Abstract:
A method and apparatus for self-calibrating control of gas flow. The gas flow rate is initially set by controlling, to a high degree of precision, the amount of opening of a flow restriction, where the design of the apparatus containing the flow restriction lends itself to achieving high precision. The gas flow rate is then measured by a pressure rate-of-drop upstream of the flow restriction, and the amount of flow restriction opening is adjusted, if need be, to obtain exactly the desired flow.

Description:
RELATED APPLICATION 
       [0001]    This application is a divisional of U.S. patent application Ser. No. 12/906,058, filed Oct. 15, 2010, which claims priority benefit from U.S. Provisional Patent Application No. 61/252,143, filed Oct. 15, 2009, the disclosures of which are incorporated herein by reference in their entireties. 
     
    
     BACKGROUND 
       [0002]    1. Field 
         [0003]    This invention is in the field of fluid flow control and, more specifically the field of high accuracy flow control such as required for, e.g., semiconductor processing, plat panel display fabrication, solar cell fabrication, etc. 
         [0004]    2. Related Art 
         [0005]    Metering the mass-flow rate of a gas is important to many industrial processes. In the case of the semiconductor industry, metering must be especially accurate, because deviations in the flow rate of only several percent can lead to process failures. 
         [0006]    Mass flow is the result of a pressure gradient existing in a system. As long as no external work is done on the system, mass will flow from areas of high pressure to low pressure. This is the working principle in all flow control devices. In order to control the rate of flow from the high pressure region to the low pressure region, a flow restriction is used. The flow restriction is positioned such that all flow in the system must pass through the restriction. Depending on the characteristics of the restriction, mass flow rate through the flow control device is a function of some or all of the following: dimensions of the flow restriction, the magnitude of the pressures both upstream and downstream of the flow restriction, the temperature of the system, and the physical properties of the gas, such as density and dynamic viscosity. The flow rate can be controlled by varying one or more of these parameters. In general, the physical properties of the gas and the temperature of the system are difficult to change or control, so flow is controlled by varying the pressures in the system, the dimensions of the flow restriction, or both. 
         [0007]    The industry-standard flow control device is a mass flow controller (MFC) containing a flow restriction in the form of a valve that can be partially opened to allow increased flow or partially closed to decrease flow. The opening of the valve is controlled by a closed loop feedback circuit that minimizes the difference between an externally provided set point and the reading from an internal flow measuring device. The flow measuring device uses a thermal sensor with two resistance-thermometer elements wound around the outside of a tube through which the gas flows. The elements are heated by applying an electric current. As the gas flows through the tube, it picks up heat from the first element and transfers it to the second element. The resulting temperature differential between the two elements is a measure of the mass flow rate of the gas. In the newer, pressure insensitive MFCs, a pressure transducer is included between the thermal sensor and the control valve to account for the effects of changing pressure on flow. 
         [0008]    A consequence of the thermal sensor flow measurement used in the MFC is that accurate flow control requires regular calibration of the device. Without regular calibration, the actual flow rate through the MFC can drift to unacceptable values due to errors in the flow measuring device. This calibration is often performed by flowing gas through the MFC into or out of a known volume and measuring the pressure rise or drop in the volume. The actual flow rate can be determined by calculating the rate of pressure rise or drop and using established pressure-temperature-volume gas relations. This type of measurement is known as a rate-of-rise calibration. 
         [0009]    The rate-of-rise flow calibration is based on primary flow measurements, and is therefore a primary calibration standard—that is, flow is determined only by measurements of mass, pressure, volume, and time. There are only three types of known primary flow measurements: gravimetric, measuring the change in mass over time; volumetric, measuring the change in volume at constant pressure over time; and rate-of-rise, measuring the change in pressure at constant volume over time. All other types of flow measurement are secondary measurements and must be calibrated to a primary measurement. 
         [0010]    Another method of metering the flow rate of a gas is to vary the pressure of the gas upstream of a critical orifice. The volume-flow rate of a gas through a critical orifice at constant temperature is independent of the upstream or downstream pressure, provided that certain pressure requirements are met, e.g., the upstream pressure is twice that of the downstream pressure. By controlling the density of the upstream gas, which is proportional to pressure, the mass-flow rate through the critical orifice can be controlled. 
         [0011]    In this type of flow control, the pressure is controlled using a control valve in a closed loop control circuit with a pressure transducer positioned between the control valve and the critical orifice. The control valve is opened or closed to maintain a specified pressure upstream of the critical orifice. Mass flow rate is determined from the pressure upstream of a critical orifice and the established characteristics of the critical orifice. Accurate flow metering, therefore, is dependent not only on the performance of the pressure controlling system, but also on the mechanical integrity and stability of the dimensions of the orifice. Since the orifice is susceptible to being restricted with particulate contamination or eroded with reaction by the gases flowing through it, it is desirable to calibrate the pressure-flow relationship on a regular basis. This is performed using the same rate-of-rise measurement that is used for the MFC. 
         [0012]    Both of the above mentioned methods control mass flow using a closed loop control scheme in which mass flow is ultimately the result of a pressure gradient acting across a flow restriction. Viewed as a control system, the output variable of these devices is mass flow, and the input variables are pressure and flow restriction characteristics. 
         [0013]    In the case of the MFC, it controls the dimensions of the flow restriction based on a second-order measurement of mass flow rate. The actual dimensional characteristics of the flow restriction are unknown, but can be adjusted proportionally to increase or decrease flow restriction as desired. In terms of the process variables, flow restriction and pressure, only pressure is observable by the device (for the pressure-insensitive MFCs), and only the flow restriction can be controlled. 
         [0014]    The critical orifice device controls flow by monitoring and controlling the upstream pressure while maintaining presumably constant flow restriction characteristics. The critical orifice device does not monitor or control the characteristics of the flow restriction beyond assuming they are constant. In terms of process variables, pressure is both observable and controllable by the device, while flow restriction is not controllable or observable. It is true that without any external influence, the characteristics of the flow restriction should not vary with time; however, in operation, the possibility exists for either chemical or mechanical perturbation of the flow restriction. This type of perturbation cannot be measured by the system, and therefore, cannot be corrected without the aid of an external calibration. 
         [0015]    The shortcomings of both of these flow control schemes, especially the need for external measurements for calibration and detection of faults, illustrate why an improved flow control scheme is desirable. 
         [0016]    A key requirement of a flow control device that is able to detect faults in its operation as well as to correct those faults through self-calibration is that there be a sufficient number of process variables that are observable and controllable. For both types of flow control devices described above, which together comprise the vast majority of flow control devices used in the semiconductor industry, there are not sufficient process variables to accomplish these tasks. 
         [0017]    In the present invention, these process variables are added by implementing a control valve that is designed to provide a highly accurate and repeatable mapping between its position and its flow restriction characteristics, and is able to achieve a very accurate measurement and control of its position. 
         [0018]    If the flow restriction can be controlled and also measured, the only additional input necessary to control the flow rate is knowledge of the pressure gradient acting on the flow restriction, because flow conductance is a knowable, repeatable function of the flow restriction dimensions. This control scheme is similar to that of the critical orifice device, except the static flow restriction is replaced with one that is variable and measureable. 
         [0019]    The benefits obtained through use of this controllable valve will depend on the type of flow control device in which it is implemented. For the critical orifice flow control device, substitution of the controllable valve for the critical orifice will remove the uncertainty of any change to the dimensions of the critical orifice. For the thermal sensor MFC, since the combination of the pressure transducer and controllable valve provides a known flow rate, this flow rate can be checked against the flow rate measured by the thermal sensor, where any discrepancy is noted as a fault. 
         [0020]    Neither of these flow control device types, however, allows self-calibration during operation. For that capability, the flow control device must incorporate a primary flow measurement as an integral part of its operation. Incorporating this type of control valve into the flow monitoring system shown in  FIG. 1  yields a flow control device that is highly accurate and self-calibrating. Initially, the position of the control valve  108 , which determines the flow restriction, would be controlled based on a rate-of-drop flow measurement carried out with valve  106  fully closed. Following the rate-of-drop measurement, valve  106  would be opened and flow would be controlled by adjusting the position of the control valve based on the pressure in the system as measured with pressure transducer  112 . 
         [0021]    A flow restriction with measurable, controllable dimensions is a key piece to a greatly improved flow control scheme, which can ultimately lead to a flow control device that is self calibrating and does not rely on secondary flow measurements. The technological challenges in making this type of control valve that is accurate enough for the semiconductor industry become apparent from an order-of-magnitude estimate of the precision required. The mass flow accuracy currently required for semiconductor processing equipment is +/−1%. In general, flow must be controlled between 1 and 10,000 sccm (standard cubic centimeters per second), and the pressure difference between the flow restriction inlet and outlet is typically between 20 and 150 psi (pounds per square inch). If we imagine an illustrative flow restriction in the form of a rectangle with a static width of 10 mm and a static length of 1 mm, with a 60 psi pressure drop across the restriction, the height must be adjusted to 0.8 um to allow flow of 1 sccm. Performing error propagation with the specification of +/−1%, the height must be controlled to within +/−1.1 nm. 
         [0022]    In fact, except for high precision metering valves, which are not well suited for the cost, space, cleanliness, and reliability requirements of semiconductor manufacturing, very little work has been done to implement control valves with measureable and controllable restrictions. U.S. Pat. No. 6,761,063-B2, entitled “True Position Sensor for Diaphragm Valves,” uses “a thin conductive member disposed between the diaphragm membrane and the actuator” to measure the capacitance between this conductive member and the valve body. The capacitance value provides an indication of the distance between the conductive member and the valve body, which gives an indication of the distance between the diaphragm and the valve body, which then gives an indication of the amount of valve opening. This type of assembly, with all of these separate parts, will at best provide control to a precision of approximately 0.001 inch, which is approximately 25,000 nm. In addition, the inventors note that the capacitance will change when fluid flows through the valve, thus making this approach even less appropriate for measuring the characteristics of the flow restriction to the level of accuracy needed in the present invention. 
       SUMMARY 
       [0023]    The following summary of the invention is included in order to provide a basic understanding of some aspects and features of the invention. This summary is not an extensive overview of the invention and as such it is not intended to particularly identify key or critical elements of the invention or to delineate the scope of the invention. Its sole purpose is to present some concepts of the invention in a simplified form as a prelude to the more detailed description that is presented below. 
         [0024]    Embodiments of the present invention provide for a controllable flow restriction in which the dimensions of the flow restriction are measurable and controllable to a very high degree of precision. The measurement and control of the dimensions are precise enough that they can be used to accomplish the self-calibrating gas-flow-control scheme shown in  FIG. 1  with the flow accuracy required by the semiconductor industry. 
         [0025]    Embodiment of the invention provide an apparatus for controlling the flow of fluid, comprising: a first block having a flow restriction surface; a second block having a complementary flow restriction surface, wherein the flow restriction surface and the complementary flow restriction surface cooperate to form a flow restriction valve; a fluid inlet hole formed in one of the first block or second block and providing fluid passage to the flow restriction valve; a fluid outlet hole formed in one of the first block or second block and providing fluid passage to the flow restriction valve; a seal provided about the flow restriction valve; and, wherein a change in the amount of the flow restriction valve opening is effected by elastic flexure of at least one of the first block or second block. 
         [0026]    Embodiments of the invention also provide for a system for precision gas delivery, comprising: a flow control valve; a pressure transducer measuring gas pressure upstream of the flow control valve; a temperature sensor; a flow regulator positioned upstream of the flow control valve; a conduit coupling the flow regulator to the flow control valve; and, a controller receiving signals from the pressure transducer and temperature sensor and controlling the operation of the flow control valve according to flow calculation; wherein the flow control valve comprises an actuator varying the amount of gas flow by elastically flexing a body part of the flow control valve. 
         [0027]    Embodiments of the invention also provide for a method for controlling flow rate through gas delivery system having a flow control valve, a flow regulator, and a known gas confinement volume coupled between the flow regulator and the flow control valve; comprising: actuating the flow control valve to deliver a desired flow rate; temporarily interrupting gas flow through the flow regulator; measuring temperature of the gas; measuring pressure drop of the gas within the known volume; using the measured temperature, pressure drop and known volume to calculate flow rate through the flow control valve; resuming flow through the flow regulator; and, using calculated flow rate to adjust the flow through the flow control valve by activating an actuator to cause elastic flexure of a body part of the flow control valve. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]    The accompanying drawings, which are incorporated in and constitute a part of this specification, exemplify the embodiments of the present invention and, together with the description, serve to explain and illustrate principles of the invention. The drawings are intended to illustrate major features of the exemplary embodiments in a diagrammatic manner. The drawings are not intended to depict every feature of actual embodiments nor relative dimensions of the depicted elements, and are not drawn to scale. 
           [0029]      FIG. 1  is a simplified schematic diagram of an embodiment of an apparatus in accordance with the present invention for self-calibrating gas flow control. 
           [0030]      FIG. 2  is a simplified schematic diagram of an embodiment of an apparatus in accordance with the present invention for a high precision controllable flow restriction, while  FIG. 2A  illustrates an alternative embodiment. 
           [0031]      FIGS. 2B-2D  illustrate examples for modifications of the embodiment of  FIG. 2 , while  FIG. 2E  illustrates an enlarged view of details of  FIG. 2D . 
           [0032]      FIG. 2F and 2G  illustrate another embodiment of the invention. 
           [0033]      FIG. 3  is a simplified schematic diagram showing the details of the flow restriction. 
           [0034]      FIG. 4  is a simplified schematic diagram showing the embodiment of  FIG. 2  with the flow restriction opened, where the amount of opening is designated by “h”. 
           [0035]      FIG. 5  is a graph showing the relationship between flow and the amount of flow restriction opening, h, for the specified inlet pressure and flow restriction radial dimensions. 
           [0036]      FIG. 6  is a simplified schematic diagram of an embodiment of an apparatus in accordance with the present invention for a high precision controllable flow restriction, including a processor and computer readable storage medium to control automatically the amount of flow restriction opening. 
       
    
    
     DETAILED DESCRIPTION 
       [0037]    Embodiments of the present invention provide for a controllable flow restriction in which the dimensions of the flow restriction are measurable and controllable to a very high degree of precision. The measurement and control of the dimensions are precise enough that they can be used to accomplish the self-calibrating gas-flow-control scheme shown in  FIG. 1  with the flow accuracy required by the semiconductor industry. 
         [0038]    In various embodiments of the present invention, this level of precision is obtained by incorporating the following characteristics:
   1. Uniaxial motion of the two opposing faces of the flow restriction, where transverse and/or rotational motion in the other two axes is limited to less than approximately 1 nm;   2. Measurement of motion in the uniaxial dimension to a precision of approximately 1 nm;   3. Actuation of motion with resolution of approximately 0.1 nm.   
 
         [0042]    An illustrative embodiment of the invention, shown in  FIG. 2 , consists of two adjacent bodies  201  and  202  with a planar contacting area that forms the flow restriction valve  211 . That is, the first block  201  has a flow restriction surface  213  and the second block  202  has a complementary flow restriction surface  212 . The flow restriction surface  213  of the first block  201  cooperates with the complementary flow restriction surface  212  of the second block  202  to thereby form flow restriction valve  211 . In the embodiment of  FIG. 2 , the flow restriction valve  211  is formed by an annular extension  215  formed on the flow restriction surface  213  of block  201 , thereby defining hole  216  (see,  FIG. 3 ). Conversely, the complementary flow restriction surface  212  is machined to be flat so as to form a perfect seal when urged against the annular extension  215 . 
         [0043]    The first body or block  201  is static in space, and the second body or block  202  is coupled to the first with a cantilever  203 . The cantilever is positioned so that the motion of the second body with respect to the first at the planar contacting area is essentially uniaxial and very predictable and reproducible. The planar faces of the bodies are patterned to form two separate cavities  204  and  205  that are isolated from each other when the two bodies are contacting, but are coupled by a flow restriction valve  211  when the bodies are displaced from each other. 
         [0044]    In  FIG. 2 , bodies  201  and  202  are machined from a single piece of material, such as, e.g., stainless steel. Of course, any material that is compatible with the gas being used and allows reliable and repeatable flexure at the cantilever could be used. For example, alternative materials include other types of steel, Inconel, Hastelloy, etc. It is noted, however, that when made from one solid piece of material, it would be difficult to machine the valve surfaces. Therefore,  FIG. 2A  illustrates an alternative embodiment, wherein bodies  201  and  202  are fabricated from two pieces, so that the machining becomes very straightforward. Of course, the one or both bodies  201  and  202  may be made from more than one single piece. The most typical way to fasten the pieces together is with fastener  220 , such as, e.g., bolts, but they could also be glued or welded together. The main requirement for the fastening is that there should be no movement at the location of the fastening, but it should allow for uniaxial movement at the flow restriction area. As both embodiments of  FIGS. 2 and 2A  would operate the same, the following description proceeds as applicable to either embodiment. 
         [0045]    An actuator  206  is installed in the first body  201  which acts on the second body  202  to induce displacement of the second body, and therefore change the flow restriction dimension. That is, as the actuator expands or contracts, it causes an elastic flexure in body  202  about the cantilever  203 . This is similar to what is sometimes referred to as flexure bearing, wherein the motion is caused by elastic flexure or deformation of the material forming the flexure bearing. Since the motion is elastic deformation, it is very precise and controllable. Also, when relaxed, the apparatus inherently assumes its natural position due to the elastic nature of the deformation. The displacement sensor  207  is installed in the first body to measure this displacement. In one embodiment, this is accomplished using a capacitive measuring device, or displacement sensor, which can measure linear displacements on the order of one nanometer. 
         [0046]    A closed loop control circuit is formed with the output of the sensor  207  and the action of the actuator  206  to accomplish control of the flow restriction  211  dimensions, and consequently, the flow conductance coupling the two cavities. Piping  208  and  209  is incorporated into the system such that gas flow is directed through hole  218  into one cavity and out of the other cavity  205  through hole  219  to pipe  209 , such that all flow must pass through the flow restriction valve  211  defined by the two bodies. 
         [0047]    By coupling the two bodies that form the flow restriction with a cantilever, as opposed to mechanical hinges or sliding assemblies, mechanical play and hysteresis are eliminated because friction sources are eliminated. Also, during actuation, there is negligible elastic deformation within the two bodies; elastic deformation is isolated to the cantilever coupling the two bodies. Both planes which define the flow restriction, therefore, are rigid. 
         [0048]    As depicted in  FIGS. 2 and 2A , body  202  is positioned as close as possible to body  201 , thus closing the flow restriction  211 . According to one embodiment, the two bodies  201  and  202  are constructed such that when they are coupled together via the fastener, the two bodies are urged against each other so as to close the flow restriction  211 . A flexible seal  210  is provided about the flow restriction  211 , so as to prevent gas flow to the atmosphere. Also, according to one embodiment, the seal  210  is constructed such that it is in tension and serves to pull the two bodies  201  and  202  together to cause the flow restriction  211  to be closed. In this particular figure, the linear actuator  206 , which is secured in body  201  and pushes against body  202 , is in its relaxed state. When the linear actuator  206  is activated, it pushes against the tension of the flexible seal  210 , moving body  202  away from body  201 , forcing body  202  to pivot on the cantilever  203  and consequently allowing the flow restriction  211  to open up. It should be appreciated that the actuator  206  may be attached to body  202  and press against body  201 . 
         [0049]    This flow restriction  211 , as viewed from the top, forms a circle as shown in  FIG. 3 , where the inside dimension of the flow restriction  211  is r 1  and the outside dimension is r 2 . Gas flow is from the inside of the flow restriction  211 , across the flow restriction  211 , to the outside of the flow restriction  211 . That is, with reference to  FIG. 4 , gas flows from inlet piping  208 , to cavity  204 , to cavity  205  (when the flow restriction  211  is open) and, since it&#39;s blocked by seal  210 , proceeds to outlet piping  209 . Consequently, when the two bodies  201  and  202  are closed against each other as shown in  FIG. 2 , the flow restriction  211  is closed, and no gas can flow. When the linear actuator  206  is activated, the flow restriction  211  opens up, and gas can flow from the inlet  208  to the outlet  209 . In general, the flow of gas will increase as the flow restriction opens. 
         [0050]    Since both body  201  and body  202  are rigid, and the only motion that can occur in the apparatus is flexure of the body at the cantilever  203 , the movement of body  202  with respect to body  201  is very well defined. For small movements, where the opening of the flow restriction  211  is on the order of micrometers, which is much smaller than the distance between the flow restriction and the flexure, the movement of body  202  with respect to body  201  at the flow restriction will be essentially uniaxial in a direction perpendicular to the plane of the flow restriction  211 . This well defined movement is critical for reproducible gas flow characteristics of the apparatus. 
         [0051]    As can be appreciated, the embodiment of  FIGS. 2  is provided only as one illustration and it may be varied without detracting from its effectiveness. For example,  FIG. 2B  illustrates an embodiment wherein one body, here body  201 , includes the hole for the gas inlet, while the other body, here body  202 , includes the hole for the outlet. Of course, the reverse can also be done with the same result.  FIG. 2C  illustrates an embodiment wherein the two bodies are not connected to each other. Rather, body  201  is anchored and does not move, while body  202  is anchored independently via a cantilever arrangement, such that it can be elastically flexured to control the opening of the flow restriction. 
         [0052]    Additionally,  FIGS. 2D and 2E  illustrate how the seal can be implemented such that it is also controlling the amount of flow through the valve. As shown in  FIG. 2D  and in the detail view of  FIG. 2E , seal  210  is provided about cavities  204  and  205 . Its periphery is fixedly attached to stationary body  201 , while its central region is fixedly attached to flexure body  202 . In this manner, when actuator  206  is actuated, it pulls on body  202 , which in turn pulls on seal  210 . Consequently, seal  210  elastically deforms such that it creates an opening of height “h” to enable gas to flow from cavity  204  to cavity  205 . 
         [0053]      FIGS. 2F and 2G  illustrate yet another embodiment of the invention, wherein  FIG. 2F  illustrates the closed, i.e., no flow condition, and  FIG. 2G  illustrates the open position. As shown, body  202  is joined to body  201  via flexures  221 . In one embodiment, body  201  and body  202  are cylindrical and the flexure parts  221  are round disks extending from body  202  and may be machined from the same block as body  202  or maybe simply attached to body  202  by, e.g., welding. While other shapes are possible, circular shapes would provide uniform and balanced movement. In this embodiment, the lower flexure part  221  also functions as the seal  210 , although it is clearly possible to provide a separate seal, such as with the other embodiments. Linear actuator  206  is provided between lever  240  and the top portion of body  201 , such that when the actuator  206  expands, it raises the lever so as to raise body  202  and elastically flex the flexure parts of body  202 , as illustrated in  FIG. 2G . In the elevated position, the bottom surface of body  202 , which forms the flow restriction surface, is raised a distance “h” from the complementary flow restriction surface of body  201 , to thereby allow controlled fluid flow through the flow restriction valve  211 . In this embodiment the two cylindrical flexures would limit relative motion between the bodies  201  and  202  to one degree of freedom (vertical), and would restrict rotation of the bodies with respect to each other in the plane of the page. This enables high accurate control of the fluid flow through the flow restriction  211 . 
         [0054]    If we quantify the amount of flow restriction opening as “h”, as shown in  FIG. 4 , we can write the following equation for the flow of gas as a function of the opening, h: 
         [0000]      Flow=2π P   in   2   h   3 /3 RTμ 1 n ( r   1   /r   2 )   Equation (1)
 
         [0055]    where
   P in  is the pressure of the gas at the inlet  208     R is the universal gas constant=1.986 calories per mol per K   T is the absolute temperature in K   μ is the viscosity of the gas   and h, r 1 , and r 2  are the dimensions shown in  FIGS. 3 and 4 .   
 
         [0061]    For most gas flow applications, Equation (1), which describes laminar flow through the flow restriction, will provide a sufficiently accurate answer; however, for those cases where the downstream pressure, i.e., the pressure of the gas at the outlet  209 , P out , is sufficiently high compared to the pressure, P in , at the inlet  208 , the flow determined in Equation (1) must be multiplied by cos(arcsin(P out /P in )). 
         [0062]      FIG. 5  shows the gas flow for an inlet pressure of 0.2 MPa (approximately 30 psi), absolute. One of the advantages of the configuration of the restriction is that the flow is a function of the cube of the restriction opening, h. This means that one order of magnitude change in the amount of flow restriction opening can control three orders of magnitude of flow, giving the apparatus a very large range of flow rate control. 
         [0063]    The linear actuator  206  can be of various types, such as a solenoid or piezoelectric actuator. A typical example is a piezoelectric actuator, part number P830.30, from Physik Instrumente, GmbH of Karlsruhe/Palmbach, Germany. The displacement sensor can also be of various types, such as a strain gauge or capacitance position sensor. A typical example is a capacitance position sensor, part number D510.050, also from Physik Instrumente. 
         [0064]    To be useful as a gas flow controller, the apparatus of  FIG. 2  must have some means to control the amount of the flow restriction opening, h.  FIG. 6  shows such an embodiment, with a controller  601  that measures the output of the displacement sensor, and using values stored in the computer readable storage medium, determines the amount of flow restriction opening, h. The controller then controls the linear actuator to move body  202  until the value indicated by the displacement sensor is consistent with the desired opening, i.e., the position set point. This control can be carried out with a standard control loop, such as a PID (proportional-integral-derivative) controller. 
         [0065]    As indicated by Equation (1), in addition to the known values of h, r 1 , and r 2 , effective control of the gas flow rate also requires that P in  and T be known. The determination of these parameters can be carried out with the apparatus shown in  FIG. 1 . In this embodiment, the apparatus  600  of  FIG. 6  is represented by the control valve  108  of  FIG. 1 . The controller  601  of  FIG. 6  is part of the control valve  108  of  FIG. 1  and represents a control loop that is nested within the control loop of controller  120  of  FIG. 1 . 
         [0066]    The controller  120  of  FIG. 1  has stored within its computer readable storage medium the values that allow it to determine the required amount of flow restriction opening, h, that is necessary to obtain the desired flow rate for a given gas pressure and temperature. The determination of the required opening can be carried out using an equation such as Equation (1) or alternatively, using a lookup table that is determined ahead of time by measuring the gas flow rate for a wide range of values of P in , T, and h. 
         [0067]    The gas flow controller of  FIG. 1  has a sufficient number of observable and controllable parameters to be able to perform self-diagnostics and self-calibration. Furthermore, these self-diagnostics and self-calibration can take place while the gas flow controller is delivering gas at a desired flow rate to a process chamber. 
         [0068]    As shown in  FIG. 1 , the apparatus comprises a gas line  101  having an inlet  103  in fluid communication with a gas source  104 , and an outlet  105  in fluid communication with a process chamber (not shown). Under standard process conditions, the valve  106  would be open and gas would be flowing through the volume  110 , through the control valve  108 , and then ultimately into the process chamber. 
         [0069]    The volume  110  represents the total fixed volume between the valve  106  and the control valve  108 . A pressure transducer  112  is configured to measure the pressure in this volume V  110 . A temperature sensor  114  is positioned to measure the temperature of the components. In certain embodiments, the sensor  114  may be a specialized sensor in direct thermal communication with one or more components. In other embodiments, where the environment is temperature-controlled and it is not expected that the temperature will vary greatly from place to place or time to time, a thermometer positioned near the gas delivery system will provide sufficient information regarding the temperature of interest. 
         [0070]    The procedure for testing the flow of gas through the control valve  108  may be summarized as follows:
   1. The control valve  108  is set to a desired flow rate, and a flow of gas is established.   2. The valve  106  is closed.   3. While the valve  106  is closed, the pressure is measured at regular periods, typically ranging from 1 to 100 milliseconds, by the pressure transducer.   4. After the pressure has dropped by some amount (typically 1-10% of the starting value), the valve  106  is opened, and the testing procedure concluded.   5. At some point during this measurement, the reading of the temperature sensor  114  is noted.   There is some amount of flexibility in the ordering of these steps; for example, steps 1 and 2 can be interchanged. Step  5  can be done at any time during the testing procedure.   
 
         [0077]    Some elaboration on the valve  106  is warranted. In its simplest form, valve  106  would be an on/off shutoff valve. A potential disadvantage of this type of valve is that in step  4 , when the valve is opened, there will be a rapid rise in pressure inside the volume V  110 . This rapid rise in pressure might make it difficult for the control valve  108  to change the amount of flow restriction opening sufficiently fast to keep a constant flow of gas flowing to the process chamber. A good alternative to the shutoff valve is a metering valve (as indicated in  FIG. 1 ), which is a valve designed to provide varying gas flow rates over a range of settings. When metering valve  106  is opened at the end of the measurement period, the controller controls the amount of valve opening such that the rise in pressure, as determined with pressure transducer  112 , is maintained at a certain rate that is sufficiently low so that the flow through the control valve  108  is not perturbed. In other words, the opening of metering valve  106  is performed gradually rather than abruptly, so that the gas flow is not perturbed. Alternatively, rather than raising the pressure at all during the process step, the pressure could be held constant at the end of the measurement period and then raised once the process step was terminated. This approach would have the least effect on any perturbation of the flow rate through the control valve  108 . 
         [0078]    According to the ideal gas equation, the amount of gas in the volume V  110 , is given by: 
         [0000]        n=PV/RT,    Equation (2)
 
         [0000]    where
   n=amount of gas (measured in moles)   P=pressure measured by the pressure transducer   V=volume of gas   R=ideal gas constant=1.987 calories per mol per K   T=absolute temperature in K.   
 
         [0084]    To some extent, all real gases are non-ideal. For these non-ideal gases, Equation (2) can be rewritten as: 
         [0000]        n=PV/ZRT,  where   Equation (3)
   Z=compressibility factor.   
 
         [0086]    The compressibility factor can be found in various handbooks or it can be determined from experimental measurements for any particular gas, and is a function of temperature and pressure. 
         [0087]    The flow rate of a gas can be written as the change in the amount of gas per unit time; i.e.: 
         [0000]      flow rate=Δ n/Δt,    Equation (4)
   where t=time.   
 
         [0089]    Substituting into Equation (4) from Equation (3), yields: 
         [0000]      flow rate=(Δ P/Δt ) V/ZRT.    Equation (5)
 
         [0090]    The first factor (ΔP/Δt) is merely the slope of the pressure measurements as a function of time taken in step 3 of the procedure above. Thus, taking these pressure measurements in conjunction with the volume, temperature, and the compressibility factor, the actual rate of flow of the gas through the control valve  108  can be determined according to embodiments of the present invention, thus providing two independent measurements of the gas flow rate into the process chamber. 
         [0091]    One or more steps of the various embodiments of the present invention could be performed with manual or automatic operation. For example, the steps of opening/closing valves and taking pressure readings could be conducted automatically according to computer control. Alternatively, one or more of the various valves could be actuated manually, with the resulting flow rate calculated automatically from the detected pressure drop. Automatic operation of one or more steps could be accomplished based upon instructions stored in a computer readable storage medium, utilizing communication through control lines as indicated in  FIG. 1 . 
         [0092]    Another benefit of this measurement system is that if a discrepancy is found between the desired flow rate and the measured flow rate, the setting of the control valve  108  can be changed to correct for the discrepancy and provide the desired flow rate. This type of correction is particularly appropriate considering that the pressure rate-of-drop measurement provides a primary calibration standard. This correction can be done in the same process step or in a subsequent process step. This type of correction is greatly simplified if the system is under computer control. 
         [0093]    It should be understood that processes and techniques described herein are not inherently related to any particular apparatus and may be implemented by any suitable combination of components. Further, various types of general purpose devices may be used in accordance with the teachings described herein. It may also prove advantageous to construct specialized apparatus to perform the method steps described herein. 
         [0094]    The present invention has been described in relation to particular examples, which are intended in all respects to be illustrative rather than restrictive. Those skilled in the art will appreciate that many different combinations of hardware, software, and firmware will be suitable for practicing the present invention. Moreover, other implementations of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.