Patent Publication Number: US-2022220986-A1

Title: Laminar flow restrictor and seal for same

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is (1) a continuation in part of U.S. patent application Ser. No. 16/985,540, filed Aug. 5, 2020, which in turn claims the benefit of U.S. Provisional Patent Application No. 62/882,794, filed Aug. 5, 2019; and (2) a continuation in part of U.S. patent application Ser. No. 16/985,635, filed Aug. 5, 2020, which in turn claims the benefit of U.S. Provisional Patent Application No. 62/882,814, filed Aug. 5, 2019, the entireties of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Mass flow control has been one of the key technologies in semiconductor chip fabrication. Apparatuses for controlling mass flow are important for delivering known flow rates of process gases for semiconductor fabrication and other industrial processes. Such devices are used to measure and accurately control the flow of fluids for a variety of applications. This control may be achieved through the use of precisely calibrated laminar flow restrictors which are effectively sealed to prevent bypass flow pas the laminar flow restrictors. 
     As the technology of chip fabrication has improved, so has the demand on the apparatuses for controlling flow. Semiconductor fabrication processes increasingly require increased performance, including more accurate measurements, lower equipment costs, improved transient response times, and more consistency in timing in the delivery of gases. In order to improve the consistency in gas delivery, improved flow restrictors and associated seals are desired. 
     SUMMARY OF THE INVENTION 
     The present technology is directed to a laminar flow restrictor for use in a mass flow controller or other gas delivery device and seals to seal the aforementioned laminar flow restrictors. One or more of these gas delivery devices may be used in a wide range of processes such as semiconductor chip fabrication, solar panel fabrication, etc. 
     In one implementation, the invention is a flow restrictor for restricting the flow of a gas. The flow restrictor has a first end, a second end, and a longitudinal axis extending from the first end to the second end. A plurality of first layers extend from the first end to the second end along the longitudinal axis. A plurality of second layers extend from the first end to the second end along the longitudinal axis. A first aperture at the first end is defined by a first layer of the plurality of first layers and the plurality of second layers. A second aperture at the second end is defined by the first layer of the plurality of first layers and the plurality of second layers. A flow passage is defined by the first layer of the plurality of first layers and the plurality of second layers, the flow passage extending from the first aperture to the second aperture. 
     In another implementation, the invention is a mass flow control apparatus for delivery of a fluid, the mass flow control apparatus having a valve comprising an inlet passage, an outlet passage, a valve seat, and a closure member. The mass flow control apparatus also has a flow restrictor, the flow restrictor positioned in one of the inlet passage or the outlet passage. The flow restrictor has a first end, a second end, and a longitudinal axis extending from the first end to the second end. A plurality of layers extend substantially parallel to the longitudinal axis. A first aperture is located at the first end and a second aperture is located at the second end. A flow passage is defined by the plurality of layers, the flow passage fluidly coupled to the first aperture and the second aperture. 
     In yet another implementation, the invention is a method of manufacturing a flow restrictor. First, a plurality of layer blanks are provided, the layer blanks having a first edge, a second edge opposite the first edge, a third edge, a fourth edge opposite the third edge, a front face, and a rear face opposite the front face. A first cavity is formed in the front face of a first one of the plurality of layer blanks. The plurality of layer blanks are stacked. Subsequently, the plurality of layer blanks are bonded to form a resistor stack having a first unfinished end and an opposite second unfinished end. The first unfinished end of the resistor stack is formed by the first edges of the plurality of layer blanks and the second unfinished end of the resistor stack is formed by the second edges of the plurality of layer blanks. Finally, material is removed from the first unfinished end of the layer stack to expose the first cavity and form a first aperture. 
     In one implementation, the invention is a seal for a gas flow restrictor, the seal having a first end, a second end, and an aperture for receiving the flow restrictor to form a fluid tight connection between the flow restrictor and the seal. 
     In another implementation, the invention is a valve assembly, the valve assembly having a valve, a flow restrictor, and a seal. The valve has a passage. The flow restrictor has a first end, a second end, a longitudinal axis extending from the first end to the second end, and a sealing portion located between the first end and the second end along the longitudinal axis. The seal is in contact with the sealing portion of the flow restrictor and the passage of the valve. 
     In yet a further implementation, the invention is a valve assembly, the valve assembly having a valve, the valve having a first passage, a second passage, a first sealing recess, and a second recess. The valve assembly has a base having a third sealing recess and a fourth sealing recess. The valve assembly has a flow restrictor, the flow restrictor having a first end, a second end, a longitudinal axis extending from the first end to the second end, and a surface of the flow restrictor located between the first end and the second end along the longitudinal axis. Finally, the valve assembly has a seal in contact with the surface of the flow restrictor and the first sealing recess of the valve. 
     In another implementation, the invention is a valve assembly, the valve assembly having a valve, a flow restrictor, and a seal. The valve has a port, a passage, and a basin, the passage extending between the port and a floor of the basin. The flow restrictor has a first end, a second end, a longitudinal axis extending from the first end to the second end, and a sealing portion located between the first end and the second end along the longitudinal axis. The seal is in contact with both the sealing portion of the flow restrictor and the floor of the basin. 
     Further areas of applicability of the present technology will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred implementation, are intended for purposes of illustration only and are not intended to limit the scope of the technology. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention of the present disclosure will become more fully understood from the detailed description and the accompanying drawings, wherein: 
         FIG. 1  is a schematic of a process utilizing one or more laminar flow restrictors. 
         FIG. 2  is a schematic of a mass flow controller as may be utilized in the process of  FIG. 1 . 
         FIG. 3  is a perspective view of a first embodiment of a laminar flow restrictor as may be utilized in the mass flow controller of  FIG. 2 . 
         FIG. 4  is a perspective view illustrating a portion of the layers forming the flow restrictor of  FIG. 3 . 
         FIG. 5A  is an end view of the portion of the flow restrictor of  FIG. 4 . 
         FIG. 5B  is a detail view of the area VB of  FIG. 5A . 
         FIG. 6  is an exploded perspective view of the portion of the flow restrictor of  FIG. 4 . 
         FIG. 7  is a cross-sectional view of the portion of the flow restrictor of  FIG. 4 , taken along line VII-VII. 
         FIG. 8  is a top view of a first layer of the flow restrictor of  FIG. 3 . 
         FIG. 9  is a top view of a second layer of the flow restrictor of  FIG. 3 . 
         FIG. 10  is a perspective view of a second embodiment of a laminar flow restrictor. 
         FIG. 11  is a perspective view illustrating a portion of the layers forming the flow restrictor of  FIG. 10 . 
         FIG. 12A  is an end view of the portion of the flow restrictor of  FIG. 11 . 
         FIG. 12B  is a detail view of the area XIIB of  FIG. 12A . 
         FIG. 13  is an exploded perspective view of the portion of the flow restrictor of  FIG. 11 . 
         FIG. 14  is a cross-sectional view of the portion of the flow restrictor of  FIG. 11 , taken along line XIV-XIV. 
         FIG. 15  is a top view a first layer of the flow restrictor of  FIG. 10 . 
         FIG. 16  is a top view a second layer of the flow restrictor of  FIG. 10 . 
         FIG. 17  is a perspective view of a portion of a third embodiment of a laminar flow restrictor. 
         FIG. 18  is an end view of the portion of the flow restrictor of  FIG. 17 . 
         FIG. 19  is an exploded perspective view of the portion of the flow restrictor of  FIG. 17 . 
         FIG. 20  is a cross-sectional view of the portion of the flow restrictor of  FIG. 17 , taken along line XX-XX. 
         FIG. 21  is a top view of a first layer of the flow restrictor of  FIG. 17 . 
         FIG. 22  is a top view of a second layer of the flow restrictor of  FIG. 17 . 
         FIG. 23  is a perspective view of a portion of a fourth embodiment of a laminar flow restrictor. 
         FIG. 24  is an end view of the portion of the flow restrictor of  FIG. 23 . 
         FIG. 25  is an exploded perspective view of the portion of the flow restrictor of  FIG. 23 . 
         FIG. 26  is a cross-sectional view of the portion of the flow restrictor of  FIG. 23 , taken along line XXVI-XXVI. 
         FIG. 27  is a top view of a first layer of the flow restrictor of  FIG. 23 . 
         FIG. 28  is a top view of a second layer of the flow restrictor of  FIG. 23 . 
         FIG. 29  is a top view of a third layer of the flow restrictor of  FIG. 23 . 
         FIG. 30  is a perspective view of a fifth embodiment of a laminar flow restrictor. 
         FIG. 31  is a perspective view illustrating a portion of the layers forming the flow restrictor of  FIG. 30 . 
         FIG. 32  is an end view of the portion of the flow restrictor of  FIG. 31 . 
         FIG. 33  is an exploded perspective view of the portion of the flow restrictor of  FIG. 31 . 
         FIG. 34  is a cross-sectional view of the portion of the flow restrictor of  FIG. 31 , taken along line XXXIV-XXXIV. 
         FIG. 35  is a top view a first layer of the flow restrictor of  FIG. 31 . 
         FIG. 36  is a top view a second layer of the flow restrictor of  FIG. 31 . 
         FIG. 37  is an exploded perspective view of a plurality of layer blanks illustrating methods of manufacturing the disclosed flow restrictors. 
         FIG. 38  is a top view of a first layer of the invention of  FIG. 37 . 
         FIG. 39  is a top view of a second layer of the invention of  FIG. 37 . 
         FIG. 40  is a perspective view of a resistor stack prior to finishing according to the invention of  FIG. 37 . 
         FIG. 41  is a perspective view of a resistor stack after finishing according to the invention of  FIG. 37 . 
         FIG. 42  is a schematic of a process utilizing one or more flow restrictors. 
         FIG. 43  is a schematic of a mass flow controller as may be utilized in the process of  FIG. 42 . 
         FIG. 44  is a schematic view of a valve incorporating a first embodiment of a flow restrictor and seal as may be utilized in the mass flow controller of  FIG. 43 . 
         FIG. 45  is a perspective view of the first embodiment of the flow restrictor and seal as may be utilized in the valve of  FIG. 44 . 
         FIG. 46  is a cross-sectional view of the flow restrictor and seal of  FIG. 45 , taken along line XLVI-XLVI. 
         FIG. 47  is a perspective view of the flow restrictor of  FIG. 45  without the seal. 
         FIG. 48  is a perspective view of the seal of  FIG. 45  without the flow restrictor. 
         FIG. 49  is a schematic view of a valve incorporating a second embodiment of a flow restrictor and seal as may be utilized in the mass flow controller of  FIG. 43 . 
         FIG. 50  is a perspective view of the second embodiment of the flow restrictor and seal as may be utilized in the valve of  FIG. 49 . 
         FIG. 51  is a cross-sectional view of the flow restrictor and seal of  FIG. 50 , taken along line LI-LI. 
         FIG. 52  is a perspective view of the seal of  FIG. 50  without the flow restrictor. 
         FIG. 53  is a cross-sectional view of the seal of  FIG. 52 , taken along line LIII-LIII. 
         FIG. 54  is a front view of the seal of  FIG. 52 . 
         FIG. 55  is a top view of the seal of  FIG. 55 . 
         FIG. 56  is a perspective view of another embodiment of a laminar flow restrictor. 
         FIG. 57  is a perspective view illustrating a portion of the layers forming the flow restrictor of  FIG. 56 . 
         FIG. 58  is an end view of the portion of the flow restrictor of  FIG. 57 . 
         FIG. 59  is an exploded perspective view of the portion of the flow restrictor of  FIG. 57 . 
         FIG. 60  is a cross-sectional view of the portion of the flow restrictor of  FIG. 57 , taken along line LX-LX. 
         FIG. 61  is a top view a first layer of the flow restrictor of  FIG. 57 . 
         FIG. 62  is a top view a second layer of the flow restrictor of  FIG. 67 . 
         FIG. 63  is a perspective view of an apparatus for controlling flow. 
         FIG. 64  is a cross-sectional view of the apparatus for controlling flow of  FIG. 63 , taken along line LXIV-LXIV. 
         FIG. 65  is an enlarged view of a portion of the cross-sectional view of  FIG. 64 . 
     
    
    
     DETAILED DESCRIPTION 
     The description of illustrative embodiments according to principles of the present invention is intended to be read in connection with the accompanying drawings, which are to be considered part of the entire written description. In the description of embodiments of the invention disclosed herein, any reference to direction or orientation is merely intended for convenience of description and is not intended in any way to limit the scope of the present invention. Relative terms such as “lower,” “upper,” “horizontal,” “vertical,” “above,” “below,” “up,” “down,” “left,” “right,” “top” and “bottom” as well as derivatives thereof (e.g., “horizontally,” “downwardly,” “upwardly,” etc.) should be construed to refer to the orientation as then described or as shown in the drawing under discussion. These relative terms are for convenience of description only and do not require that the apparatus be constructed or operated in a particular orientation unless explicitly indicated as such. Terms such as “attached,” “affixed,” “connected,” “coupled,” “interconnected,” and similar refer to a relationship wherein structures are secured or attached to one another either directly or indirectly through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise. Moreover, the features and benefits of the invention are illustrated by reference to the preferred embodiments. Accordingly, the invention expressly should not be limited to such preferred embodiments illustrating some possible non-limiting combinations of features that may exist alone or in other combinations of features; the scope of the invention being defined by the claims appended hereto. 
     Section I 
     The present invention is directed to a laminar flow restrictor for use in an apparatus for controlling gas flow. In some embodiments, the apparatus may function as a mass flow controller to deliver a known mass flow of gas to a semiconductor or similar process. Semiconductor fabrication is one industry which demands high performance in control of gas flows. As semiconductor fabrication techniques have advanced, customers have recognized the need for flow control devices with increased accuracy and repeatability in the mass of the delivered gas flows. Modern semiconductor processes require that the mass of the gas flow is tightly controlled, the response time minimized, and the gas flow is highly accurate. The present invention delivers improved accuracy and repeatability in the delivered flows. 
       FIG. 1  shows a schematic of an exemplary processing system  1000  utilizing one or more laminar flow restrictors. The processing system  1000  may utilize a plurality of apparatus for controlling flow  100  fluidly coupled to a processing chamber  1300 . The plurality of apparatus for controlling flow  100  are used to supply one or more different process gases to the processing chamber  1300 . Articles such as semiconductors may be processed within the processing chamber  1300 . Valves  1100  isolate each of the apparatus for controlling flow  100  from the processing chamber  1300 , enabling each of the apparatus for controlling flow  100  to be selectively connected or isolated from the processing chamber  1300 , facilitating a wide variety of different processing steps. The processing chamber  1300  may contain an applicator to apply process gases delivered by the plurality of apparatus for controlling flow  100 , enabling selective or diffuse distribution of the gas supplied by the plurality of apparatus for controlling flow  100 . In addition, the processing system  1000  may further comprise a vacuum source  1200  which is isolated from the processing chamber  1300  by a valve  1100  to enable evacuation of process gases or facilitate purging one or more of the apparatus for controlling flow  100  to enable switching between process gases in the same apparatus for controlling flow  100 . Optionally, the apparatus for controlling flow  100  may be mass flow controllers, flow splitters, or any other device which controls the flow of a process gas in a processing system. Furthermore, the valves  1100  may be integrated into the apparatus for controlling flow  100  if so desired. 
     Processes that may be performed in the processing system  100  may include wet cleaning, photolithography, ion implantation, dry etching, atomic layer etching, wet etching, plasma ashing, rapid thermal annealing, furnace annealing, thermal oxidation, chemical vapor deposition, atomic layer deposition, physical vapor deposition, molecular beam epitaxy, laser lift-off, electrochemical deposition, chemical-mechanical polishing, wafer testing, or any other process utilizing controlled volumes of a process gas. 
       FIG. 2  shows a schematic of an exemplary mass flow controller  101 , which is one type of apparatus for controlling flow  100  that may be utilized in the processing system  1000 . The mass flow controller  101  has a gas supply of a process gas fluidly coupled to an inlet  104 . The inlet is fluidly coupled to a proportional valve  120  which is capable of varying the volume of process gas flowing through the proportional valve  120 . The proportional valve  120  meters the mass flow of process gas which passes to the P 1  volume  106 . The proportional valve  120  is capable of providing proportional control of the process gas such that it need not be fully open or closed, but instead may have intermediate states to permit control of the mass flow rate of process gas. 
     A P 1  volume  106  is fluidly coupled to the proportional valve  120 , the P 1  volume  106  being the sum of all the volume within the mass flow controller  101  between the proportional valve  120  and a flow restrictor  160 . A pressure transducer  130  is fluidly coupled to the P 1  volume  106  to enable measurement of the pressure within the P 1  volume  106 . An on/off valve  150  is located between the flow restrictor  160  and the proportional valve  120  and may be used to completely halt flow of the process gas out of the P 1  volume  106 . Optionally, the flow restrictor  160  may be located between the on/off valve  150  and the proportional valve  120  in an alternate configuration. Finally, the flow restrictor  160  is fluidly coupled to an outlet  110  of the mass flow controller  101 . In the processing system, the outlet  110  is fluidly coupled to a valve  1100  or directly to the processing chamber  1300 . 
     Internal to the first on/off valve  150  is a valve seat and a closure member. When the apparatus  100  is delivering process gas, the first on/off valve  150  is in an open state, such that the valve seat and the closure member are not in contact. This permits flow of the process gas, and provides a negligible restriction to fluid flow. When the first on/off valve  150  is in a closed state the closure member and the valve seat are biased into contact by a spring, stopping the flow of process gas through the first on/off valve  150 . 
     The flow restrictor  160  is used, in combination with the proportional valve  120 , to meter flow of the process gas. In most embodiments, the flow restrictor  160  provides a known restriction to fluid flow. The first characterized flow restrictor  160  may be selected to have a specific flow impedance so as to deliver a desired range of mass flow rates of a given process gas. The flow restrictor  160  has a greater resistance to flow than the passages upstream and downstream of the flow restrictor  160 . 
     Optionally, the mass flow controller  101  comprises one or more P 2  pressure transducers downstream of the flow restrictor  160  and the on/off valve  150 . The P 2  pressure transducer is used to measure the pressure differential across the flow restrictor  160 . In some embodiments, the P 2  pressure downstream of the flow restrictor  160  may be obtained from another apparatus  100  connected to the processing chamber, with the readings communicated to the mass flow controller  101 . 
     Optionally, temperature sensors may be employed to further enhance the accuracy of the mass flow controller  101 . They may be mounted in the base of the mass flow controller  101  near the P 1  volume  106 . Additional temperature sensors may be employed in a variety of locations, including the proportional valve  120 , the pressure transducer  130 , and the on/off valve  150 . 
     Turning to  FIGS. 3-9 , a first embodiment of the flow restrictor  160  is shown in greater detail. The flow restrictor  160  is constructed as a plurality of layers forming a restrictor stack  170 . The restrictor stack  170  may take the form of an elongated rectangular shape as shown in  FIG. 3 . The flow restrictor  160  extends from a first end  161  to a second end  162  along a longitudinal axis A-A. A plurality of layers  210  comprising flow passages are sandwiched between a plurality of outer layers  220  which do not comprise flow passages. The flow restrictor  160  has a first side  163  formed of the pluralities of layers  210 ,  220  and an opposite second side  164 . The flow restrictor  160  further comprises a front face  165  and an opposite rear face  166 . The outer layers  220  enclose the flow passages on opposite sides of the layers  210  comprising flow passages. The outer layers  220  may or may not have the same thickness as the layers  210  comprising flow passages. A selection of the layers  210  is shown in  FIG. 4 , which illustrates portions of the flow passages and the configuration of the layers  210 . Each of the layers  210  extend from a first end  213  to a second end  214 . Portions of the plurality of flow passages can be seen in  FIG. 4 . The details of the flow passages will be discussed in greater detail below. 
     Turning to  FIGS. 5A and 5B , the layers  210  comprise a plurality of apertures  212  formed at opposite ends  213 ,  214  of the layers  210 . This enables gas to flow along the layers  210  from the first end  213  to the second end  214  along the longitudinal axis A-A. In alternate embodiments, the apertures  212  need not be on opposite ends and may instead be formed on adjacent sides or may be formed exclusively on a single end. The apertures  212  may also be formed so that gas flows across the shorter direction of the rectangular layers  210 , perpendicular to the longitudinal axis A-A. The layers  210  also need not be rectangular and may be square or any other desired shape. It is further contemplated that an aperture may be formed into the plane of the layers  210 , permitting gas to flow perpendicular to the planes of the layers  210 , then turn a corner and flow in the plane of the layers  210 . The specific arrangement of the apertures  212 , the shape of the layers  210 , and the shape of the resulting flow restrictor  160  may be adapted as desired depending on the shape of the flow passage which receives the resulting flow restrictor  160 . It is even contemplated that the flow restrictor  160  may have an annular configuration, with apertures  212  formed into a circumference of the flow restrictor  160  and/or apertures  212  formed so that gas flows perpendicular to the planes of some or all of the layers  210 . 
       FIG. 6  shows an exploded view of the layers  210 . The layers  210  comprise two first layers  230  and two second layers  260 . As best seen in  FIGS. 8 and 9 , the first layer  230  has a first side  231 , a second side  232 , a third side  233 , a fourth side  234 , a front face  235 , and an opposite rear face  236 . The second layer  260  has a first side  261 , a second side  262 , a third side  263 , a fourth side  264 , a front face  265 , and an opposite rear face  266 . The first layer  230  has a series of flow passages comprising entry passages  237 , U passages  238 , and longitudinal passages  239 . The entry passages and the U passages are each only formed into a portion of the thickness of the first layer  230  while the longitudinal passages  239  extend through the entirety of the thickness of the first layer  230 . The second layer  260  also has entry passages  267  and U passages  268  formed into the front face  265  that correspond to the entry passages  237  and U passages  238  of the first layer  240 . When a first layer  230  and a second layer  260  are stacked with the front faces  235 ,  265  facing one another, the entry passages  237 ,  267  form apertures  212  on the first and second sides  231 ,  261 ,  232 ,  262  of the layers  230 ,  260 . As is best shown in  FIG. 7 , in combination with additional first layers  230  and second layers  260 , a plurality of flow passages  270  are formed, extending from apertures  212  on one end  213  of the plurality of layers  210  to the opposite second end  214  of the plurality of layers  210 . 
     Returning to  FIG. 5A , the apertures  212  have a first edge  215 , a second edge  216 , a third edge  217 , and a fourth edge  218 . The first edge  215  is formed by the first layer  230 , the second edge  216  is formed by the second layer  260 , and the third and fourth edges  217 ,  218  are each formed by a portion of the first layer  230  and a portion of the second layer  260 . 
     The flow passages  270  may be varied in any desired manner to achieve a desired flow impedance. For instance, the number of flow passages  270  may be increased or decreased by reducing or increasing the number of the plurality of layers  210 . Furthermore, the length of the flow passages  270  may be increased or decreased by changing the number of times that the flow passages  270  double back on themselves, changing the resulting number of U passages  238 ,  268  and longitudinal passages  239 . A greater or fewer number of flow passages  270  may be formed into pairs of first and second layers  230 ,  260 . The width of the flow passages  270  may also be increased or decreased, and the thickness of the first and second layers  230 ,  260  may be varied. Indeed, it is not necessary that the same thickness be used for every pair of first and second layers  230 ,  260 . Each layer within the plurality of layers  210  could be individually varied to alter the resulting flow impedance of the flow restrictor  160 . 
     The flow restrictor  160  is manufactured by first etching each of the layers  210  individually or in an array. The layers  210  may all be formed of the same material or may be formed of different materials. The etching may be carried out in a single step or in a series of steps to achieve the multiple depths required. Alternative processes such as laser ablation, micromachining, or other known processes may also be used. Once the plurality of layers  210  have been formed, they are assembled with the non-etched outer layers  220  and joined by diffusion bonding. Again, alternative techniques such as conventional bonding with adhesives, welding, or similar processes may also be used as is known in the art. The resulting stack of layers  210 ,  220  is joined, sealing the flow passages  270  and forming the flow restrictor  160 . Subsequent finishing steps can be performed to alter the overall shape or size of the flow restrictor  160  to suit the dimensions of the flow passages into which the flow restrictor  160  is installed. These processes may include grinding, machining, laser cutting, water jetting, or other known techniques. Indeed, the flow restrictor  160  does not need to remain rectangular and may be formed into cylindrical shapes as will be discussed further below. 
     Turning to  FIGS. 10-16 , a second embodiment of the flow restrictor  300  is best shown in  FIG. 10 . Where not explicitly noted, the reference numerals are identical to those of the first embodiment of the flow restrictor  160 . The second embodiment of the flow restrictor  300  extends from a first end  302  to a second end  303  along a longitudinal axis A-A and is also formed of a plurality of layers  310  having flow passages and a plurality of outer layers  320  which do not have flow passages. After bonding, the layers  310 ,  320  are post-processed into a cylindrical shape which facilitates insertion into a cylindrical bore, enabling easy installation of the flow restrictor  300  into a valve or other flow device. 
     As shown in  FIG. 11 , a selection of the layers  310  are shown in perspective. The layers  310  extend from a first end  313  to a second end  314  opposite the first end  313 .  FIGS. 12A and 12B  best illustrate the apertures  312  formed into the first end  313  of the layers  310 . As can also be seen, the layers  310  comprise two first layers  330  and two second layers  360 . As best seen in  FIG. 12B , the apertures  312  have a first edge  315 , a second edge  316  opposite the first edge  315 , a third edge  317 , and a fourth edge  318  opposite the third edge  317 . The first and second edges  315 ,  316  are formed by the first layers  330 . The third and fourth edges  317 ,  318  are each formed by the second layer  360 . 
     An exploded view of the layers  310  is shown in  FIG. 13 , better illustrating the flow passages of the restrictor  300 .  FIGS. 15 and 16  illustrate the first layer  330  and the second layer  360 , respectively. The first layer  330  has a first side  331 , a second side  332 , a third side  333 , a fourth side  334 , a front face  335 , and an opposite rear face  336 . The second layer  360  has a first side  361 , a second side  362 , a third side  363 , a fourth side  364 , a front face  365 , and an opposite rear face  366 . The first layer  330  has a series of longitudinal passages  339  that terminate in layer transition apertures  340 . The longitudinal passages  339  and the layer transition apertures  340  extend through the entirety of the first layer  330 . The second layer  360  has notches  369  that extend from the first and second sides  361 ,  362 . The notches  369  also extend through the entirety of the second layer  360 . As can be best seen in  FIG. 14 , the apertures  312  are formed by the open ends of the notches  369  when the layers  330 ,  360  are alternately stacked as shown. Flow passages  370  are formed by the stacking of the layers  330 ,  360  as shown. In alternate embodiments, the layer transition apertures may be formed in a variety of shapes and may be formed with or without flow passage contouring at the ends of the channel, or with contouring of different shapes. 
     Once again, a plurality of the layers  330 ,  360  are stacked and assembled with the outer layers  320 . The layers are then bonded through diffusion bonding or a similar technique. The resulting resistor stack is then ground or machined into a cylindrical shape as shown in  FIG. 10 . This cylindrical shape also incorporates annular grooves which facilitate the mounting of a seal which seals the flow restrictor  300  into a bore of a device to ensure that the only gas passing by the flow restrictor  300  must pass through the passages  370 . In other embodiments, the final part may be machined into different shapes, or alternatively left in its raw shape formed by the bonded resistor stack. 
     A third embodiment of the flow restrictor  400  is shown in  FIGS. 17-22 .  FIG. 17  shows a selection of the plurality of layers  410  forming the flow passages of the flow restrictor  400 . The outer layers are not shown in this embodiment as they are substantially identical to those of the other embodiments. The plurality of layers  410  extend from a first end  413  to a second end  414  opposite the first end  413 . As best shown in  FIG. 18 , apertures  412  are formed in the first end  413  and the second end  414  to permit passage of gas into and out of the flow restrictor  400 .  FIG. 19  shows an exploded view of the plurality of layers  410  to better illustrate the flow passages. As can be seen, the plurality of layers  410  comprise two first layers  430  and two second layers  460 . 
       FIGS. 21 and 22  illustrate the first layer  430  and the second layer  460 , respectively. The first layer  430  has a first side  431 , a second side  432 , a third side  433 , a fourth side  434 , a front face  435 , and an opposite rear face  436 . The second layer  460  has a first side  461 , a second side  462 , a third side  463 , a fourth side  464 , a front face  465 , and an opposite rear face  466 . The first layer  430  has a series of longitudinal passages  439  having an elongated configuration with straight sides and a radius at each end. The second layer  460  has notches  469  that transition from a u-shape having parallel sides to angled sides which increase in width as they approach the first side  461  or second side  462  of the second layer  460 . The notches  469  overlap with the longitudinal passages  439  when the first and second layers are aligned. The second layer  460  also has D-shaped apertures  468  which allow the connection of two adjacent longitudinal passages  439  to increase the effective length of the flow passage from one aperture  412  to another aperture  412 . There is no limit to the number of D-shaped apertures  468  which may be employed. Furthermore, there is no need to limit the apertures  468  to a D shape, and they may be any desired shape to facilitate a connection between adjacent longitudinal passages  439 . In alternate embodiments the notches  469  can be shaped differently. For instance, shapes such as rectangular, wedge, or other shapes may be used. Additionally, longitudinal passages  439  can have contouring in them to improve flow characteristics. Thus, the longitudinal passages  439  need not be formed with a constant width, and may have varying widths at either ends or anywhere along their length. In yet further embodiments a third layer (or a plurality of layers) can be interleaved between the first layer  430  and the second layer  460  such that each first layer  430  only contacts one second layer  460 , and the apertures  468  between subsequent sheets do not allow flow transitions except for adjacent first and second layers  430 ,  460 . 
     As can be best seen in  FIG. 20 , the apertures  412  are formed by the open ends of the notches  469  when the layers  430 ,  460  are alternately stacked as shown. Flow passages  470  are formed by the stacking of the layers  430 ,  460  as shown. The layers  430 ,  460  are of equal thickness in this embodiment, but may have different thicknesses if desired. 
     A fourth embodiment of the flow restrictor  500  is shown in  FIGS. 23-29 .  FIG. 23  shows a selection of the plurality of layers  510  forming the flow passages of the flow restrictor  500 . The outer layers are not shown in this embodiment as they are substantially identical to those of the other embodiments. The plurality of layers  510  extend from a first end  513  to a second end  514  opposite the first end  513 . As best shown in  FIG. 24 , apertures  512  are formed in the first end  513  and the second end  514  to permit passage of gas into and out of the flow restrictor  500 .  FIG. 25  shows an exploded view of the plurality of layers  510  to better illustrate the flow passages. As can be seen, the plurality of layers  510  comprise a first layer  530 , a second layer  560 , and a third layer  580 . 
       FIGS. 27-29  illustrate the first layer  530 , the second layer  560 , and the third layer  580 , respectively. The first layer  530  has a first side  531 , a second side  532 , a third side  533 , a fourth side  534 , a front face  535 , and an opposite rear face  536 . The second layer  560  has a first side  561 , a second side  562 , a third side  563 , a fourth side  564 , a front face  565 , and an opposite rear face  566 . The first layer  530  has a series of longitudinal passages  539  having an elongate configuration with straight sides and a radius at each end. The second layer  560  has notches  569  that transition from a u-shape having parallel sides to angled sides which increase in width as they approach the first side  561  or second side  562  of the second layer  560 . The notches  569  overlap with the longitudinal passages  539  when the first and second layers are aligned. The third layer  580  has a first side  581 , a second side  582 , a third side  583 , a fourth side  584 , a front face  585 , and an opposite rear face  586 . As can be best seen in  FIG. 26 , the apertures  512  are formed by the open ends of the notches  569  when the layers  530 ,  560  are alternately stacked as shown. Flow passages  570  are formed by the stacking of the layers  530 ,  560  as shown. The layers  530 ,  560  are of equal thickness in this embodiment, but may have different thicknesses if desired. The third layer may be useful for decreasing the density of the flow passages, ensuring that flow is more evenly distributed across the cross-sectional area of the flow restrictor  500 . This is particularly useful for producing very high flow impedance flow restrictors. 
     A fifth embodiment of the flow restrictor  600  is shown in  FIGS. 30-36 .  FIG. 30  shows the flow restrictor  600  in perspective. The flow restrictor  600  extends from a first end  602  to a second end  603  and has outer layers  620  which surround layers  610  which have flow passages therein. A selection of the layers  610  are shown in  FIG. 31  in perspective view. These layers  610  extend from a first end  613  to a second end  614 , with apertures  612  on the first and second ends  613 ,  614 . An exploded view of the layers  610  is shown in  FIG. 33 , illustrating two first layers  630  and two second layers  660 . 
     The first layer  630  and the second layer  660  are illustrated in  FIGS. 35 and 36 . The first layer  630  has a first side  631 , a second side  632 , a third side  633 , a fourth side  634 , a front face  635 , and an opposite rear face  636 . The second layer  660  has a first side  661 , a second side  662 , a third side  663 , a fourth side  664 , a front face  665 , and an opposite rear face  666 . The first layer  630  has a series of longitudinal passages  639  having an elongated configuration which meet with U shaped portions  640  or with openings  641 . The second layer  660  is free of any flow passages or other features. As can be seen, in the flow restrictor  600 , gas remains exclusively on a single layer  630  and does not transition between first and second layers  630 ,  660 . Instead, it enters through an opening  641  at the first side  631 , travels down a longitudinal passage  639 , returns along a U shaped portion  640  at least two times, then exits through an opening  641  on the second side  632 . The exact flow path may be altered to zig-zag, utilize more than two U shaped portions  640 , no U shaped portions  640 , or take any other path on the layer  630 . However, it never flows through the second layer  660  in this embodiment. The longitudinal passages  639 , U shaped portions  640 , and openings  641  all extend through the entirety of the thickness of the first layer  630 . In alternate configurations, single sheet flow may be obtained by forming the flow passage depth only partially through the sheet such that the sheet dimensions remain intact during assembly prior to bonding. 
     As best shown in  FIG. 34 , flow passages  670  are formed by the stacking of the layers  630 ,  660  as shown. The layers  630 ,  660  are of equal thickness in this embodiment, but may have different thicknesses if desired. The layers  630 ,  660  are formed individually of different materials having a different reactivity when subjected to etching chemicals. The material of the first layer  630  may be more reactive than the material of the second layer  660 , facilitating effective etching of the first layer  630  without significant etching of the second layer  660 . Layer pairs are formed by assembling one first layer  630  with one second layer  660 . The layer pairs are then diffusion bonded so they cannot be readily separated. As discussed above, other bonding techniques may be utilized. Then, the layer pairs are etched so that the flow passages  670  are formed into the first layer  630  without etching the second layer  660 . The layer pairs are then assembled into the plurality of layers  610  having flow passages  670 . Outer layers  620  are also assembled with the plurality of layers  610  having the flow passages  670 . Finally, the layers  610 ,  620  are diffusion bonded together. Optionally, post processing such as grinding may be used to form the flow restrictor  600  and adapt it for installation into a flow passage of a device. 
     It should be noted that the flow passages do not need to extend straight from one end of the flow restrictor to the other end of the flow restrictor, or double back in parallel rows. Instead, it is conceived that the flow passages may zig-zag, arc, or take any other path needed to achieve the desired flow impedance in the completed flow restrictor. Multiple layer transitions may also be made, enabling the use of flow passages which fork and rejoin, transition across more than two or three layers, or the like. It is further conceived that flow restrictors may incorporate features of specific embodiments in combination, such that a hybrid of the disclosed embodiments may be constructed. The above-disclosed restrictor designs can be used to achieve highly laminar flow and high part to part reproducibility. This high reproducibility reduces calibration requirements when manufacturing flow control devices utilizing one or more laminar flow elements. 
     Details illustrating a method of forming the flow restrictors according to the present invention are shown in  FIGS. 37-41 .  FIG. 37  shows a plurality of layer blanks  710  in an exploded view. Each of the layer blanks has a first edge  711 , a second edge  712  opposite the first edge, a third edge  713 , and a fourth edge  714  opposite the third edge. The layer blanks  710  further comprise a front face  715  and a rear face  716  opposite the front face  715 . The layer blanks  710  are formed into first layers  730  and second layers  760  as further illustrated in  FIGS. 38 and 39 . The first layer  730  is modified from a layer blank  710  by forming a second cavity  732  into the first layer  730 . The second layer  760  is modified from a layer blank  710  by forming a first cavity  761  and a third cavity  763  into the second layer  760 . The first, second, and third cavities  761 ,  732 ,  763  are formed into the front faces  715  of their respective first and second layers  730 ,  760 . Preferably the cavities  761 ,  732 ,  763  are formed through the thickness of the layers  730 ,  760 . In some embodiments, some or all of the cavities  761 ,  732 ,  763  may be formed only partially through the thickness of the layers  730 ,  760 . In the illustrated method, the cavities  761 ,  732 ,  763  are formed from the front face  715  to the rear face  716 . The cavities  761 ,  732 ,  763  are spaced from the first, second, third, and fourth edges  711 ,  712 ,  713 ,  714  of the layer blanks  710 . 
     The cavities  761 ,  732 ,  763  are formed by etching the layer blanks  710 . Alternate processes are available such as micromachining, laser ablation, or other known techniques. As illustrated in  FIG. 40 , a resistor stack  770  is formed from the plurality of layers  730 ,  760 . Subsequent to formation of the cavities  761 ,  732 ,  763 , the layers  730 ,  760  are stacked in alternating layers, ensuring that the layers  730 ,  760  are kept in alignment so that the second cavity  732  overlaps with the first and third cavities  761 ,  763 . The layers  730 ,  760  are then bonded to form the resistor stack  770  as a unitary component. The layers  730 ,  760  may be bonded by diffusion bonding, welding, gluing, or any other known technique. In yet other embodiments, the second cavity  732  may be the only cavity and the first and third cavities  761 ,  763  may be omitted. Thus, it is conceived that the second cavity  732  may be the only cavity required where the flow passages are formed into a single layer. 
     The resistor stack  770  comprises a first unfinished end  771  formed by the first edges  711  of the first and second layers  730 ,  760 . An opposite second unfinished end  772  is formed by the second edges  712  of the first and second layers  730 ,  760  of the resistor stack  770 . As can be seen, no cavities are exposed on the unfinished ends  771 ,  772 . In alternate embodiments, only one of the layers  730 ,  760  need have cavities, with the other layers  730 ,  760  being free of cavities. This allows formation of resistors such as those shown in  FIGS. 30-36 . In yet other embodiments, three or more different types of layers may be utilized such as is shown in  FIGS. 23-27 . The layers need not be alternately stacked, but instead may simply be separated from each other. Thus, un-modified layer blanks  710  may be interleaved with the first and second layers if so desired. Any combination of layers can be made so long as at least one flow passage is formed in the finished flow resistor. 
       FIG. 41  illustrates the resistor stack  770  after finishing operations have been completed. These finishing operations can take one of two alternative forms. In the first process, the unfinished ends  771 ,  772  are broken off of the resistor stack  770  to expose the first and third cavities  761 ,  763 . The exposed first and third cavities  761 ,  763  form apertures  712  on first and second finished ends  773 ,  774 . This results in flow passages extending from the apertures  712  on the first finished end  773  to the apertures  712  on the second finished end. Optionally, additional material removal operations can be done to the resistor stack  770  prior to removal of the unfinished ends  771 ,  772 . This has the benefit of minimizing the amount of debris which enters the flow passages, ensuring that the resulting flow restriction closely matches the theoretical flow restriction provided by the flow restrictor. Furthermore, manufacturing repeatability is greatly improved by ensuring that debris cannot enter the flow passages. 
     In an alternative second process, the unfinished ends  771 ,  772  of the resistor stack  770  are removed through conventional material removal processes such as machining, milling turning, sawing, grinding, electrical discharge machining, or etching. Once the unfinished ends  771 ,  772  are removed to form the finished ends  773 ,  774 , the resistor stack  770  is rinsed with deionized water. An electropolish process is used to dissolve any remaining metal particles and produce a surface having very low roughness. Next, deionized water is pumped through the flow passages to flush the electropolishing solution. The resistor stack  770  is then dried and subsequently a nitric acid solution is used to remove any remaining free iron, phosphates, and sulfates. This results in a surface which is extremely clean and free of contaminants. 
     Section II 
     The present invention is directed to a seal for a flow restrictor for use in an apparatus for controlling gas flow. In some embodiments, the apparatus may function as a mass flow controller to deliver a known mass flow of gas to a semiconductor or similar process. Semiconductor fabrication is one industry which demands high performance in control of gas flows. As semiconductor fabrication techniques have advanced, customers have recognized the need for flow control devices with increased accuracy and repeatability in the mass of the delivered gas flows. Modern semiconductor processes require that the mass of the gas flow is tightly controlled, the response time minimized, and the gas flow is highly accurate. The present seals ensure that the flow restrictor is sealed into its flow passage more effectively and at a reduced cost. 
       FIG. 42  shows a schematic of an exemplary processing system  1000 A utilizing one or more flow restrictors. The processing system  1000 A may utilize a plurality of apparatus for controlling flow  100 A fluidly coupled to a processing chamber  1300 A. The plurality of apparatus for controlling flow  100 A are used to supply one or more different process gases to the processing chamber  1300 A. Articles such as semiconductors may be processed within the processing chamber  1300 A. Valves  1100 A isolate each of the apparatus for controlling flow  100 A from the processing chamber  1300 A, enabling each of the apparatus for controlling flow  100 A to be selectively connected or isolated from the processing chamber  1300 A, facilitating a wide variety of different processing steps. The processing chamber  1300 A may contain an applicator to apply process gases delivered by the plurality of apparatus for controlling flow  100 A, enabling selective or diffuse distribution of the gas supplied by the plurality of apparatus for controlling flow  100 A. In addition, the processing system  1000 A may further comprise a vacuum source  1200 A which is isolated from the processing chamber  1300 A by a valve  1100 A to enable evacuation of process gases or facilitate purging one or more of the apparatus for controlling flow  100 A to enable switching between process gases in the same apparatus for controlling flow  100 A. Optionally, the apparatus for controlling flow  100 A may be mass flow controllers, flow splitters, or any other device which controls the flow of a process gas in a processing system. Furthermore, the valves  1100 A may be integrated into the apparatus for controlling flow  100 A if so desired. 
     Processes that may be performed in the processing system  100 A may include wet cleaning, photolithography, ion implantation, dry etching, atomic layer etching, wet etching, plasma ashing, rapid thermal annealing, furnace annealing, thermal oxidation, chemical vapor deposition, atomic layer deposition, physical vapor deposition, molecular beam epitaxy, laser lift-off, electrochemical deposition, chemical-mechanical polishing, wafer testing, or any other process utilizing controlled volumes of a process gas. 
       FIG. 43  shows a schematic of an exemplary mass flow controller  101 A, which is one type of apparatus for controlling flow  100 A that may be utilized in the processing system  1000 A. The mass flow controller  101 A has a gas supply of a process gas fluidly coupled to an inlet  104 A. The inlet  104 A is fluidly coupled to a proportional valve  120 A which is capable of varying the volume of process gas flowing through the proportional valve  120 A. The proportional valve  120 A meters the mass flow of process gas which passes to the P 1  volume  106 A. The proportional valve  120 A is capable of providing proportional control of the process gas such that it need not be fully open or closed, but instead may have intermediate states to permit control of the mass flow rate of process gas. 
     A P 1  volume  106 A is fluidly coupled to the proportional valve  120 A, the P 1  volume  106 A being the sum of all the volume within the mass flow controller  101 A between the proportional valve  120 A and a flow restrictor  160 A. A pressure transducer  130 A is fluidly coupled to the P 1  volume  106 A to enable measurement of the pressure within the P 1  volume  106 A. An on/off valve  150 A is located between the flow restrictor  160 A and the proportional valve  120 A and may be used to completely halt flow of the process gas out of the P 1  volume  106 A. Optionally, the flow restrictor  160 A may be located between the on/off valve  150 A and the proportional valve  120 A in an alternate configuration. Finally, the flow restrictor  160 A is fluidly coupled to an outlet  110 A of the mass flow controller  101 A. In the processing system, the outlet  110 A is fluidly coupled to a valve  1100 A or directly to the processing chamber  1300 A. In the present embodiment, the flow restrictor  160 A is located between the on/off valve  150 A and the outlet  110 A. In an alternate embodiment, the on/off valve  150 A is located between the flow restrictor  160 A and the outlet  110 A. Thus, the arrangement of the on/off valve  150 A and the flow restrictor  160 A may be reversed. 
     Internal to the first on/off valve  150 A is a valve seat and a closure member. When the apparatus  100 A is delivering process gas, the first on/off valve  150 A is in an open state, such that the valve seat and the closure member are not in contact. This permits flow of the process gas and provides a negligible restriction to fluid flow. When the first on/off valve  150 A is in a closed state the closure member and the valve seat are biased into contact by a spring, stopping the flow of process gas through the first on/off valve  150 A. 
     The flow restrictor  160 A is used, in combination with the proportional valve  120 A, to meter flow of the process gas. In most embodiments, the flow restrictor  160 A provides a known restriction to fluid flow. The first characterized flow restrictor  160 A may be selected to have a specific flow impedance so as to deliver a desired range of mass flow rates of a given process gas. The flow restrictor  160 A has a greater resistance to flow than the passages upstream and downstream of the flow restrictor  160 A. 
     Optionally, the mass flow controller  101 A comprises one or more P 2  pressure transducers downstream of the flow restrictor  160 A and the on/off valve  150 A. The P 2  pressure transducer is used to measure the pressure differential across the flow restrictor  160 A. In some embodiments, the P 2  pressure downstream of the flow restrictor  160 A may be obtained from another apparatus  100 A connected to the processing chamber, with the readings communicated to the mass flow controller  101 A. 
     Optionally, temperature sensors may be employed to further enhance the accuracy of the mass flow controller  101 A. They may be mounted in the base of the mass flow controller  101 A near the P 1  volume  106 A. Additional temperature sensors may be employed in a variety of locations, including the proportional valve  120 A, the pressure transducer  130 A, and the on/off valve  150 A. 
     Turning to  FIG. 44 , a schematic of an on/off valve  150 A is shown with a first embodiment of the flow restrictor  160 A located within an outlet passage  157 A of the on/off valve  150 A. The on/off valve  150 A has an inlet passage  158 A which allows process gas to flow into the valve  150 A. A spring  156 A biases a closure member  154 A into contact with a valve seat  152 A, preventing process gas from flowing when the valve  150 A is in a closed state. When in an open state, the closure member  154 A is moved so that it is spaced from the valve seat  152 A, allowing process gas to pass the valve seat  152 A into the outlet  157 A. The outlet  157 A is formed as a cylindrical bore, but may also be formed as an oval, polygon, or any other shape. The flow restrictor  160 A is inserted into the outlet  157 A with a seal  170 A preventing gas flow between the flow restrictor  160 A and the wall  159 A of the outlet  157 A. 
     Turning to  FIGS. 45-48 , the flow restrictor  160 A and the seal  170 A are shown in greater detail.  FIG. 45  shows a perspective view of the flow restrictor  160 A and the seal  170 A. The flow restrictor  160 A extends from a first end  161 A to a second end  162 A along a longitudinal axis A-A. The seal  170 A is fitted to the flow restrictor  160 A. The seal  170 A circumferentially surrounds the flow restrictor  160 A and has an outer surface  171 A. The seal  170 A extends between a first end  172 A and a second end  173 A along a longitudinal axis B-B. The longitudinal axis B-B of the seal  170 A is collinear with the longitudinal axis A-A of the flow restrictor  160 A. However, in alternate embodiments, the longitudinal axis B-B of the seal  170 A may not be collinear with the longitudinal axis A-A of the flow restrictor  170 A. In some embodiments, the longitudinal axis B-B of the seal is angled with respect to the longitudinal axis A-A of the flow restrictor  160 A. In yet other embodiments, the longitudinal axis B-B of the seal may be spaced but parallel to the longitudinal axis A-A of the flow restrictor  160 A. In yet other embodiments, the axes may be both angled and spaced from one another. 
     As best seen in  FIG. 46 , the flow restrictor  160 A has a sealing portion  163 A and an unsealed portion  166 A. The unsealed portion  166 A has a first diameter D 1 A and the sealing portion  163 A has a second diameter D 2 A, the first diameter D 1 A being greater than the second diameter D 2 A. The seal  170 A further comprises an inner surface  174 A which is in surface contact with the sealing portion  163 A of the flow restrictor  160 A. The outer surface  171 A has a third diameter D 3 A which is greater than either of the first and second diameters D 1 A, D 2 A. This results in an interference fit between the wall  159 A and the outer surface  171 A and ensures that the seal  170 A seals against the wall  159 A of the outlet  157 A while simultaneously preventing contact between the flow restrictor  160 A and the wall  159 A. The inner surface  174 A defines an aperture through which the flow restrictor  160 A is received and through which all gas flows generally along the axis B-B from the first end  161 A to the second end  162 A of the flow restrictor  160 A. In yet other embodiments, the sealing portion  163 A extends the entire length of the flow restrictor  160 A. In yet further embodiments, the first diameter DIA may be the same diameter as the second diameter D 2 A. Preferably, the third diameter D 3 A has an interference fit with the wall  159 A. The third diameter D 3 A may also be the same diameter as the second diameter D 2 A. Furthermore, the gas need not enter from the first end  161 A and exit the second end  162 A of the flow restrictor, but may also enter through the circumference of the flow restrictor  160 A. Flow of gas within the flow restrictor  160 A need not flow strictly along the axis B-B, but need only pass through the flow restrictor  160 A and past the seal  170 A rather than around it. 
     The sealing portion  163 A has a seal receiving surface  165 A and a plurality of ridges  164 A used to improve sealing and retain the seal in place. The second diameter D 2 A is reduced as compared with the first diameter D 1 A so as to provide room for the seal  170 A and enhance retention of the seal  170 A on the flow restrictor  160 A. The ridges  164 A have a triangular cross-section and encircle the flow restrictor  160 A. When the seal  170 A is installed onto the sealing portion  163 A of the flow restrictor  160 A, the ridges  164 A deform the seal  170 A to further enhance the retention of the seal  170 A. This ensures that the seal  170 A is maintained on the flow restrictor  160 A when the flow restrictor is pressed into the outlet  157 A. The third diameter D 3 A is typically an interference fit with the outlet  157 A, so substantial force may be required to press the seal  170 A into the outlet  157 A depending on the extent of the interference. In the exemplary embodiment, the sealing portion  163 A has two ridges  164 A. In alternate embodiments, the sealing portion  163 A may have greater or fewer ridges  164 A. The cross-sectional profile of the ridges  164 A may be rectangular, trapezoidal, or any other shape. In yet further variations, a texture may be formed on the seal receiving surface  165 A. This texture may be formed by knurling, grinding, or any other known process. In alternate embodiments, a single model of flow restrictor  160 A may be installed into a plurality of outlets  157 A having differing diameters by modifying the thickness of the seal such that the third diameter D 3 A is modified to have a suitable interference with the wall  159 A of each of the respective outlets  157 A. This configuration beneficially allows the restrictor to be installed directly against the seat of the valve, greatly reducing the volume enclosed between the valve seat and the flow restrictor  160 A. In addition, multiple valve geometries, bore sizes, and fitting geometries can be accommodated by positioning the flow restrictor  160 A within the outlet  157 A. 
     In use, process gas flows through the flow restrictor  160 A from the first end  161 A to the second end  162 A. The seal  170 A provides a close fit with both the flow restrictor  160 A and the wall  159 A of the outlet  157 A so as to prevent process gas from flowing around the flow restrictor  160 A. Although some leakage of gas is possible, this leaking is reduced to at least 1×10{circumflex over ( )}-7 atm-cc/sec when Helium is used as a process gas. This leak rate ensures that a negligible volume of process gas flows around the flow restrictor  160 A rather than through the flow restrictor  160 A. 
     The seal  170 A is preferably formed of a non-metallic material such as a plastic material. One exemplary material could be Polytetrafluoroethylene (also known as “PTFE” or “Teflon”). Alternate materials may include metals, ceramics, or composite materials. The seal  170 A is preferably shrunk or stretched onto the flow restrictor  160 A so as to ensure a tight fit between the seal receiving surface  165 A and the inner surface  174 A. However, other methods are contemplated. In yet further embodiments, the seal may be welded, bonded, or pressed onto the flow restrictor  160 A so as to achieve a secure gas tight connection between the seal  170 A and the flow restrictor  160 A. In yet another embodiment, a plurality of identical flow restrictors  160 A are mounted to differing seals  170 A to allow installation into different size outlets  157 A. 
     Turning to  FIGS. 49-55 , a second embodiment of a flow restrictor  260 A is shown with a seal  270 A. As can be seen in the schematic of  FIG. 49 , a valve  150 A is illustrated. The valve  150 A is substantially identical to the valve  150 A of  FIG. 44 . However, instead of having a flow restrictor pressed into the outlet  157 A, a seal  270 A is mounted between a sealing surface  153 A of the valve  150 A and a sealing surface  291 A of a base  290 A, the base  290 A comprising flow passages  292 A which connect the on/off valve  150 A to the various components of the mass flow controller  101 A or other apparatus for controlling flow  100 A. The seal  270 A is installed between the sealing surface  153 A and the sealing surface  291 A and has a first seal ring  271 A and a second seal ring  272 A as best shown in  FIGS. 50 and 51 . The first seal ring  271 A and second seal ring  272 A are mounted to a gasket sheet  273 A and extend beyond the gasket sheet  273 A to engage sealing recesses  155 A,  295 A of the valve  150 A and the base  290 A, respectively. A plurality of apertures  274 A are provided through the gasket sheet  273 A to allow the passage of fasteners used to join the valve  150 A to the base  290 A. Additional holes  275 A may be used to facilitate manufacturing of the seal  270 A or for other purposes such as to seal additional flow passages. 
     As can be seen in  FIG. 51 , the first seal ring  271 A of the seal  270 A receives the flow restrictor  260 A. The flow restrictor  260 A extends from a first end  261 A to a second end  262 A along a longitudinal axis A-A. As best seen in  FIGS. 51 and 52 , the first seal ring  271 A has a first side  276 A and a second side  277 A opposite the first side  276 A, a longitudinal axis B-B extending through the first seal ring  271 A perpendicular to the first and second sides  276 A,  277 A. The first and second sides  276 A,  277 A engage the sealing recesses  155 A,  295 A and are compressed between them when the valve  150 A is mounted to the base  290 A. The first seal ring  271 A also has an inner surface  278 A which is generally cylindrical and a sealing web  279 A which extends across the inner surface  278 A. A flow aperture  280 A is formed in the sealing web  279 A to receive the flow restrictor  260 A. The flow aperture  280 A has a generally rectangular shape in the present embodiment, but in other embodiments it may be circular, elliptical, or any other shape suitable to accommodate a corresponding flow restrictor. The flow restrictor  260 A has a generally rectangular profile along the longitudinal axis and is a close fit within the flow aperture  280 A. Once the flow restrictor  260 A is installed in the flow aperture  280 A, it can be welded, bonded, or press fit to achieve a gas tight seal between the outer surface of the flow restrictor  260 A and the sealing web  279 A, ensuring that no process gas escapes past the flow restrictor  260 A without passing through the flow restrictor  260 A. The first seal ring  271 A also has an outer surface  285 A which may be of any size or diameter so long as the first seal ring  271 A can nest within the sealing recesses  155 A,  295 A. In alternate configurations, the sealing recesses  155 A,  295 A may be omitted. In yet further configurations, the inner surface  278 A and outer surface  285 A need not be cylindrical, and may be rectangular, ellipsoid, polygonal, or any other shape. 
     The second seal ring  272 A also has a first side  281 A and a second side  282 A. However, the second seal ring  272 A differs from the first seal ring  271 A in that it has no corresponding sealing web. Instead, the inner surface  283 A defines a flow aperture that enables the passage of process gas without significant flow impedance. Ideally, the flow passages and the second seal ring  272 A provide no restriction to fluid flow. In alternate embodiments, the seal  270 A may comprise only the first seal ring  271 A and be free of the second seal ring  272 A or any other components. Alternately, there may be more than one of the first or second seal rings  271 A,  272 A. 
     In alternate embodiments, the flow aperture  280 A of the first seal ring  271 A may be circular, rectangular, have a polygon shape, may comprise arcs, or may have any known shape. Thus, any cross-section of flow restrictor may be accommodated in the seal ring  271 A. In yet further embodiments, the seal ring  271 A may be press fit, welded, bonded, or otherwise secured directly within a flow passage such as the outlet  157 A of the valve  150 A or the flow passages  292 A of the base  290 A. In yet further embodiments, the gasket sheet  273 A may be omitted, such that the seal is comprised only of the seal ring  271 A. The seal  270 A is preferably constructed at least partially of a metal material. In the most preferred embodiments, the first and second seal rings  271 A,  272 A are metallic. 
     During assembly, the seal  270 A is placed between the valve  150 A and the base  290 A and aligned so that the first and second seal rings  271 A,  272 A align with the sealing recesses  155 A,  295 A. The flow restrictor  260 A then extends into the outlet  157 A and the corresponding flow passage  292 A in the base  290 A. The flow restrictor  260 A may be attached to the first seal ring  271 A so that the seal is halfway along the length of the flow restrictor  260 A, or it may be attached at any point along the length of the flow restrictor  260 A. It may even be attached substantially flush with either the first or second end  261 A,  262 A. Furthermore, the seal  270 A may be installed such that it is located within a portion of the valve  150 A to minimize the distance between the valve seat  152 A and the flow restrictor  260 A, minimizing the volume therebetween. As noted previously, the seal  270 A may also be configured so that the flow restrictor  260 A is positioned upstream of the valve seat  152 A and positioned in the inlet  158 A instead of the outlet  157 A. The seal of this embodiment can reliably produce a seal with a Helium leak rate better than 1×10{circumflex over ( )}-11 atm-cc/sec, substantially eliminating all flow of process gas around the flow restrictor  260 A. 
     Section III 
     Yet another embodiment of a flow restrictor  800  is shown in  FIGS. 56-62 .  FIG. 56  shows the flow restrictor  800  in perspective. The flow restrictor  800  extends from a first end  802  to a second end  803  and has outer layers  820  which surround layers  810  which have flow passages therein. A selection of the layers  810  are shown in  FIG. 57  in perspective view. These layers  810  extend from a first end  813  to a second end  814 , with apertures  812  on the first and second ends  813 ,  814 . The apertures  812  are not exposed at the first and second ends  813 ,  814  but will be exposed during subsequent processing steps described in greater detail below. The apertures need not have a different width than the rest of the flow passage, and instead may merely be formed by exposing the flow passage in a subsequent material removal operation. 
     A plurality of alignment features  815  are formed around the periphery of the layers  810 ,  820  to facilitate alignment and bonding of the layers  810 ,  820  to form the flow restrictor  800 . The alignment features  815  may also be formed internal to the layers  810 ,  820  and may be formed as holes, slots, protuberances, or any other geometry that permits alignment. The alignment features  815  may also be used to facilitate mass production, ensure that layers  810 ,  820  are not flipped or otherwise upside-down, or for any other purpose. An exploded view of the layers  810  is shown in  FIG. 59 , illustrating two first layers  830  and two second layers  860 . Flow passages  870  are formed in the first layers  830 . 
     The first layer  830  and the second layer  860  are illustrated in  FIGS. 61 and 62 . The first layer  830  has a first side  831 , a second side  832 , a third side  833 , a fourth side  834 , a front face  835 , and an opposite rear face  836 . The second layer  860  has a first side  861 , a second side  862 , a third side  863 , a fourth side  864 , a front face  865 , and an opposite rear face  866 . The first layer  830  has a series of longitudinal passages  839  having an elongated configuration which extend from the first side  831  to the second side  832 . 
     The second layer  860  is free of any flow passages or other features. As can be seen, in the flow restrictor  800 , gas remains exclusively on a single layer  830  and does not transition between first and second layers  830 ,  860 . The second layers form upper and lower boundaries of the flow passages, but do not have flow passages formed therein. The longitudinal passages  839  form the flow passages  870  when bounded by the second layers  860  on the front face  865  and the opposite rear face  866 . Gas enters through an opening  841  at the first side  831 , travels down a longitudinal passage  839 , then exits through an opening  841  on the second side  832 . The openings  841  are exposed in subsequent material removal operations as noted above to form the apertures  812 . In some embodiments, the flow path may zig-zag, change direction, or take any other path on the layer  830 . However, it never flows through the second layer  860  in this embodiment. The longitudinal passages  839  and openings  841  all extend through the entirety of the thickness of the first layer  830 . In alternate configurations, single sheet flow may be obtained by forming the flow passage depth only partially through the sheet such that the sheet dimensions remain intact during assembly prior to bonding. 
     As best shown in  FIG. 58 , the flow passages  870  are formed by the stacking of the layers  830 ,  860  as shown. The layers  830 ,  860  are of unequal thickness in this embodiment, but may have the same thickness if desired. Furthermore, thickness of the layers  830  or the number of flow passages  870  can be altered to alter the restriction to fluid flow. Each of the first layers  830  may be etched individually, then later bonded in an alternating sequence with the second layers  860  to form the plurality of layers  810  having a plurality of flow passages  870  therein. Subsequently or concurrently, the outer layers  820  may be bonded together with the plurality of layers  810  to form the flow restrictor  800 . Finally, post-processing is performed which exposes the openings  841  to form apertures  812  and allow fluid flow through the flow passages  870 . Post-processing may include machining, grinding, or other techniques. 
     In other embodiments, the layers  830 ,  860  may be formed individually of different materials having a different reactivity when subjected to etching chemicals or may be formed of identical materials having the same reactivity when subjected to etching chemicals. Layers may be formed in pairs are formed by assembling one first layer  830  with one second layer  860 . The layer pairs are then diffusion bonded so they cannot be readily separated. As discussed above, other bonding techniques may be utilized. Then, the layer pairs are etched so that the flow passages  870  are formed into the first layer  830  without etching the second layer  860 . The layer pairs are then assembled into the plurality of layers  810  having flow passages  870 . Outer layers  820  are also assembled with the plurality of layers  810  having the flow passages  870 . Finally, the layers  810 ,  820  are diffusion bonded together. Optionally, post processing such as grinding may be used to form the flow restrictor  800  and adapt it for installation into a flow passage of a device. 
     In one method of finishing the flow restrictor  800 , the flow restrictor  800  is formed by bonding the plurality of layers  810  and the outer layers  820  as discussed above. Subsequent to bonding of the layers  810 ,  820 , the flow restrictor is machined to expose the outlets  841  and form the apertures  812 . During the machining process, the flow restrictor  800  is machined to form a generally cylindrical shape suitable for insertion into a passage of a valve. 
     Subsequently, the machined flow restrictor  800  is ultrasonically cleaned. Nitrogen is then flowed through the flow passages  870  to eliminate particles. An electropolish process is then used to further clean the flow passages  870 . Deionized water is used to rinse the flow passages  870  and remove any electropolish solution within the flow passages  870 . A nitrogen purge is then flowed through the flow passages  870  to remove the deionized water. Nitric acid is then flowed through the flow passages  870  to further remove particles and debris, followed by another deionized water purge and nitrogen purge. Finally, another deionized water rinse is performed and the flow restrictor  800  is dried using a heated gas flow. This results in clean flow passages  870  which are free of debris or other particles such as machining remnants and the like. The flow restrictors  800  are clean and deliver highly predictable restrictions to fluid flow as a result of the processing operations performed thereon. 
     Turning to  FIGS. 63 to 65 , an exemplary apparatus for controlling fluid flow  100  is illustrated. The apparatus  100  has a valve  900 , the valve  900  being either a proportional valve or an on/off valve. The valve  900  has a passage  902  through which a fluid flows. The passage extends from a port  904  to a basin  906 . The basin  906  has a floor  908  and a sidewall  910 . A seal  912  serves as a seat for the valve  900 . A closure member  914  engages the seal  912  to permit or prevent fluid flow through the valve  900 . 
     The seal  912  is illustrated in greater detail in  FIG. 65 . The seal  912  has an inner surface  920  which engages a sealing surface  880  of the flow restrictor  800 . The inner surface  920  forms an aperture which receives the flow restrictor  800  to form a fluid-tight connection between the flow restrictor and the seal. The inner surface  920  forms a first seal which seals against the sealing surface  880  of the flow restrictor. 
     The sealing surface  880  also engages an inner surface  916  of the passage  902 . The sealing surface  880  may form an interference fit with the passage  902  and with the inner surface  920  of the seal  912 . This enables a fluid-tight connection between the flow restrictor  800  and both the passage  902  and the seal  912 . Alternately, the sealing surface  880  may only be sealed against one of the inner surface  920  of the seal  912  or the inner surface  916  of the passage  902 . The sealing surface  880  may also be referred to as a sealing portion because it interfaces with the inner surface  210  of the seal  912  to form the first seal. 
     The seal further comprises a seat surface  922 , a floor surface  924 , and a flange  926 . The flange  926  engages a retainer component  927  which maintains the seal  912  in position within the basin  906 . The floor surface  924  rests against the floor  908  of the basin  906 . The interface between the floor surface  924  of the seal  912  and the floor  908  of the basin  906  may also provide a second seal to prevent leakage of fluid past the seal  912  and into the passage  902 . The seat surface  922  engages the closure member  914  of the valve  900  to prevent fluid flow through the flow restrictor  800 . Optionally, the seal  912  may be formed of a non-metallic material. The seal  912  may be formed of a polymer material such as polytetrafluoroethylene. Alternately, it may be formed of a metallic or composite material. 
     As can be seen in  FIGS. 64 and 65 , the flow restrictor  800  also has a clearance surface  882  which has a smaller diameter than the sealing surface  880 . This is done to provide clearance for the flow restrictor  800  within the passage  902 . The first end  813  of the flow restrictor  800  is recessed with respect to the seat surface  922  to ensure that the flow restrictor  800  does not interfere with the closure member  914  during operation of the valve  900 . The second end  814  extends into the passage  902  and does not extend to the port  904 . 
     While the invention has been described with respect to specific examples including presently preferred modes of carrying out the invention, those skilled in the art will appreciate that there are numerous variations and permutations of the above described systems and techniques. It is to be understood that other embodiments may be utilized, and structural and functional modifications may be made without departing from the scope of the present invention. Thus, the spirit and scope of the invention should be construed broadly as set forth in the appended claims.