Repetition: Physical Deposition Processes PVD (Physical Vapour Deposition) Evaporation Sputtering Diode-system Triode-system Magnetron-system ("balanced/unbalanced") Ion beam-system Ionplating DC-glow-discharge RF-glow-discharge Magnetron- discharge Arc-discharge Ion-Cluster-beam Reactive versions of the above processes Repetition: Rates and Cooling Rates PVD Effusion cell, Ion Gun High rate Evaporation electron gun High rate Sputtering magnetron -2 -1 3 10 10 1 10 10 10 R[nm/s] 29 3 6 2.9·10 2.9·10 R T [K/s] Eparticle =0.1eV 377 4 7 3.77·10 3.77·10 R T [K/s] Eparticle =1eV These extremely high achievable cooling rates show, that PVD processes (apart from being a direct transition from vapor solid state) often can be considered as non equilibrium processes . Vacuum Physics Central Termini: Mean free path: the way a gas particle (or a film particle) can travel without a collision with another particle. Impingement rate: number of particles which hit a surface per second and unit area at constant pressure. Coverage time: time needed for the formation of a full monolayer. Mean Free Path I Collision of two particles, 1 and 2 with radius r = R/2: R 1 r 2 If both particles are considered as points then a collision happens, if particle 1 is located within a disk of the area = ·R2. is called the collision cross section . Mean Free Path II Aparticle moves straight for a distance l through a gas. Within a cylinder of the volume V = l· it will collide with each particle located in V. l The cylinder contains N = n · V particles. For straight movement this is the collision number . Mean Free Path III One collision happens if N = 1. This yields the mean free path as: N 1 n V n 1 1 1 1 n n R2 4 n 2 r Macroscopic information: Particle density n, from the ideal gas equation. Microscoic information: Collision cross section contains energy dependent atom/molecule radii or the general interaction cross sections of the colliding particles. Mean Free Path IV State of movement f theo ackgroundb gas: Energetic Gas particle: coating article: relative p relative movement movement may may not be neglected be neglected 1 1 4 n2 r 2 4 n2 r Example- Free Path Mean 1 N p p2 V N B k T n 4 n r V kB T p = 0.1 Pa -23 kB=1,38·10 J/K T = 300K r = 1.5·100-1m k T B 4 p2 r 1 . 38 10 [ J23 / K ] 300 [ K ] 4 0 . 1 [ J m ]3 1 . 510 10 2 [ m ] 14 . 6 cm Mean Free Path - Rough Estimate p=5mmPa p = 1 Pa = 5 mm -4 p = 10 Pa = 50 m 100 He 10 CO ; Ar; N 2 2 1 H O 2 0,1 0,01 1E-3 Mittlere Freie Weglänge Freie Mittlere [m] 1E-4 10-5 10-4 10-3 10-2 10-1 100 101 102 Druck [Pa] ConsiderationFree Path: Scale Mean CERN – LHC: U = 2·4.3 · = 27 km p=5mmPa 5 [ mm ] p [ Pa ] 5 5 p [ Pa ] [ mm2 . ] 7 7 10 1 . 8 10 Pa7 1 . 89 10 mbar Within LHC a pressure of approx. 10-9 mbar has to be maintained, to exclude interparticle collisions. Gas Phase Transport Clausius' law of distance: x N ( x ) N ( 0 ) exp This means: A significant number of collisions happens before the mean free path is reached . Only approx. 37% of the particles reach without a collision. The mean free path is only a statistical measure. Gas Phase Transport - Statistics Consider large ensemble of single situations: dn d1 d2 Calculate the expectation value of free throw distances: x x exp d 0 x exp 0 Areal Impingement Rate I Initial situation: Gas molecules hit surface Wanted: number of gas molecules, which hit the unit surface within 1 second. Areal Impingement Rate II Approach: cylinder with unit top areas, heigth u. Only particles with a velocity component u in the direction of e1, which trespass the top cylinder surface reach the surface within unit time. u e1 1 Differential areal u du)u(n1udz cylinder particle impingement rate: volume density Areal Impingement Rate III Differential arealdz uu 1 n ( u ) du cylinder particle impingement rate: volume density Total areal Z dz n u ( u ) du impingement rate: u 0 0 m 2 u Maxwell-distribution m 2 k T of one velocity- ( u ) e B 2 m k T component: B Areal impingement rate IV Calculation of the total areal impingement rate: Z dz n u ( u ) du u 0 0 m 2 u m m k T n u e 2 kB T du n B 2 k B T 2 k B Tm 0 kB T m N p p m n V kB T m 2 k B T Areal Impingement Rate V Z = Z(p,T,m)= p m = m 2 k B T 6-2 m= 5.3·10 kg (O2) -23 kB=1,38.10 J/K T = 300K p = 0.1 Pa p = 10-4 Pa Z = 2.7·1017 s-1cm-2 Z = 2.7·10 14 s-1cm-2 etwa 270 ML/s etwa 0.2 ML/s Areal Impingement Rate - Graphic Types of Vacuum Name Pressure [Pa] Mean free Coverage time path [mm] O2, 300K [ML/s] Rough vacuum Atm15·10-552.7·105 2700 Fine vacuum 1 0.1 5 50 2700 270 High vacuum (HV) 0.1 10-5 505·105 270 0.027 -5 -10 5 10 -7 Ultra high vacuum (UHV) 10 10 5·10 5·10 0.027 2.7·10 -10 10 -7 Extreme UHV (XHV) <10 5·10 2.7·10 5·105 mm ≡ 500 m 5·1010 mm ≡ 50 000 km (!) Types of Pumps Gas transporting: + Rotary pump Rough vacuum/fine vacuum + Diffusion pump High vacuum + Turbomolecular pump High vacuum Gas adsorbing: + Cold traps Fine vacuum + Cryo pumps High vacuum/UHV + Sublimation pumps UHV + Getter pumps UHV reactive gases + Ione getter pumps UHV inert molecules (activation) Flow Types Flow through a pipe, diameter d: Laminar/turbulent: Rough vacuum/fine vacuum d d Particle collisions probable, global flow Molecular: High vacuum, UHV d d Wall collisions probable, no flow Flow Types and Pumping Systems Efficient in the laminar region: + Gas transporting pumps: Rotary pump Ejector pump + Rotary pumps, except Turbomolecular pumps Efficient in the molecular region : + Gas transporting pumps: Diffusion pump Turbomolecular pump + Gas adsorbing pumps Design Criteria for Vacuum Systems Mean free path : + Choice of pump type + Pump velocity + Dimension of pipe diameters Areal impingement rate Z: + Coverage times (e. g. surface analytics) + Impurity content in coatings (ratio of impingement rate of the coating particles and of the background gas particles) Impurities Sticking ZDes Z ... Ipingement rate 1 Z ... Desorption rate coefficient : Z Des High sticking coefficient ≈ 1 (ZDes ≈ 0): Reactive gases: O2 H20 Complex carbohydrates (pump oil) Low sticking coefficient << 1 (ZDes ≈ Z): Inert gases: Noble gases N2 CH4 Carbohydrates without reactive groups Impurities: Example Coating aterial:m Al, m = 4.5·10-26 kg 19 2 -1 Rate Al: 10 nm/s = 3 ·10 At/(m s ) -26 Impurity: O2, m = .3 ·105 kg Sticking coefficient : pprox. 1 für Al und Oa2 Temperture: 300K Wanted: Background gas pressure, at which % 1 Oxygen is incorporated unto the coating Z 1 p m O2102 O2 Z 3 1019 m 2 k T Al O2 B 2 k T p 102 3 19 10 m 1B . 11 105 Pa O2 m O2 Design Criteria: Summary Mean free path : Influences gas dynamics. Even at rather high pressures (10-2 Pa) the mean free path reaches the dimensions of average deposition chambers . Areal impingement rate Z: Crucial for coating purity. The pressure of the background gas has to be at least in the medium high vacuum to guarantee sufficient film purity. .