CHAPTER 6

Flow Meters

Flow measurements are performed to characterize components and to monitor and control systems. Pump manufacturers and some users measure the speed of pumps; they require measurement of gas flow to determine pumping speed. Process engineers control the gas flow in systems for plasma deposition or etching, chemical vapor deposition, reactive sputtering, or ion milling. Scientists measure the gas flow into a chamber to calibrate systems used for studying gas desorption kinetics. For some applications, accuracy is important; however, repeatability is important for other applications.

At atmospheric pressure a moderately large 50-L/s (1 00-cfin) mechanical pump has a gas throughput of 5 ~ 1 0 ~ Pa-L/s (3.75~10~ Torr-L/s). A small lOO-L/s ion pump operating at Pa pumps 10” Pa-L/s (7 .5~10-~ Torr- L/s)--a range of more than nine orders of magnitude. Figure 6.1 illustrates the flow ranges of several pumps and processes, along with the capabilities of some flow meters. No one gauge covers the entire range. Old techniques such as moving oil or mercury pellets, and time to exhaust a reservoir, and so on [ 1-31, are still used to measure the very low flows needed to make pumping speed measurements.

In this chapter we defrne molar flow and mass flow, relate them to throughput, and review several methods and devices for flow measurement.

6.1 MOLAR FLOW, MASS FLOW AND THROUGHPUT

Gas flow can be expressed in two ways. It is frequently expressed in units of throughput, such as Pa-m3/s or Torr-L/s. It may also be expressed in term of the consewable quantities kg-molesh or kg/s. Conhsion arises because the two ways of expressing flow are not dimensionally the same and throughput does not conserve energy. In SI, throughput has units of Pa-m3/s. Although we do not express it in these dimensions, throughput has the dimensions of power and 1 Pa-m3/s = 1 J/s = 1W. This is the power

109

A User’s Guide to Vacuum Technology, 3rd Edition. John F. O’Hanlon Copyright 0 2003 John Wiley & Sons, Inc.

ISBN: 0-471-27052-0

110

E t? L 0 v) v) a, 0 0 fi

0) 3 u c r 0

.-

F L 0 a, a, 3

FLOW METERS

Molecular FI ow

I I I I 1 I I I I I 1

Mechanical Pumps

d

Hiah Vacuum PumDs

------ I I I I I I I I I I I

RPE

RIE, Plasma, LPCVD

Sputtering

Sonic Choke -

Rotameters

Thermal Mass Flow

Laminar Flow

Fig. 6.1 Gas flow requirements and instrument ranges: Top: Gas flow ranges of some pumps and flow requirements for several processes. Bottom: Gas flow ranges of flow measuring instruments and devices.

required to trunsporr the gas. One Pa-m3 is the quantity of gas contained in 1 m3 at a pressure of 1 Pa. Molar flow and mass flow have dimensions of kg-moles/time or masdtime, respectively. These can be related to throughput, only if the temperature of the gas is known.

Mass conservation is a second distinction between mass flow and through ut. Throughput is not a conservable quantity. The numerical value of Pa-m does not uniquely define the number of molecules. One Pa-m3 of air could contain 2 . 4 5 ~ lo2' molecules/m3 at 300 K, or it could contain 1 . 2 2 5 ~ 1 0 ~ ~ molecules/m3 at 600 K. Moles and mass are conservable quantities. Knowledge of the number of moles/s, or kgh, flowing through a system allows us to perform calculations when the system temperature is

Y

6.1 MOLAR FLOW, MASS FLOW AND THROUGHPUT 111

not uniform. We need to know when it is appropriate to use molar flow or throughput, and how to convert from throughput to mass or molar flow.

The molar flow rate N’ has SI units of (kg-moles)/s and represents the total number of kg-moles of gas passing a plane in one second. Molar flow and throughput are related through the ideal gas law. If we replace n in (2.13) with”, we get

where N’ is the molar quantity (kg-moles) of gas, and R = No k = 8314.3 kJ/(K-kg mole). The molar flow rate at constant temperature is obtained by taking the time derivative of (6.1).

d dN’ dt dt - (PV) = Q = RT-

m’ Q - (kg - moles/$ = - = 1.2 1 x dt RT

b(6.2)

Sometimes we wish to express the flow as mass flow. Its units will be kg/s in SI; we recall that each kg-mole has a mass of Mkg.

- dm (kg/s) = (z) = 1.21 x 10- 4 (7) MQ dr

b (6.3)

A4 is the molecular weight and Q has units of Pa-m3/s at temperature T. The flow may be expressed alternatively as the number of molecules per second passing a plane: r (molecules/s) = N&‘/dt. Using these relationships, we can convert from throughput Q to molar flow rate dN’/dt, mass flow rate dnddt, or molecular flow rate r. Ehrlich [4] notes that it is customary to label standard leaks with units of “atm-cc/s at T.” He reminds us that the value given is numerically equal to Q and not to kg-moles/s. The statement “at 7” is included to allow conversion from throughput to molar flow. Some of the equations given here have flow given with dimensions of throughput and others with molar or mass flow.

Throughput, mass flow, or molar flow can be used in calculations. Throughput is a convenient term to use when the system is at a constant temperature for measurements such as pumping speed calculations. Molar flow is best used for studying reaction kinetics and for calculations, which would otherwise have to be referred to several temperatures. For example, a calibrated leak labeled in “Pa-m3/s at 23°C” is connected to a system whose chamber is at 35°C and pump is at 50°C. In this example it would be much easier to have the leak labeled in kg-moles/s. The important concept to remember is the fimdamental difference between throughput Q and molar flow dNYdt. Throughput is dimensionally distinct from molar

112 FLOW METERS

flow and is not a quantity that is conserved. A kg-mole of gas is a fixed, known number of molecules that does not change with temperature.

6.2 ROTAMETERS AND CHOKES

A rotameter [5 ] is a flow-measuring device constructed from a precision tapered bore that contains a ball of accurately ground diameter and known mass. See Fig. 6 . 2 ~ . The gas flow through the tube raises the ball to a height proportional to the throughput or mass flow. The general equation for continuum flow in an orifice is

The equation for continuum flow in a rotameter with a low pressure drop can be obtained from this by letting P2 = (PI - AP). When AP is small compared to PI or P2, we get

(6.5)

Except for a geometrical factor, which accounts for the nonzero thickness of the orifice, (6.5) describes gas flow through a rotameter. The gas flow is a function of the inlet pressure PI, gas temperature, molecular weight, height h, and mass of the ball. The mass of the ball is constant and creates a constant pressure difference AP.

f h

I Fig. 6.2 (a) Rotameter, and (b) choke flow element.

6.2 ROTAMETERS AND CHOKES

The mass flow rate can be expressed as

113

(6.6)

From (6.6) and (6.7) we see that the inlet pressure and temperature must be known to calibrate the throughput and mass flow. Rotameters are initially calibrated for one gas and must be recalibrated for use with any other gas. Rotameters are made for flows ranging fiom 5x103-to-5x106 Pa-L/s. The accuracy of these instruments is of order 10-20% full scale, whereas repeatability is about 2-3%.

Chokes [6,7] (Fig. 6.2b) are used to measure, or more commonly set, the throughput in the range 5 ~ 1 0 ~ to lo7 Pa-Ws. After the flow through an orifice reaches its sonic limit (P2/P1< 0.52), it is practically independent of outlet pressure and is expressed as

for air at 22'32,

Q(Pa - Ws) = 2 x 1O5GC'A(m2) (6.9)

The mass flow rate is given by

(6.10)

for air at 22OC,

b(6.11)

Again the throughput is dependent on the area, inlet pressure, temperature, and gas species. These devices are not accurate in small sizes (less than 1- mm diameter), because the nature of the choke is critically dependent on the length of the hole as well as the radius and shape of the entrance edge. Van Atta [7] discusses large radius orifices, which are designed to make the flow more uniform and repeatable. Chokes are useful as flow restricting devices where accuracy and repeatability are not necessary. Chokes are used to limit flow fiom gas cylinders and to control turbulence during venting and rough pumping.

dm -(kg/~) = 2 . 5 8 ~ 10-3plCf A(m2) dt

114 FLOW METERS

6.3 DIFFERENTIAL PRESSURE TECHNIQUES

Rotameters and chokes measure gas flow at a known inlet pressure and an essentially constant pressure drop. They do not operate in the flow ranges below 5x103 Pa-L/s (50 Torr-L/s). Low flow rates are easily measured in the molecular or laminar viscous flow region by measuring the pressure drop across a known conductance. The concept is the same for low, medium, and high vacuum. Only the form of the conductance and the pressure gauge differ. High and ultrahigh vacuum flow measurements are almost always limited to pumping speed measurements and are treated separately in Chapter 7.

A molecular or laminar viscous element is used in combination with a capacitance manometer to measure the gas flow in the low and medium vacuum range. A laminar flow element [8] is incorporated into a flow meter as sketched in Fig. 6 .3~ . It is simply a capillary tube long enough to satisfj the Poiseuille equation. See Section 3.3.

(6.12)

The flow is proportional to AP and the average pressure in the tube. Flow measurement with a long capillary requires two pressure gauges and knowledge of the temperature as well as the gas species. This is an accurate technique, but not the most convenient. It is most often used for calibration of thermal mass flow meters.

Molecular-flow elements [9] are constructed from a parallel bundle of capillaries, v-grooves or similar shapes. See Fig. 6.3b. The diameter of each channel must be kept small for the flow to remain molecular at usably high pressures, say 100 Pa. Typically, a single channel will have a diameter of a fraction of a millimeter. The conductance of one channel is of order lo4 L/s so that a large number of parallel channels (>10,000) are necessary to achieve a practical device. The flow through such an element can be expressed as

Q-+

Q

Fig. 6.3 Differential pressure flow elements, (a) laminar and (b) molecular.

6.3 DIFFERENTIAL PRESSURE TECHNIQUES 115

V Q =CAP = xu’-AP

4 (6.13)

where x is the number of channels and a ’is the transmission probability of one channel. We see the flow to be proportional to (T’M)’”. As long as the line pressure is less than 100 Pa, it is not necessary to know its value. These devices are available commercially for use in the range 0.01-100 Pa-L/s, attitude-insensitive, stable and easy to use. However, the holes can become clogged. They have a slow response time (5-60 s), can have a high pressure drop; they cannot be used at inlet pressures greater than 100 Pa. The output of the capacitance manometer that measures AP can be used to control the opening and closing of an adjacent valve and achieve closed loop flow control.

6.4 THERMAL MASS FLOW TECHNIQUE

Mass flow can be calculated fiom the quantity of heat per unit time required to raise the temperature of a gas stream a known amount. Flow meters have been constructed which are sensitive to either thermal conductivity [ 10-1 21 or heat capacity [ 13,141. Devices sensitive to heat capacity have become widely accepted, because of their accuracy and ability to measure large gas flows with low power input. When combined with a rapidly acting valve, they become mass flow controllers.

6.4.1 Mass Flow Meter

The concept of the Thomas thermal mass flow meter [ 1 51 is illustrated in Fig. 6.4. We can measure the gas flow by applying constant power to the

m I

Fig. 6.4 Principle of thermal mass flow measurement

116 FLOW METERS

m' 3

0 sccm

10 sccm

30 sccm

Fig. 6.5 Thermal mass flow sensor and temperature profile. Upper: Cross-sectional view of the sensor tube, resistance thermometers, and heat sinks. Lower: Temperature profile. Temperature profile reproduced with permission from An Improved Thermal Mass Flow Controll#er for Hazardous and Precision Applications, William J. Alvesteffer, M. S. Thesis, Old Dominion University. Copyright 2000, William J. Alvesteffer.

uniformly spaced grid and observing the temperature rise of the gas on the downstream side of the grid. The amount of heat that is required to warm the gas stream is linearly dependent on the mass flow and the specific heat

(6.14)

For example, if we apply a nitrogen mass flow of 0.001 kg/s to this device we will observe a temperature rise of 10°C for each 8.1 J/s of heat input to the grid. The change in thermal capacity with temperature is small and has only a slight effect on the measurement of mass flow. Typical thermal coefficients due to heat capacity variations range from +O.O75%/"C (COZ) to +O.O025%/"C (Ar).

Operation of a thermal mass flow meter is based on (6.14). One early form of the device is sketched in Fig. 6.5. Heat is externally applied at the center of the tube. While there is no gas flow, the temperature profile is

6.4 THERMAL MASS FLOW TECHNIQUE 117

Fig. 6.6 Constant power mass flow controller circuit. Reproduced with permission of Luke Hinkle, Copyright 2000, Luke Hinkle.

symmetrical. With gas flow, the thermal profile is skewed. Two thermocouples (or resistance thermometers) measure the change in temperature profile between the no-flow and flow condition. The meter must be mounted in the position shown, as the heat distribution is attitude sensitive. Another form of the device is illustrated in Fig. 6.6. It uses a bridge circuit to keep the temperatures constant. With this technique, the mass flow is proportional to the amount of power required to maintain constant temperatures. Sampling tubes of 0.2-0.8-mm internal diameter are usually made from stainless steel; however, Inconel or Monel can be used for corrosive gases. Flow meter manufacturers prefer units of standard cubic centimeters per minute (sccm) for display of small flows and standard liters per minute for large gas flows. Flow meters are manufactured with full-scale deflections ranging from 1 sccm (1.6 Pa-L/s) to 500 standard liters per minute (-lo6 Pa-Lh). Devices that measure flows greater than 10-200 sccm (-20-3500 Pa-L/s) use a laminar flow bypass, which diverts a fixed percentage of the flow to the small tube. Hinkle and Marino have shown that the linearity of the flow bypass is design- dependent; the bypass ratio was affected by end effects. The thermal properties of the system are dependent on the Nusselt number, which varied with flow; if the boundary conditions vary, it is also a function of position [16]. These effects can be addressed by software algorithms.

118 FLOW METERS

Table 6.1 Thermal Mass Flow Meter Correction Factors"

Gas

Heat Capacity Density Correction

J/( kg-OC) (kg/m3) at O°C Factor f

1004.2 2058.5

520.5 488.3 535.1 692.5 478.7 692.0

2125.5 627.6

1714.2 5192.3 1430.0 360.0

1455.6 248 1.5 2229.2 1029.3 974.0

1039.7 808.8 75 1.9 917.6 993.3

1334.3 531.4 666.1 673.6 338.9 158.2

1.293 0.760 1.782 3.478 5.227 6.86 3.163 3.926 1.235 4.506 1.342 0.1786 0.0899 3.61 0.893 3.793 0.715 0.9 1.339 1.250 2.052 3.168 1.427 1.517 1.433 7.58 6.516 8.36

13.28 5.856

1 .oo 0.73 1.45 0.67 0.41 0.3 1 0.86 0.42 0.44 0.40 0.50 1.45 1.01 1 .oo 1 .oo 1.54 0.72 1.46 0.99 1.00 0.74 0.48 1 .oo 0.76 0.60 0.60 0.26 0.20" 0.25 1.32

Reproduced with permission from MKS Instruments, 6 Shattuck Road, Andover, MA 01810. ' Qx =fQmeter.

at 60°C.

A thermal mass flow meter directly measures the amount of heat absorbed by the gas stream, and therefore indirectly measures the mass flow. However, the gauge scales are normally calibrated in units of throughput-usually air. We can convert throughput to mass flow with the aid of (6.3). A gauge calibrated in units of throughput has a different temperature coefficient than one calibrated in units of mass flow, because throughput is density-dependent. According to (6.3), a mass flow of kg/s (air) at a temperature of 20°C corresponds to a throughput of 83.64

6.4 THERMAL MASS FLOW TECHNIQUE

Pa-Ws. If the gas were heated to 30°C, a mass flow of lo6 kg/s would correspond to a throughput of 86.5 Pa-L/s. Heated air is less dense than room temperature air. Near room temperature the temperature coefficient due to density changes is about -0.33%/"C. The temperature coeficient for throughput is therefore slightly less than this because of the small positive temperature coefficient of the heat capacity previously discussed. Temperature stability is improved by use of an insulation layer. Adding insulation increases the response time from 1-2 s to 6-10 s.

The mass flow sensor will have to be readjusted for gases other than air. We can purchase a sensor especially calibrated for one gas, or we can multiply the meter reading by a correction factor. To first order, the meter deflection is proportional to the gas density and heat capacity, so we can make an approximate correction with the aid of (6.15).

119

b(6.15)

The factor in parentheses is known as the meter correction factor$ This factor is approximate. The actual correction may differ due to small changes in gas viscosity, specific heat with temperature, or the rate at which a gas transfers heat to and ikom the tube wall. Example correction factors are given in Table 6.1. Hinkle and Marino [ 161 have shown that a function, not a factor is required for some gases. The factors were found to

C 0

0 C

U

.- CI

3 1.4 - C -Experiment

0 H, Simulation

0 0 v) m (3

.- 0 - x He Simulation CI

1.2 - -

1.0 1 I 1

0 20 40 60 80 100 Flow (sccm)

Fig. 6.7 Simulation and experimental gas correction functions for He and H2 relative to Nz. Reproduced with permission from J. Vuc. Sci. Technol. A, 9, 2043, L. D. Hinkle and C. F. Marino. Copyright 1991, AVS-The Science and Technology Society.

120 FLOW METERS

be correct for small gas flows. For high flows, they demonstrated that significant error could be introduced when measuring gases with different thermal diffusion constants. Figure 6.7 illustrates this error for two gases, helium and hydrogen, when measured in a flow sensor calibrated for nitrogen. A flow of 100 sccm introduced a 7% error in the helium correction factor, whereas the same flow of hydrogen introduced a 12% error in the correction factor.

Thermal mass flow sensors have the advantages of convenience, stability, accuracy (4 %) and moderately short response time. These sensors are attitude-sensitive and have a high temperature coefficient. Designs using very-small-diameter tubes can clog, especially when reactive gases contact minute impurities of water vapor.

6.4.2 Mass Flow Controller

A thermal mass flow controller (MFC) consists of a thermal mass flow sensor, a rapidly acting valve, and an electronic control system. In its basic form, a mass flow controller can maintain a constant, operator-set flow. Complex instruments can maintain ratios of gas flows or be integrated into process control systems. Flow valves may be controlled by a solenoid, a piezoelectric stack. For ultraclean applications, a piezoelectric controller with a metal diaphragm will produce the fewest particles.

The maximum flow and the pressure drop across the flow sensor and valve must be known to choose the proper size combination. We first determine the equivalent air throughput from Qmeter = Qx lfx. We then choose a flow meter with the next largest full-scale meter deflection. From the manufacturer's data we determine the pressure drop AP across the meter and valve combination at maximum flow. The value of AP is little concern, if the delivery pressure is above atmosphere. Vapors e.g., CCld, which are liquid at room temperature, have vapor pressures below atmospheric pressure. If the gas or vapor source is at a reduced pressure, we must size the meter and valve so that the pressure drop is less than the difference between PI and P2, the delivery and chamber pressures, respectively. AP < (PI - P2). The pressure drop can be reduced by choosing a low conductance valve or, if necessary, a somewhat larger flow meter than might otherwise be desired.

6.4.3 Mass Flow Meter Calibration

Calibration of a mass flow meter can be done by comparison with primary or secondary standards. Primary standards are most often maintained at National laboratories. They determine flow by comparison with independently calibrated fundamental measurements. Secondary standards

6.4 THERMAL MASS FLOW TECHNIQUE

are instruments that have been calibrated against primary standards. Secondary standards are found in the laboratories of large research institutions or manufacturing fms. Volumetric piston and rate of rise techniques are used as primary standards, whereas the pressure drop across a laminar flow element or another mass flow meter can be used as secondary standards. No AVS recommended practices have been published for calibration of mass flow meters. Methods for low throughput measurement are found in the AVS recommended procedure for pumping speed measurement [3]. Hinkle and Uttaro have reviewed primary and secondary standards and presented some data on long-term mass flow meter stability [ 171.

121

REFERENCES

1. C. E. Normand, 1961 Trans. 8th. Nut? Vac. W p . , L. E. Preuss, ed., Pergamon Press, Elmsford, NY, 1962, p. 534.

2. D. J. Stevenson, 1961 Trans. 8th. Vac. Symp., L. E. Preuss, ed., Pergamon Press, Elmsford, NY, 1962, p. 555.

3. M. Hablanian, J. Vac. Sci. Technol. A, 5, 2552 (1987). (American Vacuum Society Recommended Procedure for Measuring Pumping Speeds; see Appendix A).

4. C. Ehrlich, J. Vac. Sci. Technol. A, 4,2384, 1986. 5. C. M. Van Atta, Vacuum Science & Engineering, McGraw-Hill, New York, 1965,

Chapter 7. 6. R. W. K m a , in Flow-its Measurement and Control in Science and Industry, Vol. 2,

W. W. Durgin, Ed., Instrument Society of America, Research Triangle Park, NC, 1981, p. 741.

7. Flow Measurement, PTC 19.5.4 American Society of Mechanical Engineers, New York, 1959, Chaper 4.

8. D. A. Todd, Jr., in Flow-Its Measurement and Control in Science and Industry, Vol. 2, W. W. Durgin, Ed., Instrument Society of America, Research Triangle Park, NC, 1981, p. 695.

9. R. M. Kiesling, J. J. Sullivan, and D. J. Santeler, J. Vac. Sci. Technol., 15,771 (1978). 10. C. E. Hastings and C. R. Wcislo, AIEE, March, 1951. 11. F. Mac Donald, Instrum. and Control Syst., October (1969). 12. J. H. Laub, Electrical Engineering, December 1947. 13. J. M. Benson, W. C. Baker, and E. Easter, Instrum. Control Syst., p. 85 ( 1 970). 14. C. E. Hawk and W. C. Baker, J. Vac. Sci. Technol., 6,255 (1969). 15. C. C. Thomas, J. Franklin Institute, 152,411 (191 1). 16. L. D. Hinkle and C. F. Marino, J. Vac. Sci. Technol. A , 9,2043 (1 992). 17. L. D. Hinkle and F. L. Uttaro, Vacuum, 47,523 (1996).

PROBLEMS

6.1 T What is the basic difference between mass flow and throughput?

122 FLOW METERS

6.2 (a) What is the mass flow rate in kg/s of 1000 Pa-L/s of air at 20"C? Express this as (b) a molecular flow rate and (c) a molar flow rate.

6.3 What is the limiting flow of 20°C atmospheric pressure air through a sonic choke whose diameter is 3.5 mm?

6.4 t A OS-L/s molecular flow element is used with a capacitance manometer with a range of 0.01 to 100 Pa. (a) What range of flow can it measure (a) for air and (b) for argon?

6.5 A laminar flow tube is being used to calibrate a 0-200 SCCM thermal mass flow meter for air. The tube is 1 mm in diameter and 5 cm long. The room temperature air supply has a maximum pressure of lo5 Pa, and the differential capacitance manometer has a full-scale reading of 200 Pa. Does this calibrated source provide enough air flow to calibrate the flow meter?

6.6 7 What are two advantages and disadvantages of a thermal mass flow meter?

6.7 How much power is absorbed fiom a heater that causes air (heat capacity of 1004.16 J/(kg-K) flowing at the rate of 0.06 kg/min to rise 2"C?

6.8 A thermal mass flow sensor with a full-scale value of 100 sccm reads 0 sccm at 20°C with no pressure drop across the sensor. At a temperature of 30°C the indicated flow through the device is +0.16 sccm. What is the zero flow temperature coefficient in units of parts per million (ppm) of full scale per degree Celsius.

6.9 The sketch of sensor tube temperature versus position illustrated in Fig. 6.5 indicates that the maximum tube temperature decreases as the gas flow increases. Why is this true?

6.10 1,1,2-Trichloro-l,2,2-trifluorethane (CC12FCClF2) is a liquid with a vapor pressure of 37,730 Pa (288 Torr) at 20°C. (a) What is the maximum flow that can be read on a thermal flow meter that is calibrated for a full-scale nitrogen flow of 500 SCCM (844 Pa-Lh)? (b) This flow meter is used in series with a control valve to regulate the flow into a vacuum chamber held at a pressure of 10 Pa. For trichlorotrifluoroethane the flow in the meter-valve combination can be expressed as Q(Pa-L/s) = 2~10'~P,,, AP. Can this meter-valve combination provide a trichlorotrifluoroethane flow equal to the full- scale value of the flow meter?