Sierra Instruments, Inc.

Process gas mass flow controllers - An overview

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Courtesy of Sierra Instruments, Inc.

A mass How controller (MFC) is used 10 control the How of gases in a wide range of microelectronic processes. A well-designed MFC maintains a constant tlow within I percent of the full-scale flow, has a repeatability of 0.2 percent of full scale, and has a response time of 1 second to reach within 2 percent of the desired (command) flow, all of this is in response to any changes in command flow. upstream pressure, downstream pressure, gas temperature, or any otner variations imposed on the instrument, for enhanced accuracy, simplicity, and cost-effectiveness the MFC should directly monitor gas mass (molecular) flow without the separate measurement ol temperature and pressure.

A mass flow controller consists of a mass flow monitor (MFM) and a servo-control valve. In operation, to be described in rrvore detail later, an output signal from the MFM is compared to a previously esiabhsned command signal to automatically open or close the servo-control valve.

Several methods are currently used to monitor gas (low [1-4]. Turbine meters, positive-displacement meters, vortex-shedding meters, ultrasonic meters, and magnetohydrodynamic meters all monitor volumetric tlow. To obtain mass flow, the volumetric flow is multiplied by the gas density, requiring the separate measurement of gas temperature and pressure. For incompress ble flows, orifices, and Venturis measure the square of the flow and thus require not only measurement of temperature and pressure but atso square-'oot extraction. Rotameters monitor volumetric flow and respond to temperature and pressure in a complex nonlinear fashion which is different for each flow tube. Flow meters based on the Cor-iolis force directly monitor mass flow but generally do not have sufficient sensitivity for gases.

Thermal techniques offer the best alternative for direct monitoring of gas mass flow rate. With these techniques, as the gas molecules carry heat away from a hot surface, the rate of heat loss is transduced with temperature sensitive elements in an electronic bridge circuit which directly monitors mass flow.

Mass Flow Monitors

Figure 1 describes two types of thermal MFMs. the immersibie type ana the capiliary-tube type [5,6],

Immersibie thermal MFMs have two sensors immersed in the flow one which is sell-heated and monitors mass flow and the other which monitors gas tempe*ature and automatically corrects for temperature changes Typically, each sensor is a resistance temperature detector (RTD) which is either a single wire, a wire wound on a ceramic mandrel, or a resistive 'ilm. The sensors are usually electrically driven as a constant-temperature or constant-current anemometer. For high flows, the dual sensor probe is inserted into a duct or pipe. The wetted surfaces of the sensors are either glass, alumina, or 316 stainless steel. For low flows, the MFM consists of one or more micromachmed rectangular channels, each with a separate suspended resistive film mass flow sensor and temperature sensor. In this case, the sensors ana How channels are coated with a ceramic, such as silicon nitride.

Immersibie thermal MFMs generally are Mow caiioratea with theaciualgas for which tney are deployed. Since many of the gases commonly used in the microelectronics industry are Hazardous, the actual gas cannot be used tor calibration purposes. Unfortunately, calibrating with non-hazardous reference gases is difficult oecause the heat-transfer correlations are complex, non-linear functions involving temper-atu'e-dependent transDort parameters, such as gas viscosity and (hernial conductivity.

Capillary-tubethermalMFMs. however, have a simple principle o! operation facilitating straightforward calibration with refe'ence gases. The capillary-tube thermal MFM is the one most commonly used in the microelectronics industry.

Capillary-Tube Thermal MFM

Figure 1 shows the flow paths in a typical capillary-tube thermal MFM. The total mass flow (m) enters the MFM and divides into two paths, one (m,) through the sensor tube, the other (m2) throjgh the bypass. A pressure-drop (AP = P,-Pi) is created, forcing a small fraction of the mass flow through the sensor tube that is then rnon tored. An accurate MFM must have a constant ratio of bypass flow to sensed flow (m/m,). Different flow ranges can be obtained by changing the bypass to eflect a higher or lower ratio of bypass flow to sensed flow.

Figure 2 shows the principle of operation of capillary-tube thermal MFMs. The sensor tube has a relatively small diameter and large length-to-diameter ratio in the range of 50:1 to 100:1. Both features are characteristic of capillary tubes. In capillary-tube MFCs, the Reynolds number is sufficiently low (less than 2000) and the length-to-diameter ratio sufficiently high to create a pure laminar flow in the sensor tube. Pure laminar flow is described by the Hagen-Poiseuille equation in which the oressure drop (P,-P2) is linearly proportional to the sensor's mass flow rate (mt), Fig. 2 shows two coils surrounding the sensor. The coils direct a constant amount of heat (H) through the thin walls of the sensor tube into the gas. Also, the RTD coils sense changes in temperature through changes in their resistance. In actual operation. the mass flow carries heat from the upstream coil to the downstream coil; therefore, the latter is hotter than the former. The long length-to-diameter ratio of the tube insures that the entire cross-section of the stream is heated by the coils. This means the first law of thermodynamics can be applied in its simplest form. Figure 2 describes the mass flow through the sensor tube as inversely proportional to the temperature difference (AT= T2-T,) of the coils. A full theoretical analysis reveals a more complex relationship, but this simplified description is adequate for a general understanding of the principle of operation. The coils are legs of a bridge circuit with a constant current input. The output voltage is in direct proportion to the difference (R2-Ri) in the coils' resistance; the result is the temperature difference (A7). The other two parameters, heat input {H) and specific heat (C/.) are both constant. C,, is a desirable transport parameter, unlike gas viscosity and heat conductivity, because it is essentially constant for a given gas over wide range of temperature and pressure. Although the output is not intrinsically linear with mass flow, it is nearly linear over the normal operating range. True linearity is achieved with multiple breakpoint linearization (e.g., 0. 25, 50, 75, and 100 percent of full scale).

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