Method for determining key process parameters in chamber vacuum pumping and breaking process

Abstract

This invention discloses a method for determining key process parameters in the vacuuming and devastation process of a chamber. The method is applicable to pressure ranges spanning 10... ‑5 Up to 10 5 This method covers pressures exceeding 10 orders of magnitude. It proposes using a modified Knudsen number as the partitioning criterion to divide the vacuum chamber exhaust process into different flow intervals. Each segment is solved using a k-ω shear stress transport turbulence model, a laminar flow + velocity slip model, a free molecular flow model, and a coupled ordinary differential equation model. Coupled calculations across a wide pressure range are achieved through data transfer between modules. Simultaneously, this method considers material venting and leakage to obtain pressure-time evolution results that better reflect actual operating conditions. This method can provide a reliable basis for vacuum chamber exhaust design, pump matching, material selection, and process optimization.

Description

Technical Field

[0001] This invention relates to the fields of vacuum science and technology, computational fluid dynamics and numerical simulation technology, and specifically to a method for determining key process parameters in the process of vacuuming and breaking vacuum in a chamber. Background Technology

[0002] Vacuum pumping and devastation processes are crucial steps in the operation of high-end manufacturing and research equipment, such as semiconductor manufacturing, thin film deposition, and surface analysis. The gas flow state involved in this process changes significantly with decreasing pressure, exhibiting complex characteristics involving multiple scales and physical mechanisms: In the initial stage, the gas in the chamber is in a high-density continuous flow state, typically exhibiting turbulent flow. Subsequently, the gas enters a continuous slip flow region, where significant wall slip effects occur. In the final stage, the gas enters a transitional flow and even a free molecular flow state, where the continuous medium assumption gradually fails, necessitating the use of molecular kinetic theory methods to describe the transport behavior.

[0003] In existing technologies, it is difficult to achieve scientific calculations that balance computational accuracy, efficiency, and physical consistency for gas processes over a wide pressure range. A single simulation software or physical model typically cannot cover the entire pressure range from continuous flow to rarefied flow. For example, computational fluid dynamics (CFD) methods based on the Navier-Stokes (NS) equations have high accuracy in the continuous flow region, but their applicability decreases significantly in the rarefied flow region. While free molecular flow models based on molecular kinetic theory can effectively describe transport behavior in rarefied regions, their complexity and computational cost increase dramatically with the number of particles in high-pressure, strong continuous flow regions, making them impractical. Furthermore, gas processes with wide pressure ranges cannot be scientifically described by simply segmenting and splicing different models. On the one hand, due to the continuous flow characteristics of gas inside the cavity, the local pressure, velocity, and flow state at different locations at the same time may not be consistent. This results in different regions of the same device being within the applicable range of different models at the same time. If a segmented processing method is used, the continuous spatial transmission and mutual influence of gas are ignored, which lacks physical rationality. On the other hand, the switching between different models does not only depend on the change of pressure value range, but also needs to inherit the final state information calculated by the previous model. The final state information includes at least the gas pressure, velocity, flow direction, and corresponding boundary state at different locations in the cavity. If a simple splicing method is used without the continuous transmission of the above state quantities, it is difficult to guarantee the continuity and accuracy of the calculation results across ranges.

[0004] Therefore, there is an urgent need for a numerical simulation and parameter determination method applicable to gas processes over a wide pressure range. This method should not only enable automatic selection, stable switching, and continuous cross-scale coupling calculations between different physical models based on flow state criteria, but also retain and transfer the final state information of the previous stage during model switching. This allows subsequent models to continue solving based on the pressure distribution, velocity distribution, flow direction, and boundary states at various locations within the cavity, thus avoiding physical distortions caused by simple segmented splicing. Furthermore, this method can uniformly couple the material gas emission rate and system leakage rate into the whole-process pressure evolution model, thereby improving the accuracy and engineering applicability of vacuum process simulation, ultimate vacuum prediction, and determination of key process parameters. Summary of the Invention

[0005] This invention aims to overcome the shortcomings of existing technologies and provide a method for determining key process parameters in the vacuuming and devastation processes of a chamber. This method uses a modified Knudsen number as a criterion to divide the vacuuming process into multiple pressure zones, employing different models in each zone, and achieving full-process coupling through data transmission.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for determining process parameters of a chamber vacuuming process, comprising the following steps:

[0007] Step 1: Construct the geometric model of the vacuum chamber and its internal components; set the equipment and material parameters; calculate and correct the Knudsen number of the system;

[0008] Step Two: In ≤10 -3 In the continuous flow region, the pressure and velocity fields within the chamber are solved, the pressure-time curves for this region are obtained and recorded, and the pressure-time curves are extracted. =10 -3 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step.

[0009] Step 3: Using the pressure field and velocity field state variables at the final state time of Step 2 as input, in 10 -3 < ≤10 -1 Within the slip flow region, the pressure and velocity fields within the chamber are solved, the pressure-time curves for this region are obtained and recorded, and the pressure-time curves are extracted. =10 -1 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step.

[0010] Step 4: Using the pressure field and velocity field state variables at the final state in Step 3 as input, in >10 -1Within the high vacuum region, the pressure field and velocity field inside the chamber are solved, and the pressure-time curve of this region is obtained and recorded. The pressure-time curves obtained in steps two, three, and four are connected to derive the pressure-time curve of the entire process.

[0011] Step 5: Determine whether the pressure-time curve of the entire process meets the preset requirements; if it meets the preset requirements, output the equipment parameters and material parameters corresponding to the pressure-time curve; if it does not meet the preset requirements, adjust the equipment parameters and material parameters, return to Step 2 for iterative calculation, until the preset requirements are met or the number of iterations reaches the upper limit.

[0012] Specifically, the equipment parameters include cavity size, vacuum pump pumping speed, pumping position, inlet position, and vacuum pump opening and closing strategy.

[0013] Specifically, material parameters include material gas output rate and gas leakage rate.

[0014] Specifically, in step two, the k-ω shear stress transport (SST) turbulence model is used to solve for the pressure and velocity fields inside the cavity.

[0015] Specifically, in step three, the laminar flow + velocity slip model is used to solve for the pressure field and velocity field inside the cavity.

[0016] Specifically, in step four, the pressure field and velocity field inside the cavity are solved using a free molecular flow model and a coupled ordinary differential equation (ODE) model.

[0017] Furthermore, step one is implemented through the following sub-steps:

[0018] (1.1) Construct a geometric model of the equipment, which includes the closed three-dimensional structure of the vacuum chamber and the three-dimensional structure of the internal components within the chamber;

[0019] Specifically, the positions of the extraction port and the inlet, the cavity size and their relative arrangement with the internal components of the cavity are defined in the geometric model, and the extraction port is associated with the boundary conditions of the vacuum pump for the inheritance of boundary conditions and data transfer in subsequent segmented solutions.

[0020] (1.2) The material gas emission rate and leakage rate are set as functions of pressure;

[0021] Specifically, the leakage rate Q_leak(P) = k(P_ext - P) n Where k is the leakage coefficient, n is the empirical index, P_ext-P represents the pressure difference between the inside and outside of the system, and the total gas output rate is expressed as the sum of the products of the gas output rate of each component and its surface area: Q_des = Σ(q_i·A_i).

[0022] (1.3) Setting the pumping strategy includes: setting the pumping rate or equivalent pumping speed of the vacuum pump, the start and stop time of the vacuum pump and the opening and closing logic; wherein, the pumping rate or equivalent pumping speed should be a piecewise function that varies with the chamber pressure in order to simulate the real situation.

[0023] (1.4) Calculate and correct the Knudsen number of the system as follows:

[0024]

[0025] In the formula, M is the backtracking window length. The time decay weight is used, where t is the time interval. The hysteresis time constant is used to characterize the degree to which historical Knudsen numbers retain the current criterion. The larger the cavity, the stronger the inertia of the criterion, and the better it can suppress high-frequency switching near the boundary region. The larger the cavity, the more complex the internal piping. The larger the value, Take one-tenth of the transition time (i.e., model switching time). Kn is the Knudsen number, calculated as follows:

[0026]

[0027] Where λ is the mean free path of gas molecules, L is the pipe diameter whose characteristic dimension depends on the device geometry modeling, and k B Where is Boltzmann's constant, T is temperature, d is molecular diameter, and P is gas pressure.

[0028] Furthermore, the criteria and calculation methods for dividing the intervals in steps two, three, and four are as follows:

[0029] The first pressure range corresponds to the modified Knudsen number. ≤10 -3 The compressibility of the gas needs to be considered. The SST turbulence model is used for calculation. The enhanced wall function is used to handle the near-wall flow, and the ideal gas law is enabled to account for density changes.

[0030] The second pressure range corresponds to a modified Knudsen number of 10. -3 < ≤10 -1 The velocity-slip wall condition needs to be considered, and a laminar flow + velocity-slip model is used for calculation; the velocity-slip wall condition adopts the Maxwell slip model, and the slip length is determined based on the current conditions. Dynamic calculation of the number of molecules and the mean free path of gas molecules.

[0031] The third pressure range corresponds to a corrected Knudsen number of 10. -1 < The environment is close to a free molecular flow. The free molecular flow model and the coupled ordinary differential model are used for calculation, and the angle coefficient resolution is improved to ensure the accuracy of molecular flux calculation.

[0032] Furthermore, the ordinary differential equation model is the vacuum pumping balance equation: V·(dP / dt) = -S·P + Q_des+ Q_leak, where V is the chamber volume, S is the effective pumping speed at the pump inlet, Q_des is the total exhaust rate, and Q_leak is the total leakage rate.

[0033] Furthermore, step five includes threshold determination in the form of inequalities: for at least one specified pressure P i Determine when the time t is reached. i Does t satisfy? i ≤t i,set ; For example, setting multiple specified pressure-time nodes (P i , t i,set Each node is combined using logical relationships of "AND" or "OR" for comprehensive judgment.

[0034] Furthermore, the parameter adjustment algorithm in step six adopts the gradient descent method, or the preset parameter space adopts grid search.

[0035] Furthermore, the calculation processes in steps two, three, and four are controlled by the following convergence criterion.

[0036]

[0037] in, and The first Second and third The pressure value of the pumping curve obtained in the next iteration. This represents the rate of change of pressure. These are the weighting coefficients. To prevent tiny positive numbers with a denominator of zero, This is the convergence threshold. This criterion considers both the calculation errors of the pressure value and the rate of pressure change to ensure the stability and convergence of the numerical solution of the pumping curve.

[0038] Furthermore, the algorithms in steps two, three, and four incorporate Gaussian noise into the pressure variable to account for measurement errors in the pressure signal. After introducing noise, the pressure is corrected to...

[0039]

[0040] in The corrected pressure is P, which is the pressure calculated directly from the model in steps two, three, and four. It is a Gaussian noise term, satisfying... Gaussian distribution It refers to the measurement accuracy of the instrument's pressure sensor.

[0041] This invention also provides a method for determining process parameters of a chamber vacuum breaking process. The calculation method for the vacuum pumping process described above is also applicable to the calculation of the vacuum breaking process. The vacuum breaking process is the reverse process of vacuum pumping, in which the gas pressure changes from low to high. The solution process first performs calculations using a free molecular flow + coupled ordinary differential equation model, then performs calculations using a laminar flow + velocity slip model, and finally performs calculations using a k-ω shear stress transport turbulence model. The method is consistent with the vacuum pumping calculation method and specifically includes the following steps:

[0042] Step 1: Construct the geometric model of the vacuum chamber and its internal components, set the equipment and material parameters, and calculate and correct the Knudsen number of the system. ;

[0043] Step Two: In >10 -1 Within the high vacuum region, the pressure and velocity fields within the chamber were solved using a free molecular flow model and a coupled ordinary differential equation model. The pressure-time curves for this region were obtained and recorded, and the pressure was extracted. =10 -1 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step;

[0044] Step 3: Using the pressure field, velocity field, and other state variables at the final state in Step 2 as inputs, in 10... -3 < ≤10 -1 Within the slip flow region, a laminar flow + velocity slip model was used to solve for the pressure and velocity fields within the cavity. The pressure-time curves for this region were obtained and recorded, and the pressure was extracted. =10 -3 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step;

[0045] Step 4: Using the pressure field and velocity field state variables at the final state in Step 3 as input, in ≤10 -3 In the continuous flow region, the pressure and velocity fields inside the cavity are solved using the k-ω shear stress transport turbulence model. The pressure-time curves of this region are obtained and recorded. The pressure-time curves obtained in steps two, three, and four are connected to derive the pressure-time curves of the entire process.

[0046] Step 5: Determine whether the pressure-time curve of the entire process meets the preset requirements (such as whether the time to reach the specified pressure meets the preset threshold); if the preset requirements are met, output the equipment parameters and material parameters corresponding to the pressure-time curve; if the preset requirements are not met, adjust the equipment parameters and material parameters, return to Step 2 for iterative calculation, until the preset requirements are met or the number of iterations reaches the upper limit.

[0047] Furthermore, the gas used in the vacuuming and devastating processes can be air, nitrogen, argon, or other process gases.

[0048] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for determining process parameters of a chamber vacuuming process or the above-described method for determining process parameters of a chamber vacuum breaking process.

[0049] The beneficial effects of this invention are as follows: It proposes a cross-scale unified criterion based on dynamically modified Knudsen numbers, which can achieve stable switching and continuous coupling calculation between different physical models over a wide pressure range, accurately covering 10 5 Pa to 10 -5 This invention addresses the challenge of completing scientific calculations across a pressure range spanning ten orders of magnitude, overcoming the limitations of single software and models in achieving full-process scientific computation. The proposed dynamic correction Knudsen number cross-scale unified criterion fully considers the actual situation where different locations within the cavity may be in different flow ranges at the same time, avoiding physical distortions caused by forcibly fragmenting the continuous flow process. Simultaneously, it retains and transmits the final state information obtained from the previous stage during model switching, ensuring the continuity, stability, and scientific rigor of cross-range solutions. Furthermore, this invention couples material gas emission rate with system leakage rate, establishing a pressure evolution equation that includes effective pumping speed, gas emission term, and leakage term, enabling more accurate prediction of the vacuuming process and ultimate vacuum level. This method provides quantitative basis for system vacuum performance evaluation, cavity vacuuming strategy optimization, pump configuration optimization, and material selection, significantly improving simulation accuracy, parameter determination capabilities, and engineering application efficiency in vacuum equipment development. Moreover, this invention employs a general algorithm framework, independent of specific commercial software platforms, thus facilitating portability and reproduction in different equipment, cavity structures, and production line scenarios. Attached Figure Description

[0050] Figure 1 A schematic flowchart illustrating a method for determining key process parameters for chamber vacuuming and breaking processes applicable to a wide pressure range, provided by an embodiment of the present invention;

[0051] Figure 2 This is a schematic diagram of a typical vacuum cavity calculation model;

[0052] Figure 3 A schematic diagram of the connection structure between the vacuum chamber evacuation port and the molecular pump;

[0053] Figure 4 The diagram shows the pumping speed curves of the pumps, where (A) is the pumping speed curve of the roughing pump and (B) is the pumping speed curve of the molecular pump.

[0054] Figure 5 The results are the calculation results of the pressure-time curve for the entire process;

[0055] Figure 6 The result is a calculation of the three-dimensional distribution of gas pressure at a specific moment.

[0056] Figure 7 Solving for pressure 10 using a free molecular flow + coupled ordinary differential equation model -5 Up to 10 1 The calculated pressure-time curve at Pa. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the implementation of the present invention is not limited thereto.

[0058] This invention provides a method for determining process parameters during a chamber evacuation process. The method is described in detail in simulating the entire process of evacuating a vacuum chamber from atmospheric pressure to a high vacuum. It is applicable to a wide pressure range, and this embodiment can cover 10... 5 Pa to 10 -5 Pressure ranges up to 10 orders of magnitude Pa, see [link / reference]. Figure 1 Specifically, it includes the following steps:

[0059] Step 1: See Figure 2 A three-dimensional model is established, including the chamber, internal components (evaporation source, substrate stage, and substrate), and pump port (in this embodiment, the internal components within the chamber are also considered). The positions of the extraction and inlet ports, the chamber dimensions, and their relative arrangement with the internal components are defined in this model. The extraction port is then associated with the boundary conditions of the vacuum pump. A mesh is generated, and the mesh is refined locally in the near-wall region. The initial pressure is set to 101325 Pa (one atmosphere), the initial velocity is zero, and the temperature is 293 K. The pump port is set as the pressure outlet (i.e., the extraction port), and its pressure decreases over time according to the pump's pumping speed characteristic curve.

[0060] This embodiment sets the pumping strategy as follows: setting the pumping rate or equivalent pumping speed of the vacuum pump, the start and stop times of the vacuum pump, and the opening and closing logic; specifically, a high vacuum environment is achieved through the coordinated operation of a rough pump and a molecular pump, with the rough pump operating within a range of 10... 5 -10 -1 Pa, in amounts less than 10 -1The molecular pump starts operating at a pressure of Pa. Therefore, the extraction port is segmented. See also... Figure 3 The inlets of the roughing pump and the molecular pump are connected to the evacuation port of the vacuum chamber, and a first valve and a second valve are respectively installed on the connecting pipes. The working process is as follows: First, the first valve is opened and the second valve is closed, and the roughing pump starts pumping, set to pump to 10... -1 Pa stops (an atmospheric pressure detection device is installed inside the vacuum chamber); II. The pressure inside the vacuum chamber is less than or equal to 10. -1 At pressure Pa, the first valve closes, the second valve opens, and the molecular pump begins pumping, stopping when the preset pressure is reached; the pumping rates of the roughing pump and the molecular pump are shown in [reference needed]. Figure 4 .

[0061] Calculate and correct the Knudsen number of the system:

[0062]

[0063] In the formula, M is the backtracking window length, which is 0.1s. The weighting is time-decayed. Since the time from continuous flow to slip flow is relatively short, piecewise weighting is adopted during the continuous flow phase. Taking 0.008, the slip flow and free molecular flow stages It is 0.08. The hysteresis time constant is set to 0.1s to characterize the degree to which historical Knudsen numbers retain the current criterion. Kn is the Knudsen number, calculated as follows:

[0064]

[0065] Where, k B The Boltzmann constant is 1.38 × 10⁻⁶. -23 J / K, characteristic dimension L is 0.6 mm, T is temperature 293 K, and d is molecular diameter 3.7 × 10⁻⁶. -10 Where m and P are gas pressures, the first pressure range, second pressure range, and third pressure range can be calculated using the above formula. In this embodiment, the first pressure range, second pressure range, and third pressure range are each 10. 2 ~10 5 Pa, 10 1 ~10 2 Pa and 10 -5 ~10 1 Pa.

[0066] Step 2: In an atmospheric pressure environment Much less than 10 -3 The calculations were performed using a transient, density-based solver, based on the k-omega SST turbulence model, energy equations, and the ideal gas law. The time step was set to 10. -4On the order of s, calculations continue until... Rise to 10 -3 Store the calculation results as follows Figure 5 As shown by the black curve in the middle, the pressure field and velocity field distribution at the end of this stage are extracted as the boundary conditions for step three.

[0067] Step 3: In 10 -3 < ≤10 -1 For the interval, a transient, pressure-based solver was used, and the model was switched to laminar flow. Slip wall boundary conditions were considered, based on the Maxwell slip model, and the calculation continued until... Increase to 10 1 Store the calculation results as follows: Figure 5 As shown by the red curve in the middle, the pressure field and velocity field distribution at the end of this stage are extracted as the boundary conditions for step three.

[0068] Step Four: The scope of the study is >10 1 Based on the pressure distribution at the end of step three and the type of gas, estimate the molecular number density at this point as the initial value. Before proceeding to step four, unit conversion is required: convert the pressure field (in Pa) at the end of step three into the initial molecular number density distribution (n = Pa / (kJ / kPa)). B Since the pressure is low at this point, the gas venting rate of the material cannot be ignored, and the cavity wall becomes the venting boundary. The gas venting rate of the stainless steel material is defined as q_ss = 10. -8 Pa·m³ / (s·m²), rubber sealing ring air output rate q_rubber = 10 -6 Pa·m³ / (s·m²). Total gas output rate Q_des = q_ss·A_ss + q_rubber·A_rubber, with the initial estimate of the total system leakage rate Q_leak set to 10. -7 Pa·m³ / s. These parameters are used as source terms in the ODE equations to solve the ODE equations. A transient solver is configured, and the calculation is set to 10. -5 Pa stops, and the calculated data is as follows: Figure 5 The blue curve is shown. Combining the results of steps two and three, the pressure-time curve at the center of the cavity is derived, as shown below. Figure 5 As shown, the pressure change is continuous, with no abrupt changes over time. Importing the pressure distribution results at different times into the 3D model file is illustrated below. Figure 6 As shown, the pressure change within the chamber is continuous and there are no abrupt changes in space, proving the scientific rationality of the calculation method.

[0069] Step 5: The qualification standard for the vacuum system is: the cavity pressure is reduced to 1×10⁻⁶ within 5000 seconds.-4 Below Pa, such as Figure 7 The pressure in the vacuum chamber shown is less than 1 × 10⁻⁶ after 5000 s. -4 If Pa meets the judgment criteria, derive the equipment parameters and material parameters.

[0070] In another embodiment, multiple specified pressure-time nodes (P) can also be set. i , t i,set Each node is judged comprehensively based on logical relationships.

[0071] This invention also provides a method for determining process parameters of a chamber vacuum breaking process. The calculation method for the vacuum pumping process described above is also applicable to the calculation of the vacuum breaking process. The vacuum breaking process is the reverse process of vacuum pumping, in which the gas pressure changes from low to high. The solution process first performs calculations using a free molecular flow + coupled ordinary differential equation model, then performs calculations using a laminar flow + velocity slip model, and finally performs calculations using a k-ω shear stress transport turbulence model. The method is consistent with the vacuum pumping calculation method and specifically includes the following steps:

[0072] Step 1: Construct the geometric model of the vacuum chamber and its internal components, set the equipment and material parameters, and calculate and correct the Knudsen number of the system. ;

[0073] Step Two: In >10 -1 Within the high vacuum region, the pressure and velocity fields within the chamber were solved using a free molecular flow model and a coupled ordinary differential equation model. The pressure-time curves for this region were obtained and recorded, and the pressure was extracted. =10 -1 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step;

[0074] Step 3: Using the pressure field, velocity field, and other state variables at the final state in Step 2 as inputs, in 10... -3 < ≤10 -1 Within the slip flow region, a laminar flow + velocity slip model was used to solve for the pressure and velocity fields within the cavity. The pressure-time curves for this region were obtained and recorded, and the pressure was extracted. =10 -3 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step;

[0075] Step 4: Using the pressure field and velocity field state variables at the final state in Step 3 as input, in ≤10 -3In the continuous flow region, the pressure and velocity fields inside the cavity are solved using the k-ω shear stress transport turbulence model. The pressure-time curves of this region are obtained and recorded. The pressure-time curves obtained in steps two, three, and four are connected to derive the pressure-time curves of the entire process.

[0076] Step 5: Determine whether the pressure-time curve of the entire process meets the preset requirements (such as whether the time to reach the specified pressure meets the preset threshold); if the preset requirements are met, output the equipment parameters and material parameters corresponding to the pressure-time curve; if the preset requirements are not met, adjust the equipment parameters and material parameters, return to Step 2 for iterative calculation, until the preset requirements are met or the number of iterations reaches the upper limit.

[0077] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for determining key process parameters of a chamber vacuuming process or the above-described method for determining process parameters of a chamber vacuum breaking process.

[0078] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0079] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0080] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0081] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0082] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A method for determining process parameters in a chamber vacuuming process, characterized in that, Includes the following steps: Step 1: Construct the geometric model of the vacuum chamber and its internal components; set the equipment and material parameters, and calculate and correct the Knudsen number of the system. ; Step Two: In ≤10 -3 In the continuous flow region, the pressure and velocity fields within the chamber are solved, the pressure-time curves for this region are obtained and recorded, and the pressure-time curves are extracted. =10 -3 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step; Step 3: Using the pressure field and velocity field state variables at the final state time of Step 2 as input, in 10 -3 < ≤10 -1 Within the slip flow region, the pressure and velocity fields within the chamber are solved, the pressure-time curves for this region are obtained and recorded, and the pressure-time curves are extracted. =10 -1 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step; Step 4: Using the pressure field and velocity field state variables at the final state in Step 3 as input, in >10 -1 Within the high vacuum region, the pressure field and velocity field inside the chamber are solved, and the pressure-time curve of this region is obtained and recorded. The pressure-time curves obtained in steps two, three, and four are connected to derive the pressure-time curve of the entire process. Step 5: Determine whether the pressure-time curve of the entire process meets the preset requirements; if it meets the preset requirements, output the equipment parameters and material parameters corresponding to the pressure-time curve; if it does not meet the preset requirements, adjust the equipment parameters and material parameters, return to Step 2 for iterative calculation, until the preset requirements are met or the number of iterations reaches the upper limit.

2. The method according to claim 1, characterized in that, Step one is achieved through the following sub-steps: (1.1) Construct a geometric model of the equipment, which includes the closed three-dimensional structure of the vacuum chamber and the three-dimensional structure of the internal components within the chamber; (1.2) The material gas emission rate and leakage rate are set as functions of pressure; (1.3) Setting the pumping strategy includes: setting the pumping rate or equivalent pumping speed of the vacuum pump, the start and stop time of the vacuum pump and the opening and closing logic; wherein, the pumping rate or equivalent pumping speed must be a piecewise function that varies with the chamber pressure. (1.4) Calculate and correct the Knudsen number of the system as follows: In the formula, M is the backtracking window length. The time decay weight is Kn, where Kn is the Knudsen number and t is time. is the hysteresis time constant, used to characterize the degree to which historical Knudsen numbers retain the current criterion.

3. The method according to claim 1, characterized in that, The criteria and calculation methods for dividing the intervals in steps two, three, and four are as follows: The first pressure range corresponds to the modified Knudsen number. ≤10 -3 Considering the compressibility of the gas, the SST turbulence model is used for calculation, the enhanced wall function is used to handle the near-wall flow, and the ideal gas law is enabled to account for density changes. The second pressure range corresponds to a modified Knudsen number of 10. -3 < ≤10 -1 Considering velocity-slip wall conditions, a laminar flow + velocity-slip model is used for calculation; the velocity-slip wall conditions adopt the Maxwell slip model, and the slip length is determined based on the current conditions. Dynamic calculation of the number of molecules and the mean free path of gas molecules; The third pressure range corresponds to a corrected Knudsen number of 10. -1 < The environment is a free molecular flow. The free molecular flow model and the coupled ordinary differential model are used for calculation, and the angular coefficient resolution is improved to ensure the accuracy of molecular flux calculation.

4. The method according to claim 3, characterized in that, The ordinary differential equation model is the vacuum pumping balance equation: V·(dP / dt) = -S·P + Q_des + Q_leak, where V is the chamber volume, S is the effective pumping speed at the pump inlet, Q_des is the total outflow rate, and Q_leak is the total leakage rate.

5. The method according to claim 1, characterized in that, Step five includes threshold determination in the form of inequalities: for at least one specified pressure P i Determine when the time t is reached. i Does t satisfy? i ≤t i,set .

6. The method according to claim 1, characterized in that, The parameter adjustment algorithm in step six uses gradient descent or grid search in the preset parameter space.

7. The method according to claim 1, characterized in that, The calculation process in steps two, three, and four adopts the following convergence criterion. control: in, and The first Second and third The pressure value of the pumping curve obtained in the next iteration. and The first Second and third The rate of change of pressure obtained in the next iteration. These are the weighting coefficients. To prevent tiny positive numbers with a denominator of zero, As a convergence threshold, this criterion considers both the calculation errors of the pressure value and the rate of change of pressure to ensure the stability and convergence of the numerical solution of the pumping curve.

8. The method according to claim 1, characterized in that, The algorithms in steps two, three, and four consider the measurement error of the pressure signal and introduce a Gaussian noise term into the pressure variable; after introducing noise, the pressure correction is as follows: Where P' is the corrected pressure, and P is the pressure directly calculated from the model in steps two, three, and four. It is a Gaussian noise term, satisfying... Gaussian distribution It refers to the measurement accuracy of the instrument's pressure sensor.

9. A method for determining process parameters in a chamber vacuum breaking process, characterized in that, Includes the following steps: Step 1: Construct the geometric model of the vacuum chamber and its internal components, set the equipment and material parameters, and calculate and correct the Knudsen number of the system. ; Step Two: In >10 -1 Within the high vacuum region, the pressure and velocity fields within the chamber are solved, the pressure-time curves for this region are obtained and recorded, and the pressure-time curves are extracted. =10 -1 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step; Step 3: Using the pressure field and velocity field state variables at the final state time of Step 2 as input, in 10 -3 < ≤10 -1 Within the slip flow region, the pressure and velocity fields within the chamber are solved, the pressure-time curves for this region are obtained and recorded, and the pressure-time curves are extracted. =10 -3 The pressure field and velocity field corresponding to the time are used as the initial and boundary conditions for the next step; Step 4: Using the pressure field and velocity field state variables at the final state in Step 3 as input, in ≤10 -3 In the continuous flow region, solve the pressure field and velocity field in the chamber, obtain and record the pressure-time curve of this region, connect the pressure-time curves obtained in steps two, three and four, and derive the pressure-time curve of the entire process. Step 5: Determine whether the pressure-time curve of the entire process meets the preset requirements; if it meets the preset requirements, output the equipment parameters and material parameters corresponding to the pressure-time curve; if it does not meet the preset requirements, adjust the equipment parameters and material parameters, return to Step 2 for iterative calculation, until the preset requirements are met or the number of iterations reaches the upper limit.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements a method for determining process parameters of a chamber vacuuming process as described in any one of claims 1-8 or a method for determining process parameters of a chamber vacuum breaking process as described in claim 9.

Images