Deep learning-based BGA packaging welding spot form prediction method

Abstract

The invention relates to the technical field of chip packaging, in particular to a BGA packaging welding spot form prediction method based on deep learning, and the method comprises the following steps: S1, taking the initial diameter of a welding ball, the thickness of a solder mask and the size of a bonding pad as key parameters; during finite element modeling, the volume of a cylinder with the same volume is used for replacing the volume of a welded ball after welding is completed to simplify establishment of a finite element model, and the height value and the width value of the welded ball with the corresponding size after welding is completed are obtained through simulation; s2, training the height value and the width value obtained by simulation by using a deep learning method, and training to obtain an optimal network model; and obtaining the final height value and width value of the welding spot under the conditions of certain initial diameter of the welding ball, certain thickness of the solder mask and certain size of the bonding pad by using the optimal network model. According to the scheme, the shape of the solder ball obtained through simulation has high consistency with measured data, the model obtained through final training can rapidly and accurately predict the final size of the solder ball under certain parameters, and the working efficiency can be greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of chip packaging technology, and in particular to a BGA packaging solder joint morphology prediction method based on deep learning. Background Art

[0002] In BGA package products, due to differences in package size, I / O quantity, etc., under certain package design rules, designers will select the corresponding BGA solder ball size to meet the size and I / O quantity requirements. During the packaging process, the BGA solder ball is interconnected with the pad on the substrate through reflow soldering. During the soldering process, due to the surface tension and gravity of the solder ball, a ball-like shape will be formed. Different pad sizes, initial solder ball diameters, and solder mask thicknesses will affect the final shape of the solder ball after soldering.

[0003] At present, the industry generally estimates the final height of the solder ball after soldering based on 80% of the diameter of the solder ball before soldering, but actual test data shows that there is a 10% error between the final height of the solder ball and the empirical value. A large error value will affect the package size of the final product, resulting in a large tolerance between it and the size on the drawing, affecting product quality. In order to solve the above problem, it is necessary to design a BGA package solder joint morphology prediction method.

[0004] There are two main methods for predicting the shape of package solder joints in the prior art: one method is to obtain the final shape of the BGA solder ball after soldering, usually by first using the finite element method to establish a package model, and then solve it by setting the corresponding material parameters, dividing the grid and setting the boundary conditions. However, this method generally takes a long time to solve and requires a certain finite element modeling and simulation foundation. The difference in finite element models will also lead to limited accuracy of the results. Another method is to obtain the actual product data through experimental testing. This method requires a lot of time and materials, which will greatly increase labor costs and material costs, and is not conducive to improving work efficiency.

[0005] In summary, how to provide a BGA package solder joint morphology prediction method with high working efficiency and strong versatility is a problem that needs to be solved urgently. Summary of the invention

[0006] In order to solve the above problems, the present invention provides a BGA package solder joint morphology prediction method based on deep learning, which can improve simulation accuracy and work efficiency.

[0007] The present invention provides a BGA package solder joint morphology prediction method based on deep learning, comprising the following steps:

[0008] S1: Taking the initial diameter of the solder ball, the thickness of the solder mask layer and the size of the pad as key parameters, the volume of the solder ball after welding is replaced by the volume of a cylinder of equal volume to simplify the finite element model, and simulate the height and width of the solder ball after welding under the corresponding size;

[0009] S2: Use deep learning methods to train the simulated height and width values, and train to obtain the optimal network model; then use the optimal network model to obtain the final height and width values ​​of the solder joint under a certain initial solder ball diameter, solder mask thickness and pad size.

[0010] Furthermore, the method for simplifying the establishment of the finite element model in S1 is as follows:

[0011] S11: Before welding, assume that the initial solder ball is sphere 1, then the radius of sphere 1 is R1, and the initial volume of the solder ball is the volume of sphere 1 V1 = 4 / 3*π*R1 3 ;

[0012] S12: After welding, the solder ball forms an irregular spherical part and a cylindrical part; the irregular spherical part is assumed to be sphere 2, the volume of sphere 2 is V3, and the cylindrical part is assumed to be cylinder 1, the volume of cylinder 1 is V2;

[0013] Then V1=V2+V3;

[0014] V2=π*R2 2 *h1, where R2 is the radius of the pad and h1 is the thickness of the solder mask;

[0015] S13: Simplify the volume V2 of cylinder 1, represent sphere 2 as cylinder 2, define the volume of cylinder 2 as V4, then V4 = V1 - V2;

[0016] S14: Set the radius R3 of cylinder 2 to be equal to the pad radius R2, and the height of cylinder 2 to be h2, then V4 is π*R3 2 *h2;

[0017] We can obtain: π*R3 2 *h2=4 / 3*π*R1 3 -π*R2 2 *h1;

[0018] In this way, the height h2 of the second cylinder of the corresponding finite element model under the corresponding initial diameter of the solder ball, the thickness of the solder mask layer and the size of the pad can be calculated.

[0019] Furthermore, when deep learning is performed in S2, a fully connected neural network (FCNN) is used for model training, which can be expressed as follows:

[0020] y j =σ(ω i，j x i +b j ) where X is the hidden layer input value of the nth layer, X = [x1, x2, ..., x i ]; Y is the output value of the nth layer, Y=[y1,y2,...,y j ]; σ is the activation function; i, j are the number of neurons in the n-1th layer and the nth layer respectively; ω and b represent the weight and bias respectively.

[0021] Furthermore, the Relu function is selected as the activation function σ:

[0022]

[0023] Furthermore, the mean square error loss function is used to update the network parameters. The mean square error loss function is:

[0024]

[0025] Where L(θ) represents the loss function of the network prediction value and the actual value; M is the number of data used each time the network parameters are updated during the training process; k is one of the data in the M groups; S θ (Y k ) is the predicted value of the network forward propagation, S(Y k ) are the actual values ​​corresponding to the training data.

[0026] Furthermore, the mean square error loss function is always positive. When the mean square error loss function value is the smallest, the prediction of the network model reaches the optimal value, which can be expressed by mathematical formula:

[0027]

[0028] Furthermore, the objective function L(θ) is minimized and the parameter value is updated along the direction of the objective function gradient descent until the minimum value of the function is found, that is, downward along the surface slope direction created by the objective function until the valley is reached, which can be expressed as:

[0029]

[0030] Among them, θ is specifically θ(ω,b), that is, θ here is the set of ω and b; θ t Represents the parameters before network update; θ t+1 Represents the updated parameters of the network; η represents the learning rate; β is a constant; represents the derivative of L(θ); represents the derivative of θ.

[0031] Furthermore, Adam is used to calculate the adaptive learning rate of each parameter, which is expressed as:

[0032] m t =β1m t-1 +(1-β1)g t

[0033]

[0034] Among them, mt and vt represent the estimates of the first matrix and the second matrix of the gradient respectively; g t Represents the gradient of the loss function at time t.

[0035] Furthermore, mt and vt are calculated and corrected, which can be expressed as:

[0036]

[0037] Among them, β1 and β2 are close to 1.

[0038] Furthermore, the modified mt and vt are used to update the parameters, which can be expressed as:

[0039]

[0040] The default value of ∈ is 10. 18 .

[0041] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0042] 1. The present invention simplifies the simulation model in finite element modeling, replacing the volume of the solder ball after welding with a cylinder of equal volume. The surface tension and gravity of the solder ball are taken into account in the simulation. The final solder ball morphology obtained by the simulation method has a high consistency with the measured data, and the simulation accuracy can reach 98%.

[0043] 2. The present invention processes the solder ball size data obtained by finite element simulation according to a deep learning algorithm, and the model finally trained can quickly and accurately predict the final size of the solder ball under a certain solder ball initial diameter, pad size and solder mask thickness. This method greatly improves work efficiency and can be used by personnel who do not have relevant finite element simulation and data processing expertise, which greatly improves versatility and simplifies operation difficulty. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic diagram of an initial solder ball provided according to an embodiment of the present invention;

[0045] Figure 2 is a schematic diagram of a solder ball after soldering according to an embodiment of the present invention;

[0046] Figure 3 is a schematic diagram of a solder ball finite element model provided according to an embodiment of the present invention;

[0047] Figure 4 is a schematic diagram of a solder ball finite element simulation process provided by an embodiment of the present invention;

[0048] Figure 5 is a comparison diagram of network prediction values ​​and measured values ​​provided according to an embodiment of the present invention (line a is solder ball height, line c is solder ball width, point b is predicted height, and point d is predicted width);

[0049] Figure 6 is a loss function error graph of network training provided according to an embodiment of the present invention;

[0050] Figure 7 It is an overall flow chart of the package solder joint morphology prediction method provided according to an embodiment of the present invention.

[0051] The reference numerals include: sphere one 1, sphere two 2, cylinder one 3, cylinder two 4, pad 5, solder resist layer 6. DETAILED DESCRIPTION

[0052] In the following, reference will be made to the Figure 1-7 Embodiments of the present invention are described. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following Figure 1-7 It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0054] A BGA package solder joint morphology prediction method based on deep learning includes the following steps:

[0055] S1: Taking the initial diameter of the solder ball, the thickness of the solder mask layer and the size of the pad as key parameters, the volume of the solder ball after welding is replaced by the volume of a cylinder of equal volume to simplify the establishment of the finite element model, and simulate the height and width of the solder ball after welding under the corresponding size. The method of simplifying the establishment of the finite element model is as follows:

[0056] S11: Figure 1 As shown, before welding, the initial solder ball is sphere 1, then the radius of sphere 1 is R1, and the initial volume of the solder ball is the volume of sphere 1 V1 = 4 / 3*π*r1 3 ;

[0057] S12: Figure 2 As shown, after welding, the solder ball forms an irregular spherical part and a cylindrical part; let the irregular spherical part be sphere 2, and the volume of sphere 2 be V3; let the cylindrical part be cylinder 1 3, and the volume of cylinder 1 3 be V2;

[0058] Then V1=V2+V3;

[0059] V2=π*R2 2 *h1, where R2 is the radius of the pad 5 and h1 is the thickness of the solder resist layer 6;

[0060] S13: Figure 2 , Figure 3 As shown, the volume V2 of the cylinder 1 3 is simplified, the sphere 2 is represented as the cylinder 2 4, and the volume of the cylinder 2 4 is defined as V4, then V4 = V1-V2;

[0061] S14: Set the radius R3 of cylinder 24 to be equal to the radius R2 of pad 5, and the height of cylinder 24 to be h2, then V4 is π*R3 2 *h2;

[0062] We can obtain: π*R3 2 *h2=4 / 3*π*R1 3 -π*R2 2 *h1;

[0063] In this way, the height h2 of the corresponding finite element model cylinder 24 under the corresponding solder ball initial diameter, solder mask thickness and pad size can be calculated.

[0064] After establishing the above finite element model, the height and width of the solder ball after reflow soldering can be solved in the corresponding finite element analysis software by considering the surface tension of the solder ball, gravity and other conditions. The specific finite element analysis process is as follows: Figure 4 As shown, the left side is the cylinder 2 4, and the right side is the solder ball after reflow soldering.

[0065] The following table is Table 1. The data in the table are the measured solder ball height values ​​when the solder ball diameter is 0.76mm, the pad radius is 0.6mm, and the solder mask thickness is constant. From Table 1, it can be seen that the average height value is 0.61512mm. At the same time, the finite element simulation height value obtained by the above finite element model analysis is 0.6167mm, and the simulation value has higher simulation accuracy than the measured value. It is worth noting that during the test, the height value and the width value are a set of data obtained by both actual measurement and simulation. In order to simplify the description in this scheme, only the height value is used as an example for explanation.

[0066]

[0067] The following table is Table 2. The data in the table are the measured solder ball height values ​​when the solder ball diameter is 0.45mm, the pad radius is 0.4mm, and the solder mask thickness is constant. Tables 1 and 2 are measured under the condition of the same solder mask thickness. It can be seen from Table 2 that the average height value is 0.33644mm. At the same time, the finite element simulation height value obtained by the above finite element model analysis is 0.3459mm, and the simulation value has higher simulation accuracy than the measured value. It is worth noting that during the test, the height value and the width value are a set of data obtained by both actual measurement and simulation. In order to simplify the description in this scheme, only the height value is used as an example for explanation.

[0068]

[0069] In this embodiment, the volume of the solder ball remains basically unchanged before and after welding, so when finite element modeling is performed, a cylinder of equal volume is used to replace the volume of the solder ball when welding is completed (i.e., the volume filled in the solder mask layer + the volume of the ball on the upper part of the solder mask layer, such as Figure 2 As shown in ), the surface tension and gravity of the solder ball are taken into account in the simulation, and the cylinder will eventually form an incomplete sphere-like shape. From the two examples in Table 1 and Table 2, it can be seen that the final solder ball shape obtained by the simulation method has a high consistency with the measured data, and the simulation accuracy is as high as about 98%. The initial diameter of the solder ball, the thickness of the solder mask layer and the pad size are used as key parameters to simplify the establishment of the finite element model. After finite element analysis, the simulation data is slightly different from the measured data, and the simulation accuracy is high. The most commonly used solder ball material in actual production is SAC305. In this scheme, the material of the solder ball is determined as a constant.

[0070] S2: Use deep learning methods to train the simulated height and width values, and train to obtain the optimal network model; then use the optimal network model to obtain the final height and width values ​​of the solder joint under a certain initial solder ball diameter, solder mask thickness and pad size.

[0071] Since the data set is in the form of vectors, when performing deep learning, a fully connected neural network (FCNN) is used for model training, which can be expressed as follows:

[0072] y j =σ(ω i，j x i +b j )

[0073] Among them, X is the hidden layer input value of the nth layer, X=[x1,x2,...,x i ]; Y is the output value of the nth layer, Y=[y1,y2,...,y j]; σ is the activation function. In the actual network training process, gradient disappearance, gradient explosion and overfitting problems often occur. One of the functions of the activation function is to alleviate the above problems as much as possible; i, j are the number of neurons in the n-1th layer and the nth layer respectively; ω and b represent weights and biases respectively. The weight is used to measure the connection strength between neurons, and the bias represents the threshold of the neuron.

[0074] The structure of the fully connected neural network is divided into an input layer, a hidden layer, and an output layer. In this embodiment, the input layer of the network is a key factor affecting the morphological change. In this embodiment, the pad window size, the substrate green oil layer thickness and the original size of the solder ball are selected as the output layer of the fully connected neural network. The output layer is the morphological change of the solder ball after the reflow process, that is, the height and width of the solder ball.

[0075] Select the Relu function as the activation function σ:

[0076]

[0077] The Relu function is not differentiable in the entire interval, but it can perfectly solve the problem of gradient disappearance in the positive interval, and its calculation speed and convergence speed are better than Sigmoid and Tanh functions. Therefore, the Relu function is selected as the activation function.

[0078] After the network forward propagates and outputs the predicted value, a loss function needs to be constructed to measure the difference between the predicted value and the actual value, so that the optimizer can be used to update the network parameters so that the predicted result gradually approaches the true value. In this experiment, the mean square error loss function is used to update the network parameters. The mean square error loss function is:

[0079]

[0080] Where L(θ) represents the loss function of the network prediction value and the actual value; M is the number of data used each time the network parameters are updated during the training process; k is one of the data in the M groups; S θ (Y k ) is the predicted value of the network forward propagation, S(Y k ) are the actual values ​​corresponding to the training data.

[0081] The mean square error loss function is always positive. When the mean square error loss function value is the smallest, the prediction of the network model reaches the optimal value, which can be expressed as follows:

[0082]

[0083] To update the neural network in reverse according to the gradient, this cycle is repeated. In back propagation, after the gradients of all parameters are calculated through the loss function, the optimization algorithm can be used to adjust the network parameters (i.e. weights and biases) with the goal of minimizing the loss function and making the network's predicted value gradually approach the true value.

[0084] Minimize the objective function L(θ) and update the parameter value along the direction of the objective function gradient descent until the minimum value of the function is found, that is, go down along the surface slope created by the objective function until you reach the valley, which can be expressed as:

[0085]

[0086] Among them, θ is specifically θ(ω,b), that is, θ here is the set of ω and b; θ t Represents the parameters before network update; θ t+1 Represents the updated parameters of the network; η represents the learning rate, which determines the size of the steps taken to achieve the minimum value of the optimization problem; β is a constant; represents the derivative of L(θ); represents the derivative of θ.

[0087] Adam is used to calculate the adaptive learning rate of each parameter. In addition to storing the past gradient square v t In addition to the exponential decay average of the past gradient m t The exponential decay average value of is expressed as:

[0088] m t =β1m t-1 +(1-β1)g t

[0089]

[0090] Among them, mt and vt represent the estimates of the first matrix and the second matrix of the gradient respectively; g t Represents the gradient of the loss function at time t.

[0091] mt and vt tend to be biased towards 0 during the initial step, especially when the learning rate is small, so it is necessary to calculate and correct mt and vt to offset these deviations, expressed as:

[0092]

[0093] Among them, β1 and β2 are close to 1. In actual calculations, the default value of β1 is 0.9, and the default value of β2 is 0.999.

[0094] The modified mt and vt are used to update the parameters, which can be expressed as:

[0095]

[0096] The default value of ∈ is 10. 18 .

[0097] In this embodiment, a total of 200 sets of data were generated using finite element analysis software, of which 10 sets were randomly selected as test sets and the others were used as training sets for network training. 40 sets of data were randomly selected for network update in each iteration to ensure that the data extracted each time were not exactly the same, and a total of 1500 iterations were performed. The above-mentioned trained neural network can quickly output the predicted values ​​of the solder ball morphology of the corresponding parameters within 2 seconds, with an accuracy rate of up to 98%, saving a lot of manpower and time costs.

[0098] Figure 5 This is a comparison between the network predicted values ​​and the actual values. Line a and line c represent the actual height and width values ​​of 10 random groups of solder balls after reflow, respectively. Points b and c represent the predicted values. It can be clearly seen from the figure that the actual values ​​are in good agreement with the predicted values.

[0099] Figure 6 This is the loss function error of the network training. It can be seen that it has basically converged dynamically in 5000 batches.

[0100] The following is a comparison between the network prediction value and the actual value. The lines represent the actual height and width of 10 random groups of solder balls after reflow, and the points represent the predicted values. The blue line is the actual solder ball height value, the yellow line is the actual solder ball width value, the red point is the network predicted solder ball height value, and the green point is the network predicted solder ball width value. It can be clearly seen from the figure that the actual value and the predicted value are in good agreement.

[0101] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

[0102] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A BGA package solder joint morphology prediction method based on deep learning, characterized in that: The steps include: S1: Taking the initial diameter of the solder ball, the thickness of the solder mask layer and the size of the pad as key parameters, the volume of the solder ball after welding is replaced by the volume of a cylinder of equal volume to simplify the finite element model, and simulate the height and width of the solder ball after welding under the corresponding size; S2: Use deep learning methods to train the simulated height and width values, and train to obtain the optimal network model; then use the optimal network model to obtain the final height and width values ​​of the solder joint under a certain initial solder ball diameter, solder mask thickness and pad size.

2. The BGA package solder joint morphology prediction method based on deep learning according to claim 1, characterized in that: The simplified method of establishing the finite element model in S1 is as follows: S11: Before welding, assume that the initial solder ball is sphere 1 (1), then the radius of sphere 1 (1) is R1, and the initial volume of the solder ball, i.e. the volume of sphere 1 (1), is V1 = 4 / 3*π*R1 3 ; S12: After welding, the solder ball forms an irregular spherical part and a cylindrical part; let the irregular spherical part be sphere two (2), and the volume of sphere two (2) be V3; let the cylindrical part be cylinder one (3), and the volume of cylinder one (3) be V2; Then V1=V2+V3; V2=π*R2 2 *h1, where R2 is the radius of the pad (5) and h1 is the thickness of the solder mask (6); S13: Simplify the volume V2 of cylinder 1 (3), express sphere 2 (2) as cylinder 2 (4), define the volume of cylinder 2 (4) as V4, then V4 = V1 - V2; S14: Set the radius R3 of cylinder 2 (4) equal to the radius R2 of pad (5), and the height of cylinder 2 (4) is h2, then V4 is π*R3 2 *h2; We can obtain: π*R3 2 *h2=4 / 3*π*R1 3 -π*R2 2 *h1; In this way, the height h2 of the corresponding finite element model cylinder 2 (4) under the corresponding solder ball initial diameter, solder mask thickness and pad size can be calculated.

3. The BGA package solder joint morphology prediction method based on deep learning according to claim 2 is characterized in that: When deep learning is performed in S2, a fully connected neural network (FCNN) is used for model training, which can be expressed as: y j =σ(ω i，j x i +b j ) Among them, X is the hidden layer input value of the nth layer, X=[x1,x2,...,x i ]; Y is the output value of the nth layer, Y=[y1,y2,...,y j ]; σ is the activation function; i, j are the number of neurons in the n-1th layer and the nth layer respectively; ω and b represent the weight and bias respectively.

4. The BGA package solder joint morphology prediction method based on deep learning according to claim 3 is characterized in that: Select the Relu function as the activation function σ:

5. The BGA package solder joint morphology prediction method based on deep learning according to claim 4, characterized in that: The mean square error loss function is used to update the network parameters. The mean square error loss function is: Where L(θ) represents the loss function of the network prediction value and the actual value; M is the number of data used each time the network parameters are updated during the training process; k is one of the data in the M groups; S θ (Y k ) is the predicted value of the network forward propagation, S(Y k ) are the actual values ​​corresponding to the training data.

6. The BGA package solder joint morphology prediction method based on deep learning according to claim 5, characterized in that: The mean square error loss function is always positive. When the mean square error loss function value is the smallest, the prediction of the network model reaches the optimal value, which can be expressed as follows:

7. The BGA package solder joint morphology prediction method based on deep learning according to claim 6, characterized in that: Minimize the objective function L(θ) and update the parameter value along the direction of the objective function gradient descent until the minimum value of the function is found, that is, go down along the surface slope created by the objective function until you reach the valley, which can be expressed as: Among them, θ is specifically θ(ω,b), that is, θ here is the set of ω and b; θ t Represents the parameters before network update; θ t+1 Represents the updated parameters of the network; η represents the learning rate; β is a constant; represents the derivative of L(θ); represents the derivative of θ.

8. The BGA package solder joint morphology prediction method based on deep learning according to claim 7, characterized in that: Adam is used to calculate the adaptive learning rate of each parameter, which is expressed as follows: m t =β1m t-1 +(1-β1)g t Among them, mt and vt represent the estimates of the first matrix and the second matrix of the gradient respectively; g t Represents the gradient of the loss function at time t.

9. The BGA package solder joint morphology prediction method based on deep learning according to claim 8, characterized in that: Calculate and correct mt and vt, expressed as: Among them, β1 and β2 are close to 1.

10. The BGA package solder joint morphology prediction method based on deep learning according to claim 9, characterized in that: The modified mt and vt are used to update the parameters, which can be expressed as: The default value of ∈ is 10. 18 .

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