Uses of Vacuum in Microfabrication Rough Vacuum High Vacuum Ultra-High Vacuum wafer chucks evaporation surface analysis load locks ion implantation molecular beam epitaxy (MBE) sputtering Fundamentals of Micromachining reactive ion etching (RIE) low pressure chemical vapor deposition (LPCVD) Vacuum Systems Units of Pressure Measurement Outline • 1 atmosphere = • Vacuum principles – 760 mm Hg = 760 torr • Vacuum pumps – 760,000 millitorr or microns • Vacuum materials and components – 29.9213 in. Hg • Vacuum instrumentation – 14.6959 psi • Vacuum systems – 1.01325 bar 760 mm Hg – 1013.25 millibar 33.93 ft H2O – 101,325 pascals (Pa) – 407.189 in. H2O – 33.9324 ft. H2O 1 Pascal = 1 N/m2 1 Torr = 1 mm Hg 1 micron = 1 µm Hg Ideal Gas Law - 1 Vacuum Ranges • V = volume of enclosure • Low or Rough Vacuum (LV) • N = number of molecules – 760 to 10-3 torr • Nm = number of moles = N/NA • n = particle density = N/V • High Vacuum (HV) -3 -8 • P = pressure –10 to 10 torr • T = absolute temperature • Ultra-High Vacuum (UHV) -23 • kB = Boltzmann’s constant = 1.381 x 10 J/K –10-8 to 10-12 torr 23 • NA = Avogadro’s number = 6.022 x 10 particles/mole • R = Gas constant = NAkB = 8.315 J/mole-K = PV Nm RT = PV NkBT = P nkBT Ideal Gas Law - 2 Partial Pressures of Gases in Air at STP • Historical Laws: Gas Symbol Volume Percent Partial Pressure, Torr – Boyle’s Law: P1V1 = P2V2 at constant T Nitrogen N2 78 593 V /T = V /T P – Charles’ Law: 1 1 2 2 at constant Oxygen O2 21 159 Argon Ar 0.93 7.1 – Gay-Lussac’s Law: V = V0(1 + T/273) Carbon Dioxide CO2 0.03 0.25 Neon Ne 0.0018 1.4 x 10-2 Helium He 0.0005 4.0 x 10-3 Krypton Kr 0.0001 8.7 x 10-4 -4 Hydrogen H2 0.00005 4.0 x 10 Xenon Xe 0.0000087 6.6 x 10-5 Water H2O Variable 5 to 50, typ. Distribution Functions - 2 Kinetic Gas Theory r = + + • A mathematical solution to the above equations has the • Velocity of a molecule is v vxˆx vy yˆ vz zˆ form of (A and vm are constants): − 2 2 2 2 2 2 φ 2 = vx / vm • Mean square velocity is v = v +v + v (vx ) Ae x y z = 2 • Normalization of the distribution functions: • Pressure exerted on a wall in the x-direction is Px nmvx ∞ ∞ − 2 2 − dN = NAe vx / vm dv = NA πv2 = N A = (πv2 ) 1/ 2 ∫ vx ∫ x m m 2 = 2 −∞ −∞ • If velocities for all directions are distributed uniformly,v 3vx ∞ ∞ 4 − 2 2 2 1 2 4v v / vm 3 2 3kBT v = v dN = e dv = v = 1 2 1 2 3 ∫ v ∫ 3 2 m • Thus, = = = π P 3 nmv nkBT 2 mv 2 kBT N 0 0 vm m 2k T 1/ 2 2 = B dv dv dv = 4πv dv vm x y z m • Each molecular DOF has an average excitation of kBT/2. Distribution Functions - 3 Distribution Functions - 1 • Normalized distribution function for a single velocity • Boltzmann’s postulates for an ideal gas: component (Gaussian): – The number of molecules with x-components of velocity in the 1/ 2 2 2 range of v to v + dv is proportional to some function φ of v m mv x x x x φ(v2 ) = exp− x x π only: 2 kBT 2kBT dN dN dN vx =φ (v2 ) dv vy =φ (v2 ) dv vz = φ(v2 ) dv • Normalized distribution function for velocity magnitude N x x N y y N z z 3/ 2 (Gaussian): 2 – The distribution function for speed v must be the product of the 2 m mv ψ (v ) = exp− individual and identical distribution functions for each velocity 2πk T 2k T B B component: • Normalized distribution function for a randomly directed dN velocity (Maxwellian): vx,vy,vz =ψ(v2) dv dv dv =φ (v2 )φ (v2 )φ(v2 ) dv dv dv N x y z x y z x y z 3/ 2 m mv2 Φ(v2 ) = 4π v2 exp− π 2 kBT 2kBT Gas Flow - 1 • Viscous Flow – occurs for pressures greater than 10-2 torr – gas molecules constantly collide with one another – collisions with each other are more frequent than wall collisions – gas behaves like a coherent, collective medium; it acts like a fluid • Free Molecular Flow – occurs for pressures less than 10-2 torr – gas molecules travel for large distances between collisions – collisions with walls are more frequent than with each other – gas molecules fly independently of each other Gas Flow - 2 Impingement Rates • Pipe of radius r and length l: • The number of molecules with a velocity fromv x to vx + dvx 1/ 2 φ 2 • Viscous Flow 2 f mk T is dNvx = N (vx ) dvx. η = B – Poiseuille’s equation: πσ 2 π • A = area under consideration. • Only those molecules within striking distance vxdt will hit π r 4 the wall after dt seconds. Q = C (P − P ) = ()P2 − P2 vis 2 1 η 2 1 16 l • The number of molecules with velocities from vx to vx + dvx impinging upon the wall per time dt is • Free Molecular Flow ∞ 1/ 2 2 N 2 2 k T d N = Av φ(v ) dv dt integrate: ∫ v φ(v ) dv = B vx x x x x x x π – Knudsen’s equation: V 0 2 m 1/ 2 2 r 3 8k T = − = π B − 1/ 2 Q Cmol (P2 P1) (P2 P1) dN N k T − 3 l π m i = B = ()2πmk T 1/ 2 P Adt V 2πm B Mean Free Path • MFP is the average distance a gas molecule travels before colliding with another gas molecule or the container walls. • σ is the diameter of the particles • πσ 2 is the cross-sectional area for hard-sphere collisions V k T MFP = = B Nπσ 2 2 Pπσ 2 2 For common gases, {H2O, He, CO2, CH4, Ar, O2, N2, H2}, at T = 300 K: 5 x 10-3 torr-cm Mean Free Path (cm) = Pressure (torr) Vacuum Pump Pressure Ranges Gas Throughput Ultra-High Vacuum High Vacuum Rough Vacuum • Q = PS VENTURI PUMP ROTARY PISTON MECHANICAL PUMP • P = gas pressure in torr DRY MECHANICAL PUMP ROTARY VANE MECHANICAL PUMP • S = pumping or leaking speed in liters/second (L/s) SORPTION PUMP BLOWER/BOOSTER PUMP • Q = gas throughput in torr-liters/second (torr-L/s) LIQUID NITROGEN TRAP – This is the quantity of gas moving through an orifice per unit time. DIFFUSION PUMP CRYOPUMP • Q is directly related to the power needed to move the gas: TURBOPUMP ION PUMP – 1 Watt = 7.50 torr-L/sec = 1000 Pa-L/sec TI SUBLIMATION PUMP • C = gas conductance in liters/second (L/s) • Q = C(P2 - P1) -12 -10 -8 -6 -4 -2 0 +2 Pressure in Torr (units are exponents of ten) Rotary Vane Mechanical Pumps - 2 Vacuum Pumps • Two fundamental types: Discharge Valve Interstage Relief Valve – Concentration pumps • Gas entering the inlet is compressed and expelled out an outlet • Can run continuously – Entrainment pumps Gas • Gas entering the inlet is trapped inside Ballast Valve • Must be regenerated to empty the trapped gas Second Stage First Stage Rotary Vane Mechanical Pumps - 3 Rotary Vane Mechanical Pumps - 1 • Gases are removed by compressing them slightly above Gas atmospheric pressure and then forcing them through a Ballast Inlet Outlet Valve check valve. Electric Motor • The rotary vane modules are immersed in an oil bath. Oil Fill • The purpose of the oil is to: Oil Sight – cool the pump Glass – lubricate the rotary vanes Oil – provide a lip seal for the vanes Drain – open the second stage exhaust valve at low inlet pressures Frame • They are powered by an electric motor: Oil-Filled Pump Body – Belt drive: 250 to 400 rpm – Direct drive: 1725 rpm (most common type) Sorption Pumps - 2 Rotary Vane Mechanical Pumps - 4 Neck Flange • Potential Problems: Blow-Out Plug – Oil must have low vapor pressure to achieve desired performance • Water or dirt or impurities in the oil will raise the vapor pressure – Backstreaming of oil vapor can occur at low pressures • This can be trapped in a molecular sieve filter Aluminum Body • Most often responsible for the oily smell in a vacuum chamber with Internal Fins – Large gas loads can froth the oil and prevent sealing • Gas ballast can be opened to allow froth to settle • Roughing valves should be opened slowly (feathered) to prevent this Molecular Sieve Liquid Nitrogen Bath – Belts can break on belt-drive pumps • Direct drive pumps eliminate this problem Styrofoam LN2 Bucket Sorption Pumps - 3 Sorption Pumps - 1 • Gases are pumped by – Cryocondensation: gases freeze into solid phase on cold surfaces – Cryosorption: gases are trapped in a porous molecular sieve • Vessel is cooled by immersion in liquid nitrogen (LN2) which reaches -196° C, or 77° K. • Pumping is completely oil free and has no moving parts. • Each sorption pump requires about 2-3 gallons of LN2 and about 20 minutes to cool down. • Several sorption pumps are often combined on a manifold. • Pumps must be regenerated by heating to 250° C for 30 mins. to melt frost and degas the molecular sieve material. Roots Blowers / Booster Pumps - 1 Venturi Pumps - 1 Inlet Low Pressure Roots Blower Venturi Booster Pump High Pressure Supply Air Muffler Low Vacuum Suction Outlet Rotary Vane Mechanical Pump Roots Blowers / Booster Pumps - 2 Venturi Pumps - 2 • Bernoulli’s principle is used to pull vacuum from the Inlet pinched midsection of a flow restriction.