Multi-target prediction method for thermal fatigue life and electrical performance of wire bonding

Abstract

The invention discloses a multi-target prediction method for wire bonding thermal fatigue life and electrical performance, which belongs to the technical field of microwave interconnection and comprises the following steps: determining physical property parameters and structural parameters of a wire bonding interconnection structure; obtaining a mathematical description of a lead bonding form; establishing a thermal analysis model and a structure-electromagnetic analysis model of the lead bonding interconnection structure; comprehensive experiments are designed, and various performance indexes are obtained; establishing a mapping relation model from the geometric parameters of the lead to each performance index; and establishing a thermal fatigue life prediction model and completing reliability life prediction. The method can be used for carrying out accurate parameterization representation on a lead bonding interconnection structure model, multi-target prediction of the lead bonding thermal fatigue life and the electrical performance is rapidly achieved, and structural design and optimization of lead bonding packaging are guided.

Description

Technical Field

[0001] The invention relates to the field of microwave interconnection technology, and in particular to a multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding. Background Art

[0002] With the continuous development of semiconductor technology, electronic equipment is required to develop in the direction of lightweight, miniaturization and high performance, especially active phased array radar. Due to its special working environment, it is necessary to use microwave components with small size, light weight, high performance and high reliability. In traditional high-density microwave components, wire bonding is often used to achieve the interconnection of chips, electronic components and microwave transmission lines. In order to meet the requirements of high density, high operating frequency, high reliability and miniaturization of microwave components, it is necessary to continuously improve the conductivity and reliability of wire bonding. The lead structure is the main factor affecting the electrical performance and reliability of microwave components. Parameters such as the lead diameter, arch height, two-pin position, platform length, etc. have a great influence on the thermal reliability and microwave transmission of microwave components.

[0003] Wire bonding packaging has a wide range of applications in practical engineering. At present, domestic and foreign research is mainly carried out from three aspects: one is to study the reliability of wire bonding interconnection structure for the manufacturing process and process parameters of wire bonding packaging; one is to study the reliability of wire bonding interconnection structure under different service environments such as temperature and vibration for the physical structure parameters of wire bonding; one is to judge the signal integrity problem caused by interconnection leads in the circuit mainly with the help of software simulation tools. Judging its performance often takes a lot of time to establish interconnection structure model and perform software simulation, and because of the single prediction effect, it is often impossible to comprehensively consider the influence of service environment and electrical performance, and provide specific regulation guidance for reference. These problems are the biggest obstacles to improving the prediction and regulation of wire bonding interconnection structure performance in engineering practice, which limits the development of wire bonding packaging.

[0004] The above problems need to be solved urgently. To this end, the present invention provides a multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding. Summary of the invention

[0005] The technical problem to be solved by the present invention is: how to solve the problems existing in the above-mentioned prior art and realize multi-objective prediction of thermal fatigue life and electrical performance of wire bonding. A multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding is provided, which can be used to accurately parameterize the wire bonding interconnection structure model, quickly realize multi-objective prediction of thermal fatigue life and electrical performance of wire bonding, and guide the structural design and optimization of wire bonding packaging.

[0006] The present invention solves the above technical problems through the following technical solutions, and the present invention comprises the following steps:

[0007] Step 1: Determine the geometric parameters and physical parameters of the wire bonding interconnection structure according to the specific requirements of the interconnection in the high-frequency microwave component;

[0008] Step 2: parametrically characterize the geometric parameters of each interconnect structure in the microwave component to obtain a mathematical description of the wire bonding morphology;

[0009] Step 3: Based on the determined geometric parameters, physical parameters and parametric characterization of the wire bonding interconnection in the microwave component, a thermal analysis model and a structural-electromagnetic analysis model of the wire bonding interconnection structure are established respectively;

[0010] Step 4: According to the control factors, temperature cycle reliability and electromagnetic transmission performance indicators in microwave components, a comprehensive experiment on wire bonding interconnection morphological parameters, temperature cycle reliability and electromagnetic transmission performance is designed to obtain the average stress and strain variation range of the wire bonding interconnection structure during the thermal simulation process of each experimental item and the insertion loss of the wire bonding interconnection structure obtained by electromagnetic simulation;

[0011] Step 5: Based on comprehensive experimental data, a mapping relationship model between wire bonding interconnection morphological parameters and temperature cycle reliability indicators and electromagnetic transmission performance indicators based on CNN convolutional neural network is established, and the electromagnetic transmission performance prediction of wire bonding interconnection structure is completed;

[0012] Step 6: Establish a thermal fatigue life prediction model. Based on the mapping relationship model between the wire bonding interconnection morphological parameters and the temperature cycle reliability index obtained in step 5, complete the thermal fatigue life prediction of the wire bonding interconnection structure.

[0013] Furthermore, in the step 1, the geometric parameters of the wire bonding interconnection structure are determined to include the wire diameter D, the arch height h1, the wire span L, the platform length xL, the pad diameter D1, the pad height h3, the chip length L1, the chip width W1, the chip height h2, the dielectric substrate length L2, the dielectric substrate width W2, and the dielectric substrate height h4; the physical parameters of the wire bonding interconnection structure are determined to include the signal transmission frequency f, the dielectric constant ε of each component g , loss tangent θ g , density d g , elastic modulus E g , Poisson's ratio λ g 、Coefficient of thermal expansion α g , and the tensile strength of the lead wire σ b , section shrinkage rate ψ.

[0014] Furthermore, in step 2, the specific processing process is as follows:

[0015] Step 2a: Obtain a mathematical description of the first segment of the wire bonding by using the formula f(x)=y, where x represents the position of the first segment of the wire in the x-axis direction, x=0, and y represents the position of the first segment of the wire in the y-axis direction, y∈[h2+h3,h1+h2+h3];

[0016] Step 2b: Obtain a mathematical description of the second segment of the wire bonding morphology by using the formula f(x)=h1+h2+h3, where x is in the range of [0,xL];

[0017] Step (2c): By formula Get a mathematical description of the third segment of the wire bond morphology, where x is in the range [xL,L].

[0018] Furthermore, in step three, the specific processing process is as follows:

[0019] Step 3a: Based on the geometric parameters and physical parameters determined in step 1 and the parametric characterization of wire bonding in step 2, a thermal analysis model of the wire bonding interconnection structure is established in ANSYS Apdl software;

[0020] Step 3b: Based on the geometric parameters and physical parameters determined in step 1 and the parametric characterization of wire bonding in step 2, a wire bonding interconnect structure-electromagnetic analysis model is established in full-wave three-dimensional electromagnetic wave simulation software.

[0021] Furthermore, in step 4, the specific processing process is as follows:

[0022] Step 4a: According to the wire bonding interconnection morphology, the wire diameter D, the arch height h1, the wire span L and the platform length xL are used as control factors of the wire bonding interconnection structure;

[0023] Step 4b: Determine the range of the four control factors for wire bonding interconnection: wire diameter D∈[D min ,D max ]、Lead arch height h1∈[h min ,h max ]、Lead span L∈[L min ,L max ]、Lead platform length xL∈[xL min ,xL max ],in,() min Represents the minimum value of a certain control factor, () max Indicates the maximum value of a certain control factor;

[0024] Step 4c: using a Latin hypercube uniform sampling method to extract N sampling points within the variation range of the four control factors, to obtain N groups of wire bonding interconnection morphological parameter data, where N is a positive integer;

[0025] Step 4d: taking the average stress and strain variation range of the wire bonding interconnection structure during the thermal simulation as a temperature cycle reliability indicator, and taking the insertion loss as an electromagnetic transmission performance indicator;

[0026] Step 4e: Input the N groups of data obtained by Latin hypercube sampling as input parameters into ANSYS Apdl software to conduct a comprehensive experiment on the morphological parameters and temperature cycle reliability of wire bonding interconnection, and obtain the average stress and strain variation range of the wire bonding interconnection structure during the thermal simulation process;

[0027] Step 4f: Use the N groups of data obtained by Latin hypercube sampling as input parameters to input into the full-wave three-dimensional electromagnetic wave simulation software, conduct a comprehensive experiment on the wire bonding interconnection morphological parameters and electromagnetic transmission performance, and obtain the insertion loss.

[0028] Furthermore, in step 5, the specific processing process is as follows:

[0029] Step 5a: randomly arranging the obtained wire bonding interconnection morphological parameters and the comprehensive experimental data of the thermal analysis model and the structural-electromagnetic analysis model, and dividing the first 90% of the data into a training group and the remaining 10% of the data into a test group;

[0030] Step 5b: The obtained wire bonding interconnection morphological parameters and the four regulating factors of the wire bonding interconnection structure in the comprehensive experimental data of the thermal analysis model and the structural-electromagnetic analysis model, namely, the wire diameter D, the arch height h1, the wire span L, and the platform length xL, are used as the input of the CNN convolutional neural network mapping relationship model, and the average stress of the wire bonding interconnection structure, the strain variation range of the wire bonding interconnection structure, and the insertion loss of the wire bonding interconnection structure are used as the output;

[0031] Step 5c: Use the formula Normalize the input and output data, limit the data to [0,1], and eliminate the influence of the dimension of each parameter. 标准 represents the normalized value of an experimental data, x represents the actual value of an experimental data, and x max Indicates the maximum value of a certain experimental data range, x min Indicates the minimum value of a certain experimental data range;

[0032] Step 5d: Establish a CNN convolutional neural network topology with 4 inputs and 3 outputs. The network structure includes an input layer, a convolution layer, an activation layer, a maximum pooling layer, a fully connected layer, and a regression layer. The activation layer selects a RELU activation function whose mathematical expression is f(x)=max(0,x);

[0033] Step 5e: Input various experimental data into the network and use the SGDM gradient descent method to learn and train the network;

[0034] Step 5f: Denormalize the output prediction value and save the model, establish a mapping relationship between the wire bonding interconnection morphological parameters and the average stress of the wire bonding interconnection structure, the strain variation range of the wire bonding interconnection structure, and the insertion loss of the wire bonding interconnection structure. The model relationship is as follows:

[0035] σ m =Y1(D,h1,L,xL)

[0036] Δε=Y2(D,h1,L,xL)

[0037] S 21 =Y3(D,h1,L,xL)

[0038] Among them, σ m is the predicted average stress of the wire bonding interconnection structure, Δε is the predicted strain variation range of the wire bonding interconnection structure, S 21 To predict the insertion loss of the wire bonding interconnection structure, Y1 is the mapping relationship between the four regulating factors and the average stress of the wire bonding interconnection structure, Y2 is the mapping relationship between the four regulating factors and the strain variation range of the wire bonding interconnection structure, and Y3 is the mapping relationship between the four regulating factors and the insertion loss of the wire bonding interconnection structure. The electromagnetic transmission performance of the wire bonding interconnection structure can be predicted through the mapping relationship Y3.

[0039] Furthermore, in step six, the specific processing process is as follows:

[0040] Step 6a: The thermal fatigue life of the wire bonding interconnection structure is predicted from three aspects: junction temperature fluctuation, plastic strain and elastic deformation, and then a thermal fatigue life prediction model is established. The calculation formula is as follows:

[0041]

[0042] Among them, Δε is the strain variation range, σ' r is the material fatigue strength coefficient, σ m is the average stress in one cycle, N f is the number of failure cycles, i.e. thermal fatigue life, b is the fatigue strength index, ε r ' is the fatigue ductility coefficient, c is the fatigue ductility index, and E is the elastic modulus;

[0043] Step 6b: Determine the calculation formulas for the material fatigue strength coefficient, fatigue strength index, fatigue ductility coefficient and fatigue ductility index as follows:

[0044] b=-0.12

[0045] c=-0.6

[0046] σ' r =3.5σ r

[0047]

[0048] Among them, σ r is the fracture strength coefficient, ε r is the fracture ductility coefficient;

[0049] The calculation formulas for the fracture strength coefficient and fracture ductility coefficient are as follows:

[0050] σ r =σ b ln(1+ψ)

[0051] ε r = -ln(1-ψ)

[0052] Among them, σb is the tensile strength, ψ is the section reduction rate;

[0053] Step 6c: Substitute the parameter calculation formulas in step 6b into the thermal fatigue life prediction model calculation formula in step 6a to obtain:

[0054]

[0055] Step 6d: Substitute the average stress and strain variation range of the bonding wire interconnection structure predicted by the corresponding mapping relationship model into the calculation formula of the thermal fatigue life prediction model to calculate the predicted thermal fatigue life of the wire bonding interconnection structure.

[0056] Compared with the prior art, the present invention has the following advantages:

[0057] 1. The present invention uses ANSYS Apdl software and full-wave three-dimensional electromagnetic wave simulation software to respectively establish accurate parameterized models for thermal analysis and structural-electromagnetic analysis of wire bonding interconnection structures, designs comprehensive experiments on wire bonding interconnection morphological parameters, temperature cycle reliability and electrical performance, obtains reliability indicators and electromagnetic transmission performance indicators of wire bonding packages in a service environment, and establishes a multi-objective prediction model from wire bonding interconnection structural parameters to temperature cycle reliability indicators and electromagnetic transmission performance indicators based on a CNN convolutional neural network. The model can be used to study the influence of wire bonding interconnection structural parameters on its reliability and signal transmission performance, and solves the problem that it is currently impossible to quickly perform accurate parameterized modeling based on wire bonding interconnection structural parameters and accurately predict the temperature cycle reliability and electromagnetic transmission performance of wire bonding interconnection structures.

[0058] 2. By establishing a multi-objective prediction model based on CNN convolutional neural network, which transforms wire bonding interconnection structure parameters to temperature cycle reliability index and electromagnetic transmission performance index, the mapping relationship between wire bonding interconnection structure parameters and temperature cycle reliability and electromagnetic transmission performance can be obtained quickly and accurately, which can be used to judge the rationality of wire bonding interconnection structure design scheme and its impact on reliability and electromagnetic transmission performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic flow chart of a multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding in an embodiment of the present invention;

[0060] Figure 2 It is a dimensioning diagram of a substrate and a chip of a thermal analysis model of a wire bonding interconnection structure in an embodiment of the present invention;

[0061] Figure 3 It is a dimensioning diagram of a single bonding wire and a pad in a thermal analysis model of a wire bonding interconnection structure in an embodiment of the present invention;

[0062] Figure 4 It is a dimension annotation diagram of the wire bonding interconnection structure-electromagnetic analysis model in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given, but the protection scope of the present invention is not limited to the following embodiment.

[0064] Embodiment 1

[0065] This embodiment provides a technical solution: a multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding, the specific steps are as follows:

[0066] Step 1: Determine the physical and structural parameters of the wire bonding interconnect structure

[0067] The structural parameters of the thermal analysis model of wire bonding interconnection structure are as follows: Figure 2 , Figure 3 As shown in the figure, the structural parameters include the length, width, height, diameter, span and platform length of the dielectric substrate, chip, lead and pad, the physical property parameters include the density, elastic modulus, Poisson's ratio, thermal expansion coefficient, etc. of each part of the material, and the working parameters include the highest temperature T during thermal analysis. max , minimum temperature T min ;

[0068] Wire bonding interconnect structure - Structural parameters of electromagnetic analysis model are as follows Figure 4As shown, the structural parameters include the length, width, height, diameter, span and platform length of the dielectric substrate, chip, lead and pad; the physical parameters include the relative dielectric constant and loss tangent of each part of the material; and the working parameters include the signal transmission frequency f of the wire bonding interconnection structure.

[0069] Step 2: Obtain a mathematical description of the wire bonding morphology

[0070] In step 2, the specific processing process is as follows:

[0071] (2a): The mathematical description of the morphology of the first section of the wire bond is obtained by the formula f(x)=y, where x represents the position of the first section of the wire in the x-axis direction, x=0, and y represents the position of the first section of the wire in the y-axis direction, and the variable range is y∈[h2+h3,h1+h2+h3];

[0072] (2b): The mathematical description of the morphology of the second section of the wire bond is obtained by the formula f(x)=h1+h2+h3, where the variable range of x is [0,xL];

[0073] (2c): By formula Get a mathematical description of the morphology of the third segment of the wire bond, where x can vary in the range [xL,L].

[0074] Step 3: Establish thermal analysis model and structural-electromagnetic analysis model of wire bonding interconnect structure

[0075] In step three, the specific processing process is as follows:

[0076] (3a): Based on the geometric parameters (structural parameters) and physical parameters determined in step 1, and the parametric characterization of wire bonding in step 2, a thermal analysis model of the wire bonding interconnection structure is established in ANSYS Apdl software;

[0077] (3b): Based on the geometric parameters and physical parameters determined in step one and the parametric characterization of wire bonding in step two, a wire bonding interconnect structure-electromagnetic analysis model is established in a full-wave three-dimensional electromagnetic wave simulation software.

[0078] Step 4: Design a comprehensive experiment and obtain various performance indicators

[0079] In step 4, the specific processing process is as follows:

[0080] (4a): According to the wire bonding interconnection morphology, the wire diameter D, the arch height h1, the wire span L and the platform length xL are used as the regulating factors of the wire bonding interconnection;

[0081] (4b): Determine the variable range of the four control factors of wire bonding interconnection: wire diameter D∈[D min,D max ]、Lead arch height h1∈[h min ,h max ]、Lead span L∈[L min ,L max ]、Lead platform length xL∈[xL min ,xL max ],in,() min Represents the minimum value of a certain control factor, () max Indicates the maximum value of a certain control factor;

[0082] (4c): Using the Latin hypercube uniform sampling method, 200 sampling points are extracted within the range of the four geometric parameters (control factors) to obtain 200 sets of structural parameter data;

[0083] (4d): Based on the actual investigation of wire bonding packaging of (high-frequency) microwave components, the average stress and strain variation range of the wire bonding interconnect structure during thermal simulation is used as the temperature cycling reliability indicator, and the insertion loss is used as the electromagnetic transmission performance indicator;

[0084] (4e): 200 sets of data obtained by Latin hypercube sampling were input into ANSYS Apdl software as input parameters to conduct comprehensive experiments on wire bonding interconnection morphological parameters and temperature cycle reliability, and obtain the average stress and strain variation range of the wire bonding interconnection structure during thermal simulation;

[0085] (4f): The 200 sets of data obtained by Latin hypercube sampling are input as input parameters into the full-wave three-dimensional electromagnetic wave simulation software to conduct a comprehensive experiment on the wire bonding interconnection morphological parameters and electromagnetic transmission performance to obtain the insertion loss.

[0086] In (4e), the wire bonding interconnect morphology parameters are the four control factors mentioned above.

[0087] Step 5: Establish a mapping relationship model from wire bonding interconnection morphology parameters to various performance indicators

[0088] In step five, the specific processing process is as follows:

[0089] (5a): The obtained wire bonding interconnection morphological parameters and the comprehensive experimental data of the thermal analysis model and the structural-electromagnetic analysis model are randomly arranged, and the first 90% of the obtained 200 groups of experimental data are divided into a training group, and the remaining 10% of the data are divided into a test group; (the comprehensive experimental data specifically includes data such as thermal analysis results and structural-electromagnetic analysis results under different wire bonding interconnection morphological parameters, and the experimental items refer to the experimental items corresponding to the above four control factors)

[0090] (5b): The obtained wire bonding interconnection morphological parameters and the four control factors of the wire bonding interconnection structure in the comprehensive experimental data of the thermal analysis model and the structural-electromagnetic analysis model, namely, the wire diameter D, the arch height h1, the wire span L and the platform length xL, are used as the input of the CNN convolutional neural network mapping relationship model, and the average stress of the wire bonding interconnection structure, the strain variation range of the wire bonding interconnection structure and the insertion loss of the wire bonding interconnection structure are used as the output;

[0091] (5c) Using the formula Normalize the input and output data, limit the data to [0,1], and eliminate the influence of the dimension of each parameter. 标准 represents the normalized value of an experimental data, x represents the actual value of an experimental data, and x max Indicates the maximum value of a certain experimental data range, x min Indicates the minimum value of a certain experimental data range;

[0092] (5d): Establish a CNN convolutional neural network topology with 4 inputs and 3 outputs. The network structure includes input layer, convolution layer, activation layer, maximum pooling layer, fully connected layer and regression layer. The activation layer selects the RELU activation function with the mathematical expression of f(x)=max(0,x);

[0093] (5e): The network is trained using the SGDM gradient descent method. The initial learning rate is set to 0.01, and the learning rate reduction factor is set to 0.1. The experimental data is put into the network for training and testing. 30 samples are set for each training, and the maximum number of training times is 1200.

[0094] (5f): The output prediction value is denormalized and the model is saved to establish a mapping relationship between the wire bonding interconnection morphological parameters and the average stress of the wire bonding interconnection structure, the strain variation range of the wire bonding interconnection structure, and the insertion loss of the wire bonding interconnection structure. The model relationship is as follows:

[0095] σ m =Y1(D,h1,L,xL)

[0096] Δε=Y2(D,h1,L,xL)

[0097] S 21 =Y3(D,h1,L,xL)

[0098] Among them, σ m is the predicted average stress of the wire bonding interconnection structure, Δε is the predicted strain variation range of the wire bonding interconnection structure, S 21To predict the insertion loss of the wire bonding interconnection structure, Y1 is the mapping relationship between the four regulating factors and the average stress of the wire bonding interconnection structure, Y2 is the mapping relationship between the four regulating factors and the strain variation range of the wire bonding interconnection structure, and Y3 is the mapping relationship between the four regulating factors and the insertion loss of the wire bonding interconnection structure. The electromagnetic transmission performance of the wire bonding interconnection structure can be predicted through the mapping relationship Y3.

[0099] Step 6: Establish a thermal fatigue life prediction model and complete reliability life prediction

[0100] In step six, the specific processing process is as follows:

[0101] (6a): The thermal fatigue life of wire bonding interconnection structure is predicted from three aspects: junction temperature fluctuation, plastic strain and elastic deformation. The calculation formula is as follows:

[0102]

[0103] Among them, Δε is the strain variation range, σ' r is the material fatigue strength coefficient, σ m is the average stress in one cycle, N f is the number of failure cycles, i.e. thermal fatigue life, b is the fatigue strength index, ε r ' is the fatigue ductility coefficient, c is the fatigue ductility index, and E is the elastic modulus;

[0104] (6b): Through the summary of fatigue tests on various metal materials by some researchers, the four constant values ​​of material fatigue strength coefficient, fatigue strength index, fatigue ductility coefficient and fatigue ductility index can be determined by the following formula:

[0105] b=-0.12

[0106] c=-0.6

[0107] σ' r =3.5σ r

[0108]

[0109] Among them, σ r is the fracture strength coefficient, ε r is the fracture ductility coefficient;

[0110] (6c): The calculation formulas for the fracture strength coefficient and the fracture ductility coefficient are as follows:

[0111] σ r =σ b ln(1+ψ)

[0112] εr = -ln(1-ψ)

[0113] Among them, σb is the tensile strength, ψ is the section reduction rate;

[0114] (6d): Based on the above content, the calculation formula for the thermal fatigue life of the wire bonding interconnection structure under thermal load is as follows:

[0115]

[0116] Among them, σ m is the predicted average stress, Δε is the predicted strain variation range, and the predicted average stress and strain variation range are substituted into the thermal fatigue life prediction model (i.e., the calculation formula in 6(a) above) to calculate the predicted thermal fatigue life of the wire bonding interconnection structure.

[0117] Embodiment 2

[0118] The advantages of the present invention can be further illustrated by the following simulation experiments:

[0119] 1. Determine the basic parameters of wire bonding interconnection structure

[0120] In this embodiment, the thermal analysis simulation takes the wire bonding interconnection structure as an example, with the highest temperature of 100°C and the lowest temperature of -25°C in the temperature cycle, the physical parameters as shown in Table 1, and the structural parameters as shown in Table 2. Figure 2 , Figure 3 shown.

[0121] Table 1 Thermal analysis physical property parameters of wire bonding interconnection structure

[0122]

[0123] Table 2 Thermal analysis structural parameters of wire bonding interconnection structure

[0124]

[0125] In this embodiment, the electromagnetic analysis takes the wire bonding interconnection structure with an operating frequency of 5 GHz, physical properties, and structural parameters as shown in Table 3 as an example. Figure 4 shown.

[0126] Table 3 Basic parameters of electromagnetic analysis model for wire bonding interconnection structure

[0127]

[0128]

[0129] 2. Prediction of thermal fatigue life and electrical performance of wire bond interconnect structures

[0130] Based on the multi-objective prediction method for wire bonding thermal fatigue life and electrical performance proposed in the present invention, a mapping relationship model between the wire bonding interconnection morphological parameters and the average stress of the wire bonding interconnection structure, the strain variation range of the wire bonding interconnection structure, and the insertion loss of the wire bonding interconnection structure is established. The model relationship is as follows:

[0131] σ m =Y1(D,h1,L,xL)

[0132] Δε=Y2(D,h1,L,xL)

[0133] S 21 =Y3(D,h1,L,xL)

[0134] According to the mapping relationship S 21 =Y3(D,h1,L,xL) can complete the prediction of the electromagnetic transmission performance of the wire bonding interconnection structure. Based on the multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding proposed in the present invention, the thermal fatigue life prediction formula is as follows:

[0135]

[0136] Among them, the four constant values ​​of material fatigue strength coefficient, fatigue strength index, fatigue ductility coefficient and fatigue ductility index can be determined by the following formula:

[0137] b=-0.12

[0138] c=-0.6

[0139] σ' r =3.5σ r

[0140]

[0141] Among them, the calculation formulas of fracture strength coefficient and fracture ductility coefficient are as follows:

[0142] σ r =σ b ln(1+ψ)

[0143] ε r = -ln(1-ψ)

[0144] By substituting the average stress and strain variation range of the wire bonding interconnection structure predicted by the CNN convolutional neural network into the thermal fatigue life prediction formula, the thermal fatigue life of the wire bonding interconnection structure can be calculated.

[0145] The obtained formula is packaged in MATLAB software, and the basic material parameter table of the thermal analysis model and electromagnetic analysis model of the wire bonding interconnection structure is called. The thermal fatigue life of the wire bonding interconnection structure under the current thermal and electromagnetic conditions is 2.1764×10 5 The insertion loss is -4.1041dB and the calculation time is 1min54s.

[0146] 3. Comparative Analysis of Simulation Results

[0147] The accurate parameterized model of wire bonding interconnection structure is established in ANSYS Apdl software by using the structure and physical property parameters of the thermal analysis model of wire bonding interconnection structure in Table 1 and Table 2. Through thermal simulation, the average stress of wire bonding interconnection structure under the current physical property, structure and thermal parameters of wire bonding interconnection is 103.9747MPa and the strain range is 0.002258. The average stress and strain range are substituted into the thermal fatigue life calculation formula, and the thermal fatigue life is calculated to be 2.3423×10 5 The simulation and calculation time is 85min21s;

[0148] An accurate parameterized model of the wire bonding interconnect structure is established in the full-wave three-dimensional electromagnetic wave simulation software using the wire bonding interconnect structure-electromagnetic analysis model structure and physical property parameters in Table 3. Through electromagnetic simulation, the insertion loss of the current wire bonding interconnect structure under physical, structural and thermal parameters is obtained to be -4.0533 dB, and the simulation time is 2 min 43 s.

[0149] By comparing the prediction method proposed in the present invention with the results obtained by simulating with the thermal simulation software ANSYS Apdl and the electromagnetic simulation software HFSS, it can be seen that the thermal fatigue life error and insertion loss error predicted by the wire bonding interconnection structure electrical performance prediction method proposed in the present invention are very small, and the prediction accuracy is high. From the perspective of analysis time, the time consumed by the prediction method of the present invention is 2.16% of the time consumed by the thermal simulation software and electromagnetic software simulation, which greatly saves time cost, especially when a large number of wire bonding interconnection structures are analyzed simultaneously in engineering practice. Therefore, the wire bonding interconnection structure performance prediction method proposed in the present invention can realize the accurate prediction of the thermal fatigue life and signal transmission performance of the wire bonding interconnection structure, and effectively reduce the time cost of analysis, which is conducive to guiding the design and optimization of the wire bonding interconnection structure.

[0150] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding, characterized in that: The following steps are involved: Step 1: Determine the geometric parameters and physical parameters of the wire bonding interconnection structure according to the specific requirements of the interconnection in the high-frequency microwave component; Step 2: parametrically characterize the geometric parameters of each interconnect structure in the microwave component to obtain a mathematical description of the wire bonding morphology; Step 3: Based on the determined geometric parameters, physical parameters and parametric characterization of the wire bonding interconnection in the microwave component, a thermal analysis model and a structural-electromagnetic analysis model of the wire bonding interconnection structure are established respectively; Step 4: According to the control factors, temperature cycle reliability and electromagnetic transmission performance indicators in microwave components, a comprehensive experiment on wire bonding interconnection morphological parameters, temperature cycle reliability and electromagnetic transmission performance is designed to obtain the average stress and strain variation range of the wire bonding interconnection structure during the thermal simulation process of each experimental item and the insertion loss of the wire bonding interconnection structure obtained by electromagnetic simulation; Step 5: Based on comprehensive experimental data, a mapping relationship model between wire bonding interconnection morphological parameters and temperature cycle reliability indicators and electromagnetic transmission performance indicators based on CNN convolutional neural network is established, and the electromagnetic transmission performance prediction of wire bonding interconnection structure is completed; Step 6: Establish a thermal fatigue life prediction model. Based on the mapping relationship model between the wire bonding interconnection morphological parameters and the temperature cycle reliability index obtained in step 5, complete the thermal fatigue life prediction of the wire bonding interconnection structure.

2. The multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding according to claim 1, characterized in that: In the step 1, the geometric parameters of the wire bonding interconnection structure are determined, including the wire diameter D, the arch height h1, the wire span L, the platform length xL, the pad diameter D1, the pad height h3, the chip length L1, the chip width W1, the chip height h2, the dielectric substrate length L2, the dielectric substrate width W2, and the dielectric substrate height h4; the physical parameters of the wire bonding interconnection structure are determined, including the signal transmission frequency f, the dielectric constant ε of each component g , loss tangent θ g , density d g , elastic modulus E g , Poisson's ratio λ g 、Coefficient of thermal expansion α g , and the tensile strength of the lead wire σ b , section shrinkage rate ψ.

3. The multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding according to claim 2, characterized in that: In the step 2, the specific processing process is as follows: Step 2a: Obtain a mathematical description of the first segment of the wire bonding by using the formula f(x)=y, where x represents the position of the first segment of the wire in the x-axis direction, x=0, and y represents the position of the first segment of the wire in the y-axis direction, y∈[h2+h3,h1+h2+h3]; Step 2b: Obtain a mathematical description of the second segment of the wire bonding morphology by using the formula f(x)=h1+h2+h3, where x is in the range of [0,xL]; Step (2c): By formula Get a mathematical description of the third segment of the wire bond morphology, where x is in the range [xL,L].

4. The multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding according to claim 3, characterized in that: In step three, the specific processing process is as follows: Step 3a: Based on the geometric parameters and physical parameters determined in step 1 and the parametric characterization of wire bonding in step 2, a thermal analysis model of the wire bonding interconnection structure is established in ANSYS Apdl software; Step 3b: Based on the geometric parameters and physical parameters determined in step 1 and the parametric characterization of wire bonding in step 2, a wire bonding interconnect structure-electromagnetic analysis model is established in full-wave three-dimensional electromagnetic wave simulation software.

5. The multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding according to claim 4, characterized in that: In step 4, the specific processing process is as follows: Step 4a: According to the wire bonding interconnection morphology, the wire diameter D, the arch height h1, the wire span L and the platform length xL are used as control factors of the wire bonding interconnection structure; Step 4b: Determine the range of the four control factors for wire bonding interconnection: wire diameter D∈[D min ,D max ]、Lead arch height h1∈[h min ,h max ]、Lead span L∈[L min ,L max ]、Lead platform length xL∈[xL min ,xL max ], where ()min represents the minimum value of a certain control factor, () max Indicates the maximum value of a certain control factor; Step 4c: using a Latin hypercube uniform sampling method to extract N sampling points within the variation range of the four control factors, to obtain N groups of wire bonding interconnection morphological parameter data, where N is a positive integer; Step 4d: taking the average stress and strain variation range of the wire bonding interconnection structure during the thermal simulation as a temperature cycle reliability indicator, and taking the insertion loss as an electromagnetic transmission performance indicator; Step 4e: Input the N groups of data obtained by Latin hypercube sampling as input parameters into ANSYS Apdl software to conduct a comprehensive experiment on the morphological parameters and temperature cycle reliability of wire bonding interconnection, and obtain the average stress and strain variation range of the wire bonding interconnection structure during the thermal simulation process; Step 4f: Use the N groups of data obtained by Latin hypercube sampling as input parameters to input into the full-wave three-dimensional electromagnetic wave simulation software, conduct a comprehensive experiment on the wire bonding interconnection morphological parameters and electromagnetic transmission performance, and obtain the insertion loss.

6. The multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding according to claim 5, characterized in that: In step 5, the specific processing process is as follows: Step 5a: randomly arranging the obtained wire bonding interconnection morphological parameters and the comprehensive experimental data of the thermal analysis model and the structural-electromagnetic analysis model, and dividing the first 90% of the data into a training group and the remaining 10% of the data into a test group; Step 5b: The obtained wire bonding interconnection morphological parameters and the four regulating factors of the wire bonding interconnection structure in the comprehensive experimental data of the thermal analysis model and the structural-electromagnetic analysis model, namely, the wire diameter D, the arch height h1, the wire span L, and the platform length xL, are used as the input of the CNN convolutional neural network mapping relationship model, and the average stress of the wire bonding interconnection structure, the strain variation range of the wire bonding interconnection structure, and the insertion loss of the wire bonding interconnection structure are used as the output; Step 5c: Use the formula Normalize the input and output data, limit the data to [0,1], and eliminate the influence of the dimension of each parameter. 标准 represents the normalized value of an experimental data, x represents the actual value of an experimental data, and x max Indicates the maximum value of a certain experimental data range, x min Indicates the minimum value of a certain experimental data range; Step 5d: Establish a CNN convolutional neural network topology with 4 inputs and 3 outputs. The network structure includes an input layer, a convolution layer, an activation layer, a maximum pooling layer, a fully connected layer, and a regression layer. The activation layer selects a RELU activation function whose mathematical expression is f(x)=max(0,x); Step 5e: Input various experimental data into the network and use the SGDM gradient descent method to learn and train the network; Step 5f: Denormalize the output prediction value and save the model, establish a mapping relationship between the wire bonding interconnection morphological parameters and the average stress of the wire bonding interconnection structure, the strain variation range of the wire bonding interconnection structure, and the insertion loss of the wire bonding interconnection structure. The model relationship is as follows: s m =Y1(D,h1,L,xL) Δε=Y2(D,h1,L,xL) S 21 =Y3(D,h1,L,xL) Among them, σ m is the predicted average stress of the wire bonding interconnection structure, Δε is the predicted strain variation range of the wire bonding interconnection structure, S 21 To predict the insertion loss of the wire bonding interconnection structure, Y1 is the mapping relationship between the four regulating factors and the average stress of the wire bonding interconnection structure, Y2 is the mapping relationship between the four regulating factors and the strain variation range of the wire bonding interconnection structure, and Y3 is the mapping relationship between the four regulating factors and the insertion loss of the wire bonding interconnection structure. The electromagnetic transmission performance of the wire bonding interconnection structure can be predicted through the mapping relationship Y3.

7. The multi-objective prediction method for thermal fatigue life and electrical performance of wire bonding according to claim 6, characterized in that: In step six, the specific processing process is as follows: Step 6a: The thermal fatigue life of the wire bonding interconnection structure is predicted from three aspects: junction temperature fluctuation, plastic strain and elastic deformation, and then a thermal fatigue life prediction model is established. The calculation formula is as follows: Among them, Δε is the strain variation range, σ' r is the material fatigue strength coefficient, σm is the average stress in one cycle, N f is the number of failure cycles, i.e. thermal fatigue life, b is the fatigue strength index, ε r ' is the fatigue ductility coefficient, c is the fatigue ductility index, and E is the elastic modulus; Step 6b: Determine the calculation formulas for the material fatigue strength coefficient, fatigue strength index, fatigue ductility coefficient and fatigue ductility index as follows: b＝-0.12 c＝-0.6 in r =3.5σ r Among them, σ r is the fracture strength coefficient, ε r is the fracture ductility coefficient; The calculation formulas for the fracture strength coefficient and fracture ductility coefficient are as follows: s r =s b ln(1+ψ) e r =-ln(1-ψ) Among them, σb is the tensile strength, ψ is the section reduction rate; Step 6c: Substitute the parameter calculation formulas in step 6b into the thermal fatigue life prediction model calculation formula in step 6a to obtain: Step 6d: Substitute the average stress and strain variation range of the bonding wire interconnection structure predicted by the corresponding mapping relationship model into the calculation formula of the thermal fatigue life prediction model to calculate the predicted thermal fatigue life of the wire bonding interconnection structure.

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