Three-dimensional integrated inductor multi-objective optimization method based on TSV

Abstract

The invention discloses a TSV-based three-dimensional integrated inductor multi-objective optimization method, which specifically comprises the following steps: step 1, establishing a geometric model of a three-dimensional inductor, and determining geometric parameters to be optimized; 2, sampling the inductor structure determined in the step 1, and dividing the obtained data into a training set and a test set; step 3, performing numerical simulation on the sampled data in the step 2 to obtain an admittance parameter Y11 corresponding to each group of geometric parameters, then performing order reduction and merging processing on the parameters Y11, and outputting a merging result y; 4, determining an artificial neural network structure; and step 5, determining a target function of multi-target optimization according to the network structure in the step 4. And the optimization efficiency is improved while the optimization precision is ensured.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of computer-aided design of three-dimensional integrated circuits, and relates to a multi-objective optimization method for a three-dimensional integrated inductor based on TSV. BACKGROUND

[0002] In the development process of integrated circuits, the through-silicon via (TSV) technology is an important way to realize the miniaturization and microfabrication of integrated circuits. With the continuous development of TSV technology, TSV can not only realize the interconnection between different layers of 2.5D or 3D integrated circuits, but also can be used as part of a passive device to realize the design of a three-dimensional passive device. The three-dimensional passive device is integrated in a silicon substrate or a silicon adapter, and through the three-dimensional passive device, the miniaturization of radio frequency and microwave components can be realized. Extensive research has been conducted on three-dimensional integrated passive devices at home and abroad. However, the modeling and optimization of passive devices have always been a difficult problem. Finite element-based simulation is often very time-consuming, and in three-dimensional integrated inductors as a representative of three-dimensional integrated passive devices, the presence of TSV structure requires more grids for finite element simulation, thus requiring more computational effort and consuming longer simulation time, which greatly reduces the optimization efficiency.

[0003] In the actual simulation process of radio frequency passive devices, engineers often need to combine experience to perform each optimization iteration, which makes it difficult to effectively obtain the optimal solution. In addition, with the help of parameter scanning functions of commercial electromagnetic simulation software such as Ansys HFSS, auxiliary optimization analysis can be performed, but multi-parameter scanning analysis requires a large amount of time and is difficult to perform multi-objective optimization. Currently, advanced passive device modeling methods use artificial neural networks (ANN) to establish the relationship between the geometric parameters of the passive device and the frequency response curve such as S parameters. At the same time, vector fitting (VF) technology is used to reduce the order of the frequency response curve, so that the generalization ability of ANN is improved.

[0004] However, the current mainstream optimization method is to use a heuristic algorithm or a space mapping technique for single-objective modeling, or to add multiple objective functions using weights to combine them into one objective function. Both of these optimization strategies have problems: the former cannot uniformly optimize multiple indicators in actual engineering and compromises when the indicators conflict; the latter is still essentially a single-objective optimization, and the selection of weights depends on the subjective judgment of engineers, which may not accurately reflect the actual engineering situation.

[0005] For the inductor, the value L of the inductor at a given frequency and the quality factor Q are two important indicators of the inductor, which need to meet the inductance value close to the design value while ensuring the maximization of Q. Therefore, a comprehensive three-dimensional integrated inductor parameterized modeling and multi-objective optimization comprehensive design method needs to be proposed. SUMMARY

[0006] The purpose of the present application is to provide a TSV-based three-dimensional integrated inductor multi-objective optimization method, which can improve the optimization efficiency while ensuring the optimization accuracy.

[0007] The technical scheme adopted by the present application is a TSV-based three-dimensional integrated inductor multi-objective optimization method, which specifically includes the following steps:

[0008] Step 1, establish a geometric model of a three-dimensional inductor, and determine the geometric parameters to be optimized;

[0009] Step 2, sample the inductor structure determined in step 1, and divide the data obtained by sampling into a training set and a test set;

[0010] Step 3, perform numerical simulation on the sampling data of step 2 to obtain the admittance parameter Y corresponding to each set of geometric parameters 11 , and then perform reduction and merging processing on the Y 11 parameter to output the merging result y;

[0011] Step 4, determine the structure of an artificial neural network;

[0012] Step 5, determine the objective function of multi-objective optimization according to the network structure of step 4, and perform optimization for the objective function.

[0013] The present application has the following characteristics:

[0014] In step 1, the three-dimensional inductor model structure is: including a through silicon via TSV and a redistribution layer RDL, wherein the RDL is divided into an upper RDL and a lower RDL, the lower RDL is inclined clockwise at an angle r, and the upper RDL and the lower RDL are interconnected by the TSV;

[0015] The geometric parameters to be optimized are: the length l and the width w of the RDL, and the included angle r between the upper RDL and the lower RDL, wherein the distance from the geometric center of the TSV to the edge of the RDL is fixed as a constant; the to-be-determined geometric parameters are combined into a vector x, which is defined as:

[0016] x=[r l w] T (1).

[0017] In step 2, the Latin hypercube sampling method is used to sample the geometric parameters of the three-dimensional inductor, and the sampled data is divided into a training set and a test set.

[0018] The specific process of step 3 is as follows:

[0019] Step 3.1, numerical simulation is performed on the sampling data of step 2 using Ansys HFSS, and the admittance parameter Y corresponding to each set of geometric parameters is obtained 11 ;

[0020] Step 3.2, the vector fitting method is used to reduce the order of Y 11 parameters, as shown in the following formula (2):

[0021]

[0022] Where s represents complex frequency, c n represents residue, a n represents pole, H represents frequency response, i.e. Y 11 parameters, N represents the order of transfer function, and d and h represent the remainder.

[0023] Step 3.3, the parameters processed in step 3.2 are combined, and the output parameter y is obtained, the specific process is as follows:

[0024] y=Re[a1...a n c1...c n d h] T +Im[a1...a n c1...c n d h] T (3)。

[0025] In step 3.1, the sweep frequency range of numerical simulation is 1GHz-100GHz, and the step is 0.1Ghz.

[0026] In step 4, the multi-layer perceptron MLP is used as the structure of artificial neural network, each layer of neurons is full connection layer, GELU is used as activation function, Adam is used as optimizer, and mean square error MSE is used as loss function.

[0027] In step 4, the x of test set data is used for prediction, and the predicted y is substituted back into the pole-residue transfer function to obtain the predicted Y 11 curve; the real value of Y 11 in the test set and the predicted Y 11 are converted into the real value of inductance L and quality factor Q in the test set and L and Q respectively by the following formula (4):

[0028]

[0029] Subsequently, the prediction values and the true values of L and Q are subjected to error analysis, and the average value of the mean square error of all test sets is taken as the error, the inductance value error E L and the quality factor error E Q Defined by the following formula (5) and formula (6) respectively, when the test is completed, the corresponding layer number when the error is the smallest is taken as the final structure of ANN:

[0030]

[0031] In the formula, m is the number of test sets, length(·) represents the dimension of L and Q, i represents the test set number, j represents the sampling point number, respectively represent the predicted values of the inductance values L and Q;

[0032] The specific process of step 5 is: the objective function of multi-objective optimization is determined as minimizing the error between the inductance value and the design value and maximizing the quality factor, which is specifically as follows:

[0033]

[0034] F L = |L-L * | (8)

[0035] Wherein, L represents the actual value of inductance, Q represents the quality factor predicted by the ANN model, L * represents the design value of inductance.

[0036] The beneficial effects of the present application are that based on the present application, multi-objective optimization of computer-aided design of three-dimensional integrated inductors can be carried out. Compared with the traditional method, the present method adopts an ANN-based modeling method and introduces a multi-objective optimization algorithm. The problems of low optimization efficiency and the need for experience adjustment caused by the need for a large amount of computing resources and long computing time in the traditional simulation-based modeling optimization method can be solved, and the non-dominated solution set of the optimal solution can be calculated by the multi-objective optimization algorithm, which facilitates designers to better compromise between the advantages and disadvantages of multiple objectives. The present method can be applied to the design and optimization process of TSV-based three-dimensional integrated inductors, thereby reducing the time cost of design. Further, by changing the sampling parameters and the objective function, the present method can be applied to the design and optimization of all three-dimensional passive devices. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The flowchart of the TSV-based three-dimensional integrated inductor multi-objective optimization method of the present application;

[0038] Figure 2 The geometric parameter selection diagram of the TSV-based three-dimensional integrated inductor multi-objective optimization method of the present application;

[0039] Figure 3 This is a comparison chart of inductance value prediction and simulation results during the modeling process of the TSV-based multi-objective optimization method for three-dimensional integrated inductors in this invention.

[0040] Figure 4 This is a comparison chart of the quality factor prediction and simulation results in the modeling process of the TSV-based multi-objective optimization method for three-dimensional integrated inductors of this invention.

[0041] Figure 5 This is a comparison chart of Pareto solution sets for different iteration numbers in the TSV-based multi-objective optimization method for three-dimensional integrated inductors of this invention. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0043] Example 1

[0044] This invention presents a multi-objective optimization method for three-dimensional integrated inductors based on TSV, the process of which is as follows: Figure 1 As shown, the specific steps include the following:

[0045] Step 1: Use Ansys HFSS software to build a three-dimensional geometric model of the inductor and determine the geometric parameters to be optimized;

[0046] Step 2: Sample the inductor structure determined in Step 1. Specifically, determine the number of samples to be 200 sets, of which 160 sets are for training and 40 sets are for testing. Then, use the Latin hypercube sampling method to sample the parameters within the range of Table 1.

[0047] Step 3: Perform numerical simulation on the sampled data from Step 2 to obtain the admittance parameter Y corresponding to each set of geometric parameters. 11 Subsequently, Y 11 The parameters are reduced in order and merged, and the merged result y is output.

[0048] Step 4: Determine the structure of the artificial neural network;

[0049] Step 5: Based on the network structure in Step 4, determine the objective function for multi-objective optimization.

[0050] Example 2

[0051] The specific process of step 1 is as follows: In this method, if... Figure 2As shown, the three-dimensional inductor is composed of through silicon vias (TSVs) and a redistribution layer (RDL), wherein the RDL is divided into an upper RDL and a lower RDL, the lower RDL is inclined clockwise at an angle r, and the upper and lower RDLs are interconnected by TSVs. The geometric parameters to be optimized are the length l and the width w of the RDL, and the included angle r between the upper and lower RDLs, wherein the distance between the geometric center of the TSV and the edge of the RDL is fixed as a constant, and in the present method, the distance is selected as 10 μm. The sampling range of the geometric parameters to be optimized is:

[0052] Table 1 Sampling range of three-dimensional inductor parameters to be optimized

[0053] Parameter Lower boundary Upper boundary l 90 pm 110 pm w 12 pm 18 pm r 20° 30°

[0054] In the present method, the geometric parameters to be determined are combined into a vector x, which is defined as

[0055] x = [r l w] T (1)

[0056] Example 3

[0057] The specific process of step 3 is as follows:

[0058] The sampling data is numerically simulated using Ansys HFSS to obtain the admittance parameter Y corresponding to each set of geometric parameters 11 . Among them, the sweep range of numerical simulation is 1 GHz to 100 GHz, and the step is 0.1 GHz.

[0059] Then the vector fitting method is used to reduce the order of Y 11 parameters, wherein the transfer function of vector fitting adopts a transfer function based on poles and residues, which is specifically expressed as follows, wherein s represents complex frequency, c n represents the residue, a n represents the pole, H represents the frequency response, in the present method, Y 11 parameters, N represents the order of the transfer function, and d and h represent the remainder. In the present method, the order N is fixed as 4.

[0060]

[0061] In the present method, all Y 11 data are subjected to vector fitting processing. Through the vector fitting algorithm, a n converges to the pole of Y 11 , and a n is substituted to further obtain other parameters in formula (2).

[0062] In order to facilitate the training of step 4 neural network, the parameters obtained by vector fitting are combined, as shown in the following formula:

[0063] y = Re[a1...a n c1...c n dh] T +Im[a1...a n c1...c n dh] T (3).

[0064] Example 4

[0065] The specific process of step 4 is as follows:

[0066] Using x as the input of the ANN defined in step 1 and y as the output of the ANN defined in step 3, the training set is used for training, and the test set is used for validation. In this method, TensorFlow is used to build the ANN (Artificial Neural Network). Specifically, a multilayer perceptron (MLP) is used as the structure of the ANN, each neuron is a fully connected layer, GELU is used as the activation function, Adam is used as the optimizer, and mean squared error (MSE) is used as the loss function.

[0067] This method first trains the ANN using the training set data determined in step 2. In this method, the number of neurons in each layer is fixed at 48. The ANN training is complete when the specified number of training epochs is reached. To determine the number of layers in the ANN and verify its accuracy, predictions are made using the test set data x, and the predicted y is substituted back into the pole-residue transfer function to obtain the predicted Y. 11 Curve. The Y values ​​in the test set are respectively expressed by the following formulas. 11 Actual value and predicted Y 11 This is converted into the true values ​​of inductance L and quality factor Q in the test set, and the sum of L and Q, and the predicted values. For example... Figure 3 and Figure 4 As shown.

[0068]

[0069] Where f represents frequency.

[0070] Subsequently, error analysis was performed on the predicted and actual values ​​of L and Q. Specifically, in this method, the average of the mean squared errors of all test sets was taken as the error. The errors of the inductance value and the quality factor were defined by the following formulas.

[0071]

[0072] In the formula, m is the number of test sets, i represents the test set number, and j represents the sampling point number. respectively represent the predicted values of the inductance value L and the Q value.

[0073] In the present method, n = 40, length(·) represents the dimension of L and Q, in the present method, since the sweep range of the sample is 1GHz to 100GHz with a step of 0.1GHz, length(L) = length(Q) = 991.

[0074] In the present method, the number of layers of the ANN is set to 3 to 7 layers, and the number of layers corresponding to the minimum prediction error is taken as the actual number of layers of the ANN. The specific implementation is: the number of neurons in each layer is fixed at 48, and the number of layers is set to 3 to 7 layers, respectively. In order to reduce the test error, each group of ANN structure is trained 10 times, and the test set is used to test them respectively, and the error defined by formula (5) and formula (6) is calculated. When the test is completed, the number of layers corresponding to the minimum error is taken as the final structure of the ANN.

[0075] Example 5

[0076] The specific process of step 5 is:

[0077] After the ANN structure is determined, the ANN prediction result of each unknown variable x is taken as the objective function of the multi-objective optimization process. The specific implementation is: the objective function of the multi-objective optimization is determined to minimize the error between the inductance value and the design value and maximize the quality factor. The objective function can be represented by the following formula.

[0078]

[0079] F L = |L - L * | (8)

[0080] Wherein, L represents the actual value of the inductance, in the present method, the ANN model prediction result established in step 4 is used for approximation, Q represents the quality factor predicted by the ANN model, L * represents the design value of the inductance.

[0081] The specific implementation is that in each iteration, first, the frequency response Y 11 curve corresponding to the unknown variable x of the present iteration is predicted using the ANN model established in step 4, then the inductance value L and the quality factor Q corresponding to the present iteration are calculated using formula (4), and the values calculated in formula (7) and (8) are used as the objective function value in the present iteration. Then, the NSGA-II algorithm is used to perform Pareto optimization on the objective function. In particular, in the present method, the crossover probability of the NSGA-II algorithm is 0.9, the mutation probability is the reciprocal of the number of unknown variables, that is, 0.33, and the population size is 30.

[0082] Example 6

[0083] In the present method, the number of iterations is determined by the control variable method. Specifically, the crossover probability, mutation probability and population size of the NSGA-II algorithm are fixed, only the number of iterations is changed, and the dominance relationship between the Pareto solution sets corresponding to different numbers of iterations is compared to determine the optimal number of iterations. Specifically, the test frequency is 5 GHz, the inductance design value is 0.94 nH, and the number of iterations is selected as 30, 50 and 70 respectively, and each group of data is tested 5 times to take the optimal value. The optimal values of the three groups of data are compared as shown in FIG. 5. As can be seen from the figure, the solution set corresponding to 50 iterations has a dominance relationship with the solution set corresponding to 30 iterations, and the solution set corresponding to 70 iterations does not have a clear dominance relationship with the solution set corresponding to 50 iterations. Therefore, in the present method, the number of iterations is 50. Figure 5

[0084] The modeling and optimization time is statistically analyzed as shown in Table 2.

[0085] Table 2 Modeling and optimization time statistics

[0086] Step Number of iterations / loops Time (min) Vector fitting 200 2.43 ANN / 1.43 Optimization process (population size = 30) 50 29.16 Finite element simulation 1 2.06

[0087] As can be seen from Table 2, the total optimization time of the present method is about 33 minutes. As a comparison, the finite element simulation requires 2.06 minutes for a single time, and if the same NSGA-II algorithm is used for the optimization process with a population size of 30 and an iteration number of 50, it will take several days. Therefore, the present method is highly efficient. The solutions in the Pareto front are all optimal solutions without dominance relationship, after obtaining the Pareto front, the designer can select one solution as the design parameter according to the actual work needs, and then carry out subsequent design work. Each of the above steps is open, and by modifying the parameters of the algorithm, the optimization of passive microwave devices other than three-dimensional integrated inductors can be compatible.​

Claims

1. A method for multi-objective optimization of a TSV-based three-dimensional integrated inductor, the method comprising: Specifically comprising the following steps: Step 1, a three-dimensional inductor geometric model is established, and geometric parameters to be optimized are determined; Step 2, the inductor structure determined in step 1 is sampled, and the data obtained by sampling is divided into a training set and a test set; Step 3, numerical simulation is performed on the sampled data of step 2 to obtain the admittance parameter Y corresponding to each set of geometric parameters 11 , and then the Y 11 parameters are reduced and combined to output the combined result y; Step 4, the structure of an artificial neural network is determined; Step 5, according to the network structure of step 4, a target function of multi-objective optimization is determined.

2. The TSV-based three-dimensional integrated inductor multi-objective optimization method of claim 1, wherein: In step 1, the three-dimensional inductor model structure is: including through silicon via TSV and redistribution layer RDL, wherein the RDL is divided into upper RDL and lower RDL, wherein the lower RDL is inclined clockwise at an angle r, and the upper RDL and the lower RDL are interconnected by the TSV; The geometric parameters to be optimized are: the length l and the width w of the RDL, and the included angle r between the upper RDL and the lower RDL, wherein the distance from the geometric center of the TSV to the edge of the RDL is fixed as a constant; the to-be-determined geometric parameters are combined into a vector x, defined as x = [r l w] T (1).

3. The TSV-based three-dimensional integrated inductor multi-objective optimization method of claim 2, wherein: In step 2, the Latin hypercube sampling method is used to sample the geometric parameters of the three-dimensional inductor, and the sampled data is divided into a training set and a test set.

4. The TSV-based three-dimensional integrated inductor multi-objective optimization method of claim 3, wherein: The specific process of step 3 is: Step 3.1, numerical simulation is performed on the sampling data of Step 2 using Ansys HFSS to obtain the admittance parameter Y corresponding to each set of geometric parameters 11 ; Step 3.2, vector fitting method for Y 11 The parameters are reduced as shown in equation (2) below: where s represents a complex frequency, c n represents a residue, a n represents a pole, H represents a frequency response, i.e., Y 11 a parameter, N represents an order of the transfer function, and d and h represent remainders; Step 3.3, the parameters processed in step 3.2 are combined, and the output parameter y is output, and the specific process is as follows: y = Re[a1...a n c1...c n d h] T + Im[a1...a n c1...c n d h] T (3).

5. The TSV-based three-dimensional integrated inductor multi-objective optimization method of claim 4, wherein: In step 3.1, the sweep range of numerical simulation is 1GHz-100GHz, and the step is 0.1Ghz.

6. The TSV-based three-dimensional integrated inductor multi-objective optimization method of claim 4, wherein: In step 4, a multilayer perceptron MLP is used as the structure of the artificial neural network, each layer of neurons is a fully connected layer, GELU is used as the activation function, Adam is used as the optimizer, and mean square error MSE is used as the loss function.

7. The TSV-based three-dimensional integrated inductor multi-objective optimization method of claim 6, wherein: In step 4, the x of the test set data is used to make a prediction and the predicted y is put back into the pole-residue transfer function to get the predicted Y 11 The Y in the test set is converted to a curve; the Y in the test set is converted to a curve by the following equation (4) respectively 11 The true value and the predicted Y 11 The true value and the predicted L and Q of the inductance value L and the quality factor Q in the test set are converted Subsequently, the error analysis was performed on the predicted values and the true values of L and Q, respectively, and the average value of the mean square error of all test sets was taken as the error, the inductance value error E L and the quality factor error E Q defined by the following formula (5) and formula (6), respectively, and the layer number corresponding to the minimum error when the test was completed was taken as the final structure of ANN: In the formula, m is the number of test sets, length(·) represents the dimension of L and Q, i represents the test set number, j represents the sampling point number, respectively represent the predicted values of the inductance L and Q.

8. The TSV-based three-dimensional integrated inductor multi-objective optimization method of claim 7, wherein: The specific process of step 5 is: the target function of multi-objective optimization is to minimize the error between the inductance value and the design value and maximize the quality factor, which is specifically as follows: F L = |L - L * | (8) where L represents the actual value of the inductance, Q represents the quality factor predicted by the ANN model, and L * represents the design value of the inductance.

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