongly depends on gas sublimation > 103 l/s Non evaporable 800- 2x103 l/s A’= sublimation, A=non evaporable Zr-Al S depends on active surface saturation 75 Getter pumps With a number of panels one can obtain S > 1x104 l/s Stripes of active material Plus: Wall cooling Gas-surface weak interaction Physisorption and diffusion into the bulk But if warmed it releases the gas Advantages Pump H2 Heavy duty Low cost No contamination Disadvantages Saturation Metal vapours No rare gas pumping Pressure limit: 10-10 ÷ 10-12 mbar 76 Ion-getter pump Pumping mechanism - Gas-surface chemical interaction - Chemisorption - Solution of gas inside material - Ionization of gas molecules - Burying inside the active material Ion-getter with cathodic grinding Ti ~1 Tesla 7 KV 77 Basic processes occurring within a single cell • e- ionize molecules • Secondary e- ionize molecules Ions are accelerated to cathodes • produce secondary e• grind up cathode material • make craters Ions buried into cathode material H2: accumulates into the cathodes Produce cathode vapors Depositing also on anodes to work as getters Need regeneration by annealing 78 Ion-getter pump S: 4 ÷ 1000 l/s Advantages Heavy duty No traps No contamination Any mounting position Silent Pressure limit: 10-11 ÷ 10-12 mbar Starting operating pressure: 10-3 10-4 mbar Disadvantages High magnetic fields Low pump S for H2 Medium - high cost 79 Cryogenic pumps Pumping mechanism Liquid He cooled Cold walls - Gas – cold surface interaction - Physisorption, condensation Liquid N2 cooled Adsorbing material Adsorbing pumps Pumping mechanism - Gas – cold surface interaction - Physisorption Adsorbing porous material High surface/volume ratio Zeolites Al2O3, SiO2 H2O and N2 pumping 80 Cryopump Pumping mechanism - Gas – cold surface interaction - Physisorption and condensation Metal wall 81 vapor pressure Cryopump The gas condensation if gas pressure > vapor pressure at wall T S: 4 ÷ 100 l/s Starting operating pressure: 10-9 mbar Advantages Heavy duty No contamination Low cost Disadvantages Pressure limit: 10-10 ÷ 10-11 mbar Saturation Noisy Needs other UHV pumps 82 Ionization in gases Type of collisions: - neutral Molecule – electron - neutral Molecule – ions - neutral molecule – neutral molecule (Penning) - radiation absorption - neutral Molecule – hot metal surface Ionization of a molecule (atom) from collisions with e- - + - Ion - Ion + 83 Ionization in gases Ionization energy Electron affinity Ion - Ion + - + Less probable eV More probable 84 Atom or neutral molecule – electron collision Collision type: - elastic - atom excitation - molecule dissociation - Ionising ( e) Elastic collision Ek mev12 2 1 Ek mv 2 e 2 2 2 before collision after collision E kgas 2 2 Ek Ek 1 Ek 2 Ke 1 Ekgas Ke 1 Ek1 for gas molecules mv Relative energy loss mm e me m 2 E k E k gas 1 m me Ke me m me 10 4 10 6 m Very small energy losses 85 Elastic collision e- suffers very small energy loss for each elastic collision e- mean free path e = average space between two elastic collisions e- collision rate e = collisions number per unit time L L ete number of collisions L et e L/ Total energy loss i Ke Ek i 86 Elastic collision Apply external electric field E If e- has vin~ 0 eEe Ek 2Ke v max eE me e Maximum kinetic energy of an emoving in a gas kBT 1 e 2 r p e kBT E Ek 2 2Ke r p Depends on electric field and pressure 87 Ionization if Ek e kBT E eEe Wi 2 2Ke r p 2Ke Ionization energy e- can ionize an atom - But it can also - Increase the atom kinetic energy - Excite an e- to unoccupied bound states Ionization probability i = ionizing collisions/total collisions + - 88 Ionization e- can ionize an atom But it can also - e- trapped inside atom with formation of negative ions Due to practical measurements collisions number e- with Ek --- constant pressure --- unit lenght Specific ionization coefficient - l et e - number of (e- ion) i incidentelectron i i e p Long path to produce more ions 89 Vacuum measurement Different types of vacuometers depending on pressure range Mechanical, thermal, ionization 90 Vacuum measurement Bourdon Mechanical Membrane tube Pin wheel index To vacuum 105 102 Pa (103 1 mbar) The tube curvature changes with pressure Needs calibration Precision: 1-2% fsr 105 102 Pa (103 1 mbar) x0 R2 4T p The membrane or bellow bends with pressure Needs calibration Precision: 1-2% fsr 91 Thermal conductivity vacuometers Pirani heated filament The filament temperature, and hence the resistance depends on heat dissipation in the gas, i.e. on the gas pressure Pressure variation means T variation i.e. resistance variation. This is measured through the W. bridge V variation V W Rf 2 2 R3 R R pK gasT T 3 2 4 KfT 92 Thermal conductivity vacuometers unbalanced W V Rf 2 2 Thermal dissipation contact dissipation R3 pK gasT T 4 KfT R R 3 2 radiative dissipation = cost Stephan-Boltzmann =wire emissivity Kgas= gas thermal conductivity Kf= wire thermal conductivity =coefficient For small p, the reference bridge is 2 V02 R3 T 4 KfT W0 Rf R2 R3 Hence V V W W0 Rf 2 2 0 2 R3 R R pK gasT 3 2 p cost (V 2 V02 ) The pressure is obtained by measuring the Wheatstone voltage In general it depends on the gas type 93 Ionization vacuum gauges Hot cathode Cold cathode Based on gas ionization and current measurements 94 Ionization vacuum gauge I+ = ion current i = specific ionization coefficient I- = electron current from filament Sensitivity K = σi · λe e = electron mean free path I+ = I- i e p Directly proportional to pressure The gauge measure the total pressure Range: 10-4 – 10-12 mbar Sensitivity K = i e K depends on gas, gauge geometry, gauge potential 95 Usually one increases by designing the gometry Ionization vacuum gauge 1 tesla Cold cathode electrons from gas or field emission similar to the behavior inside the ion getter pumps Less precise due to problem of discharge current at low pressure No filament so less subject to Filament faults Range: 10-4 – 5 x10-10 mbar Note: discharge starts only by mag field to avoid high E field - induced currents 96 Mass Spectrometry Need to distinguish the intensity of specific gas molecules Collect molecules Molecule ionization Separation of different molecules Current measurement Specific mass = ion mass (a.u.)/ion charge = m ne n = ion ionization multiplicity Specific mass of Ar+ = 40 Specific mass of Ar++ = 20 For a single molecule there are many peaks, depending on n 97 Mass Spectrometry Specific mass table 98 Mass Spectrometry detector To remove secondary electrons Faraday cup All ions measured No filaments Low sensitivity sturdy Amplifier time constant large Channeltron - electron multiplyer High sensitivity Delicate Fast response 99 Quadrupole Mass Spectrometry (QMS) Storing system Detector (Channeltron) Analyser (Quadrupole field) Ion source (filament) Vacuum Chamber Quadrupole field between the rods Ions of varying mass are shot axially into the rod The applied quadrupole field deflects the ions in the X and Y directions, causing them to describe helical trajectories through the mass filter. 100 Quadrupole Mass Spectrometry (QMS) The forces are uncoupled along x,y,z axis Quadrupole potential -U-Vcos(t) U (x 2 y 2 ) r02 U+Vcos(t) r0 = rod separation Superimpose an oscillating field Vcos(t) 101 Quadrupole Mass Spectrometry (QMS) (U V cost )(x 2 y 2 ) r02 x my e y mz 0 mx e ion equation of motion x 0 r02 y my 2e (U V cost ) 2 0 r0 mz 0 mx 2e (U V cost ) Constant speed along z a 8eU m 2r02 4eV q m 2r02 Stability parameters t 2 102 Quadrupole Mass Spectrometry (QMS) d 2x (a 2q cos2 )x 0 2 d Solved numerically for different a and q d 2y (a 2q cos2 )y 0 2 d Ions oscillate in the xy plane Only some e/m values reach detector Solutions inside are real (stable trajectory) All solutions outside are imaginary and give increasing oscillation amplitudes Neutralization of the ions on the rods 103 Quadrupole Mass Spectrometry (QMS) d 2x (a 2q cos2 )x 0 d 2 Zoom to region I d 2y (a 2q cos2 )y 0 d 2 fixed U, V and the overall ion motion can (depending on the values of a and q) result in a stable trajectory causing ions of a certain m/z value to pass the quadrupole a for 8eU m 2r02 q a q Stable solutions 4eV m 2r02 U a 0,336 V 2q The line shrink to one point Only one ion with m/e ratio can reach detector V=V0cos(t) m 4V e q 2r02 104 Quadrupole Mass Spectrometry (QMS) Reducing U relative toV, an increasingly wider m/z range can be transmitted simultaneously. Zoom to region I Work line a for 8eU m r 2 2 0 q 4eV m 2r02 U a 0,336 V 2q The line enter the stable solutions region All the ions with a/q on the line will reach detector the width q of the stable region determines the resolution. By varying the magnitude of U and V at constant U/V ratio an U/V = constant scan is obtained ions of increasingly higher m/e values to travel through the quadrupole q V=V0cos(t) 105 Quadrupole Mass Spectroscopy (QMS) profiles of the residual gas H2O p ≈ 3x10-7 mbar Before bake-out H2 H2O CO+N2 CO2 p ≈ 5x10-11 mbar After bake-out 106 VACUUM SEALING Low Vacuum Clamps Viton rings No bake at high temperatures Reusable 107 VACUUM SEALING UHV HV Plastic deformation and shear Bake at high temperatures Reusable (maybe once) 108 VALVES Diaphragm Butterfly 109 VALVES Stem All metal Dynamometric sealing 110 VALVES Leak Gate High conductance UHV to air compatible Large clearance for instruments Bakeable 111 FEEDTHROUGH Multi-pin for signal or Low currents Multi-pin for high currents 112 MANIPULATION Rotation 113