A process parameter determination method, size optimization method, defect determination method, and storage medium for a passive device

Abstract

The application provides a process parameter determination method, a size optimization method, a defect determination method and a storage medium for a passive device, comprising: providing a wafer of the passive device with multiple different layout sizes under the same device process, testing and obtaining analysis results of performance parameters of the passive device; determining an actual fluctuation range of process parameters by using the analysis results of the performance parameters and Monte Carlo simulation; the process parameters include thickness of each layer of material, relative dielectric constant and metal conductivity. The method of the application corrects the fluctuation range of the process parameters in combination with actual test data, and helps to improve the stability of the process parameters of the device process.

Description

Technical Field

[0001] This invention belongs to the field of radio frequency integrated circuit design technology, specifically involving a method for determining process parameters, a size optimization method, a defect judgment method, and a storage medium for passive devices, used for the automated layout design of passive devices (such as planar spiral inductors), and involving the synergistic application of electromagnetic simulation, machine learning, and multi-objective optimization algorithms. Background Technology

[0002] Planar spiral inductors are among the most critical passive components in radio frequency (RF) integrated circuits, playing a variety of important roles in various RF unit circuits, including impedance matching, filtering, and forming oscillation networks. Circuit design requires optimizing both circuit performance and total circuit area.

[0003] Traditional design methods typically rely on iterative layout adjustments and multiple rounds of electromagnetic (EM) simulations to gradually approach the design goal of the planar spiral inductor through trial and error. However, a single simulation can take several hours, resulting in long design cycles and high costs. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining process parameters, a method for optimizing dimensions, a method for determining defects, and a storage medium for passive devices. This method, combined with actual test data, corrects the fluctuation range of process parameters, thereby helping to improve the stability of process parameters in device manufacturing.

[0005] To achieve the above objectives, the present invention provides a method for determining the process parameters of passive devices, comprising:

[0006] S1: Provide wafers of passive devices with different layout sizes under the same device process, test and obtain the analysis results of the performance parameters of the passive devices;

[0007] S2: Use the analysis results of performance parameters and Monte Carlo simulation to determine the actual fluctuation range of process parameters; process parameters include the thickness of each material layer, relative permittivity and metallic conductivity.

[0008] The passive devices include resistors, capacitors, and inductors with different layout sizes, where the layout size includes the shape type and geometric dimensions of the layout.

[0009] In step S1, the analysis results of testing and obtaining the performance parameters of the passive device include at least: obtaining the S-parameters of the passive device, extracting the performance parameters of the passive device from the S-parameters, and statistically obtaining the analysis results of the performance parameters.

[0010] Step S2 specifically includes:

[0011] S21: Write a parameterization unit for passive devices, the parameterization unit being used to automatically generate wafers of passive devices with different layout sizes based on the geometric parameters of the layout of the passive devices;

[0012] S22: Continuously adjust the standard values ​​of process parameters, perform Monte Carlo simulation within the range of ±20% of the standard values, and obtain simulation performance parameters. The standard value of the process parameters when the simulation performance parameters are closest to the actual process fluctuation range and the actual average value is taken as the final result of the process parameters.

[0013] In step S22, during Monte Carlo simulation, the sampled values ​​of process parameters are obtained by fluctuating within a range of ±20% of the standard value. The sampled values ​​of process parameters and the parameterized units of passive devices are used to generate a wafer of passive devices with the required layout size that is automatically generated. Electromagnetic simulation is performed on the generated wafer to obtain S-parameters, and simulation performance parameters are extracted from the S-parameters.

[0014] On the other hand, the present invention provides a method for optimizing the size of passive devices, comprising:

[0015] A1: Perform the process parameter determination method for passive devices described above to obtain the actual fluctuation range of the process parameters;

[0016] A2: The average value of the actual fluctuation range of the process parameters is used as the process parameters required for electromagnetic simulation. The parameter space is established based on the geometric parameters of the layout of passive devices. The Latin hypercube sampling method is used to obtain the performance parameters or component parameters of the equivalent circuit model through parameter space sampling and formula calculation, so as to establish a passive device parameter dataset.

[0017] A3: Establish a neural network model and use the passive device parameter dataset to train and optimize the neural network model to obtain a passive device model for outputting performance parameters or component parameters based on the geometric parameters of the layout.

[0018] Step A3 specifically includes:

[0019] A31: Perform data preprocessing on the passive device parameter dataset to obtain the training set and test set;

[0020] A32: Establish a three-layer backpropagation neural network model, using the geometric parameters of the layout as input parameters and the performance parameters as output parameters;

[0021] A33: Introduce a genetic algorithm to globally search for the optimal network structure and hyperparameters of the neural network model, thereby improving the model's generalization ability and prediction accuracy.

[0022] Step A3 further includes:

[0023] A34: Use the training and test sets and the Levenberg-Marquardt algorithm to perform local fine-tuning of the weights, thresholds, and learning rate of the neural network model;

[0024] A35: Evaluate the network performance of the optimized neural network model.

[0025] The method for optimizing the size of passive devices further includes: Step A4: Based on the design requirements of the passive devices, execute a multi-objective optimization algorithm to generate a Pareto optimal solution set as the optimal size that meets the design requirements.

[0026] On the other hand, the present invention provides a method for determining defects in passive devices, comprising:

[0027] B1: Perform the process parameter determination method for passive devices described above to obtain the actual fluctuation range of the process parameters;

[0028] B2: Based on the actual fluctuation range of process parameters and the geometric parameters of the layout of the passive device under test, electromagnetic simulation is used to predict the fluctuation range of the performance parameters of the passive device and determine the performance parameter threshold.

[0029] B3: Measure the performance parameters of passive devices and identify passive devices whose performance parameters exceed the performance parameter threshold as defective devices.

[0030] The method for determining the process parameters of passive devices in this invention verifies the process fluctuation range of electromagnetic process parameters through Monte Carlo simulation and corrects the fluctuation range of process parameters by combining actual test data, which helps to improve the stability of the process parameters of the device. Furthermore, the corrected process parameters ensure the reliability of the optimization results under process fluctuations, while supporting the flexible design requirements of various passive device shapes. It can construct a high-confidence passive device parameter dataset by combining Latin hypercube sampling and use the passive device parameter dataset to train the neural network parameters. In addition, this invention executes a multi-objective optimization algorithm according to the design requirements of passive devices to generate a Pareto optimal solution set for designers to choose from, significantly reducing the number of design iterations and supporting the automated design of passive devices in radio frequency integrated circuits. Attached Figure Description

[0031] Figure 1 This is an overall flowchart of the method for determining the process parameters of passive devices and the method for optimizing the size of passive devices according to the present invention;

[0032] Figure 2 These are schematic diagrams of the geometric parameters of spiral inductors of different shapes, showing the line width W, spacing S, inner diameter R, and number of turns T;

[0033] Figures 3A-3CThis is a graph showing the distribution of the quality factor Q of planar spiral inductors of the same layout size from three batches of wafers at a frequency of 3.6 GHz; among them, Figure 3A It is a wafer distribution diagram. Figure 3B It is a box diagram. Figure 3C This is a graph of the CDF cumulative distribution function;

[0034] Figure 4 This is a flowchart of the passive device size optimization method of the present invention when using a genetic algorithm to optimize neural network parameters to improve prediction accuracy.

[0035] Figure 5 This is a flowchart of the NSGA-II algorithm.

[0036] Figure 6A and Figure 6B The graph shows the prediction accuracy of the neural network model optimized by the genetic algorithm. Figure 6A The prediction accuracy of the inductance value L is shown. Figure 6B The prediction accuracy of the quality factor Q is shown.

[0037] Figure 7 The diagram shows the optimal result at 3.6 GHz, considering the trade-offs between L value, Q value, and area after employing a multi-objective optimization algorithm.

[0038] Figure 8 The diagram shows the optimal output with an inductance value of 2nH, Q value, and area trade-off at a frequency of 3.6 GHz after employing a multi-objective optimization algorithm. Detailed Implementation

[0039] The invention will be further described below with reference to specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0040] First embodiment: Method for determining process parameters of passive devices

[0041] like Figure 1 As shown, according to the first embodiment of the present invention, the method for determining the process parameters of the passive device specifically includes:

[0042] Step S1: Prepare a wafer containing passive devices with multiple different layout sizes based on the same device process, test it, and analyze the performance parameters of the passive devices based on the test results. The analysis results of the performance parameters include the actual process fluctuation range and the actual average value.

[0043] The passive devices include resistors, capacitors, and inductors with different layout sizes, where the layout size includes the shape type and geometric dimensions. In other words, layouts with the same shape type and geometric dimensions are considered to have the same layout size.

[0044] like Figure 2 As shown, in this embodiment, the passive device is an inductor. The shape of the inductor layout includes square, circular, and octagonal planar spirals. The geometric parameters include: linewidth W, spacing S, inner diameter R, and number of turns T. Its process constraints are: R≥20um, W≥5um, S≥4um, T≥1.25. The design of each process layer of the planar spiral inductor conforms to the Design Rule Check (DRC).

[0045] In other embodiments, when the passive device is an inductor, the shape of the inductor layout is not limited to a planar spiral; it can also be a square, circular, octagonal, or any other shape capable of performing inductance functions, formed by multiple layers stacked to form a spiral. Furthermore, the passive device is not limited to an inductor; it can also be a resistor or a capacitor.

[0046] Fabricating a wafer containing passive devices of various layout sizes based on the same device process specifically includes: integrating passive devices of various layout sizes in the wafer design layout based on a specified device process (such as 0.25μm GaAs RF process), and obtaining sufficient wafers as process fluctuation data samples by performing multiple batches of fabrication on the device process.

[0047] The analysis results of testing and obtaining the performance parameters of passive devices include at least acquiring the S-parameters (i.e., scattering parameters) of the passive devices, extracting the performance parameters of the passive devices from the S-parameters, and statistically analyzing the performance parameters. For a two-port network, the S-parameters of passive devices include four S-parameters. , , , The analysis results of the performance parameters include the actual process fluctuation range and the actual average value of the performance parameters.

[0048] To verify the accuracy of subsequent electromagnetic simulations and the variability of device manufacturing processes, wafer-level testing was performed on the wafers of passive devices obtained from the fabrication process to obtain the S-parameters of the passive devices.

[0049] In this embodiment, wafer-level testing to obtain the S-parameters of passive devices specifically includes:

[0050] Step S11: Confirm the wafer information of the passive device under test, namely the product ID, lot ID, and wafer ID. It should be noted that the fabrication layout on wafers from different batches is the same.

[0051] Step S12: Visually inspect the wafers for passive devices;

[0052] Step S13: Match the pin card and probe, and load the wafer of the passive device under test that has been visually inspected and found to be correct into the probe station;

[0053] Step S14: Perform whole-wafer testing on the wafer of the passive device to obtain the S-parameters of the whole-wafer device.

[0054] The process involves setting up an automatic testing program on the testing equipment, randomly sampling a small number of wafers containing passive devices, and after confirming that the wafers containing passive devices are correct, performing a whole-wafer test on all wafers containing passive devices. The test frequency range is 0.1~40GHz, and finally obtaining the S-parameters of the whole-wafer devices.

[0055] In this embodiment, the passive device is an inductor, and the performance parameters of the inductor include inductance value L, quality factor Q, and self-resonant frequency SRF. In other embodiments, when the passive device is a resistor, its performance parameter is the resistance value; when the passive device is a capacitor, the performance parameters of the capacitor include capacitance value, capacitor quality factor, and capacitor resonant frequency.

[0056] The formulas for calculating inductance value L and quality factor Q are:

[0057] ,

[0058] in, This represents the admittance parameter, which can be obtained through S-parameter transformation. Indicates the imaginary part. Indicates the real part.

[0059] The statistical analysis results of the performance parameters include: generating wafer maps, CDF plots, and box plots to visualize the data, analyze the actual process fluctuation range of each performance parameter, and calculate the actual average and actual standard deviation of each performance parameter.

[0060] like Figures 3A-3C This is a graph showing the distribution of the quality factor Q of planar spiral inductors of the same layout size from three different batches of wafers at a frequency of 3.6 GHz. Figure 3A It is a wafer distribution diagram. Figure 3B It is a box diagram. Figure 3C This is a graph of the CDF cumulative distribution function.

[0061] Step S2: Use the analysis results of performance parameters and Monte Carlo simulation based on electromagnetic simulation to determine the actual fluctuation range of process parameters; process parameters include the thickness of each material layer, relative permittivity and metallic conductivity.

[0062] Therefore, this invention verifies the process fluctuation range of electromagnetic process parameters through Monte Carlo simulation and corrects the process parameters by combining actual test data, which helps to improve the stability of the process parameters of the device.

[0063] Step S2 specifically includes:

[0064] Step S21: Write the parameterization unit for the passive device. The parameterization unit is driven by the defined geometric parameters to automatically generate a passive device model with the corresponding layout size, which is used to obtain simulation performance parameters later.

[0065] In this embodiment, the parameterized unit of the passive device is written using the AEL language. As mentioned above, the shape of the inductor includes a planar spiral square, circular, or octagonal shape; the geometric parameters of the inductor layout include: linewidth W, spacing S, inner diameter R, and number of turns T.

[0066] AEL is the built-in scripting language of Keysight's ADS (Advanced Design System), primarily used for automated layout dimension design, parametric device modeling, and batch data processing. AEL allows for parameterized dimension adjustments, improving design efficiency.

[0067] Step S22: Sample fluctuations within ±20% of the standard value of the process parameters and obtain simulation performance parameters through multiple Monte Carlo simulations; adjust the process parameters by comparing the simulation performance parameters with the actual process fluctuation range and the actual average value. When the distribution and mean of the simulation performance parameters best match the actual process fluctuation range and the actual average value, determine the current process parameters as the final result.

[0068] Therefore, by comparing the simulated performance parameters with the performance parameters obtained from the wafer-level tests described above, the accuracy of the simulation results was verified and the optimal process parameters were obtained.

[0069] Among them, the simulation performance parameters are a set of parameters with process fluctuation range; when the process fluctuation range of the simulation performance parameters all fall within the actual process fluctuation range of the performance parameters and the average value of the simulation performance parameters is closest to the actual average value of the performance parameters, it is judged that the simulation performance parameters are closest to the actual process fluctuation range and the actual average value.

[0070] During the Monte Carlo simulation, fluctuation sampling is performed within ±20% of the standard value of the process parameters to obtain multiple sets of sampled values. Combining these sampled values ​​with the parameterized units of the passive devices, a passive device model with the corresponding layout size is automatically generated. Then, electromagnetic simulation is performed to obtain S-parameters, from which simulation performance parameters, including inductance (L), quality factor (Q), and self-resonant frequency (SRF), are extracted.

[0071] In this embodiment, electromagnetic simulation is performed using ADS Momentum. ADS Momentum is a three-dimensional planar electromagnetic field simulation module in Keysight's Advanced Design System (ADS) software, primarily used for electromagnetic characteristic analysis of high-frequency circuits and antennas.

[0072] It should be noted that the process parameters are usually consistent for passive device structures with different layout sizes (i.e., different linewidths W, spacing S, inner diameters R, and number of turns T). As long as the same device process is used, the process parameters of the substrate set in the simulation will be consistent. Therefore, the process parameters obtained in step S22 can be directly used for electromagnetic simulation.

[0073] Second embodiment: Size optimization method for passive components

[0074] like Figure 1 As shown, according to a second embodiment of the present invention, the method for optimizing the size of passive devices specifically includes:

[0075] Step A1: Perform the process parameter determination method for passive devices described above to obtain the actual fluctuation range of the process parameters;

[0076] Step A2: Use the average value of the actual fluctuation range of the process parameters as the process parameters required for electromagnetic simulation, and establish a parameter space based on the geometric parameters of the passive device layout; use the Latin hypercube sampling method to obtain performance parameters through parameter space sampling and electromagnetic simulation formula calculation to establish a passive device parameter dataset;

[0077] In another embodiment, obtaining performance parameters through parameter space sampling and electromagnetic simulation to establish a passive device parameter dataset can be replaced by obtaining component parameters of the equivalent circuit model (e.g., component parameters of the π-type equivalent circuit model) through parameter space sampling and formula calculation to establish a passive device parameter dataset.

[0078] Because passive devices occupy a large area and have numerous geometric parameters, establishing a passive device parameter dataset using actual test results would require a significant amount of layout area. Therefore, we fabricate a small number of passive devices to obtain wafer-level test results, which are then compared with electromagnetic simulation results. This allows us to correct for the actual fluctuation range of the obtained process parameters and verify the accuracy of the electromagnetic simulation. Subsequently, based on the process parameters required for electromagnetic simulation, a large batch of accurate performance parameters or component parameters are generated to establish a passive device parameter dataset.

[0079] In this embodiment, the Latin hypercube sampling method is used to perform parameter space sampling and electromagnetic simulation formula calculations in the parameter space of the geometric parameters of the layout (i.e., line width W, spacing S, inner diameter R, number of turns T) to obtain a large number of electromagnetic simulation results, which serve as a passive device parameter dataset.

[0080] In this embodiment, 1296 sets of data are sampled within the design space of the geometric parameters of the layout. In other embodiments, 1000 to 8000 sets of data are sampled within the design space of the geometric parameters of the layout.

[0081] In this embodiment, the parameter space of the geometric parameters of the layout meets the process constraints and the area cannot be too large. The process constraints that the parameter space of the geometric parameters of the layout meets are: W=5~30um; S=4~25um; R=20~150um; T=1.25~5.25, and the number of turns is set to a fixed step size of 0.25.

[0082] In this embodiment, the passive device is an inductor, and the performance parameters of the passive device include inductance value L, quality factor Q, self-resonant frequency SRF, or may include S-parameters.

[0083] Step A3: Establish a neural network model, and train and optimize the neural network model using the passive device parameter dataset to obtain a passive device model for outputting performance parameters or component parameters based on the geometric parameters of the layout.

[0084] Specifically, a genetic algorithm is used to globally search and optimize the network structure and hyperparameters of the neural network model to improve prediction accuracy.

[0085] Step A3 specifically includes:

[0086] Step A31: Perform data preprocessing on the passive device parameter dataset to obtain the training set and test set;

[0087] The preprocessing of the passive device parameter dataset includes:

[0088] Step A311 (optional): Perform parameter extraction; that is, extract the performance parameters of passive devices from the S-parameters, including inductance value L, quality factor Q, and self-resonant frequency SRF.

[0089] Step A312: Data cleaning; that is, filtering out data that exceeds the self-resonant frequency;

[0090] Since inductor performance only needs to focus on the portion that remains inductive up to the self-resonant frequency, data beyond the self-resonant frequency is filtered out.

[0091] Step A313: Divide the passive device parameter dataset into a training set and a test set; that is, divide the training set and the test set in a 4:1 ratio.

[0092] Step A314: Perform data normalization.

[0093] The training and test sets are normalized using a min-max normalization method, mapping the data to the range [0,1] to eliminate dimensional differences, accelerate model convergence, and improve optimization efficiency.

[0094] The formula for data normalization is as follows:

[0095] ,

[0096] in, and These represent the maximum and minimum values ​​of the data, respectively.

[0097] Step A32: Establish a three-layer backpropagation (BP) neural network model, using the geometric parameters of the layout (i.e., line width W, spacing S, inner diameter R, number of turns T) as input parameters, and performance parameters or component parameters as output parameters.

[0098] A three-layer backpropagation (BP) neural network model is established, specifically including: setting up an input layer, hidden layers, and an output layer, with the number of neurons in the hidden layer set to [value missing]. The learning rate is The weights from the input layer to the hidden layer are The hidden layer bias threshold is The weights from the hidden layer to the output layer are The output layer bias threshold is The transfer functions available for the hidden layer include sigmoid, logsig, tansig, and purelin.

[0099] Step A33: Introduce a genetic algorithm to globally search for the optimal network structure and hyperparameters of the neural network model, thereby improving the model's generalization ability and prediction accuracy.

[0100] In step A33, the network structure and hyperparameters include the weight matrix of the neural network. Bias threshold Learning rate and the number of neurons in the hidden layer Four key parameters, thus affecting the weight matrix of the neural network. Bias threshold Learning rate and the number of neurons in the hidden layer The four key parameters are optimized simultaneously to obtain the optimal parameter combination and reconstruct the network topology.

[0101] like Figure 4 As shown, step A33 specifically includes:

[0102] Step A331: Encode the key parameters into a key parameter vector , as an individual (i.e., chromosome);

[0103] Key parameter vector The structure is as follows, where The function represents expanding a matrix into column vectors.

[0104] ,

[0105] The variable range of the key parameters is as follows: (integer); (continuous); (continuous).

[0106] Step A332: Use root mean square error to establish the fitness function;

[0107] Since the objective is to minimize the prediction error, the root mean square error is used as the fitness function. The calculation formula is as follows:

[0108]

[0109] in, To output the number of parameters, It is the j-th true value of the i-th output parameter; It is the j-th predicted value of the i-th output parameter; This is the number of samples in the test set.

[0110] Step A333: Generate key parameter vectors , to serve as individuals in the initial population;

[0111] Step A334: Decode the individuals of the current generation to generate the corresponding neural network model, train it using the training set and calculate the fitness using the test set; based on the fitness, perform selection, crossover and mutation to generate offspring individuals.

[0112] Selection: The core objective of selection strategies is to select superior individuals from the current population based on their fitness, using certain rules (such as roulette wheel selection, tournament selection, etc.), and pass them on to the next generation. In this invention, the selection adopts a roulette wheel strategy, that is, fitness is converted into the probability of being selected; the higher the probability value, the greater the chance of being selected.

[0113] The probability that the i-th individual is selected is:

[0114]

[0115] in, Represents individuals within a population. Let be the probability that the i-th individual is selected. Let be the fitness of the i-th individual.

[0116] Crossover: Simulated binary crossover is used to mix the genes of two parent individuals to generate two offspring individuals, while maintaining the diversity of solutions. The crossover probability is set to 0.7.

[0117] The formula for calculating offspring individuals during crossover is as follows:

[0118] ,

[0119] Among them, offspring, , All of them are in the form of key parameter vectors , These are the cross-weighting coefficients.

[0120] Mutation: The mutation probability is set to 0.1, using adaptive feasible mutation. The mutation amplitude δ is dynamically adjusted based on the current population diversity. Offspring individuals The mutation formula is:

[0121] ,

[0122] in, For offspring individuals, For the parent generation, The range of variation, This represents a value randomly sampled from a standard normal distribution.

[0123] Step A335: Repeat step A334 to iteratively evolve until the termination condition is met, obtain the optimal individual, and then obtain the optimal network structure and hyperparameters of the neural network model.

[0124] In addition, step A3 may also include:

[0125] Step A34: After the genetic algorithm performs a global search, the weights, thresholds, and learning rate of the neural network model are locally refined using the training set and the test set and the Levenberg-Marquardt algorithm (trainlm).

[0126] The Levenberg-Marquardt method combines gradient descent with the Gauss-Newton method, and its update formula is as follows:

[0127]

[0128] in, Let Jacobian matrix be the error versus weights. Damping factor This is the error vector.

[0129] Step A35: Evaluate the network performance of the optimized neural network model.

[0130] The quantitative metrics used in the evaluation include mean squared error (MSE), coefficient of determination (R²), and mean relative error. Furthermore, the evaluation includes a scatter plot visualizing the predicted and actual values. This allows for a comprehensive evaluation of the network's prediction accuracy and generalization ability.

[0131] Step A4 (optional): Based on the design requirements of the passive device (such as performance and area, or target values ​​of component parameters), execute a multi-objective optimization algorithm to generate a Pareto optimal solution set (Final Pareto Front) as the optimal size to meet the design requirements for the designer to choose from.

[0132] In this invention, the trade-off between the performance and area of ​​passive components such as planar spiral inductors during circuit design is regarded as a multi-objective optimization problem. It can be solved quickly using multi-objective optimization algorithms (such as NSGA-II, MOEA / D) to obtain a Pareto optimal solution set as the optimal size to meet the design requirements.

[0133] In this embodiment, the NSGA-II algorithm is selected as the multi-objective optimization algorithm to simultaneously optimize the inductance value L, quality factor Q, and area, and generate a Pareto optimal solution set. The constraints include the process size range and the self-resonant frequency SRF.

[0134] In one example, #case1, consider the following design requirements and establish the following objective function and constraints based on these requirements:

[0135] #case1: Input a fixed frequency and obtain the optimal result that balances L value, Q value, and area.

[0136] Objective function:

[0137] Constraints: .

[0138] in, Refers to the area of ​​the device. The Q value at a given frequency point. The L value at a given frequency point. It is a given frequency, and SRF is the self-resonant frequency.

[0139] In another embodiment #case2, consider the following design requirements and establish the following objective function and constraints based on these requirements:

[0140] #case2: Input a fixed frequency and the required inductance value to obtain the optimal result for Q value and area trade-off.

[0141] Objective function:

[0142] Constraints:

[0143] in, Refers to the area of ​​the device. The Q value at a given frequency point. The L value at a given frequency point. Refers to a given frequency, The L value predicted by the model at a given frequency point. The required inductance value at a given frequency point is indicated by SRF, which is the self-resonant frequency. That is, delta L.

[0144] like Figure 5 As shown, in this embodiment, when the NSGA-II algorithm is selected as the multi-objective optimization algorithm, the NSGA-II algorithm specifically includes the following steps:

[0145] Step A41: Generate a discretized initial solution that satisfies the process constraints to initialize the parent population P.

[0146] Step A42: Non-dominated sorting, divide the population into multiple non-dominated levels and sort them according to dominance relationships;

[0147] Domination relationship is defined as the relationship between individuals. Dominant Individual (recorded as) ), if and only if:

[0148]

[0149] Step A43: Calculate the crowding distance, which is used to quantify the distribution density of individuals in the same non-dominated layer and avoid local clustering.

[0150] For each objective function ,individual crowded distance for:

[0151]

[0152] Step A44: Select, crossover, and mutate to generate offspring; the selection process uses a binary tournament method, randomly selecting two individuals from the population, prioritizing individuals with lower (better) non-dominant status or higher crowding.

[0153] Step A45: Transfer the parent generation and offspring merged into Perform a non-dominated sort, and then update the parent population according to the results of the non-dominated sort.

[0154] Step A46: Return to step A43 and iterate repeatedly until the termination condition is met, and finally output the optimal Pareto front solution.

[0155] Figure 6A and Figure 6B The graph shows the prediction accuracy of the neural network model optimized by the genetic algorithm. Figure 6A The prediction accuracy of the inductance value L is shown. Figure 6B The prediction accuracy of the quality factor Q is shown.

[0156] Figure 7 The diagram shows the optimal result (i.e., #case1) at a frequency of 3.6 GHz after adopting a multi-objective optimization algorithm, considering the trade-offs between L value, Q value, and area.

[0157] Figure 8 The diagram shows the optimal results for the inductance value L of 2nH, Q value, and area trade-off output (i.e., #case2) at a frequency of 3.6 GHz after adopting the multi-objective optimization algorithm.

[0158] Third embodiment: Defect determination method for passive devices

[0159] Based on the method for determining the process parameters of passive devices described above, the defect determination method for passive devices of the present invention includes:

[0160] Step B1: Perform the process parameter determination method for passive devices described above to obtain the actual fluctuation range of the process parameters;

[0161] Step B2: Based on the actual fluctuation range of the process parameters and the geometric parameters of the layout of the passive device under test, predict the fluctuation range of the performance parameters of the passive device and determine the performance parameter threshold through electromagnetic simulation.

[0162] In this embodiment, the passive device is an inductor, and the performance parameters of the passive device include inductance value L, quality factor Q, and self-resonant frequency SRF. Preferably, the performance parameter thresholds are calculated based on the average value and standard deviation of the performance parameters of the passive device.

[0163] Step B3: Measure the performance parameters of passive devices and identify passive devices whose performance parameters exceed the performance parameter threshold as defective devices.

[0164] In this embodiment, if any one of the performance parameters exceeds the performance parameter threshold, the passive device is determined to be a defective device.

[0165] In addition, the present invention may also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the methods described above, such as the method for determining process parameters of passive devices, the method for optimizing the size of passive devices, and the method for determining defects in passive devices.

[0166] In summary, the passive device process parameter determination method of this invention verifies the process fluctuation range of electromagnetic process parameters through Monte Carlo simulation and corrects the fluctuation range of process parameters by combining actual test data, which helps to improve the stability of the device process parameters. Furthermore, the corrected process parameters ensure the reliability of the optimization results under process fluctuations, while supporting flexible design requirements for various passive device shapes. It can construct a high-confidence passive device parameter dataset by combining Latin hypercube sampling and use the passive device parameter dataset to train neural network parameters. In addition, according to the design requirements of passive devices, a multi-objective optimization algorithm is executed to generate Pareto optimal solutions, providing designers with a set of solutions to choose from, significantly reducing the number of design iterations and supporting the automated design of passive devices in RF integrated circuits. Moreover, this invention uses a genetic algorithm to optimize neural network parameters, thereby further improving prediction accuracy.

[0167] Compared with the prior art, the beneficial effects of the method for determining the process parameters of passive devices in this invention are as follows:

[0168] 1. Significantly shorten the design cycle and reduce costs: By using artificial neural networks to predict the performance parameters of passive devices with high accuracy, the number of electromagnetic simulation iterations required in the traditional trial-and-error method is greatly reduced. Combined with genetic algorithms to optimize network parameters, the model efficiency is further improved, the overall design time is shortened and the development cost is reduced.

[0169] 2. Achieve automated multi-objective trade-off optimization: The NSGA-II algorithm is used to generate Pareto optimal solution sets for performance (inductance value L, quality factor Q) and area, enabling designers to quickly obtain multi-objective balance schemes under complex constraints, overcoming the limitations of traditional single-objective optimization or manual adjustment.

[0170] 3. Enhance design robustness and adaptability: By verifying the process fluctuation range of electromagnetic process parameters through Monte Carlo simulation and correcting the fluctuation range of process parameters in combination with actual test data, it helps to improve the stability of the process parameters of the device. Furthermore, the corrected process parameters ensure the reliability of the optimization results under process fluctuations, while supporting the flexible design requirements of various passive device shapes (square, round, octagonal).

[0171] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the invention. Various variations can be made to the above embodiments of the present invention. That is, all simple and equivalent changes and modifications made based on the claims and description of this invention fall within the protection scope of the claims of this patent. All aspects not described in detail in this invention are conventional technical content.

Claims

1. A method for determining the process parameters of a passive device, characterized in that, The method comprises the following steps: Step S1: preparing a wafer containing passive devices with different layout sizes based on the same device process, testing the wafer, and analyzing the performance parameters of the passive devices based on the test results; Step S2: determining the actual fluctuation range of the process parameters by using the analysis results of the performance parameters and Monte Carlo simulation; the process parameters include the thickness of each layer of material, the relative dielectric constant, and the metal conductivity; The step S2 specifically comprises: Step S21: writing a parameterized unit of the passive device, which is driven by defined geometric parameters, and automatically generating a passive device model of a corresponding layout size for subsequent acquisition of simulation performance parameters; Step S22: performing fluctuation sampling within a range of ±20% of the standard value of the process parameters, acquiring simulation performance parameters through multiple Monte Carlo simulations, adjusting the process parameters by comparing the simulation performance parameters with the actual process fluctuation range and the actual average value, and determining the current process parameters as the final result when the distribution and average value of the simulation performance parameters best match the actual process fluctuation range and the actual average value.

2. The method of claim 1, wherein The passive device includes resistors, capacitors, and inductors with different layout sizes, and the layout sizes include the shape type and geometric size of the layout.

3. The method of claim 1, wherein In the step S1, the performance parameters of the passive devices are tested and analyzed, and the analysis results at least include: acquiring S parameters of the passive devices, extracting performance parameters of the passive devices from the S parameters, and statistically obtaining the analysis results of the performance parameters.

4. The method of claim 1, wherein In the step S22, during the Monte Carlo simulation, fluctuation sampling is performed within a range of ±20% of the standard value of the process parameters to obtain multiple sets of sampling values; corresponding layout size passive device models are automatically generated by combining these sampling values and the parameterized unit of the passive device, and electromagnetic simulation is performed to acquire S parameters, from which simulation performance parameters are extracted.

5. A method of size optimization of a passive device, characterized in that, The method comprises the following steps: Step A1: performing the process parameter determination method of the passive device according to any one of claims 1-4 to obtain the actual fluctuation range of the process parameters; Step A2: taking the average value of the actual fluctuation range of the process parameters as the process parameters required for electromagnetic simulation, and establishing a parameter space according to the geometric parameters of the layout of the passive device; Using the Latin hypercube sampling method, performance parameters or element parameters of an equivalent circuit model are obtained by parameter space sampling and electromagnetic simulation to establish a passive device parameter dataset; Step A3: establishing a neural network model, training and optimizing the neural network model by using the passive device parameter dataset, and obtaining a passive device model to output performance parameters or element parameters according to the geometric parameters of the layout.

6. The method of claim 5, wherein, The step A3 specifically comprises: Step A31: performing data preprocessing on the passive device parameter dataset to obtain a training set and a test set; Step A32: establishing a three-layer back propagation neural network model, taking the geometric parameters of the layout as input parameters, and taking performance parameters as output parameters; Step A33: introducing a genetic algorithm to globally search for an optimal network structure and hyperparameters of the neural network model, thereby improving the generalization ability and prediction accuracy of the model; Step A34: Use the training set and test set and the Levenberg-Marquardt algorithm to perform local fine-tuning of the weights, threshold, and learning rate of the neural network model; Step A35: Evaluate the network performance of the optimized neural network model.

7. The method of claim 5, wherein, It also includes: Step A4: Based on the design requirements of the passive device, execute a multi-objective optimization algorithm to generate a Pareto optimal solution set as the optimal size to meet the design requirements.

8. A method of defect determination of a passive device, characterized by, include: Step B1: Perform the process parameter determination method for passive devices according to any one of claims 1-4 to obtain the actual fluctuation range of the process parameters; Step B2: Based on the actual fluctuation range of the process parameters and the geometric parameters of the layout of the passive device under test, predict the fluctuation range of the performance parameters of the passive device and determine the performance parameter threshold through electromagnetic simulation. Step B3: Measure the performance parameters of passive devices and identify passive devices whose performance parameters exceed the performance parameter threshold as defective devices.

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, When executed by a processor, the computer program implements the method for determining the process parameters of the passive device as described in any one of claims 1-4.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, When executed by a processor, the computer program implements the size optimization method for passive devices as described in any one of claims 5-7.

11. A computer readable storage medium having stored thereon a computer program, characterized in that, When the computer program is executed by the processor, it implements the defect determination method for passive devices as described in claim 8.

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