Syllabus Changes 3/31/03 Outgassing and Permeation 4/7/03 Thin Film Deposition 4/14/03 Spring Break No Class 4/21/03 Field Trip to Semicore Equipment Corporation (coater manufacturer) 4//28/03 System Design Calculation Wrap-up Homework #3 Length 1 Length 2 12.2 inches 4.9 inches conductance, liters/second Pbar (torr) C for 25 mm C for 50 mm 1.00E-04 407 1013 3.16E-04 420 1045 1.00E-03 460 1146 3.16E-03 588 1465 1.00E-02 994 2474 3.16E-02 2275 5664 1.00E-01 6327 15753 1
Conductance Response 100 mm Angle Valve Conductance for two Gate-Seat Distances 100000 25 mm 50 mm 10000 Liters per Second 1000 100 1.00E-04 1.00E-03 1.00E-02 1.00E-01 Pbar (Torr) Limitations of Equation 19! 15,800 l/s at 0.1 Torr! Velocity = Volume Flowrate/Area! Media Velocity is 2000 meters/sec!! Sonic Velocity is about 350 meters/s for sea level air. 2
Solution! Roth suggests using an implied sonic velocity of 192 meters/sec.! This is straightforward by introducing an aperture conductance in series with the pipe! Equation 29, where C is in l/s and A is given in square inches!c=130a Example Angle Valve Calculation conductance, liters/second Pbar (torr) 25 mm Aperture 25 & Aperture 1.00E-04 407 1634 326 3.16E-04 420 1634 334 1.00E-03 460 1634 359 3.16E-03 588 1634 433 1.00E-02 994 1634 618 3.16E-02 2275 1634 951 1.00E-01 6327 1634 1298 Pbar (torr) 50 mm Aperture 50 & Aperture 1.00E-04 1013 1634 625 3.16E-04 1045 1634 637 1.00E-03 1146 1634 674 3.16E-03 1465 1634 772 1.00E-02 2474 1634 984 3.16E-02 5664 1634 1268 1.00E-01 15753 1634 1480 3
Response 100 mm Angle Valve Conductance for two Gate-Seat Distances 100000 25 mm 50 mm 25 & Aperture 50 & Aperture 10000 Liters per Second 1000 100 1.00E-04 1.00E-03 1.00E-02 1.00E-01 Pbar (Torr) Comments! The error in the molecular conductance region would diminish if the angle valve had a real pipe connected to it.! Summary: Implement an aperture conductance in series when performing pumpdown calculations or if you suspect velocities are high. 4
Question: Consider a 100 liter Chamber with a 50 l/s exhaust system How many seconds does it take to evacuate the chamber? Answer The characteristic time constant of the system is 2 seconds. What pressure do you want to achieve? 5
What is a characteristic response time? Dissipative First order Systems Many physical process have a time dependent inclination to a restoring behavior which is dissipative in nature Take the equation Y=A/X where A is a constant Let s define Y to be Theta and X to be time, such that dθ = Kθdt dt 6
Rewriting and Integrating 1 dθ = Kdt θ lnθ = Kt + C Pressure and Temperature of Dissipative Systems We define theta as a nondimensional value that lives between zero and 1 and has a tendency towards zero For Pressure For Temperature θ = θ P Po P P max T P max T o 0 P o 7
Introducing Eq. 25. t = V S P ln 1 P 2 T=time (seconds) to pump from P 1 to P 2 V=Volume (liters) to be pumped S=delivered Pumping speed in liters/sec P 1 Starting pressure, torr P 2 Ending Pressure, torr Time constant of the system is V/S Y=A/X Y=1/X Y=5/X Y=25/x 10 9 8 7 6 Y 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 X 8
For Discussion: What is the meaning of the instantaneous time rate of change? What is the natural Log (Ln) of e? What is the natural Log of 1? What is the natural Log of 0 What is the difference between e and 10 logs? What is the area under the curve Y=1/X? Back to our pop quiz! V/S = 100/50 = 2 sec! When time = V/S, then Ln(P1/P2) = 1! And P2 is 36.78% of P1! We call this the characteristic time response. x e^x % 1 0.367879 63.2% 2 0.135335 86.5% 3 0.049787 95.0% 4 0.018316 98.2% 5 0.006738 99.3% 6 0.002479 99.8% 9
Limitations: "V/S has to be nearly constant. V is usually not a problem. The solution for S is to partition the problem where conductance changes are dramatic. Fortunately, this is easy to do in Excel. Pumpdown Example! 1 meter high by 50 cm dia. Cylindrical Vessel for a 40 mm foreline! 10 long 40 mm tubulation to an! Alcatel Dry Pump 122P operating in North America! Estimate Pumpdown time from Atmosphere to 0.01 Torr 10
Partitioning the Problem! Solution accuracy increased with greater number of steps! 7 steps are chosen here from 8 points taken from Manufacturers data! Be sure to employ equations using correct units (Torr, Inches, liters/sec) Relevant Equations are 20, 23, 24, 25 t V P ln 1 1 1 1 = + + S C C S 1 = St P2 t aperture tube p C tube = 3000P D + 80D avg L 4 3 Caperture = 130A 11
Calculation using Excel P [Torr]Sp [liters/sec] Step# P avg S avg C tube C ap St V/St [sec] ln[p1/p2] Time [sec] Cum Time 760.000 21.39 1 417.5 24.3 52842 230 22.0 8.9 2.3 20.7 0.0 75.000 27.22 2 41.25 29.2 5223 230 25.8 7.6 2.3 17.6 20.7 7.500 31.11 3 4.125 30.6 524 230 25.6 7.7 2.3 17.6 38.3 0.750 30.00 4 0.4875 28.9 64 230 18.3 10.7 1.2 12.9 55.9 0.225 27.78 5 0.15 25.8 21 230 11.1 17.7 1.1 19.4 68.8 0.075 23.89 6 0.0488 19.7 8 230 5.8 34.1 1.2 41.1 88.2 0.023 15.56 7 0.015 10.6 4 230 2.9 66.8 1.1 73.4 129.3 0.008 5.56 - - - - - - - - - 202.7 Pumpdown, sec 203 This excel datafile available for download and inspection in the Miscellaneous section of the class website. The Results Pumpdow n Time 1000 100 Pressure, Torr 10 1 0.1 0.01 0.001 0.0 50.0 100.0 150.0 200.0 Time, seconds 12
Restrictions/Assumptions! System is leak tight! There are no internal gas loads. This assumption usually valid to 1.0E-02 Torr.! Humidity does play a role, and gases are assumed dry.! No safety factor included! Pumps perform to mfgr s specification! Gas is N2 equivalent Pumpdown A summary Pump usually limits behavior at atmosphere, unless pump is much larger than the tubulation. In this case aperture limits conductance. At lowest pressures, tubulation and pump (perhaps both) can dominate the pumpdown time. Results may not be accurate, but are nevertheless highly useful for system design 13