Gas flow modeling in MEMS based microvalves for next
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Gas flow modeling in MEMS based microvalves for next generation CVD reactor designs R.Sreenivasan, Raymond A.Adomaitis, Gary W.Rubloff SCHEMATIC OF A MEMS BASED MFC MOTIVATION GAS DISTRIBUTION FACILITIES FOR NEW TECHNOLOGIES POSE THE FOLLOWING CHALLENGES: NORMALLY OPEN MICROVALVE MODULE (NO) • 2. PARTICLES MUST BE REDUCED IN SIZE AND NUMBER: THIS REDUCTION REQUIRES INCREASED MATERIALS COMPATABILITY WITH PROCESS GASES (ESG COMPATIBLE) DECREASED DEAD SPACE VOLUMES, WELDS AND FACE SEALS • • • COST RELIABILITY HIGHER RESOLUTION 1. NORMALLY OPENED PROPORTIOANL VALVE RESISTOR FLOURINERT TM TEMPERATURE SENSOR 4mm VALVE SEAT 50 m z Si MEMBRANE ~50 MICRONS d MEMS BASED MICROVALVES FIXED AREA ORIFICE MODULE DOWNSTREAM PRESSURE SENSOR UPSTREAM PRESSURE SENSOR MODELING THE MICROVALVE ? ~.5mm 25 500 m Source : Redwood Microsystems ~2mm ~2mm NORMALLY OPEN MICROVALVE MODULE (NO) MICROVALVES DISCUSSED HERE ARE SLATED TO ADDRESS ALL OF THE ABOVE CHALLENGES SUCESSFULLY ~1mm ~1cm THE ‘SMALL’ PICTURE •MATERIALS IN Si BASED MICROVALVES ARE COMPATIBLE WITH A WIDE RANGE OF ESG FIXED AREA ORIFICE MODULE •DEAD SPACE COLUMES, WETTED SURFACES AND FACE SEALS ARE REDUCED DRAMATICALLY GAS FLOW LAYER 1 :PYREX INLET z 50 m OUTLET CRITICAL ORIFICE (CO) ~1Omm •GOOD RELIABILITY , AND HIGH RESOLUTION AND COMPARITIVELY LOWER COSTS OF THE DEVICES.. 1.5mm 1.5mm •THE APPROACH IS MODULAR WHERE MEMS BASED MODULES COMPRISING OF VALVES, PRESSURE SENSORS, MICROCHANNELS AND ORFICES ARE INTEGRATED TO BUILD MFC’S, PRESSURE REGULATORS AND SHUT OF VALVES FOR ESG GAS DISTRIBUTION. NOT TO SCALE ! Source : Redwood Microsystems LAYER 2 :PYREX (CAVITY FOR THERMAL FLUIDFLUORINERT) LAYER 3 : Si MEMBRANE 30 300 1cm 30 GAS FLOW THE OBJECTIVE : TO USE MEMS BASED MICROVAVLES FOR BULDING A GAS DISTRIBUTION SYSTEM FOR THE FUTURE PROGRAMMABLE REACTOR WHERE COMPACTNESS IS A KEY REQUIREMENT AMONGST OTHER THINGS . LAYER 4 : The inlet orifice and the outlet orifice layer NOT TO SCALE ! INLET OUTLET 1cm 300 Å 300 Vvalve, valve NC-1500 valve chip measures 6 mm x 6 mm x 2 mm (unpackaged). s=membrane displacement z=membrane –valve seat gap A dynamic flow rate range of 1,500sccm to 1slpm, the valve can be used for proportional control of gas flow. 1cm 3 CHANNELS 2 ORIFICES 1 VALVE SEAT REGION THE FLUID FLOW EQUATIONS Integrating the microvalve with a pressure sensor or a flow sensor and electronic feedback circuitry provides a closed-loop, programmable pressure regulator or flow regulator. ¼” PIPES THE BIG PICTURE Source : Redwood Microsystems For Channel 1 For orifice 1 32V L 32V L P0 1 2 1 Ä P1 P0 1 2 1 d1 d1 P1 2 1 2 2CD12 A012 Re *V12 * A12 [1 ( A01 / A1 ) 2 ] Ä P2 P1 1 For valve cavity with membrane For Channel 2 For orifice 2 For Channel 3 THE CONSTRAINTS FOR THE MICROVAVLE Molecular Density Mean Free Path Calculation Continuum Assumption z 1 2d 2 n ' 2 Mass Balance Equations RT Mwt V max Vsonic 2 *V2 2 * A2 2 [1 ( A02 / A2 )2 ] 2 2CD 2 A02 2 32V L 32V L P5 3 2 3 Ä Pout P5 3 2 3 d3 d3 P0 P1 1 RT P P RT Ä 0 1 1 0 2 Mwt 2 Mwt P3 P3 4 RT P3 P4 4 RT Ä 0 2 Mwt 2 Mwt P5 Pout 3 RT P P RT Ä 5 out 3 0 2 2 Mwt Mwt 1V1 A1 2V2 A2 Ä 1V1 A1 2V2 A2 0 2V2 A2 Ä 3V3 A3 2V2 A 2 Contribution of bend to pressure drop Multi dimensional case: 11 equations(some non-linear) in 11 unknowns m 4m A 2 Dmin 3 max vmax Dmax O max is at 300torr Dmax 300microns 11 equations(some non-linear) in 11 unknowns 0 Z(unknown):11 ROW VECTOR g(z) comprises 11equations 6 fluid flow-pressure drop equations 3 equations of state 2 mass balance Jacobian is a 11X11 matrix 0 Z= ÌP1 Ü Í Ý P2 Ý Í Í P3 Ý Í Ý P4 Ý Í Í P Ý Í5 Ý g= V1 Ý Í Í Ý V Í2 Ý Í V2 Ý Compute g Í Ý Í1 Ý Initial z vector z0 Í Ý Í2 Ý Ý Í Î3 Þ Compute new root vector z1 32V L Ì Ü P1 P0 12 Í Ý D Í Ý 32V L Í Ý P P 22 ÍL 2 Ý D Í 2 2 2 Ý V A A A * * [1 ( / ) ] 1 0 Í Ý P P 1 Í2 1 Ý 2CD 2 A0 2 Í Ý P P RT Í0 1 1 Ý Í 2 Ý Mwt Í Ý 11 P P RT L Í2 2 EQUATIONS Ý Í 2 Ý Mwt IN THE Í EQUATION Ý Î1V1 2V2 Þ z0 J 1 g ( z0 ) CONCLUSIONS AND FUTURE WORK Compute J Jacobian Matrix 1)MEMS based micro valves-an idea about their working and their uses and their advantages. 2) Potential use of microvalves for future generations of the programmable reactor. MATRIX Min Dia for below which sonic flow happens= 28 microns THE EXISTING GAS DISTRIBUTION SYSTEM SIMULATION RESULTS @P=100torr, T=298K 3.2268e 2kg / m3 So for laminar flow assumption to hold the the velocity in any part of the micromalve <1917m/s So subsonic flow imposes a tighter constraint VELOCITY IN CHANNEL 3 P0=300 Feed tube PRESSURE VELOCITY Capillary sampling tube Exhaust port VELOCITY IN CHANNEL 2 P3 Hexagonal showerhead P4 MICROVALVE OUTLET A 5 FT BY 3 FT CABINET Baffle P5 MICROVALVE INLET VELOCITY IN CHANNEL 1 P6 POUT Substrate heater SIMULATION GIVES THE PRESSURE DROP AND VELOCITY OF THE GAS AS IT MOVES THROUGH THE MICROVALVE. THE VELOCITY OF THE GAS IN THE ORIFICE IS NOT SHOWN IN THE FIGURE. IT IS IMPORTANT THAT THE GAS DOES NOT REACH SONIC VELOCITY. 4)Future work: Compare simulations results with real data from literature if possible. Improve modeling by using more precise structures and dimensions and flow characteristics in our models. E.g. hexagonal channels(Hydraulic radius), compressible flow. Also incorporate materials of construction in our models and carry out simulations for Ar, WF6 and H2 flow. simulations and then add more to the model bit by bit and go with the flow. No pun intended. Linear motion device P1 P2 3) Modeling methodology and computation involved- fluid flow equations, Newton Raphson Method and Microvalve Design. For fluid flow modeling: Start with assumptions to start out real simple, put down the equations, perform CURRENT GAS DISTRIBUTION SET UP 2100 REACTOR CHAMBE R known AT .5 TORR g ( z ) 0; initial guess z0 Compute new z vector z1 O .00884e 3kg /(m.s) Re max xn 1 xn some defined tolerance 0 Pout 5out 10cm f (x ) x0 ' 0 f ( x0 ) compute new root x1 The new root is updated till 1113m / s at 298 K at 100torr 1.076e 2kg / m Reynolds Number calculation For Laminar Flow assumption 32V L 32V L P3 2 2 2 V2 2 Ä P4 P3 2 2 2 V2 2 0 d2 d2 54 f ( x) 0; (nonlinear ) initial guess x0 1 dimensional case: d1 / @P=100torr, T=298K So for subsonic flow assumption to hold, the dimension of any Part of the microvalve (channel/orifice >28microns ) Re max P4 P5 P4 V2 , 2 Channel with bend 1cm V3 , 3 NOT TO SCALE ! A proportional flow valve 0 53 55 50 THE NEWTON RAPHSON METHOD: Derived from Equation 7.5-34 Bird SL ( P P2 ) ( P P2 ) P2 out s Ä P3 P2 out s z z V1 , 1 Known 300TORR Stop iterations when the updated norm falls below some defined tolerance. Easily done in Matlab. 5sccm 5*.4e 7 moles / s * 2e 3kg / mole 7.4e 9 kg / s m Vsonic 0 2CD12 A012 P3 3V3 A3 MFP at these conditions =1.1microns Molecular Dia 2.5 A So for continuum assumption to hold, the dimension of any Part of the microvalve (channel/orifice >10MFP )=11microns Velocity calculation Subsonic Flow Assumption 2 state equations Derived from Equation 6.1-4 Bird SL Hagen-Poisuille Law Substituting for f=16/Re because flow is laminar and plugging in the exp for Re 0 *V * A [1 ( A01 / A1 ) ] P1 1 P2 2 1 SOLVING THE EQUATIONS:THE MATH INVOLVED 52 51 MEMS BASED MICROVALVES WOULD DRASTICALLY MINIMIZE THE SIZE OF THE GAS DISTRIBUTION SYSTEM, AND RENDER THE PROGRAMMABLE REACTOR A PLATFROM FOR PROGRAMMABILITY PROGRAMMABLE REACTOR (MAIN CHAMBER DRAWING)
