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Metodi sperimentali della fisica moderna Luca Gavioli Dipartimento di Matematica e Fisica

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. OUTLINE. Introduction

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Metodi sperimentali della fisica moderna Luca Gavioli Dipartimento di Matematica e Fisica

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  1. 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

  2. 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

  3. 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

  4. 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

  5. Ultra High Vacuum Apparatus

  6. Ultra High Vacuum Apparatus

  7. Gas kinetics Maxwell-Boltzmann distribution 1D N = Total number of molecules kB = Boltzmann constant N=nNA = total number of molecules n = Molecular density Maxwell-Boltzmann distribution 3D In polar coordinates Mean number of particles per unit volume between v and v+dv

  8. Gas kinetics T (°C) Maxwell-Boltzmann distribution 3D Molecular speed Most likely Average Neon @ 300 K mNe = 20 • 1.67 x 10-27 kg Quadratic mean

  9. Gas kinetics Arrival rate R: number of particles landing at a surface per unit area,unit time volume Mol. per unit volume

  10. Gas kinetics Arrival rate R of atoms at a surface per unit area kB = Boltzmann’s constant (erg/K) T = Temperature (K) p = Pressure (torr) m = Molecular mass (g) 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

  11. Gas kinetics: why the UHV H2O Residual Gas CO O2 CO2 CH4 N2 Solid Surface 1 Monolayer ~ 1014 – 1015 atoms/cm2 Bulk Solid Adsorbed Atoms & Molecules

  12. 2r Gas kinetics Mean free path 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

  13. rA rB Gas kinetics For different molecules A and B Mean free path • is so large that the collisions with walls are dominant with respect to molecular collisions

  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 @ p = 1 x 10-6 torr 10 sec @ p = 1 x 10-7 torr 100 sec @ p = 1 x 10-8 torr 1,000 sec @ p = 1 x 10-9 torr 10,000 sec @ p = 1 x 10-10 torr 100,000 sec @ p = 1 x 10-11 torr Utra High Vacuum (UHV): p = 10-10-10-11 torr

  15. Plots of relevant vacuum features vs. pressure

  16. d Gas flux through a pipe pipe p = pressure on plane dV = volume change across plane dV/dt= Volumetric flow rate [Q] = [p][L]3[t]-1 Flux Volumetric flux: variation of number of molecules through an area (Throughput)

  17. Gas flux through a pipe M = total mass Mass flux Volumetric flux Variation of mass through an area 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. d Regimes of gas flux through a pipe Flux pipe (Throughput) For  < d viscous For   d intermediate For  > d molecular Viscous S = layer contact area dvx /dy = mol speed gradient The mol-mol collisions are dominant Friction force  = viscosity laminar turbulent

  19. d Regimes of gas flux through a pipe pipe Volumetric flux mass flux For a pipe with diameter d and section d2/4 Q’ mass flux per unit section  = viscosity Reynolds number Laminar: Re<1200 turbulent: Re>2200

  20. Regimes of gas flux through a pipe Reynolds number Laminar: Q < 8 103 (T/M)d [Pa m3/s] Turbulent: Q > 1.4 104 (T/M)d [Pa m3/s]

  21. d Regimes of gas flux through a pipe viscous For  < d For   d For  > d intermediate molecular Only for intermediate and molecular flux Knudsen number = d/ intermediate 3  d/  80 d/  3 molecular 10-2 p d  0.5 p d  10-2 For air at RT

  22. Flux across pipe Pipe conductance: [C] = [L]3[t]-1 Pressures at pipe ends Pipe impedance: SI: m3s-1 cgs: lt s-1 In parallel

  23. In series Q1 = Q2 = QT or gas would accumulate

  24. Pipe conductance Viscous and intermediate regime Laminar Turbulent Molecular regime Long cylindrical pipe 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. p0 Relevant physical parameters of a pumping system Q= flux through aspiration aperture p = Vessel Pressure V = Vessel Volume 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 Effective pumping speed

  26. p0 Relevant physical parameters of a pumping system Q= flux through aspiration aperture p = Vessel Pressure V = Vessel Volume C Pumping speed S = Q/p0 Effective pumping speed [S] = [L]3[t]-1 if S = C the Se is halved

  27. p0 Relevant physical parameters of a pumping system Q= flux through aspiration aperture p = Vessel Pressure V = Vessel Volume Sources of flux (molecules) 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 Q = Q0 +Q1 S = Pumping speed p = Vessel Pressure V = Vessel Volume Long time limit Short time limit True leak rate Only the gas initially present contributes Virtual leak rate Other outgassing sources contribute

  29. Pump-down equation for a constant volume system Q = Q0 +Q1 S = Pumping speed p = Vessel Pressure V = Vessel Volume Short time limit True leak rate Constant S Q = 0 Time needed to reduce p by 50 % Vol of 1 m3 = 103 L to be pumped down from 1000 mbar to 10 mbar in 10 min = 600 s V= 1000 L P0 = 133 Pa S= 20 L/s t = 331,6 s 7.5 L/s = 27 m3/h

  30. Pump-down equation for a constant volume system 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 Ultimate pressure

  31. Example

  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 P2 P1 P0 P0 C C C S2 S3 S1 S1 = Cp0/p1 S2 = Cp1/p2 S3 = Cp2/p1

  34. Gas-solid interaction H2O CO inelastic trapped elastic CO2 physical adsorption (shortened to Physisorption): bonding with structure of the molecule unchanged Chemisorption: bonding involves electron transfer or sharing between the molecule and atoms of the surface Can be thought of as a chemical reaction CH4 N2 O2 He H2

  35. Gas-solid interaction Physisorption CO Origin: Van der Waals forces H2O CH4 CO2 O2 N2 Typical q: 6 - 40 kJ/mol = 0,062 - 0,52 eV /molecule He H2 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 N2 Typical q: 40 - 1000 kJ/mol = 0,52 - 10 eV /molecule He H2 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 Boltzmann factor probability per second that a molecule will desorb

  38. Gas-solid interaction probability per second that a molecule will desorb p(t) = probability that it is still adsorbed after elapsed t p(t+dt) = p(t) x (1-dt) O2 probability of not being desorbed after dt dp = p(t+dt) - p(t) = - dt p(t) average time of stay

  39. Gas-solid interaction average time of stay At RT  1013 s−1 Molecule dependance O2 97 kJ / mol = 1 eV / molecule Temperature dependance Note: Simple model Neglects all other interactions, surface diffusion, adsorption sites so a can change

  40. Desorption P = 1000 mbar P = 10-7 mbar pumping Equilibrium Far from equilibrium till…. Experimental relation Gas flux /area  = 0.5  = 1 for metals  = 1  = 0.5 for elastomers q1 5x10−8 mbar L s−1cm-2 1 mbar L Outgassing rate  1012 molec s−1cm-2 Nat 2.46x1019

  41. Desorption H2O How important is the molecule/surface interaction energy? Rate of desorption N2 fall of pressure at RT 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 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 p2 = 1x10-8 mbar p1 = 1000 mbar H2O CO CO2 CH4 N2 O2 He H2 Residual Gas

  44. Gas-solid permeation p1 = 1000 mbar p2 = 1x10-9 mbar Permeation is a complex process Adsorption Residual Gas Dissociation Solution into the solid Diffusion Recombination Desorption

  45. Gas-solid permeation p1 = 1000 mbar p2 = 1x10-9 mbar Permeation process can be quantified trough Phenomenological quantities 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 ls-1cm-2 m3s-1m-2

  46. Gas-solid permeation For a given gas A = wall area d = wall thickness depending on diffusion mechanisms He Kp = Permeability coefficient p = 13 mbar d = 1 mm cm3s-1cm-2 Pa-1 m3s-1m-1Pa-1

  47. Gas-solid permeation Metal – gas Kp Table of gas permeability

  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) Henry’s law c = gas concentration 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 Sievert’s law Valid for low concentrations and for metals Note the high solubility of H2 in Ti,Zr

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