Method and system for calibrating MFV heat exchange coefficient based on static volume method

Abstract

The invention discloses a method and system for calibrating an MFV heat exchange coefficient based on a static volume method, and relates to the technical field of electronic devices.The method comprises the specific steps that static data and dynamic data in the air inlet process are collected, and the static data comprise initial static parameters, termination static parameters and air inlet duration; constructing a static mass flow calculation model by utilizing a static volume method based on the static data, and constructing a dynamic mass flow calculation model by utilizing a rising rate method based on the dynamic data; and the static mass flow calculation model and the dynamic mass flow calculation model are combined based on the physical principle, and the heat exchange coefficient is solved. Based on the static volume method, the convective heat transfer coefficient of the MFV chamber under the conditions of specific media, pressure and temperature can be obtained through in-situ measurement, so that the total temperature of gas in the chamber in flow measurement can be obtained on the premise that holes are not formed, and the contradiction between leakage reduction and temperature measurement accuracy improvement in an existing method is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic devices, and more particularly to a method and system for calibrating a heat transfer coefficient of a MFV based on a static volume method. Background Art

[0002] With the development of the semiconductor industry, the requirements for the gas flow control equipment used in the manufacturing process, the mass flow controller (MFC), are getting higher and higher. In order to ensure the accurate and stable gas supply during the manufacturing process of semiconductor devices, the MFC needs to be accurately calibrated. One of the traditional calibration methods is the rate of rise method (RoR method) based on a constant volume chamber. This method has been widely used in process environments such as chemical vapor deposition (CVD) chambers since the 1960s to calibrate tiny gas flows.

[0003] The basic principle of the RoR method is to estimate the gas flow rate by measuring the rate of change of the gas pressure and temperature inside the constant volume chamber over time. This process relies on the state equation of the gas, in which the mass of the gas is determined by the pressure and temperature in the chamber. However, in actual operation, if a hole is opened on the constant volume chamber to measure the pressure, additional leakage may be introduced, which is particularly critical for small flow measurements because the leakage may lead to large uncertainties. Therefore, usually only the temperature change of the outer wall of the constant volume chamber is measured.

[0004] In the 21st century, MKS of the United States developed an online rapid calibration instrument based on the RoR method, the MFV (Mass Flow Verifier), which has an accuracy of 1% of the reading. However, in order to further improve the calibration accuracy, it is necessary to have a deep understanding of the factors that affect the calibration results, especially the influence of the heat transfer process.

[0005] In 2018, NIST researchers John D. Wright and others improved the traditional RoR flow calibration method and proposed a new heat transfer model that takes into account the relationship between the water bath temperature and the gas temperature inside the chamber. The model provides a mathematical expression to describe the heat transfer process, but the determination of the convective heat transfer coefficient h remains a challenge. The h value is affected by many factors, including the physical properties of the gas, flow rate, and the geometry of the heat transfer surface, which increase the difficulty of theoretical calculations.

[0006] Therefore, how to accurately measure the true total gas temperature (average body temperature) during the steady-state intake process of the MFV chamber is an urgent problem to be solved by those skilled in the art. Summary of the invention

[0007] In view of this, the present invention provides a method and system for calibrating the heat transfer coefficient of MFV based on the static volume method, which overcomes the above-mentioned defects.

[0008] In order to achieve the above object, the present invention adopts the following technical solution:

[0009] A method for calibrating the heat transfer coefficient of MFV based on the static volume method, the specific steps are:

[0010] Collect static data and dynamic data during the intake process, wherein the static data includes initial static parameters, terminal static parameters, and intake duration;

[0011] Based on the static data, a static mass flow calculation model is constructed using a static volume method, and based on the dynamic data, a dynamic mass flow calculation model is constructed using a rate of rise method;

[0012] Based on physical principles, the static mass flow calculation model and the dynamic mass flow calculation model are combined to solve the heat transfer coefficient.

[0013] Optionally, the static mass flow calculation model is expressed as:

[0014]

[0015] Where, M is the molecular weight of the gas medium being measured; T a is the ambient temperature; R is the universal gas constant; t is the intake time, Δt is the time difference of the valve switch; V c V is the total volume between the first valve and the second valve; p is the volume from MFC to the first valve; z m,f 、z m,i 、z p,f 、z p,i are the compression coefficients of gases at corresponding pressure and temperature; p m,f is the stagnation pressure in the constant volume chamber after air intake; p m,i is the stagnation pressure in the constant volume chamber before air intake; p p,f is the stagnation pressure at the additional volume after the intake; p p,i It is the stagnation pressure at the additional volume before the intake.

[0016] Optionally, the expression of the valve switching time system difference is:

[0017]

[0018] In the formula, t is the intake time; n is the number of valve opening and closing times; q' m The actual flow rate through the first valve after the valve is switched once; q" m is the actual flow rate through the first valve after the valve is opened and closed n times; is the total mass of the valve opened and closed n times continuously; m' is the mass of the valve opened and closed once; t' is the time for the valve to open and close once, It is the sum of the time it takes for the valve to open and close n times continuously.

[0019] Optionally, the expression of the dynamic mass flow calculation model is:

[0020]

[0021] Where, T stp P is the temperature under standard conditions; stp V is the pressure under standard conditions; s is the total volume from the sonic nozzle to the downstream valve; i is the number of the pressure data; p i is the pressure value of the MFV chamber during the intake process; T is the average total temperature of the gas in the chamber when the heat exchange is balanced; N is the number of consecutive pressure measurements in the RoR method; t RoR The time required to obtain the selected dynamic data; ρ N is the gas density under standard conditions.

[0022] Optionally, the step of obtaining the heat transfer coefficient is:

[0023] Solving the average total temperature of the gas in the chamber when heat exchange is in equilibrium based on the combined static mass flow calculation model and the dynamic mass flow calculation model;

[0024] A heat transfer model between the water bath temperature and the chamber gas temperature is constructed based on the average total temperature of the gas in the chamber and the wall temperature when the heat exchange is balanced;

[0025] The heat transfer coefficient is solved according to a heat transfer model between the water bath temperature and the chamber gas temperature.

[0026] Optionally, the expression for the average total temperature of the gas in the chamber when the heat exchange is in equilibrium is:

[0027]

[0028] Where, t pVTt T is the static volumetric intake time; a is the ambient temperature; N is the number of consecutive pressure measurements in the RoR method; V s V is the total volume from the sonic nozzle to the second valve; c V is the total volume between the first valve and the second valve; p is the volume from MFC to the first valve; z m,f 、z m,i 、z p,f 、z p,i are the compression coefficients of gases at corresponding pressure and temperature; p m,f is the stagnation pressure in the constant volume chamber after air intake; p m,i is the stagnation pressure in the constant volume chamber before air intake; p p,fis the stagnation pressure at the additional volume after the intake; p p,i It is the stagnation pressure at the additional volume before the intake.

[0029] Optionally, the temperature ratio calculation expression is:

[0030]

[0031] Where, T is the average total temperature of the gas in the chamber when the heat exchange is balanced; T w is the wall temperature; T in is the initial temperature of the gas flowing into the chamber from the measured table; γ is the specific heat ratio of the gas; is the mass flow rate measured by the static volume method; t pVTt is the static volumetric intake time; m 0 is the initial mass of the gas in the chamber when the second valve is closed; Γ is a dimensionless parameter.

[0032] Optionally, when solving the heat transfer coefficient according to the temperature ratio, the temperature ratio calculation expression needs to be deformed, and the obtained deformed expression is:

[0033] Ax+B -x -1=0;

[0034]

[0035] Where A is V c The surface area of ​​the chamber; T is the average total temperature of the gas in the chamber when the heat exchange is balanced; T w is the wall temperature; γ is the gas specific heat ratio; is the mass flow rate measured by the static volume method; t pVTt is the static volumetric intake time; m 0 is the initial mass of the gas in the chamber when the second valve is closed.

[0036] Optionally, the expression of the dimensionless quantity parameter Γ is:

[0037]

[0038] Where A is V c The surface area of v is the isochoric specific heat capacity of the gas; h is the heat transfer coefficient; It is the mass flow rate measured by the static volume method.

[0039] A system for calibrating the heat transfer coefficient of an MFV based on a static volume method, the specific steps are:

[0040] A data acquisition module, used to collect static data and dynamic data during the intake process, wherein the static data includes initial static parameters, terminal static parameters and intake duration;

[0041] A model building module, used to build a static mass flow calculation model using a static volume method based on the static data, and to build a dynamic mass flow calculation model using a rate of rise method based on the dynamic data;

[0042] A calculation module is used to solve the heat transfer coefficient by combining the static mass flow calculation model and the dynamic mass flow calculation model based on physical principles.

[0043] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a method and system for calibrating the MFV heat transfer coefficient based on the static volumetric method. Based on the static volumetric method, the convective heat transfer coefficient of the MFV chamber under specific medium, pressure and temperature conditions can be measured in situ, so as to obtain the total temperature of the gas in the chamber during flow measurement without opening a hole, thereby solving the contradiction between reducing leakage and improving temperature measurement accuracy in the prior art and improving accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0045] Figure 1 A schematic diagram of the method provided by the present invention;

[0046] Figure 2 Schematic diagram of the experimental device provided by the present invention. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] On the one hand, this embodiment discloses a method for calibrating the heat transfer coefficient of an MFV based on a static volume method, and the specific steps are as follows:

[0049] Step 1: Collect static data and dynamic data during the intake process, where the static data includes initial static parameters, terminal static parameters, and intake duration;

[0050] Step 2: Based on the static data, a static mass flow calculation model is constructed by using a static volume method, and based on the dynamic data, a dynamic mass flow calculation model is constructed by using a rate of rise method;

[0051] Step 3: Based on physical principles, the static mass flow calculation model and the dynamic mass flow calculation model are combined to solve the heat transfer coefficient.

[0052] Furthermore, in step 1, the static data collection process includes:

[0053] Initial static parameters: Before the start of intake, measure and record the stagnation pressure and stagnation temperature of the MFV chamber;

[0054] Termination static parameters: When the intake is completed, the stagnation pressure and stagnation temperature of the MFV chamber are measured and recorded again;

[0055] Intake duration: records the time from the start to the end of intake, that is, the process from the closing of the second valve to the closing of the first valve.

[0056] The dynamic data collection process is as follows: based on the sensor, the pressure change rate and temperature change rate of the MFV chamber during the entire intake process are monitored.

[0057] In one embodiment, the average mass flow rate during the total intake time is calculated using a static mass flow rate calculation model, wherein the expression of the static mass flow rate calculation model is:

[0058]

[0059] Where, M is the molecular weight of the gas medium being measured; T a is the ambient temperature; R is the universal gas constant; t is the intake time, Δt is the time difference of the valve switch; V c is the total volume from the upstream valve to the downstream valve, m 3 ; V p is the volume from MFC to the upstream valve, m 3 ;z m,f 、z m,i 、z p,f 、z p,i are the compression coefficients of gases at corresponding pressure and temperature; p m,f is the stagnation pressure in the constant volume chamber after air intake; p m,i is the stagnation pressure in the constant volume chamber before air intake; p p,f is the stagnation pressure at the additional volume after the intake; p p,i It is the stagnation pressure at the additional volume before the intake.

[0060] Furthermore, in this embodiment, all MFV chambers are placed in a constant temperature box or water bath to control the ambient temperature from changing suddenly. Assuming that the ambient temperature remains stable, when the static volume method is used to measure the state parameters before and after the intake, the heat exchange has been fully completed, and the temperature and pressure no longer change. The gas temperature T in the chamber during measurement gas , wall temperature T w With ambient temperature T a (or water bath temperature) are equal, that is:

[0061] T gas =T w =T a (2).

[0062] In one embodiment, the expression of the valve switching time system difference is:

[0063]

[0064] In the formula, t is the intake time; n is the number of valve opening and closing times; q' m The actual flow rate through the first valve (i.e., the upstream valve) when the valve is switched once; q” m is the actual flow rate through the upstream valve after the valve is opened and closed n times; is the total mass of the valve opened and closed n times continuously; m' is the mass of the valve opened and closed once; t' is the time for the valve to open and close once, It is the sum of the time it takes for the valve to open and close n times continuously.

[0065] Furthermore, the time system difference at flow rates other than the test flow points can be calculated by linear interpolation. If the time system difference measured in the test is relatively large, it is necessary to increase the test points appropriately.

[0066] The method for obtaining the systematic difference Δt of the valve switching time is as follows: select the flow rate of a critical flow nozzle, and test the valve switching once within the normal measurement time according to the static volume method. Then, at this flow rate, the valve is continuously switched n times (n≥5). The sum of the measurement time of the n switches should be approximately equal to the above-mentioned normal measurement time, and the time of each n switch should be roughly equal.

[0067] The maximum, minimum and middle flow points are selected within the flow range of the ROR method device. At least three tests should be conducted at each flow point, and the arithmetic mean is taken as the time system difference at the flow point. The time system difference at the flow rate other than the test flow point can be calculated by linear interpolation. If the time system difference measured in the test is large, it is necessary to increase the test points appropriately. The time difference of the valve switch system Δt can be ignored; the experimental device is as follows Figure 2As shown in the figure, when calibrating the convection heat transfer coefficient, a pressure gauge and an MFC (mass flow controller) are connected in sequence in front of the MFV chamber. Among them, the MFC at the gas source is only used to provide a stable flow rate.

[0068] In one embodiment, the expression of the dynamic mass flow calculation model is:

[0069]

[0070] Where, T stp is the temperature under standard conditions, 273.15K; P stp is the pressure under standard conditions, 101325Pa; V s is the total volume from the sonic nozzle to the downstream valve (i.e., the second valve); i is the number of the pressure data; p i is the pressure value of the MFV chamber during the intake process; N is the number of consecutive pressure measurements in the RoR method; t RoR The time required to obtain the selected dynamic data; ρ N is the gas density under standard conditions, kg / m 3 .

[0071] In one embodiment, the steps for obtaining the heat transfer coefficient are:

[0072] The average total temperature of the gas in the chamber when heat exchange equilibrium is solved based on the combined static mass flow calculation model and dynamic mass flow calculation model;

[0073] A heat transfer model between the water bath temperature and the chamber gas temperature is constructed based on the average total temperature of the gas in the chamber and the wall temperature when the heat exchange is balanced;

[0074] The heat transfer coefficient is solved based on the heat transfer model between the water bath temperature and the chamber gas temperature.

[0075] Due to physical principles, the dynamic mass flow rate and the static mass flow rate are the same, so the average mass flow rate during the intake time calculated by the static volume method is substituted into the RoR method to obtain the expression:

[0076]

[0077] The average total temperature T of the gas in the chamber when the heat exchange is balanced in RoR measurement can be obtained by using formulas (1) and (5):

[0078]

[0079] Where, t pVTt =t-Δt, which is the static volumetric intake time, that is, the static volumetric intake time including the time difference of the switching valve system.

[0080] According to formula (6), the expression of the heat transfer model between the water bath temperature and the chamber gas temperature can be obtained, which is:

[0081]

[0082] Where, T w for K; is the initial temperature of the gas flowing into the chamber from the measured table, K; γ is the specific heat ratio of the gas (the specific heat ratio of the ideal gas that can be brought into the near vacuum); is the mass flow rate measured by the static volume method, kg / s; m 0 is the initial mass of the gas in the chamber when the downstream valve is closed, kg; Γ is a dimensionless parameter.

[0083] In one embodiment, the expression of the dimensionless quantity parameter Γ is:

[0084]

[0085] Where A is V c Surface area, m 2 ;c v is the isochoric specific heat capacity of the gas, J / (kg·K).

[0086] In one embodiment, when actually calculating the convective heat transfer coefficient, formula (7) can be further transformed to obtain the equation group:

[0087] Ax+B -x -1=0

[0088]

[0089]

[0090] Combining formula (8), the heat transfer coefficient h can be obtained as:

[0091]

[0092] On the other hand, this embodiment also discloses a system for calibrating the heat transfer coefficient of MFV based on the static volume method, and the specific steps are as follows:

[0093] A data acquisition module is used to collect static data and dynamic data during the intake process, wherein the static data includes initial static parameters, terminal static parameters and intake duration;

[0094] A model building module, used to build a static mass flow calculation model based on static data using a static volume method, and to build a dynamic mass flow calculation model based on dynamic data using a rate of rise method;

[0095] The calculation module is used to solve the heat transfer coefficient by combining the static mass flow calculation model and the dynamic mass flow calculation model based on physical principles.

[0096] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0097] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calibrating the heat transfer coefficient of a MFV based on the static volume method, characterized in that: The specific steps are: Collect static data and dynamic data during the intake process, wherein the static data includes initial static parameters, terminal static parameters, and intake duration; Based on the static data, a static mass flow calculation model is constructed using a static volume method, and based on the dynamic data, a dynamic mass flow calculation model is constructed using a rate of rise method; Based on physical principles, the static mass flow calculation model and the dynamic mass flow calculation model are combined to solve the heat transfer coefficient.

2. The method for calibrating the heat transfer coefficient of MFV based on the static volume method according to claim 1, characterized in that: The expression of the static mass flow calculation model is: Where, M is the molecular weight of the gas medium being measured; T a is the ambient temperature; R is the universal gas constant; t is the intake time, Δt is the time difference of the valve switch; V c V is the total volume between the first valve and the second valve; p is the volume from MFC to the first valve; z m,f 、z m,i 、z p,f 、z p,i are the compression coefficients of gases at corresponding pressure and temperature; p m,f is the stagnation pressure in the constant volume chamber after air intake; p m,i is the stagnation pressure in the constant volume chamber before air intake; p p,f is the stagnation pressure at the additional volume after the intake; p p,i It is the stagnation pressure at the additional volume before the intake.

3. The method for calibrating the heat transfer coefficient of MFV based on the static volume method according to claim 2, characterized in that: The expression of the time difference of the switch valve system is: In the formula, t is the intake time; n is the number of valve opening and closing times; q' m The actual flow rate through the first valve after the valve is switched once; q" m is the actual flow rate through the first valve after the valve is opened and closed n times; is the total mass of the valve opened and closed n times continuously; m' is the mass of the valve opened and closed once; t' is the time for the valve to open and close once, It is the sum of the time it takes for the valve to open and close n times continuously.

4. The method for calibrating the heat transfer coefficient of MFV based on the static volume method according to claim 1, characterized in that: The expression of the dynamic mass flow calculation model is: Where, T stp P is the temperature under standard conditions; stp V is the pressure under standard conditions; s is the total volume from the sonic nozzle to the downstream valve; i is the number of the pressure data; p i is the pressure value of the MFV chamber during the intake process; T is the average total temperature of the gas in the chamber when the heat exchange is balanced; N is the number of consecutive pressure measurements in the RoR method; t RoR The time required to obtain the selected dynamic data; ρ N is the gas density under standard conditions.

5. The method for calibrating the heat transfer coefficient of MFV based on the static volume method according to claim 1, characterized in that: The steps for obtaining the heat transfer coefficient are: Solving the average total temperature of the gas in the chamber when heat exchange is in equilibrium based on the combined static mass flow calculation model and the dynamic mass flow calculation model; A heat transfer model between the water bath temperature and the chamber gas temperature is constructed based on the average total temperature of the gas in the chamber and the wall temperature when the heat exchange is balanced; The heat transfer coefficient is solved according to a heat transfer model between the water bath temperature and the chamber gas temperature.

6. The method for calibrating the heat transfer coefficient of MFV based on the static volume method according to claim 5, characterized in that: The expression of the average total temperature of the gas in the chamber when the heat exchange is balanced is: Where, t pVTt T is the static volumetric intake time; a is the ambient temperature; N is the number of consecutive pressure measurements in the RoR method; V s V is the total volume from the sonic nozzle to the second valve; c V is the total volume between the first valve and the second valve; p is the volume from MFC to the first valve; z m,f 、z m,i 、z p,f 、z p,i are the compression coefficients of gases at corresponding pressure and temperature; p m,f is the stagnation pressure in the constant volume chamber after air intake; p m,i is the stagnation pressure in the constant volume chamber before air intake; p p,f is the stagnation pressure at the additional volume after the intake; p p,i It is the stagnation pressure at the additional volume before the intake.

7. The method for calibrating the heat transfer coefficient of MFV based on the static volume method according to claim 5, characterized in that: The expression of the heat transfer model between the water bath temperature and the chamber gas temperature is: Where, T is the average total temperature of the gas in the chamber when the heat exchange is balanced; T w is the wall temperature; T in is the initial temperature of the gas flowing into the chamber from the measured table; γ is the specific heat ratio of the gas; is the mass flow rate measured by the static volume method; t pVTt is the static volumetric intake time; m 0 is the initial mass of the gas in the chamber when the second valve is closed; Γ is a dimensionless parameter.

8. The method for calibrating the heat transfer coefficient of a MFV based on the static volume method according to claim 7, characterized in that: When solving the heat transfer coefficient according to the heat transfer model between the water bath temperature and the chamber gas temperature, the expression of the model needs to be deformed, and the deformed expression obtained is: Ax+B -x -1=0; Where A is V c The surface area of ​​the chamber; T is the average total temperature of the gas in the chamber when the heat exchange is balanced; T w is the wall temperature; γ is the gas specific heat ratio; is the mass flow rate measured by the static volume method; t pVTt is the static volumetric intake time; m 0 is the initial mass of the gas in the chamber when the second valve is closed.

9. The method for calibrating the heat transfer coefficient of MFV based on the static volume method according to claim 7, characterized in that: The expression of dimensionless parameter Γ is: Where A is V c The surface area of v is the isochoric specific heat capacity of the gas; h is the heat transfer coefficient; It is the mass flow rate measured by the static volume method.

10. A system for calibrating MFV heat transfer coefficient based on static volume method, characterized in that: The specific steps are: A data acquisition module, used to collect static data and dynamic data during the intake process, wherein the static data includes initial static parameters, terminal static parameters and intake duration; A model building module, used to build a static mass flow calculation model using a static volume method based on the static data, and to build a dynamic mass flow calculation model using a rate of rise method based on the dynamic data; The calculation module is used to solve the heat transfer coefficient by combining the static mass flow calculation model and the dynamic mass flow calculation model based on physical principles.

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