An Optimization Method for Peak Stress of Conical TSV Arrays Based on ANFIS

Abstract

The present invention discloses a method for optimizing the peak stress of a tapered TSV array based on ANFIS, including: establishing a finite element model of the thermal stress field of the tapered TSV array; performing finite element simulations according to the orthogonal design scheme to obtain a database including the design parameters of the tapered TSV array and the peak stress; establishing an optimization model of the peak stress of the tapered TSV array based on ANFIS and training it using the database to describe the mapping relationship between the design parameters of the TSV array and the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section; constructing a multi-objective optimization function for the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array; and optimizing the design parameters of the TSV array using a population optimization algorithm. The present invention uses the ANFIS optimization algorithm to optimize the design parameters of TSVs in three-dimensional integrated circuits, which can efficiently determine the design size parameters of TSVs, improve the design efficiency of integrated circuits, and shorten the development cycle of integrated circuit chips.

Description

Technical Field

[0001] The present invention belongs to the technical field of semiconductor packaging, and particularly relates to a method for optimizing the peak stress of a tapered TSV array based on ANFIS (Adaptive NeuroFuzzy Inference System). Background Art

[0002] Integrated circuits have become the basis for realizing informatization and intelligence in all walks of life. As one of the key ways to break Moore's law in the future, three-dimensional integrated circuits have been highly pursued by researchers in recent years. The development of three-dimensional integrated circuits depends more on the design experience of researchers and the repeated iterative simulation verification of software. Designers continuously adjust the size parameters of devices in the integrated circuit to obtain the desired performance indicators of circuit modules. This time-consuming and laborious design method reduces the design efficiency of integrated circuits, increases the R & D cost, and prolongs the development cycle of integrated circuit chips. Summary of the Invention

[0003] In order to solve the above problems existing in the prior art, the present invention provides a method for optimizing the peak stress of a tapered TSV array based on ANFIS. The technical problems to be solved by the present invention are realized through the following technical solutions:

[0004] The present invention provides a method for optimizing the peak stress of a tapered TSV array based on ANFIS, including:

[0005] S1: Establish a finite element model of the thermal stress field of the tapered TSV array;

[0006] S2: Conduct finite element simulations according to the orthogonal design scheme to obtain a database including the design parameters of the tapered TSV array and the peak stress;

[0007] S3: Establish an optimization model for the peak stress of the tapered TSV array based on ANFIS and train it using the database to describe the mapping relationship between the design parameters of the TSV array and the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section;

[0008] S4: Construct a multi-objective optimization function for the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array;

[0009] S5: According to the mapping relationship and the multi-objective optimization function, use the population optimization algorithm to optimize the design parameters of the TSV array to achieve intelligent optimization of the peak stress of the TSV array.

[0010] In one embodiment of the present invention, the design parameters of the tapered TSV array include the radius of the upper surface of the TSV, the radius of the lower surface of the TSV, the height of the TSV, the pitch of the TSV, the thickness of the insulating layer, and the thickness of the buffer layer; the peak stress includes the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the mid-section.

[0011] In one embodiment of the present invention, the S3 includes:

[0012] S3.1: Construct an adaptive neuro-fuzzy inference system, which includes a fuzzification layer, a rule strength release layer, a normalization layer, a defuzzification layer, and an output layer;

[0013] S3.2: Use the database to train the adaptive neuro-fuzzy inference system, update the antecedent parameters using the backpropagation algorithm, calculate the consequent parameters using the least squares estimation method, and obtain the trained adaptive neuro-fuzzy inference system to describe the mapping relationship between the TSV array design parameters and the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the mid-section.

[0014] In one embodiment of the present invention, the S3.1 includes:

[0015] S3.11: Fuzzification layer, fuzzify a set of input TSV array design parameters and calculate the membership degree to obtain the fuzziness result and membership degree value of each TSV array design parameter;

[0016] S3.12: Rule strength release layer, multiply the membership degree values of the set of TSV array design parameters to obtain the output result of the rule strength release layer;

[0017] S3.13: Normalization layer, normalize the credibility of the i-th rule to obtain the normalized credibility of the i-th rule;

[0018] S3.14: Defuzzification layer, use the normalized credibility to obtain the defuzzified result;

[0019] S3.15: Output layer, calculate the sum of the defuzzified results of a set of input TSV array design parameters.

[0020] In one embodiment of the present invention, in the S3.11, the fuzziness result is expressed as:

[0021]

[0022] where α, β, and γ are antecedent parameters, and x represents the input TSV array design parameter;

[0023] The membership degree calculation formula for the TSV array design parameter is:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Among them, x, y, z, u, v, and q respectively represent a set of input TSV upper surface radius, TSV lower surface radius, TSV height, TSV pitch, buffer layer thickness, and insulation layer thickness. And respectively represent the membership functions of the TSV upper surface radius, TSV lower surface radius, TSV height, TSV pitch, buffer layer thickness, and insulation layer thickness.

[0031] In an embodiment of the present invention, in the said S3.11, the defuzzification formula is expressed as:

[0032]

[0033] Among them, a i , b i , c i , d i , e i , h i and g i represent the consequent parameters, represents the credibility of the i-th rule after normalization.

[0034] In an embodiment of the present invention, using the backpropagation algorithm to update the antecedent parameters includes:

[0035] Using the backpropagation algorithm to update the antecedent parameter α, the update formula is:

[0036]

[0037] Among them, α ij (k) represents the antecedent parameter corresponding to the j-th input parameter under the i-th rule in the k-th backward iteration, and α ij (k + 1) represents the antecedent parameter corresponding to the j-th input parameter under the i-th rule in the (k + 1)-th backward iteration, η is the learning rate, and E is the cost function;

[0038]

[0039] Among them, a i , b i , c i , d i , e i , h i and g i represent the consequent parameters, w i represents the confidence of the i-th rule, f o is the target output of the cost function, f is the actual output of the cost function, and μ ij represents the membership degree of the j-th parameter of the i-th rule;

[0040] Update the antecedent parameters β and γ using the backpropagation algorithm.

[0041] In an embodiment of the present invention, the consequent parameters are calculated using the least squares estimation method, including:

[0042] Obtain the linear expression of the consequent parameters:

[0043]

[0044] Among them, W = [a1 b1 c1 d1 e1 h1 g1…a6 b6 c6 d6 e6 h6 g6] T , after the antecedent parameters are determined, solve for W using the least squares method:

[0045] W = (X T X) -1 X T f.

[0046] In an embodiment of the present invention, the S4 includes:

[0047] Construct a multi-objective optimization function for the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress in the middle section of the TSV array:

[0048] J = θ(LT - LT des ) 2 + μ(TT - TT des ) 2 + ρ(RT - RT des ) 2

[0049] Among them, LT, TT, and RT respectively represent the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress in the middle section of the TSV array, LT des , TT des and RT desrespectively represent the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the mid-section of the expected TSV array, and θ, μ, and ρ respectively represent the optimization weight coefficients of the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the mid-section of the TSV array.

[0050] In one embodiment of the present invention, S5 includes:

[0051] S5.1: Initialize the parameters of the particle swarm optimization algorithm;

[0052] S5.2: According to the original TSV array design parameters, use the trained peak stress optimization model of the conical TSV array based on ANFIS to predict the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the mid-section of the TSV array;

[0053] S5.3: According to the constructed multi-objective optimization function, use the peak stress optimization model of the conical TSV array based on ANFIS to optimize the TSV array design parameters;

[0054] S5.4: Determine whether the optimal TSV array design parameters are obtained according to the finite element model. If so, complete the optimization of the peak stress of the TSV array; otherwise, return to step S5.2.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] Aiming at the problems that the existing integrated circuit research and development overly rely on the experience of designers and has low efficiency, according to the formulated TSV design parameter optimization strategy in three-dimensional integrated circuits, the ANFIS optimization algorithm is used to optimize the TSV design parameters in three-dimensional integrated circuits, which can efficiently determine the design size parameters of three-dimensional integrated circuit devices, improve the integrated circuit design efficiency, reduce the research and development cost, and shorten the development cycle of integrated circuit chips. The invention and popularization and application of this method have important engineering significance for reducing the research and development cost of three-dimensional integrated circuit chips and shortening their development cycle.

[0057] The following will further elaborate on the present invention in conjunction with the drawings and embodiments. Description of the Drawings

[0058] Figure 1 is a flowchart of a method for optimizing the peak stress of a conical TSV array based on ANFIS provided by an embodiment of the present invention;

[0059] Figure 2 is a schematic structural diagram of a finite element model of the thermal stress field of a conical TSV array provided by an embodiment of the present invention;

[0060] Figure 3 is a structural diagram of a peak stress optimization model of a conical TSV array based on ANFIS provided by an embodiment of the present invention;

[0061] Figures 4a to 4c It is the comparison and verification of the intelligent optimization value and the finite element model value of the peak stress of the TSV array. Specific embodiments

[0062] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following, in combination with the accompanying drawings and specific embodiments, will detail a method for optimizing the peak stress of a conical TSV array based on ANFIS proposed according to the present invention.

[0063] The foregoing and other technical contents, features, and effects of the present invention can be clearly presented in the following detailed description of the specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the intended purpose can be obtained. However, the accompanying drawings are only for reference and illustration purposes and are not used to limit the technical solutions of the present invention.

[0064] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including", or any other variant is intended to cover non-exclusive inclusion, so that an article or device including a series of elements not only includes those elements but also includes other elements not explicitly listed. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the article or device including the said element.

[0065] Please refer to Figure 1 , Figure 1 which is a flowchart of a method for optimizing the peak stress of a conical TSV array based on ANFIS provided by an embodiment of the present invention. The method includes:

[0066] S1: Establish a finite element model of the thermal stress field of the conical TSV array.

[0067] Please refer to Figure 2 , Figure 2 which is a schematic structural diagram of a finite element model of the thermal stress field of a conical TSV array provided by an embodiment of the present invention. Specifically, a heat flux (heat source) is set on the top layer of the TSV array, so that heat propagates along the TSVs respectively.

[0068] S2: Conduct finite element simulation experiments according to the orthogonal design scheme to obtain a database including the design parameters and peak stress of the conical TSV array.

[0069] The database includes the design parameters and peak stresses of multiple groups of tapered TSVs. The design parameters of the tapered TSV array include the upper surface radius of the TSV, the lower surface radius of the TSV, the height of the TSV, the pitch of the TSVs, the thickness of the insulating layer, and the thickness of the buffer layer. The peak stresses include the upper surface peak stress, the lower surface peak stress, and the peak stress at the mid-section. Specifically, in this step, a database is obtained through simulation in the COMSOL simulation software using the aforementioned design parameters.

[0070] In this embodiment, the database includes 49 sets of data. Each set of data includes the upper surface radius of the TSV, the lower surface radius of the TSV, the height of the TSV, the pitch of the TSVs, the thickness of the insulating layer, the thickness of the buffer layer, and the corresponding upper surface peak stress, lower surface peak stress, and peak stress at the mid-section of a tapered TSV.

[0071] S3: Establish an optimization model for the peak stress of the tapered TSV array based on ANFIS and train it using the database to describe the mapping relationship between the design parameters of the TSV array and the upper surface peak stress, the lower surface peak stress, and the peak stress at the mid-section.

[0072] In this step, a peak stress database (upper surface peak stress, lower surface peak stress, and peak stress at the mid-section) is obtained through simulation in the COMSOL software based on a database of the design parameters of the tapered TSV array (upper surface radius of the TSV, lower surface radius of the TSV, height of the TSV, pitch of the TSVs, thickness of the insulating layer, and thickness of the buffer layer). Then, ANFIS training is performed using the design parameters of the tapered TSV array and the corresponding peak stresses in the database to establish a function mapping model between the design parameters of the TSV array and the upper surface peak stress, the lower surface peak stress, and the peak stress at the mid-section.

[0073] Specifically, in this step, the function mapping model for training and establishing the mapping relationship between the design parameters of the TSV array and the peak stress is trained using the backpropagation algorithm based on the database of the design parameters of the TSV array and the peak stress.

[0074] In this embodiment, please refer to Figure 3 , Figure 3 is the structural diagram of an optimization model for the peak stress of a tapered TSV array based on ANFIS provided by an embodiment of the present invention. This step S3 includes:

[0075] S3.1: Construct an adaptive neuro-fuzzy inference system, which includes a fuzzification layer, a rule strength release layer, a normalization layer, a defuzzification layer, and an output layer.

[0076] Specifically, constructing this adaptive neuro-fuzzy inference system includes the following steps:

[0077] S3.11: Fuzzification layer, which fuzzifies the input TSV array design parameter variables and calculates the membership degrees, obtaining the fuzziness results and membership degree results of each TSV array design parameter variable. The variables include the upper surface radius of the TSV, the lower surface radius of the TSV, the height of the TSV, the pitch of the TSVs, the thickness of the buffer layer, and the thickness of the insulating layer. In the embodiments of the present invention, a triangular membership function is selected for the fuzzification of the design parameters, and the output result of the fuzzification can be expressed as:

[0078]

[0079] where α, β, and γ are the antecedent parameters, x represents the input TSV array design parameter, and the membership degree calculation formula for the input TSV array design parameter is:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] where x, y, z, u, v, and q respectively represent a set of input upper surface radius of the TSV, lower surface radius of the TSV, height of the TSV, pitch of the TSVs, thickness of the buffer layer, and thickness of the insulating layer, and respectively represent the membership functions of the upper surface radius of the TSV, lower surface radius of the TSV, height of the TSV, pitch of the TSVs, thickness of the buffer layer, and thickness of the insulating layer, and the number of these six membership functions is 2 for each, The superscript 1 in represents that this result is the output result of the first layer, i.e., the fuzzification layer, and the subscript i represents a set of discrete numbers. For example, if there is a set of data for the upper surface radius, the subscript represents the number in this set of data.

[0087] S3.12: Rule strength release layer, which multiplies the membership degree values of a set of input TSV array design parameters to obtain the output result of the rule strength release layer, which can be expressed as:

[0088]

[0089] where w i represents the credibility of the i-th rule.

[0090] S3.13: Normalization layer, which normalizes the confidence of the \(i\)-th rule. The normalization formula is:

[0091]

[0092] where represents the confidence of the \(i\)-th rule after normalization;

[0093] S3.14: Defuzzification layer, which obtains the defuzzified output result using the normalized confidence. The defuzzification formula can be expressed as:

[0094]

[0095] where \(a\) i , \(b\) i , \(c\) i , \(d\) i , \(e\) i , \(h\) i and \(g\) i represent the consequent parameters.

[0096] S3.15: Output layer, which calculates the sum of the defuzzified results of a set of TSV array design parameters as input. The calculation formula is:

[0097]

[0098] S3.2: Train the adaptive neuro-fuzzy inference system using the database, update the antecedent parameters using the backpropagation algorithm, calculate the consequent parameters using the least squares estimation method, and obtain the trained adaptive neuro-fuzzy inference system to describe the mapping relationship between the TSV array design parameters and the peak stresses on the upper surface, lower surface, and middle cross-section.

[0099] Specifically, in this step, the ANFIS model is trained using the database obtained from the simulation in step S2, and the hybrid learning algorithm is used for training. The antecedent parameters are updated using the backpropagation algorithm, and the consequent parameters are calculated using the least squares estimation method. Specifically,

[0100] Updating the antecedent parameters using the backpropagation algorithm includes: The antecedent parameters are updated using the backpropagation algorithm, and the update formula is:

[0101]

[0102] where \(\alpha\) ij (k) represents the antecedent parameter corresponding to the \(j\)-th input parameter under the \(i\)-th rule in the \(k\)-th backward iteration, and \(\alpha\) ij(k + 1) represents the antecedent parameter corresponding to the j-th input parameter under the i-th rule in the (k + 1)-th backward iteration. η is the learning rate, and E is the cost function, which can be expressed as:

[0103]

[0104] where f o is the target output of the cost function, and f is the actual output of the cost function, which can be expressed as:

[0105]

[0106] where

[0107] It should be noted that the target output and the actual output are two input parameters of the cost function. At this time, they correspond to the expected peak stress and the peak stress actually obtained through finite element simulation in step S2, respectively, which are the definitions of the two parameters of the cost function. For example, if the optimal data obtained through optimization design is 90, then the target output we hope for is 90. However, the actual output may be 95, and then we calculate this cost error through this cost function.

[0108] Furthermore, according to the chain rule of partial derivatives, we can obtain:

[0109]

[0110] where

[0111] and is determined according to the specific membership function, and the final gradient of the cost function can be expressed as:

[0112]

[0113] where μ ij represents the membership degree of the j-th parameter of the i-th rule.

[0114] Similarly, the antecedent parameters β and γ are updated in the same way.

[0115] Furthermore, the least squares estimation method is used to calculate the consequent parameters, including: The final output of ANFIS can be expressed as a linear expression of the consequent parameters:

[0116]

[0117] The above formula can be expressed in matrix form:

[0118] f = XW (18)

[0119] Among them, W = [a1 b1 c1 d1 e1 h1 g1 … a6 b6 c6 d6 e6 h6 g6] T , after the current parameter is determined, W can be solved by the least squares method:

[0120] W = (X T X) -1 X T f(19)

[0121] S4: Construct a multi-objective optimization function for the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array.

[0122] Specifically, the expression of the multi-objective optimization function for the peak stress of the TSV array is as follows:

[0123] J = θ(LT - LT des ) 2 + μ(TT - TT des ) 2 + ρ(RT - RT des ) 2 (20)

[0124] Among them, J represents the multi-objective optimization criterion for the peak stress of the TSV array, LT, TT, and RT respectively represent the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array, LT des , TT des and RT des respectively represent the desired peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array, and θ, μ, and ρ respectively represent the optimization weight coefficient of the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array.

[0125] S5: Use the population optimization algorithm to optimize the design parameters of the TSV array to achieve intelligent optimization of the peak stress of the TSV array.

[0126] Specifically, step S5 of this embodiment includes the following steps:

[0127] S5.1: Initialize the parameters of the particle swarm optimization algorithm;

[0128] S5.2: According to the original TSV array design parameters, use the trained peak stress optimization model of the conical TSV array based on ANFIS to predict the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array;

[0129] S5.3: Optimize the design parameters of the TSV array by using the ANFIS-based peak stress optimization model of the conical TSV array according to the constructed multi-objective optimization function;

[0130] S5.4: Judge whether the optimal TSV array design parameters are obtained according to the finite element model. If so, complete the intelligent optimization of the peak stress of the TSV array; otherwise, return to step S5.2 and continue to execute.

[0131] It should be noted that the basic idea of the particle swarm optimization algorithm is that each particle searches for the optimal solution separately in the search space, which is recorded as the current individual extreme value. The individual extreme value is shared with other particles in the whole particle swarm, and the optimal individual extreme value is found as the current global optimal solution of the whole particle swarm. Therefore, the implementation process of the particle swarm optimization algorithm is relatively simple and easy, and there is no need to adjust too many parameters. In the framework of the particle swarm optimization algorithm, this embodiment of the invention aims at the peak stress of the TSV array and proposes a simple and effective intelligent optimization method for the design parameters of the 3D integrated circuit TSV, providing an efficient method and approach for the research of the annealing technology in the 3D integrated circuit.

[0132] Aiming at the problems that the existing integrated circuit R & D overly relies on the experience of designers and has low efficiency, according to the formulated optimization strategy for the TSV design parameters in the 3D integrated circuit, this invention uses the ANFIS optimization algorithm to optimize the design parameters of the TSV in the 3D integrated circuit, which can efficiently determine the design size parameters of the 3D integrated circuit devices, improve the integrated circuit design efficiency, reduce the R & D cost, and shorten the development cycle of the integrated circuit chip. The invention and popularization of this method have important engineering significance for reducing the R & D cost of the 3D integrated circuit chip and shortening its development cycle.

[0133] Embodiment 2

[0134] Taking the finite element model of embedding 4x4 TSVs in the 3D integrated circuit as an example in this embodiment, Cu is selected as the conductive material for the TSV, Si is the filling material, SiO2 is the insulating layer material, and a buffer layer material Ti is added between Cu and SiO2.

[0135] The implementation details of the peak stress optimization method of the conical TSV array proposed in the embodiment of this invention are introduced in detail. The method includes:

[0136] Step 1: Establish a finite element model of the thermal stress field of the conical TSV array.

[0137] The design parameters of the finite element model include the upper surface radius of the TSV, the lower surface radius of the TSV, the height of the TSV, the TSV pitch, the thickness of the insulating layer, and the thickness of the buffer layer. Its performance indicators mainly include the peak stress on the upper surface of the TSV, the peak stress on the lower surface, and the peak stress on the middle cross-section.

[0138] Step 2: According to the orthogonal design scheme, perform finite element simulation experiments to obtain a database including TSV array design parameters and peak stresses.

[0139] Step 3: Establish an adaptive neuro-fuzzy inference system model and train it using the database to obtain a trained adaptive neuro-fuzzy inference system model to describe the mapping relationship between TSV array design parameters and peak stresses on the upper surface, peak stresses on the lower surface, and peak stresses on the middle cross-section.

[0140] In this embodiment, the neural network model (i.e., the adaptive neuro-fuzzy inference system model) describing the mapping relationship between TSV array design parameters and peak stresses of the three-dimensional finite element model is obtained by COMSOL software combined with the orthogonal design method to acquire simulation experiment data and trained using the backpropagation algorithm. This neural network model includes a fuzzification layer, a rule firing layer, a normalization layer, a defuzzification layer, and an output layer.

[0141] In step 3, training and establishing the mapping relationship model between TSV array design parameters and peak stresses is based on the database of TSV array design parameters and peak stresses and trained using the backpropagation algorithm. Use ANFIS to construct the mapping relationship between TSV array design parameters and peak stresses. According to the multi-objective optimization function of peak stresses, use the particle swarm optimization algorithm to optimize the parameter values of the upper surface radius, lower surface radius, TSV height, TSV pitch, insulation layer thickness, and buffer layer thickness of the TSV to be 5.27806μm, 2.696μm, 25.42445μm, 42μm, 2.2μm, and 0.4μm respectively.

[0142] Step 4: Construct a multi-objective optimization function for peak stresses on the upper surface, lower surface, and middle cross-section of the TSV array.

[0143] The design performance indicators of the three-dimensional finite element model mainly include peak stresses on the upper surface, lower surface, and middle cross-section of the TSV array. The desired peak stresses on the upper surface of the TSV array are 600 MPa, the peak stresses on the lower surface are 450 MPa, and the peak stresses on the middle cross-section are 550 MPa. The optimization criterion for the design parameters of the three-dimensional integrated circuit TSV array can be expressed as:

[0144] J = θ(LT - LT des ) 2 + μ(TT - TT des ) 2 + ρ(RT - RT des ) 2

[0145] Among them, J represents the multi-objective optimization criterion for the peak stress of the TSV array, LT, TT, and RT represent the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the middle cross-section of the TSV array, respectively. LT des , TT des and RT des represent the expected peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the middle cross-section of the TSV array, respectively. θ, μ, and ρ represent the optimization weight coefficients of the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the middle cross-section of the TSV array, respectively.

[0146] Step 5: Optimize the design parameters of the TSV array by using a population optimization algorithm to achieve the intelligent optimization of the peak stress of the TSV array.

[0147] The particle swarm optimization algorithm is a commonly used population optimization algorithm, which has the advantages of simple structure and easy implementation. In the embodiment of the present invention, the established ANFIS and the optimization criterion are integrated into the particle swarm optimization algorithm, and the design parameters of the TSV array in the three-dimensional integrated circuit are optimized by using the particle swarm optimization algorithm with linearly decreasing inertia weight. The particle swarm optimization algorithm with linearly decreasing inertia weight can be described as:

[0148] v i (t + 1) = wv i (t) + c1r1(p i -x i (t)) + c2r2(p g -x i (t))

[0149] x i (t + 1) = x i (t) + v i (t + 1)

[0150]

[0151] Among them, t represents the t-th iteration, x i and v i represent the position vector and velocity vector of the i-th particle, respectively. w represents the inertia weight, p i represents the local optimal position, p g represents the global optimal position, c1 and c2 are constants, r1 and r2 are random numbers between [0, 1], iter represents the current iteration number, iter max represents the maximum iteration number, w max and w min represent the maximum value and minimum value of the inertia weight, respectively. The process of optimizing the design parameters of the TSV array in the three-dimensional integrated circuit by using the particle swarm optimization algorithm with linearly decreasing inertia weight is as follows:

[0152] (1) Initialize the parameters of the particle swarm optimization algorithm;

[0153] (2) According to the TSV array design parameters, use the constructed ANFIS to predict the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle section of the TSV array;

[0154] (3) According to the constructed multi-objective optimization function of the TSV array peak stress, use the particle swarm optimization algorithm to optimize the TSV array design parameters;

[0155] (4) Determine whether the optimal TSV array design parameters are obtained. If so, complete the intelligent optimization of the TSV array peak stress. Otherwise, return to step (2) and continue to execute.

[0156] In this embodiment, according to the desired performance indicators, the above-mentioned method for optimizing the peak stress of the tapered TSV array is used to optimize the design parameters of the TSV array in the three-dimensional integrated circuit. The optimized upper surface radius, lower surface radius, TSV height, TSV pitch, buffer layer thickness, and insulation layer thickness of the TSV are 5.278064 μm, 2.695968 μm, 25.42445 μm, 42 μm, 2.2 μm, and 0.4 μm respectively. According to the optimized TSV array design parameters, the optimized peak stress on the upper surface of the TSV is 600 MPa, the peak stress on the lower surface is 450 MPa, and the peak stress on the middle section is 550 MPa. According to the optimized TSV array design parameters, use the COMSOL software for finite element verification. The experimental results are as Figures 4a to 4c shown, Figures 4a to 4c is the comparison and verification between the intelligent optimization value and the finite element model value of the TSV array peak stress. Among them, the peak stress values on the upper surface, lower surface, and middle section of the TSV array are 590.96 MPa ( Figure 4a ), 429.56 MPa ( Figure 4b ), and 535.64 MPa ( Figure 4c ), almost reaching the desired performance indicators, which shows that the method proposed in this embodiment of the present invention can effectively optimize the design parameters of the TSV array in the three-dimensional integrated circuit and realize the optimized design of the TSV array.

[0157] From the above results, it can be found that the method proposed in this embodiment of the present invention can simply and effectively optimize the TSV array in the three-dimensional integrated circuit, shorten the R & D cycle of the integrated circuit, and provide a reliable way for realizing the efficient design of the integrated circuit.

[0158] Another embodiment of the present invention provides a storage medium, in which a computer program is stored, and the computer program is used to execute the steps of the ANFIS-based peak stress optimization method for the tapered TSV array in the above embodiment. Another aspect of the present invention provides an electronic device, including a memory and a processor. A computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the ANFIS-based peak stress optimization method for the tapered TSV array as described in the above embodiment are implemented. Specifically, the integrated modules implemented in the form of software function modules can be stored in a computer-readable storage medium. The above software function modules are stored in a storage medium, including several instructions for causing an electronic device (which may be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical discs that can store program codes.

[0159] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. A peak stress optimization method for conical TSV arrays based on ANFIS, characterized in that, Including: S1: Establish a finite element model of the thermal stress field of the conical TSV array; S2: Conduct finite element simulations according to the orthogonal design scheme to obtain a database including the design parameters of the conical TSV array and the peak stress; S3: Establish an optimization model for the peak stress of the conical TSV array based on ANFIS and train it using the said database to describe the mapping relationship between the TSV array design parameters and the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section; The said S3 includes: S3.1: Construct an adaptive neuro-fuzzy inference system, which includes a fuzzification layer, a rule strength release layer, a normalization layer, a defuzzification layer, and an output layer; The said S3.1 includes: S3.11: Fuzzification layer, which fuzzifies a set of input TSV array design parameters and calculates the membership degree to obtain the fuzziness result and membership degree value of each TSV array design parameter; The fuzziness result is expressed as: where α, β, and γ are antecedent parameters, and x represents the input TSV array design parameter; The membership degree calculation formula for the TSV array design parameter is: where x, y, z, u, v, and q respectively represent a set of input TSV upper surface radius, TSV lower surface radius, TSV height, TSV pitch, buffer layer thickness, and insulation layer thickness. and respectively represent the membership functions of the TSV upper surface radius, TSV lower surface radius, TSV height, TSV pitch, buffer layer thickness, and insulation layer thickness. S3.12: Rule strength release layer, which multiplies the membership degree values of the set of TSV array design parameters to obtain the output result of the rule strength release layer; S3.13: Normalization layer, which normalizes the credibility of the i-th rule to obtain the normalized credibility of the i-th rule; S3.14: Defuzzification layer, which obtains the defuzzified result using the normalized credibility; S3.15: Output layer, which calculates the sum of the defuzzified results of a set of input TSV array design parameters; S3.2: Train the adaptive neuro-fuzzy inference system using the said database, update the antecedent parameters using the backpropagation algorithm, calculate the consequent parameters using the least squares estimation method, and obtain the trained adaptive neuro-fuzzy inference system to describe the mapping relationship between the TSV array design parameters and the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section; S4: Construct a multi-objective optimization function for the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array; S5: According to the said mapping relationship and the multi-objective optimization function, use the population optimization algorithm to optimize the TSV array design parameters to achieve the intelligent optimization of the TSV array peak stress.

2. The peak stress optimization method for the conical TSV array based on ANFIS according to claim 1, characterized in that The design parameters of the conical TSV array include the upper surface radius of the TSV, the lower surface radius of the TSV, the height of the TSV, the pitch of the TSV, the thickness of the insulating layer, and the thickness of the buffer layer; the peak stress includes the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section.

3. The peak stress optimization method for the conical TSV array based on ANFIS according to claim 1, characterized in that, In the said S3.11, the defuzzification formula is expressed as: Among them, a i , b i , c i , d i , e i , h i and g i represent the consequent parameters, represents the confidence of the i-th rule after normalization.

4. The peak stress optimization method for the conical TSV array based on ANFIS according to claim 1, wherein Updating the antecedent parameters using the backpropagation algorithm includes: Updating the antecedent parameter α using the backpropagation algorithm, and the update formula is: where α ij (k) represents the antecedent parameter corresponding to the j-th input parameter under the i-th rule in the k-th backward iteration, and α ij (k + 1) represents the antecedent parameter corresponding to the j-th input parameter under the i-th rule in the (k + 1)-th backward iteration, and α ij represents the antecedent parameter corresponding to the j-th input parameter under the i-th rule, η is the learning rate, and E is the cost function; Among them, a i , b i , c i , d i , e i , h i and g i represent the consequent parameters, w i represents the confidence of the i-th rule, f o is the target output of the cost function, f is the actual output of the cost function, μ ij represents the membership degree of the j-th parameter of the i-th rule; Updating the antecedent parameters β and γ using the backpropagation algorithm.

5. The peak stress optimization method for the conical TSV array based on ANFIS according to claim 4, wherein Calculating the consequent parameters using the least squares estimation method includes: Obtaining the linear expression of the consequent parameters: Among them, W = [a1 b1 c1 d1 e1 h1 g1…a6 b6 c6 d6 e6 h6 g6] T , after the current parameter is determined, use the least squares method to solve for W: W = (X T X) -1 X T f.

6. The peak stress optimization method for the tapered TSV array based on ANFIS according to claim 1, wherein The said S4 includes: Constructing a multi-objective optimization function for the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress on the middle cross-section of the TSV array: J = θ(LT - LT des ) 2 + μ(TT - TT des ) 2 + ρ(RT - RT des ) 2 where LT, TT, and RT respectively represent the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the middle cross-section of the TSV array, and LT des , TT des , and RT des respectively represent the desired peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the middle cross-section of the TSV array, and θ, μ, and ρ respectively represent the optimization weight coefficients of the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the middle cross-section of the TSV array.

7. The peak stress optimization method for the conical TSV array based on ANFIS according to claim 1, characterized in that The said S5 includes: S5.1: Initialize the parameters of the particle swarm optimization algorithm; S5.2: According to the original TSV array design parameters, use the trained ANFIS-based conical TSV array peak stress optimization model to predict the peak stress on the upper surface, the peak stress on the lower surface, and the peak stress at the middle section of the TSV array; S5.3: According to the constructed multi-objective optimization function, use the ANFIS-based conical TSV array peak stress optimization model to optimize the TSV array design parameters; S5.4: Determine whether the optimal TSV array design parameters are obtained according to the finite element model. If so, complete the optimization of the TSV array peak stress. Otherwise, return to step S5.2.

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