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Lecture 03 Vacuum Systems

Lecture 03 Vacuum Systems - Fundamentals of Micromachining...

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Unformatted text preview: Fundamentals of Micromachining Vacuum Systems Outline •Vacuum principles •Vacuum pumps •Vacuum materials and components •Vacuum instrumentation •Vacuum systems 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 reactive ion etching (RIE) low pressure chemical vapor deposition (LPCVD) Units of Pressure Measurement •1 atmosphere = –760 mm Hg = 760 torr –760,000 millitorr or microns –29.9213 in. Hg –14.6959 psi –1.01325 bar –1013.25 millibar –101,325 pascals (Pa) –407.189 in. H 2 O –33.9324 ft. H 2 O 1 Pascal = 1 N/m 2 1 Torr = 1 mm Hg 1 micron = 1 µ m Hg 760 mm Hg 33.93 ft H 2 O Vacuum Ranges •Low or Rough Vacuum (LV) –760 to 10-3 torr •High Vacuum (HV) –10-3 to 10-8 torr •Ultra-High Vacuum (UHV) –10-8 to 10-12 torr Partial Pressures of Gases in Air at STP Gas Symbol Volume Percent Partial Pressure, Torr Nitrogen N 2 78 593 Oxygen O 2 21 159 Argon Ar 0.93 7.1 Carbon Dioxide CO 2 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 Hydrogen H 2 0.00005 4.0 x 10-4 Xenon Xe 0.0000087 6.6 x 10-5 Water H 2 O Variable 5 to 50, typ. Ideal Gas Law - 1 • V = volume of enclosure • N = number of molecules • N m = number of moles = N/N A • n = particle density = N/V • P = pressure • T = absolute temperature • k B = Boltzmann’s constant = 1.381 x 10-23 J/K • N A = Avogadro’s number = 6.022 x 10 23 particles/mole • R = Gas constant = N A k B = 8.315 J/mole-K T nk P T Nk PV RT N PV B B m = = = Ideal Gas Law - 2 •Historical Laws: –Boyle’s Law: P 1 V 1 = P 2 V 2 at constant T –Charles’ Law: V 1 /T 1 = V 2 /T 2 at constant P –Gay-Lussac’s Law: V = V (1 + T/ 273) Kinetic Gas Theory •Velocity of a molecule is •Mean square velocity is •Pressure exerted on a wall in the x-direction is •If velocities for all directions are distributed uniformly, •Thus, •Each molecular DOF has an average excitation of k B T/2. z v y v x v v z y x ˆ ˆ ˆ + + = r 2 2 2 2 z y x v v v v + + = 2 x x v nm P = 2 2 3 x v v = T nk v nm P B = = 2 3 1 T k v m B 2 3 2 2 1 = Distribution Functions - 1 •Boltzmann’s postulates for an ideal gas: –The number of molecules with x-components of velocity in the range of v x to v x + dv x is proportional to some function φ of v x 2 only: –The distribution function for speed v must be the product of the individual and identical distribution functions for each velocity component: z z vz y y vy x x vx dv v N dN dv v N dN dv v N dN ) ( ) ( ) ( 2 2 2 φ φ φ = = = z y x z y x z y x vz vy vx dv dv dv v v v dv dv dv v N dN ) ( ) ( ) ( ) ( 2 2 2 2 , , φ φ φ ψ = = Distribution Functions - 2 •A mathematical solution to the above equations has the form of ( A and v m are constants): •Normalization of the distribution functions: 2 2 / 2 ) ( m x v v x Ae v − = φ N v NA dv NAe dN m x v v vx...
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Lecture 03 Vacuum Systems - Fundamentals of Micromachining...

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