Method and apparatus for pressure-based mass flow rate control

Abstract

A system and method for splitting a single mass flow into secondary flows of desired ratios. The system and method include a laminar flow element and a secondary flow path including two pressure sensors. The nonlinear relationship between flow rate and pressure upstream and downstream of the laminar flow element can be converted to a function composed of upstream and downstream pressures that have a linear relationship with flow rate. This conversion allows for flow ratio control applications using signals from pressure sensors even in the absence of information about fluid type and flow rate into the flow ratio controller.

Description

Related Applications

[0001] This application is a continuation of U.S. Patent Application No. 16 / 800,363, filed February 25, 2020. The teachings of the above-referenced patent application are incorporated herein by reference in their entirety. [Background technology]

[0002] The fabrication of semiconductor devices often requires the careful synchronization and precisely metered delivery of as many as a dozen gases to a processing tool, such as a vacuum chamber. Various gases are used in the manufacturing process, and many separate processing steps may be required in which the semiconductor device is cleaned, polished, oxidized, masked, etched, doped, metallized, etc. The steps used, their particular sequence, and the materials involved all contribute to the creation of a particular device.

[0003] Accordingly, wafer fabrication facilities are typically organized to include areas where chemical vapor deposition, plasma deposition, plasma etching, sputtering, and other similar gas-producing processes are performed. For example, various process gases must be supplied to processing tools such as chemical vapor deposition reactors, vacuum sputtering systems, plasma etchers, or plasma-enhanced chemical vapor deposition. Pure gases must be supplied to the tools in uncontaminated, precisely metered amounts.

[0004] In a typical wafer fabrication facility, gases are stored in tanks, which are connected via pipes or conduits to a gas box. The gas box delivers uncontaminated, precisely metered amounts of pure, inert or reactive gases from the fabrication facility's tanks to the process tools. The gas box or gas metering system contains multiple gas paths with valves, pressure regulators, and gas metering units such as transducers, mass flow controllers, and filtration / purification devices. Each gas path has its own inlet for connection to a separate gas source, but all gas paths converge to a single outlet for connection to the process tools.

[0005] It may be desirable to split the combined process gas to multiple process chambers or other destinations. In such cases, a single outlet of the gas box is connected to multiple locations through secondary flow paths or lines. Flow ratio controllers (FRCs) are used to measure and control the relative proportions of secondary flows in the secondary flow lines and ensure accurate delivery of fluid to the process chambers at known, precise values ​​of secondary flow rates.

[0006] Existing flow ratio controllers use thermal flow sensors to measure and control the relative ratio of secondary flows due to the fact that thermal flow sensors have a linear response of the thermal sensor signal to flow rate and low pressure drop characteristics. However, thermal flow sensors have a tendency to zero drift, which causes their accuracy to decrease over time. In addition, exposure to high temperatures can damage the thermal flow sensor and produce undesirable chemical reactions in certain gases that further reduce its accuracy. Summary of the Invention [Problem to be solved by the invention]

[0007] A need exists for a system and method that uses a pressure-based flow sensor to divide a single mass flow into secondary flows of desired ratios. Pressure-based flow sensors can avoid the problems found in thermal flow sensors, but their relationship between pressure sensor signal and flow rate is highly nonlinear, which in turn requires knowledge of gas properties to be used in flow ratio control applications. [Means for solving the problem]

[0008] A system for dividing an inlet flow into secondary flows includes an inlet channel configured to receive the inlet flow. The system also includes secondary flow lines connected to the inlet. Each secondary flow line of the system includes a flow path configured to carry the secondary flow at a secondary flow rate, an upstream pressure sensor configured to provide an upstream pressure signal representative of the upstream pressure, a downstream pressure sensor configured to provide a downstream pressure signal representative of the downstream pressure, a pressure drop element in the flow path downstream of the upstream pressure sensor and upstream of the downstream pressure sensor configured to generate a linear response between the secondary flow rate and a function of the upstream and downstream pressures, and a valve configured to control the secondary flow based on the control signal. In some embodiments, the valve can be positioned in the flow path downstream of the pressure sensor downstream of the secondary flow line. In some embodiments, the system further includes a temperature sensor configured to measure the temperature of the inlet flow.

[0009] The system also includes a controller configured to calculate a ratio of secondary flow rates based on the upstream pressure signal and the downstream pressure signal, and the controller of the system is further configured to obtain a desired ratio of secondary flow rates by sending a control signal to the valve based on the calculated ratio of secondary flow rates and the desired ratio of secondary flow rates.

[0010] The pressure drop element in the secondary flow line can be a laminar flow element. The laminar flow element can be one of an annulus, bundled tubing, corrugated sheet, or multi-layer sheet. The pressure drop element can also be a compressed laminar flow element. The pressure drop element in the secondary flow line can also be a nozzle or orifice.

[0011] In some embodiments, a single pressure sensor can be used as the upstream pressure sensor for all secondary flow lines that have a valve located in the flow path of the secondary flow line downstream of the pressure sensor.

[0012] The function of the upstream and downstream pressure may be: f(Pu,Pd)=Pu 2 -Pd 2 where f(Pu,Pd) is the function, Pu is the upstream pressure, and Pd is the downstream pressure. The secondary flow rate can be determined by the following equation: Q=k*f(Pu,Pd) where Q is the secondary flow rate and k is a function of the dimensions of the pressure drop element, the fluid properties, and the fluid temperature. In some such embodiments, k=k(∈,d,L,mw,r,μ,T), where ∈,d, and L are the dimensions of the pressure drop element, mw, r, and μ are the fluid properties, and T is the fluid temperature.

[0013] The secondary flow rate can be determined based on a 3D map constructed from calibration points having variables Pu, Pd, and Q, where Q is the secondary flow rate, Pu is the upstream pressure, and Pd is the downstream pressure.

[0014] A method for dividing an inlet flow into desired ratios of secondary flows includes receiving the inlet flow at an inlet and dividing the inlet flow into secondary flow lines connected to the inlet. Each secondary flow line utilized by the method includes a flow path configured to carry the secondary flow at a secondary flow rate, an upstream pressure sensor configured to provide an upstream pressure signal representative of the upstream pressure, a downstream pressure sensor configured to provide a downstream pressure signal representative of the downstream pressure, a pressure drop element in the flow path downstream of the upstream pressure sensor and upstream of the downstream pressure sensor configured to generate a linear response of the secondary flow rate as a function of the upstream and downstream pressures, and a valve configured to control the secondary flow based on a control signal. The method for flow rate ratio control further includes determining, by a controller, a ratio of the secondary flow rates based on the upstream and downstream pressure signals, and obtaining the desired ratio of the secondary flow rates by sending a control signal to the valve based on the calculated ratio of the secondary flow rates and the desired ratio of the secondary flow rates. [Brief explanation of the drawings]

[0015] The foregoing will be apparent from the following more particular description of exemplary embodiments, which are illustrated in the accompanying drawings, in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the embodiments. [Figure 1] FIG. 1 is a schematic diagram illustrating an existing flow ratio controller that receives a single mass flow from a set of mass flow controllers. [Figure 2] 1 is a graph showing the relationship between the sensor output of a heat flow sensor and the flow rate at the measurement location. [Figure 3] 10 is a three-dimensional graph showing the relationship between upstream pressure, downstream pressure, and flow rate of gas N2 in a channel having laminar flow elements. [Figure 4] FIG. 1 is a schematic diagram illustrating an exemplary embodiment of a pressure-based flow ratio controller. [Figure 5]FIG. 1 is a diagram of several laminar flow elements that may be used as pressure drop elements in an exemplary embodiment of the present invention. [Figure 6] 10 is a set of graphs showing flow rate as a function of upstream and downstream pressure in a channel with laminar flow elements for the gases N2 and SF6. [Figure 7] 1 is a flow chart illustrating one exemplary embodiment of a method for utilizing a pressure sensor to split a single mass flow into secondary flows of desired ratios. [Figure 8A] FIG. 10 is a schematic diagram illustrating a first further exemplary embodiment of a pressure-based flow ratio controller. [Figure 8B] FIG. 10 is a schematic diagram illustrating a second further exemplary embodiment of a pressure-based flow ratio controller. DETAILED DESCRIPTION OF THE INVENTION

[0016] Exemplary embodiments are described below. One particular use of the disclosed apparatus, system, and method is for use with gas metering systems that deliver uncontaminated, precisely metered amounts of process and purge gases to semiconductor processing tools, chambers, and / or other systems, devices, and equipment. The disclosed apparatus, system, and method offer the advantage of operating without interfering with the performance of any upstream mass flow controllers. The disclosed apparatus, system, and method offer the advantage of allowing a single mass flow to be split into secondary flows of desired ratios using pressure sensors. The apparatus, system, and method offer the advantage of splitting a single flow of gas or liquid into multiple secondary flows of known, precise relative values ​​in desired ratios without requiring knowledge of the relatively large upstream pressure or the gas or gases that make up the flow.

[0017] FIG. 1 is a schematic diagram illustrating an existing flow ratio controller 100 that receives a single mass flow 103 from a set of mass flow controllers 101, shown for comparison. The set of mass flow controllers 101 controls the flow of a fluid 102 into an inlet line or manifold 104 of the flow ratio controller 100. The fluid may be a mixture including both process gas and purge gas drawn from an existing gas storage device, such as a gas tank. Although not shown, the fluid 102 may be monitored and controlled by additional components, such as filters, purifiers, and pressure transducers and controllers. The mass flow 102 forms an inlet flow 103 that is received by an inlet 104. In other embodiments, the inlet flow is comprised of a single fluid 102 received from a single mass flow controller, gas storage container, or other source. The inlet flow is represented by a flow rate Q t The gases 102 move to the inlet 104 at . The number of gases 102 and mass flow controllers 101 may be variable. The gases 102 may come from any potential source or gas storage device. Even if the properties of the individual gases 102 are known, the properties of the mixture 103 and the inlet flow rate Q t may be unknown due to different process recipes.

[0018] The inlet 104 is connected to secondary flow lines 105a, 105b, ..., 105N. The inlet flow is divided into secondary flows, Q1, Q2, ..., Q N The secondary flows Q1, Q2, ..., Q3 in the secondary flow lines 105 travel in the flow path of the secondary flow lines 105. The flow ratio controller can have any number of secondary flow lines and secondary flows depending on the needs of the system in which it is operating. N The sum of the formula

[0019]

number

[0020] must be equal to the inlet flow rate Q, as expressed in

[0021] Secondary flow rate Q1,Q2,…,Q N and inlet flow rate Q t The ratio of ∑ ...

[0022] r i =Q i / Q t

[0023] where r i is the flow rate of secondary flow line i. Secondary flows Q1,Q2,…,Q N and inlet flow rate Q t These can be precisely controlled once the ratio of secondary flow to secondary flow can be determined. The ratio of secondary flow is determined based on signals provided by flow sensors 106 on each secondary flow line 105, which provide signals indicative of the measured secondary flow rate.

[0024] The secondary flows can be controlled by valves 107 located in each secondary flow line 105. The controller is programmed to receive signals provided by the flow sensors 106, to determine the current ratio of secondary flows, and to send control signals to at least one of the valves 107 causing the valve 107 to vary the secondary flow in the secondary flow lines 105 to obtain the desired ratio of secondary flows. The controller receives a desired ratio of secondary flows, i.e., a mass flow ratio set point (r), from a host controller or through a user interface. spi , i=1,2...N).

[0025] The controller is programmed to receive signals indicative of the measured secondary flows provided by the flow sensors 106 and to calculate a flow rate ratio of the secondary flows in the secondary flow lines. The controller is also programmed to calculate a control signal based on the difference between the calculated ratio of the secondary flows and a desired ratio of the secondary flows using a feedback control algorithm, such as a PID or other feedback control algorithm. The controller is also programmed to send the calculated control signal to at least one of the valves 107. The control signal instructs the at least one valve 107 to adjust the at least one secondary flow. By sending the control signal to the at least one valve 107, the controller adjusts the secondary flow rate through at least one of the secondary flow lines 105 until the actual ratio of the secondary flows equals the desired ratio of the secondary flows.

[0026] In the absence of prior knowledge of the fluid or mixture of fluids being received at the inlet 104 with its inlet mass flow rate, the relationship between the signals of the flow sensors 106 and the secondary flow rates they are monitoring must be linear in order to calculate the flow ratio. A linear function f(x) has the properties f(k*x) = k*f(x) and f(x1+x2) = f(x1) + f(x2), where k is a constant. These properties are essential for the mathematical calculations used to isolate and calculate the secondary flow ratio without knowledge of the properties of the fluid 103.

[0027] If Q1=f1(x1), where Q1 is the flow rate of the secondary flow in secondary flow line 105a and f1(x1) is a linear function of the signal x1 provided by flow sensor 106a, and Q2=f2(x2), where Q2 is the flow rate of the secondary flow in secondary flow line 105b and f2(x2) is a different linear function of the signal x2 of flow sensor 106b, then the ratio r of the two secondary flow rates Q1 and Q2 can be expressed as the following equation:

[0028] r=Q1 / Q2=f1(x1) / f2(x2)

[0029] Due to the linear properties of the functions f1(x1) and f2(x2), the above equation can be transformed as:

[0030] r=f1(x1) / f2(x2)=f1(y1*x0) / f2(y2*x0)=y1*f1(x0) / y2*f2(x0)=(y1 / y2)*k0

[0031] where x0 is a constant, and therefore k0 = f1(x0) / f2(x0) is a constant. y1 = x1 / x0 and y2 = x2 / x0 are the transformed sensor signals. Functions f1(x0) and f2(x0) both contain the same variable based on the fluid properties. Because function f1(x0) is divided by function f2(x0) to generate k0, the variables based on the unknown fluid properties found in functions f1(x0) and f2(x0) cancel out and are no longer needed to calculate the flow ratio r. Therefore, the flow ratio Q1 / Q2 is equivalent to the ratio of the transformed sensor signals y1 / y2. This relationship allows for the determination of the secondary flow ratio based on the signal provided by the flow sensor 106. The secondary flow ratio is a function of the gas or fluid 103 at the inlet 104 and / or the inlet flow rate Q t This can be determined even when there is no prior information about

[0032] 1, the mathematical limitations of the transformation used to determine the ratio of secondary flows necessitate the use of flow sensors 106 that have a linear response between their signals and the flows they are measuring in secondary flow lines 105. Thermal flow sensors typically used in flow ratio controllers have such a linear response.

[0033] FIG. 2 is a graph 200 illustrating the relationship 201 between the sensor output of a thermal flow sensor and the flow rate at a measurement location. The thermal flow sensor has a sensor output that is related to the measured flow rate by a linear function 201, as shown in graph 200. Additionally, thermal flow sensors also have a low pressure drop, which is beneficial in certain situations requiring flow rate control. However, there are drawbacks to using thermal flow sensors. Specifically, thermal flow sensors have long-term drift in their measurements, which introduces inaccuracies into flow rate controllers that use thermal flow sensors. Additionally, high temperatures on thermal flow sensors can produce undesirable chemical reactions when used in combination with certain reactive gas species, such as HBr and Cl. These reactions can further reduce the accuracy of the thermal sensor.

[0034] Pressure-based mass flow measurement techniques and sensors offer an alternative to thermal-based mass flow sensors. Flow ratio controllers using pressure sensors can have better performance than existing thermal-based flow ratio controllers in terms of zero drift, corrosion resistance, and high-temperature performance. However, pressure-based mass flow measurements typically have a highly nonlinear relationship between pressure sensor output and flow rate. This relationship can be quite complex and can include fluid properties as important variables. For example, the flow rate (Q) of a nozzle under unthrottled flow conditions is determined by the following equation:

[0035]

number

[0036] where C' is the discharge coefficient, A is the nozzle throat area, Pu is the pressure upstream of the nozzle, Pd is the pressure downstream of the nozzle, R is the Universal Gas Constant, T is the fluid temperature, M is the fluid molecular weight, and γ is the specific heat ratio of the gas. Due to this and other highly nonlinear relationships, fluid properties are required to directly determine the flow rate using measurements from pressure sensors. However, when a pressure-drop element, such as a laminar flow element, is placed in the channel carrying the flow, this creates a new relationship between the pressure upstream of the element, the pressure downstream of the element, and the flow rate.

[0037] In mass flow ratio control applications, the gas properties of the inlet flow may not be known to the flow ratio controller. These properties include, without limitation, the specific heat of the gas, the molecular weight of the gas, and the viscosity of the gas, which are required to determine the absolute secondary flow rates in each of the secondary flow channels. Also, the inlet mass flow may be composed of an unknown mixture of at least two components.

[0038] The secondary flow rate can generally be determined by the following formula:

[0039] Q=f(∈,d,L,mw,r,μ,T,Pu,Pd)

[0040] where Q is the secondary flow rate and f() is a function of the dimensions of the pressure drop element (∈, d, L), the fluid properties (mw, r, μ), the fluid temperature (T), the upstream pressure (Pu), and the downstream pressure (Pd). For laminar flow elements, the function f() can have the form:

[0041] Q=f(∈,d,L,mw,r,μ,T,Pu,Pd)=k(∈,d,L,mw,r,μ,T)*(Pu 2 -Pd 2 )

[0042] where k() is a function that does not include pressure, i.e., Pu and Pd. In other words, the effect of the upstream and downstream pressures on the flow rate Q can be separated from other factors.

[0043] 3 is a three-dimensional graph 300 showing the relationship 301 between upstream pressure, downstream pressure, and flow rate of gas N2 in a channel having a laminar flow element. Graph 300 displays the relationship 301 between the pressure Pu upstream of the element, the pressure Pd downstream of the element, and the flow rate in channel Q, and includes specific data points 302. The relationship 301 between Q, Pu, and Pd is still highly nonlinear.

[0044] Q=k(∈,d,L,mw,r,μ,T)*(Pu 2 -Pd 2 )

[0045] where k(∈,d,L,mw,r,μ,T) is a function that depends on the geometry of the laminar flow element (∈,d,L), the fluid properties (mw,r,μ), and the gas temperature T. For the function k(∈,d,L,mw,r,μ,T), ∈ is the porosity of the laminar flow element if it is a porous medium, d is the inner diameter of the laminar flow element of the annular bypass or bundled tubing, and L is the length of the laminar flow element. However, all of the variables in k() can be kept constant across the secondary flow line of the flow ratio controller, and therefore k() can be treated as a mathematical constant by assuming a fixed gas temperature. When k() is a constant, the flow rate in a channel with a laminar flow element is linearly related to the difference between the square of the pressure upstream of the element and the square of the pressure downstream of the element. The following example vector transformation sequence can be used to derive vector variables from two pressures Pu and Pd that are linearly related to flow rate Q. The two vectors can be defined as follows:

[0046] (1) Modified pressure vector

[0047]

number

[0048]

number

[0049] This is a column vector with scalar variables for the upstream and downstream pressures, where [ ]' is the vector transpose operator, and

[0050] (2) Transformation vector

[0051]

number

[0052]

number

[0053] This is a row vector of scalar constant functions k(∈,d,L,mw,r,μ,T). The relationship between Q, Pu, and Pd can be rewritten as follows using the two vectors mentioned above:

[0054] Q=k(∈,d,L,mw,r,μ,T)*(Pu 2 -Pd 2 )

[0055] Q=[k(∈,d,L,mw,r,μ,T),-k(∈,d,L,mw,r,μ,T)]·[Pu 2 ,Pd 2 ]'

[0056]

number

[0057] where · is the dot product operator for matrices / vectors. The rewritten flow rate Q is the modified pressure vector derived from the upstream and downstream pressures Pu and Pd of each of the secondary flow channels.

[0058]

number

[0059] In other words, the use of a laminar flow element as the pressure drop element in a pressure-based flow ratio controller provides a linear relationship between the flow rate Q and the modified pressure vector variable

[0060]

number

[0061] This allows for mass flow rate control of an unknown inlet fluid.

[0062] FIG. 4 is a schematic diagram illustrating an example embodiment of a pressure-based flow ratio controller 400. The flow ratio controller 400 of FIG. 4 can be part of a multi-channel gas supply and selectively receives individual gases or a mixture of gases, including, for example, several process gases and a purge gas, from a gas supply (e.g., gas tank). The flow ratio controller 400 is configured to receive pressure signals from pressure sensors 406, 408 to determine and precisely control the ratio of secondary flows through each secondary flow line 405. The flow ratio controller 400 can be configured to obtain a gas temperature signal from a temperature sensor 411. The temperature sensor 411 is configured to provide a gas temperature signal representative of the temperature of the inlet flow. In an alternative embodiment, a temperature sensor 411 can be disposed in each of the secondary flow lines 405 and provide a gas temperature signal representative of the temperature of the secondary flow. The one or more provided temperature signals can be used to normalize k(∈, d, L, mw, r, μ, T) during a calibration process of the flow ratio controller 400.

[0063] The flow ratio controller 400 and associated method provide the benefit of dividing a single mass flow of gas or liquid into multiple secondary flows having known, precise relative values ​​and desired ratios of the secondary flows, without requiring relatively high upstream pressures and without requiring knowledge of the gas properties. Pressure sensors 406 and 408 generate signals representative of the measured pressures upstream and downstream of pressure drop element 409, respectively.

[0064] Inlet 404 is connected to secondary flow lines 405a, 405b, ..., 405N. The inlet flow of fluid 403 is directed through secondary flow lines 405 at flow rates Q1, Q2, ..., Q N The inlet flow rate Q at the inlet 404 is t are the secondary flow rates Q1, Q2, ..., Q in the secondary flow lines 405 N is equal to the sum of

[0065]

number

[0066] The flow ratio controller can have any number of secondary flow lines 405 depending on the needs of the system in which it is operating. The outlets of the secondary flow lines can each be connected to an equal number of locations, such as processing chambers in a single process tool or locations in two or more process tools. The outlets of the secondary flow lines can be connected to any device or destination required by the system.

[0067] Each secondary flow line 405a, 405b, ..., 405N includes in its path a pressure drop element 409a, 409b, ..., 409N, an upstream pressure sensor 406a, 406b, ..., 406N disposed upstream of the pressure drop element 409, and a downstream pressure sensor 408a, 408b, ..., 408N disposed downstream of the pressure drop element 409. The upstream pressure sensor 406 generates a signal corresponding to the pressure upstream of the pressure drop element and can be used as an input for the variable Pui for the respective secondary flow line 405. The downstream pressure sensor 408 generates a signal corresponding to the pressure downstream of the pressure drop element and can be used as an input for the variable Pdi for the respective secondary flow line 405. Thus, the secondary flow rates Q1, Q2, ..., Q3 in the secondary flow lines 405 are N is the pressure signal (Pui 2 -Pdi 2 ) or vector

[0068]

number

[0069] is linearly related to the function of

[0070] Qi=ki(∈i,di,Li,mw,r,μ,T)·(Pui 2 -Pdi 2), or

[0071]

number

[0072] These linear relationships are expressed as the secondary flow rates Q1, Q2, ..., Q in the secondary flow lines 405. N and the inlet flow rate, i.e., r i =Q i / Q t , can be determined using the signals provided by pressure sensors 406i and 408i. This allows the fluid 403 at the inlet 404, the properties of the fluid 403, and the absolute true flow rate Q of the fluid 403 t Fluid 403 may be a mixture of several component fluids, and the component fluids may be known or unknown.

[0073] The controller 410 may be a computer, such as a microprocessor, having a memory and a processor. Alternatively, the controller 410 may be any similar device capable of performing mathematical processes. The controller 410 is programmed to receive signals provided by the upstream pressure sensor 406 and the downstream pressure sensor 408. The controller 410 generates a transformed sensor response vector for each secondary flow line 405.

[0074]

number

[0075] The system is further programmed to use signals from the upstream pressure sensor 406 and the downstream pressure sensor 408 to derive the transformed sensor response vector

[0076]

number

[0077] are the secondary flow rates Q1, Q2, …, Q in the secondary flow lines. N The controller 410 controls the secondary flow rates Q1, Q2, ..., Q in the secondary flow lines 405. N The transformed sensor response vector to determine the ratio of

[0078]

number

[0079] The ratio of the secondary flows Q1, Q2, ..., Q3 of all the secondary flow lines 405a, 405b, ..., 405N is N and inlet flow rate Q t It can be determined from the following equation:

[0080]

number

[0081] Each secondary flow line 405 has a secondary flow rate Q1, Q2, ..., Q in the secondary flow line 405 in which it is located. N The secondary flow rate controller 410 includes a valve 407 configured to control the secondary flows Q1, Q2, ..., Q3 based on the pressure signals from the pressure sensors 406 and 408. The valve 407 can be located upstream or downstream of the pressure flow sensors 406 and 408. The controller 410 can be configured to send a control signal to control the valve 407 to obtain a target or desired ratio of secondary flows. The controller 410 can control the secondary flows Q1, Q2, ..., Q3 based on the pressure signals from the pressure sensors 406 and 408. NThe controller 410 may then send a control signal to at least one of the valves 407, and in response to the control signal, at least one of the valves 407 will modify the secondary flow in its secondary flow line 405. By sending the control signal to at least one of the valves 407, the controller 410 adjusts the secondary flow in at least one secondary flow line 405 until the ratio of the secondary flow rates equals the desired ratio.

[0082] The controller 410 can be configured to receive a desired ratio or flow rate ratio set point for the secondary flows. The controller 410 can then calculate the current secondary flows Q1, Q2, ..., Q N , the current ratio of the secondary flow rate, the target ratio of the secondary flow rate, i.e., the mass flow rate set point (r spi ,i=1,2,…,N), the secondary flows Q1,Q2,…,Q that will generate the target ratio of secondary flows N , and the secondary flows Q1, Q2, ..., Q3 to determine a control signal to be sent to at least one of the valves 407 that will induce a target ratio of secondary flows. N and the signals from pressure flow sensors 406 and 408 can be used. Controller 410 can include a feedback control module that calculates and sends control signals to each valve in the secondary flow channels based on the calculated ratio of secondary flows s and the desired ratio of secondary flows to regulate the flow ratio in each of the secondary flow channels to a desired flow ratio set point. Controller 410 also calculates and sends control signals to each valve in the secondary flow channels based on the calculated ratio of secondary flows s and the desired ratio of secondary flows to regulate the flow ratio in each of the secondary flow channels to a desired flow ratio set point. t It can also be configured to calculate

[0083] The flow ratio controller 400, due to its use of two pressure sensors 406 and 408 to measure flow rate and, therefore, flow ratio, offers several advantages over existing thermal mass flow ratio controllers. First, it provides the ability to perform pressure-based mass flow ratio control by utilizing the linear relationship between the secondary flow rate and the converted signals of the pressure sensors 406 and 408. Second, pressure-based flow sensors are more stable than prior art thermal-based flow sensors. Pressure-based flow sensors also have greater corrosion resistance than thermal-based flow sensors. Furthermore, pressure-based flow sensors are superior in high temperature applications than thermal-based flow sensors.

[0084] In one embodiment, the pressure drop element 409 is a laminar flow element. It is comprised of upstream and / or downstream pressures that have a linear relationship to the secondary flow rate Q (Pu 2 -Pd 2 Other pressure drop elements 409 besides laminar flow elements can be used in the flow ratio controller 400, as long as there is a function equivalent to ( ). One exemplary alternative is a critical flow nozzle / orifice, where the secondary flow rate is directly linearly related to the pressure upstream of the nozzle. However, the large pressure drop that can be induced by a critical flow nozzle can be a concern in some applications of the flow ratio controller. One benefit of using a laminar flow element as the pressure drop element 409 is that it has a smaller pressure drop compared to a critical flow nozzle / orifice.

[0085] 8A and 8B are schematic diagrams illustrating two additional exemplary embodiments of a pressure-based flow ratio controller 800. In FIG. 8A, the flow ratio controller 800A includes an upstream pressure sensor 806i, a downstream pressure sensor 808i, and a pressure drop element 809i for each of the secondary flow channels 805i (i=a, b, ..., N), all upstream of the flow control valve 807i. Because all of the upstream pressure sensors 806i are connected in flow communication with the inlet 804, the pressure difference between the measurements can be very small. Therefore, the number of upstream pressure sensors 806i can be reduced, thereby reducing the cost of the flow ratio controller 800. For example, the flow ratio controller 800B of FIG. 8B includes only one upstream pressure sensor 806 that provides upstream pressure measurements for all of the secondary flow channels 805i. The number of upstream pressure sensors 806 can vary from 1 to N depending on the upstream pressure difference between the secondary flow channels 805i in the flow ratio controller 800. Both flow ratio controllers 800A and 800B can be configured to obtain a gas temperature signal from a temperature sensor 811.

[0086] FIG. 5 is a diagram of several laminar flow elements that can be used as pressure drop elements in one embodiment of the present invention. Several different types of laminar flow elements can be used as pressure drop elements. Potential types of laminar flow elements include a corrugated laminar flow element 501, a bundled-tube laminar flow element 502, and an annular laminar flow element 503. Other laminar flow elements include parallel-plate laminar flow elements and compressed laminar flow elements, such as sintered porous metal filters or other porous media. The laminar flow elements are precisely engineered with excellent consistency. They also maintain the relationship between flow rate, upstream pressure, and downstream pressure, even in low pressure ranges. Each laminar flow element includes an outer casing 500a, 500b, 500c that forces flow through the interior of the element. The interior of each laminar flow element contains one or more obstacles that induce laminar flow in the fluid moving through the element. In the case of the corrugated laminar flow element 501, the interior is filled with raised or recessed laminar metal plates 504. In the case of bundled-tube laminar flow element 502, the interior is filled with tubes 505 whose length is parallel to the flow direction. In the case of annular laminar flow element 503, the interior includes a solid cylinder 506 whose length is parallel to the flow direction, creating a ring-shaped gap 507 between the outer casing 500c and the central cylinder 506. Any variation and configuration of laminar flow elements, including without limitation those shown in Figure 5, can be utilized by the present invention, so long as they are capable of inducing laminar flow in the secondary flow lines.

[0087] FIG. 6 is a set of graphs showing the relationship between flow rate and the upstream and downstream pressures in a channel having laminar flow elements for the gases N2 and SF6. To collect the data used to generate FIG. 6, an annular laminar flow element 600 was used as a pressure drop element in the channel, with pressure sensors located upstream and downstream of the annular laminar flow element 600. The flow of fluid in the channel was controlled using a mass flow controller. Graph 601 shows the flow rate in the channel as a function of the pressure measured upstream of the annular laminar flow element 600 (Pu) and the pressure measured downstream of the annular laminar flow element 600 (Pd) (Pu). 2-Pd 2 ) as a function of the flow rate in the channel when the fluid was SF6 gas, and the pressure measured upstream of the annular laminar flow element 600 (Pu) and downstream of the annular laminar flow element 600 (Pd). Points 605 are experimental data points used to derive the relationship 603. Graph 602 shows the relationship between the flow rate in the channel and the pressure measured upstream of the annular laminar flow element 600 (Pu) and downstream of the annular laminar flow element 600 (Pd) as a function of the flow rate in the channel when the fluid was SF6 gas. 2 -Pd 2 ) and point 606 is the experimental data point used to derive relationship 604. From both graphs 601 and 602, it can be seen that the function (Pu 2 -Pd 2 ) has a linear relationship with the flow rate in the channel. Due to this linear relationship, a flow ratio controller can use signals corresponding to the pressure measured upstream of the annulus laminar flow element 600 (Pu) and the pressure measured downstream of the annulus laminar flow element 600 (Pd) to determine and control the ratio of the secondary flow of an unknown fluid composed of an unknown gas or gas mixture. The strong linear relationships 603 and 604 allow for accurate flow ratio measurement and control when using a pressure drop element such as the annulus laminar flow element 600 in flow ratio control, as shown in FIG.

[0088] In some embodiments, each secondary flow channel needs to be calibrated to provide flow measurement for flow ratio control applications. A calibration gas, such as N2, can be used to determine the coefficient of k(∈, d, L, mw, r, μ, T) in the i-th secondary flow channel (i=1, 2, ..., N) for the following flow calculation formula:

[0089] Qi=ki(∈i,di,Li,mw,r,μ,T)·(Pui 2 -Pdi 2 ), or

[0090]

number

[0091] During the calibration process, multiple calibration points of (Pui, Pdi, Qi) can be collected over the entire operating range. In addition, temperature sensors can be used to determine the T of the inlet flow and / or secondary flow. The calibration points can be used to determine the coefficients of k(∈,d,L,mw,r,μ,T).

[0092] An alternative flow calculation method involves constructing a 3D map of the variables Pui, Pdi, and Qi as shown in Figure 3 for each secondary flow channel during calibration. The flow ratio controller 410, 810 can use the 3D map as a look-up table to determine the flow rate Qi based on the measured upstream pressure Pui and downstream pressure Pdi for the ith flow channel. If the inlet gas is an unknown gas, the flow ratio controller 400, 800 can treat the inlet gas as a calibration gas (e.g., N2) and determine the secondary flow rate Qi as the calibration gas and then the corresponding flow ratio r i A 3D map of the calibrated coefficients k i (∈ i, di, Li, mw, r, μ, T) or (P ui, P di, Q i ) can be used to calculate the flow rate Q i in each secondary flow line, as a function of the modified pressure vector

[0093]

number

[0094] Since there is a linear relationship between i is accurate even if the calculated flow rate Qi is based on a calibration gas rather than the actual gas.

[0095] FIG. 7 is a flowchart 700 illustrating an exemplary embodiment of a method for splitting an inlet flow into secondary flows of desired ratios using pressure sensors. The method illustrated in flowchart 700 can be implemented using a flow ratio controller having pressure drop elements, valves, pressure sensors, controllers, and other elements configured in the manner illustrated by FIGS. 4, 8A, and 8B. A first step 701 is receiving an inlet flow at an inlet channel. The inlet flow, fluid properties, and flow rate at the inlet may be unknown. In a next step 702, the inlet flow is split into secondary flows. The secondary flows are carried by paths of secondary flow lines connected to the inlets. The secondary flows travel at secondary flow rates in the secondary flow lines. For each secondary flow line, the following steps 703 and 704 are performed: in step 703, a first pressure sensor measures the pressure in the secondary flow line upstream of the pressure drop element, and in step 704, a second pressure sensor measures the pressure in the secondary flow line downstream of the pressure drop element.

[0096] The next step 705 is performed by the controller, which uses the pressures measured upstream and downstream of the pressure drop element to determine the ratio of the flow rate and the secondary flow rate. This is possible due to laminar flow elements in the secondary flow line channel, and the secondary flow rate is a function of the upstream and downstream pressures, specifically (Pu 2 -Pd 2) is linearly related to the secondary flow rates. In a final step 706, the controller calculates and sends a control signal to at least one of the valves disposed in the secondary flow lines to control at least one of the secondary flow rates in the secondary flow lines to obtain a specified or desired ratio of secondary flow rates. The controller may use a feedback control algorithm to complete step 706. The manner in which the control signal controls at least one of the valves depends on the determined ratio of the secondary flow rates and the desired ratio of the secondary flow rates. The method illustrated in flowchart 700 may be performed continuously during operation of the flow ratio controller and may be used to achieve a sequence of desired ratios of secondary flow rates with a high degree of accuracy.

[0097] While exemplary embodiments have been particularly shown and described, those skilled in the art will recognize that various changes in form and detail may be made therein without departing from the scope of the embodiments encompassed by the appended claims.

Claims

1. 1. A system for dividing a single mass flow into secondary flows, comprising: an inlet configured to receive an inlet flow; secondary flow lines connected to the inlet, each secondary flow line comprising: a flow path configured to carry the secondary flow at a secondary rate; an upstream pressure sensor configured to provide an upstream pressure signal representative of the upstream pressure; a downstream pressure sensor configured to provide a downstream pressure signal representative of the downstream pressure; a pressure drop element in the flow path downstream of the upstream pressure sensor and upstream of the downstream pressure sensor, configured to generate a linear relationship between the secondary flow rate and a function of the upstream pressure and the downstream pressure; and a valve configured to control the secondary flow rate based on a control signal; a secondary flow line including: a controller configured to calculate a secondary flow ratio for each secondary flow line based on the upstream pressure signal and the downstream pressure signal using the linear relationship, and further configured to obtain the desired secondary flow ratio by sending the control signal to the valve based on the calculated ratio and a desired secondary flow ratio; A system having:

2. The system of claim 1 , wherein the pressure drop element is a laminar flow element.

3. The system of claim 1 , wherein the pressure drop element is a compressed laminar flow element.

4. The system of claim 2 , wherein the laminar flow element is one of a ring, a bundled tube, a corrugated plate, or a multi-layer plate.

5. The system of claim 1 , wherein the pressure drop element is a flow nozzle or an orifice.

6. The system of claim 1 , further comprising a temperature sensor configured to measure a temperature of the inlet flow.

7. The system of claim 1 , wherein the valve is disposed in the flow path of the secondary flow line upstream of the upstream pressure sensor.

8. The system of claim 1 , wherein the valve is disposed in the flow path of the secondary flow line downstream of the upstream pressure sensor and the downstream pressure sensor.

9. A system for dividing a single mass flow into secondary flows, comprising: an upstream pressure sensor configured to provide an upstream pressure signal representative of the upstream pressure; an inlet configured to receive an inlet flow; secondary flow lines connected to the inlet, each secondary flow line comprising: a flow path configured to carry the secondary flow at a secondary rate; a downstream pressure sensor configured to provide a downstream pressure signal representative of the downstream pressure; a pressure drop element in the flow path downstream of the upstream pressure sensor and upstream of the downstream pressure sensor, configured to generate a linear relationship between the secondary flow rate and a function of the upstream pressure and the downstream pressure; and a valve configured to control the secondary flow rate based on a control signal; a secondary flow line including: a controller configured to calculate a secondary flow ratio for each secondary flow line based on the upstream pressure signal and the downstream pressure signal using the linear relationship, and further configured to obtain the desired secondary flow ratio by sending the control signal to the valve based on the calculated ratio and a desired secondary flow ratio; and the valve is disposed in the flow path of the secondary flow line downstream of the upstream pressure sensor and the downstream pressure sensor; The system wherein the upstream pressure sensor is a single pressure sensor located upstream to all of the secondary flow lines.

10. The function of the upstream pressure and the downstream pressure is: f(Pu,Pd)=Pu ２ -Pd ２ 2. The system of claim 1, wherein f(Pu, Pd) is the function, Pu is the upstream pressure, and Pd is the downstream pressure.

11. The secondary flow rate can be calculated by the following formula: Q=k*f(Pu, Pd) 2. The system of claim 1, wherein Q is the secondary flow rate, f(Pu, Pd) is the function of the upstream pressure and the downstream pressure, and k is a function of the pressure drop element dimensions, fluid properties, and fluid temperature.

12. 12. The system of claim 11, wherein k = k(∈, d, L, mw, r, μ, T), where ∈, d, and L are dimensions of the pressure drop element, mw, r, and μ are the fluid properties, and T is the temperature of the fluid.

13. 10. The system of claim 1, wherein the secondary flow rate can be determined based on a 3D map constructed of calibration points having variables Pu, Pd, and Q, where Q is the secondary flow rate, Pu is the upstream pressure, and Pd is the downstream pressure.

14. 1. A method for dividing a single mass flow into secondary flows of desired ratios, comprising: receiving an ingress flow at an ingress; dividing the inlet flow into secondary flow lines connected to the inlet, each secondary flow line comprising: a flow path configured to carry the secondary flow at a secondary rate; an upstream pressure sensor configured to provide an upstream pressure signal representative of the upstream pressure; a downstream pressure sensor configured to provide a downstream pressure signal representative of the downstream pressure; a pressure drop element in the flow path downstream of the upstream pressure sensor and upstream of the downstream pressure sensor, configured to generate a linear relationship between the secondary flow rate and a function of the upstream pressure and the downstream pressure; and a valve configured to control the secondary flow rate based on a control signal; and calculating, by a controller, a secondary flow rate ratio for each secondary flow line based on the upstream pressure signal and the downstream pressure signal using the linear relationship; obtaining, by the controller, the desired ratio of secondary flow rates by sending the control signal to the valve based on the calculated ratio and a desired ratio of secondary flow rates; A method having the following.

15. The method of claim 14, wherein the pressure drop element is a laminar flow element.

16. 15. The method of claim 14, wherein the pressure drop element is a compressed laminar flow element.

17. 16. The method of claim 15, wherein the laminar flow element is one of a ring, a bundled tube, a corrugated plate, or a multi-layer plate.

18. 15. The method of claim 14, further comprising measuring the temperature of the inlet flow using a temperature sensor.

19. A method for dividing a single mass flow into secondary flows of desired ratios, comprising: receiving an ingress flow at an ingress; splitting the inlet flow into secondary flow lines connected to the inlet; the upstream pressure sensor is a single pressure sensor used as the upstream pressure sensor for all of the secondary flow lines and configured to provide an upstream pressure signal representative of the upstream pressure; Each secondary flow line is a flow path configured to carry the secondary flow at a secondary rate; a downstream pressure sensor configured to provide a downstream pressure signal representative of the downstream pressure; a pressure drop element in the flow path downstream of the upstream pressure sensor and upstream of the downstream pressure sensor, configured to generate a linear relationship between the secondary flow rate and a function of the upstream pressure and the downstream pressure; and a valve configured to control the secondary flow rate based on a control signal; and calculating, by a controller, a secondary flow rate ratio for each secondary flow line based on the upstream pressure signal and the downstream pressure signal using the linear relationship; obtaining, by the controller, the desired ratio of secondary flow rates by sending the control signal to the valve based on the calculated ratio and a desired ratio of secondary flow rates; A method having the following.

20. The function of the upstream pressure and the downstream pressure is: f(Pu,Pd)=Pu ２ -Pd ２ 15. The method of claim 14, wherein f(Pu, Pd) is the function, Pu being the upstream pressure, and Pd being the downstream pressure.

21. The secondary flow rate may be determined by the following formula: Q=k*f(Pu, Pd) 15. The method of claim 14, wherein Q is the secondary flow rate, f(Pu, Pd) is the function of the upstream pressure and the downstream pressure, and k is a function of the pressure drop element dimensions, fluid properties, and fluid temperature.

22. 22. The method of claim 21, wherein k = k(∈, d, L, mw, r, μ, T), where ∈, d, and L are dimensions of the pressure drop element, mw, r, and μ are the fluid properties, and T is the temperature of the fluid.

23. 15. The method of claim 14, further comprising generating a 3D map comprised of calibration points having variables Pu, Pd, and Q, where Q is the secondary flow rate, Pu is the upstream pressure, and Pd is the downstream pressure, and the controller determines the secondary flow rate, which can be determined based on the 3D map.

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