Classifications

• • G—PHYSICS
  • G05—CONTROLLING; REGULATING
  • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
  • G05D7/00—Control of flow
  • G05D7/06—Control of flow characterised by the use of electric means
  • G05D7/0617—Control of flow characterised by the use of electric means specially adapted for fluid materials
  • G05D7/0629—Control of flow characterised by the use of electric means specially adapted for fluid materials characterised by the type of regulator means
  • G05D7/0635—Control of flow characterised by the use of electric means specially adapted for fluid materials characterised by the type of regulator means by action on throttling means
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
  • G01F25/00—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume
  • G01F25/10—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of flowmeters
  • G01F25/15—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of flowmeters specially adapted for gas meters
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
  • G01F25/00—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume
  • G01F25/10—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of flowmeters
  • G01F25/17—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of flowmeters using calibrated reservoirs

Definitions

• the invention relates in general to methods and systems for validating the performance of a mass flow controller, and more particularly, to validating the performance of a mass flow controller using a rate of rise flow standard.
• a gas panel may be used to. deliver these process gasses to a process tool with one or more chambers or reactors.
• a gas panel is an enclosure containing one or more gas pallets dedicated to deliver process gases to the process tool.
• the gas panel is in turn composed of a group of gas pallets, which is itself composed of a group of gas sticks.
• a gas stick assembly may contain several discrete components such as an inlet fitting, manual isolation valve, binary controlled pneumatic isolation valves, gas filters, pressure regulators, pressure transducers, inline pressure displays, mass flow controllers and an outlet fitting. Each of these components is serially coupled to a common flow path or dedicated channel for one particular process gas. A manifold and a valve matrix channel the outlet of each gas stick to the process chamber.
• a process tool controller asserts setpoints to the mass flow controllers, and sequences the valve matrices, associated with certain gas sticks.
• the indicated flow value is output by the mass flow controller of each gas stick and monitored by the process tool controller.
• a mass flow controller is constructed by interfacing a flow sensor and proportioning control valve to a control system.
• the flow sensor is coupled to the control system by ah analog to digital converter.
• the control valve is driven by a current controlled solenoid valve drive circuit.
• a mass flow measurement system is located upstream of the control valve.
• the control system monitors the setpoint input and flow sensor output while refreshing the control valve input " and indicated flow output.
• Closed loop control algorithms executed by the embedded control system operate to regulate the mass flow of process gas sourced at the inlet fitting through the proportioning control valve and outlet fitting such that the real-time difference or error between the setpoint input and indicated flow output approaches zero or null as fast as possible with minimal overshoot and as small a control time as possible.
• FIGURE 1 depicts one such prior art system where process chamber 130 is used as a flow verification tool.
• process chamber 130 is used as a flow verification tool.
• a setpoint signal is input to mass flow controller 120 which in turn begins flowing gas to process chamber 130.
• a primary flow measurement technique known as rate-of-rise may be utilize to measure the flow into that volume. This method utilizes the conservation of mass principle and the equation of state of the gas to derive a relationship between the pressure in a fixed volume and the flow (mass flow) into that volume. The equation is given as,
• ⁇ P is the change in pressure over the interval ⁇ t
• R is the universal gas constant
• T is the absolute temperature of the gas
• V is the volume of the measurement chamber.
• Eq. 1 utilizes the ideal gas equation as the equation of state; similar equations can be derived for other equations of state.
• process chamber 130 which may be on the order of 20 to 60 liters makes measurements of small flow extraordinarily time consuming. Additionally, process chamber 130 may exhibit large temperature gradients throughout its volume, distorting both the measurement and calculation of the mass flow into process chamber 130.
• FIGURE 2 shows the amount of time required to achieve a given change in pressure for some typical flow rates using typical process chamber 130 of between 20 and 60 liters. Due to many other constraints, a minimum pressure of 0.1 Torr may be required to initiate the measurement, and 0.3 Torr minimum accumulated pressure required to make the measurement. As a result, to perform a single flow point validation of a 2 seem flow can require up to 5 minutes and verification of a mass flow controller may then take as long as 30 minutes. This lengthy validation cycle decreases the tool availability and adds cost to the user.
• the accuracy of the measurement is typically no better than +/-5% of the reading.
• the primary contributing errors are: errors in temperature, errors in chamber volume, and unaccounted for gases (adsorption or desorption) .
• two volumes may be used in conjunction to accurately determine a total volume during a measurement sequence, minimize false flow conditions and reduce sensitivity to pressure transients.
• a mass flow controller may be coupled to a measurement system. The mass flow controller may be commanded to a specified flow and the system may begin flow measurement. Gas is accumulated in a volume between the mass flow controller and the measurement, system and the pressure measured within this volume. Gas may then flow Into a known volume and the pressure measured. The various measurements taken during the two intervals may then be used to calculate the volume between the mass flow controller and the measurement system and the flow rate. The flow rate, in turn, may be used to determine the accuracy of the mass flow controller relative to a setpoint.
• first data pertaining to a first volume is collected during a first interval is collected
• second data pertaining to a second volume is collected during a second interval
• the first volume is determined and the flow calculated.
• the first volume comprises calculating the first volume based on the first data and the second data.
• the first data includes the change in pressure over the first interval and the second data includes the change in pressure over the second interval.
• the first volume is determined by receiving an input.
• a system for measuring a flow through a mass flow controller is coupled to the mass flow controller downstream of the mass flow controller, the system includes a chamber, a first valve coupled to the chamber upstream of the chamber, a second valve coupled to the chamber downstream of the .chamber and a pressure sensor coupled to the chamber upstream of the first valve.
• the system is operable to collect first data pertaining to a first volume during a first interval and collect second data pertaining to a second volume during a second interval;
• the second data is collected before the first data is collected.
• the first data is collected before the second data is collected.
• a choking orifice may be used in conjunction with a volume to accurately determine a flow rate irrespective of the geometry or pressure of the volume upstream of the choking orifice.
• an error curve may be derived and fitted utilizing error points determined using the choking orifice. Subsequently, flow may be calculated without use of the choking orifice and adjusted based on the derived and fitted error curve.
• a mass flow controller may be coupled to a measurement system. The mass flow controller may be commanded to a specified flow and the system may begin flow measurement. The various measurements taken during this interval may then be used to calculate the flow rate. The flow rate, in turn, may be used to determine the accuracy of the mass flow controller relative to a setpoint.
• first data pertaining to a first volume is collected during a first interval, a first flow is then calculated and adjusted based on an error curve.
• the, error curve is determined by fitting a derived error curve to a set of error points, including a set of determined error points, wherein • each determined error point is determined by: collecting second data pertaining to the first volume during a second interval at a first setpoint, with a choking orifice in an open position; calculating a second flow based on the second data; collecting third data pertaining to the first volume during a third interval at the first setpoint, with the choking orifice in a choked position; calculating a third flow based on the third data; and comparing the second flow with the third flow.
• the choking orifice is operable to create a pressure gradient in the choked position, where the pressure upstream of the choking orifice is approximately twice that of the pressure downstream of the choking orifice.
• the choking orifice is operable to create the pressure gradient when the first setpoint is at least 500 seem.
• each of the set of determined error points represents an error where the first setpoint is at least 500 seem.
• the set of error points includes a set of observed error points, wherein each observed error point is determined by: collecting fourth data pertaining to the first volume during a fourth interval at a second setpoint and calculating a fourth flow based on the fourth data.
• the error curve is adjusted based on a type of gas.
• a system is coupled to the mass flow controller downstream of the mass flow controller, the system comprising, a chamber, a first valve coupled to the chamber upstream of the chamber, a pressure sensor coupled to the chamber downstream of the chamber and a choking orifice coupled to the chamber upstream of the pressure sensor.
• the system is operable to collect first data pertaining to a first volume during a first interval and calculate a first flow.
• FIG. 1 includes an illustration of a conventional prior art system for validating a mass flow controller using a process chamber.
• FIG. 2 includes a graph of the time required to achieve a change in pressure for some typical flow rates when utilizing a process chamber in the flow verification process.
• FIG. 3 includes a block diagram of one embodiment of a system for the validation of a mass flow controller.
• FIG. 4 includes a graph of pressure as a function of time utilizing one embodiment of the methods depicted.
• FIGs. 5-8 include flowcharts depicting various embodiments of methods to perform flow verification or validate the operation of a mass flow controller.
• FIG. 9 includes a block diagram of one embodiment of a system for the validation of a mass flow controller.
• FIG. 10 includes a block diagram of one embodiment of the geometry of a path between a mass flow controller and a system like that depicted in FIG. 9.
• FIG. 11 includes a block diagram of one embodiment of the geometry of a path between a mass flow controller and a system like that depicted in FIG. 9.
• FIG. 12 includes a flowchart depicting one embodiment of a method to perform flow verification or validate the operation of a mass flow controller using the system depicted in FIG. 9. DESCRIPTION OF PREFERRED EMBODIMENTS
• two volumes may be used in conjunction to accurately determine a total volume during the measurement sequence, minimize false flow conditions and reduce sensitivity to pressure transients.
• the mass flow controller may be coupled to a measurement system.
• the mass flow controller may be commanded to a specified flow ' and the system may begin flow measurement. Gas may be accumulated in a volume between the mass flow controller and the measurement system and the pressure measured within this volume. Gas may then flow into a known volume and the pressure measured.
• the various measurements taken during the two intervals may then be used to calculate the volume between the mass flow controller and the measurement system and the flow rate, the flow rate in turn may be used to determine the accuracy of a mass flow controller relative to a setpoint.
• these systems and methods may also allow the testing of the leak through of valves within a mass flow controller. By signaling a flow rate of zero to a mass flow controller, detected changes in pressure may be attributed to leak through of those valves.
• Rate of rise system (ROR) 300 may be utilized to measure the accuracy of mass flow controller 120 with respect to a setpoint. Rate of rise system 300 may be incorporated in the flow of gas through gas stick 302 to process chamber 130.
• valve.s 350, 370 are downstream of mass flow controller 120 and upstream of process chamber 130.
• ROR 300 may contain chamber 305 between valves 330, 310 and pressure sensor 320 downstream of valve 310.
• Pressure sensor may be of the type commonly known in the art, capable of measuring pressures from .1 Torr to 1000 Torr.
• Chamber 305 typically has a volume of anywhere from lOcc up to a liter, compared with a typical volume of between 10 and 60 liters for process chamber 130.
• ROR 300 may be coupled into the flow of gas downstream of mass flow controller 120 and valve 350, and upstream of valve 370 and process chamber 130.
• the physical volume of the coupling between valves 350, 370 and 310 is represented by volume 360.
• ROR 300 is coupled to the gas stick using 316L stainless steel tubing with a .25 to .5 inch diameter, though other material such as nickel or tungsten may used in the case where gas stick 302 is being utilized to transport a specialized gas.
• Gas flows from gas supply 110 to mass flow controller 120, which regulates the volume of gas which passes through in response to a setpoint, usually between .1 seem and 100 liters a minute. If valves 310, 350 are open and valve 370 is closed, gas flows from mass flow controller 120 into chamber 305, however, if valves 350, 370 are open and valve 310 is closed gas flows from mass flow controller 120 into process chamber 130.
• valve 370 is closed to process chamber 130, valve 350 is opened to mass flow controller 120 and valve 310 within ROR 300 is closed. Mass flow controller 120 is commanded to a specified flow and ROR system 300 begins the flow measurement.
• the gas is accumulated in volume 360 between valves 350, 370 and valve 310 within ROR system 300.
• Pressure sensor 320 within ROR 300 is upstream ' of, valve 310 and this geometry enables the measurement of pressure within volume 360.
• the pressure change as a function of time may be measured to be used later for quantification of the flow measurement.
• ⁇ ti valve 330 is closed and valve 310 is opened allowing gas to flow into chamber 305 of ROR 300, a known volume. The pressure continues to be monitored as a function of time with pressure sensor 320 in ROR 300.
• FIGURE 4 A typical plot of the pressure change as a function of time is given in FIGURE 4.
• the initial pressure change depicted is that occurring in a sample volume 360 and the pressure change and time interval are ⁇ Pi and ⁇ ti receptively.
• the second slope starting at approximately 10 seconds is when valve 310 is open and valve 330 is closed.
• the accumulating volume is the combination of volume 360, and the known volume of chamber 305.
• the pressure change with time is ⁇ P 2 over the time interval ⁇ t 2 .
• Volume 360 may then be calculated using the expression below.
• Eq. 3 may then be used in conjunction with Eq. 2 to determine the flow.
• the determined flow may then be compared against the setpoint of mass flow controller to determine the accuracy of mass flow controller 120.
• FIGURE 5 a flowchart for one embodiment of a method for measuring flow attributes and validating the accuracy of a mass flow controller is ⁇ depicted. This particular method may be advantageous when measuring large flows (greater than 200 seem) , as a larger volume is utilized during the initial transient measurement of the flow, reducing measurement uncertainties.
• valve 370 may be closed by a control system indicating that a testing or validation of mass flow controller is to be conducted.
• 330 are opened and a vacuum is drawn (step 510) by pump 380.
• Valve 330 is then closed and data may be taken for the initial state (Step 520) .
• mass flow controller 120 flowing based on a certain setpoint, data may then be collected for a first interval (Step 530) .
• Time, pressure and temperature may be monitored for a certain period using sensors known in the art, such as pressure sensor 320. In some embodiments, the length of this period may be determined by a pressure or time checkpoint.
• the first interval may be concluded.
• the pressure at which the first interval concludes may vary greatly depending on the flow being measured, but is usually between 10 Torr and 1000 Torr.
• the first interval may also be concluded after a predetermined amount of time, usually at least 10 seconds, but not more than 60, seconds.
• valve 310 may then be closed (Step 540) and data collected for a second interval (Step 550) .
• this data may include pressure, temperature and time, and the length of the second interval may be determined using the same criteria as discussed with respect to the first interval above.
• volume 360 and flow attributes may then be calculated (Steps 570, 580) using Eq. 2 and Eq. 3.
• volume 360 may be input (Step 590) and then flow attributes may be calculated (Step 580) using the entered volume. The flow may then be compared to the original setpoint of mass flow controller 120 to determine the accuracy of mass flow controller 120.
• FIGURE 6 is a flowchart of a method for measuring flow and validating mass flow controller 120 which may be advantageous for moderate flows (20sccm- 200 seem) where using the larger volume of chamber 305 during the initial transient phase is not necessarily useful.
• valve 370 may be closed by a control system indicating that a flow measurement or validation of mass flow controller 120 is to be conducted.
• valves 310, 330 are opened and a vacuum is drawn (Step 610) by pump 380.
• Valve 310 is then closed and data may be taken for the initial state (Step 620) .
• mass flow controller 120 flowing- based on a certain setpoint, data may then be collected for a first interval (Step " 630) .
• Time, pressure and temperature may be monitored for a certain period using sensors known in the art, such as pressure sensor 320. The length of this period may be determined by a pressure or time checkpoint, as discussed above with respect to FIGURE 5.
• valve 330 may then be closed valve 310 opened (Step 640) and data collected for a second interval (Step 550) .
• this data may include pressure, temperature and time, and the length of the second interval may be determined using the same criteria as discussed with respect to the first interval above.
• volume 360 and flow attributes may then be calculated (Steps 670, 680) using Eq. 2 and Eq. 3.
• volume 360 may be input (Step 690) and then flow attributes may be calculated (Step 680) using the entered volume. The flow may then be compared to the original setpoint of mass flow controller 120 to determine the accuracy of mass flow controller 120.
• volume 360 between valves 350, 370 and 310 is determined, flow measurement may be conducted using only volume 360.
• volume 360 is small (less than 20cc) , consequently the pressure change for a specified flow rate easier to measure, typically reducing the measurement time for a given flow rate by a factor of five.
• FIGURE 7 illustrates one method for utilizing volume 360 for measuring flow attributes or verification of mass flow controller 120. This method may be particularly effective for flow rates less than 20sccm, and allow the use of a much shorter measurement interval.
• Valve 370 may be closed by a control system indicating that a flow measurement or validation of mass flow controller 120 is to be conducted.
• valves 310, 330 are opened and a vacuum is drawn (Step 710) by pump 380.
• Valve 310 is then closed and data taken for the initial state (Step 720) . With mass flow controller 120 flowing based on a certain setpoint, data may then be collected over a first interval (Step 730) , as discussed above.
• valve 310 may be opened and valve 330 closed (Step 740) . In certain cases it may be advantageous to open valve 330 before valve 310 so pressure is maintained in volume 360 throughout the entire first interval.
• flow attributes may then be calculated (Step 780) using Eq. 2 and Eq. 3 and the previously determined measurement of volume 360 (Step 770) .
• volume 360 may be input manually by a user (Step 790) and then flow attributes may be calculated (Step 780) . The calculated flow may then be compared to the setpoint of mass flow controller 120 to determine the accuracy of mass flow controller 120.
• volume 360 between mass flow controller valve and valve may be determined. This may be useful for high flow volumes where a large measurement volume is desirable.
• FIGURE 8 illustrates one method for utilizing volume
• Valve 370 may be closed by a control system indicating that a flow measurement or validation of mass flow controller 120 is to be conducted.
• valves 310, 330 are opened and a vacuum is drawn (Step 810) by pump 380.
• Valve 330 is then closed and data taken for the initial state (Step 820) .
• data may then be collected over a first interval (Step 830), as discussed above.
• valve 330 may then be opened (Step 840), and flow attributes may then be calculated (Step 880) using Eq. 2 and Eq. 3, the previously determined measurement of volume 360 (Step 870), and the know volume of chamber 305.
• volume 360 may be input manually by a user (Step 890) and then flow attributes calculated (Step 880) . The flow is then compared to the setpoint of mass flow controller 120 to determine the accuracy of mass flow controller 120.
• the error introduced into a rate of rise calculation may become significant. More particularly, as flow rates rise, the length of the line comprising volume 360 or other fluid elements in the path, such as valve 350, may alter the rate of change of pressure within volume 360 relative to the rate of change of pressure within the known volume of chamber 305.
• the alteration of the rate of change of pressure in volume 360 depends on the geometry of volume 360, the flow rate of mass flow controller 120, and upon the properties of the gas flowing through gas stick 302, and consequently can make the calculation of a flow rate and the commensurate .verification of mass flow controller 120 difficult. These effects may become particularly pronounced at flow rates above 200 seem.
• a choking orifice may be used in conjunction with a volume to accurately determine a flow rate irrespective of the geometry or pressure of the volume upstream of the choking orifice.
• an error curve may be derived and fitted utilizing error points determined using the choking orifice. Subsequently, flow may be calculated without use of the choking orifice and adjusted based on the derived and fitted error curve.
• FIGURE 9 depicts one embodiment of a hardware arrangement which may be incorporated into the flow of gas in parallel to a process chamber which can physically compensate for the upstream pressure dependence through fluid shorting, or choking of the flow upstream of the measuring device.
• rate of rise system (ROR) 300 may be incorporated in the flow of gas through gas stick 302 to process chamber 130.
• a choked orifrce 322 is coupled between ROR 300 and valve 350, immediate to ROR 300. Choked orifice 322 may serve to diminish the effects of the geometry of volume 360 on pressure measurement and improve the usability and accuracy of ROR 300.
• Choking orifice 322 may decrease the sensitivity of ROR 300 to the geometry of volume 360 through the use of a technique termed "fluid shorting". This technique narrows the fluid path so that pressure in volume 360 is greater than that upstream of choking orifice 322. While many pressure gradients may serve to diminish the effects of the geometry of volume 360, for ideal efficacy choking orifice 322 should create a pressure gradient such that the pressure in volume 360 is at least twice the pressure upstream of choking orifice 322. This may cause the pressure upstream of choking orifice 322 to remain substantially constant during a constant rate of flow.
• choking orifice 322 may be a multi-position valve which can be positioned according to the flow rate of mass flow controller 120 to create the proper pressure gradient between volume 360 and ROR 300.
• choking orifice 322 may be a three way valve having the positions open, closed and choked as is known in the art.
• Gas stick 302 and process chamber 130 may function normally with choking orifice 322 in the closed position.
• ROR 300 may function with gas stick 302 and process chamber 130 as described with respect to FIGURES 5-8.
• a pressure gradient may be created between volume 360 and ROR 300 which allows a flow rate to be determined in ROR 300 independently of upstream pressure or volume. Because a flow rate in ROR 300 may be determined independently of volume 360 there is no need to take measurements for determining the geometry of volume 360.
• valve 370 may be closed by a control system indicating that a testing or validation of mass flow controller is to be conducted.
• a control system indicating that a testing or validation of mass flow controller is to be conducted.
• 330 are opened and a vacuum is drawn (step 510) by pump 380.
• Valve 330 is then closed, choked orifice 322 may be set to the choked position and data may be taken for the initial state (Step 520) .
• mass flow controller 120 flowing based on a certain setpoint, data may then be collected for a first interval (Step 530) .
• Time, pressure and temperature may be monitored for a certain period using sensors known in the art, such as pressure sensor 320.
• the length of this period may be determined by a pressure or time checkpoint.
• the first interval may be concluded.
• the pressure at which the first interval concludes may vary greatly depending on the flow being measured, but is usually between 10 Torr and 1000 Torr.
• the first interval may also be concluded after a predetermined amount of time, usually at least 10 seconds, but not more than 60, seconds.
• Step 530 flow attributes may then be calculated (Steps 580) using Eq. 2 and Eq. 3, without regards to volume 360. Consequently, a second interval is not needed and steps 540-570 and 590 may be eliminated solely by virtue of utilizing choking orifice 322.
• choking orifice 322 may be tuned for utilization with any flow rate
• choking orifice 322 may be a three position valve wherein the choking orifice is tuned for use in creating a pressure gradient wherein the pressure in volume 360 is greater than two times the pressure upstream of choking orifice 322 for flow rates of 500 seem or greater.
• volume 360 may be compensated for mathematically.
• an equation for an error term as a function of major variables, including the flow rate, geometry and type of gas may be derived for a particular geometry of volume 360.
• the equation may give the shape of the curve for the error introduced by a particular geometry of volume 360.
• an equation can be derived for a flow correction term which for a case where volume 360 is like that depicted in FIGURE 10, wherein volume 360 is a constant diameter tube. More specifically, an equation can be developed that shows the relationship between the average pressure in volume 360 and the average pressure in chamber 305 which is measured. This is given as:
• volume 360 is then composed of two sections: volume 360 and chamber 305.
• the A term is the pressure derivative in the chamber 305.
• the expected flow may then be given by adding the results of Eq. 9 to Eq. 2.
• a second common geometry may be the introduction of valve 310 directly upstream of chamber 305, as depicted in FIGURE 11.
• a 2 is the pressure derivative directly upstream of valve 330.
• the actual error induced by a particular instance of volume 360 may then be empirically observed for flows over 500 seem by using ROR 300 to calculate a flow rate at a series of flow settings for mass flow controller 120 while choking orifice 322 is in an open position versus calculating flow rates at the identical series of flow settings while choking orifice 322 in the choked position.
• a set of points corresponding to an error curve for flow rates above 500 seem may be determined.
• the curve described by the derived equation for example Eq. 10, may then be fit to the empirically determined error points which occur above 500 seem to generate an error equation describing a curve representing the error induced by the geometry of volume 360 at all flows.
• this error curve may be used to correct for the error introduced by volume 360 at all flow rates with choking orifice 322 in the open position allowing the volume of chamber 305 to be utilized during a single transient phase to more accurately determine a flow rate and validate mass flow controller 120.
• FIGURE 12 depicts one embodiment of a methodology for calculating a flow rate using ROR 300 and the equation describing the error curve, as elaborated on above.
• valve 370 may be closed by a control system indicating that a testing or validation of mass flow controller is to be conducted.
• 330 are opened and a vacuum is drawn (step 1210) by pump 380.
• Valve 330 is then closed and data taken for the initial state (Step 1220) .
• Step 1230 Time, pressure and temperature may be monitored for a certain period using sensors known in the art, such as pressure sensor 320.
• the length of this period may be determined by a pressure or time checkpoint. For example, when the pressure within volume reaches a certain Torr, the first interval may be concluded. The pressure at which the first interval concludes may vary greatly depending on the flow being measured, but is usually between 10 Torr and 1000 Torr. The first interval may also be concluded after a predetermined amount of time, usually at least 10 seconds, but not more than 60, seconds.
• flow attributes may then be calculated (Steps 1240) using Eq. 2 and Eq. 3, without regards to volume 360. These flow attributes may then be corrected for the error introduced by volume 360 by using a previously determined error equation (Step 1250) , as described above. Consequently, a second interval is not needed and an accurate flow rate may be calculated at any flow setting with choking orifice 322 in an open position.
• these equations may also be tailored to take into account the gas flowing through gas stick 302 when determining the error introduced when a flow rate is calculated using ROR 300. This may be done through the use of the gas viscosity term (G as shown in Eq. 10) whose value is determined based on the gas flowing through gas stick 302 or ROR 300.
• gas term (G) may be one value for nitrogen gas and another value for one type of fluoride gas, etc.
• the resulting error curve can not only correct the calculated flow for the shape of volume 360, but can also correct the calculated flow for the viscosity of the gas flowing through gas stick 302.
• the empirically determined points used to fit the curve described by the equation will be determined based on the tuning and optimization of choking orifice 322. For example, if choking orifice 322 is tuned for use in creating a pressure gradient wherein the pressure in volume 360 is greater than two times the pressure upstream of choking orifice 322 for flow rates of 200 seem or greater, the empirically determined points may be at flow rates of 200 seem and higher.

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