A deep learning-based BGA package solder joint morphology prediction method

Abstract

The present application relates to the technical field of chip packaging, and particularly relates to a BGA packaging solder joint form prediction method based on deep learning, which comprises the following steps: S1: taking the solder ball initial diameter, solder resist thickness and pad size as key parameters, replacing the volume of the solder ball after welding is completed with an equal-volume cylinder volume to simplify the establishment of a finite element model in finite element modeling, and simulating the height value and width value of the solder ball after welding is completed under the corresponding size; S2: training the simulated height value and width value by using a deep learning method, and training an optimal network model; and obtaining the final height value and width value of the solder joint under a certain solder ball initial diameter, solder resist thickness and pad size by using the optimal network model. In the present scheme, the simulated solder ball form has high consistency with the measured data, the finally trained model can rapidly and accurately predict the final size of the solder ball under certain parameters, and the work efficiency can be greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of chip packaging, and particularly relates to a BGA packaging solder joint form prediction method based on deep learning. BACKGROUND

[0002] In a BGA packaging product, due to differences in packaging size, I / O quantity and the like, under certain packaging design rules, a designer will select a corresponding BGA solder ball size to meet the size and I / O quantity requirements. In the packaging process, the BGA solder ball is interconnected with the pads on the substrate by means of reflow soldering. Due to the surface tension and gravity of the solder ball during the soldering process, a shape close to a sphere is formed. Different pad sizes, initial diameters of the solder ball and thicknesses of the solder resist layer will all affect the final form of the solder ball after soldering is completed.

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

[0004] There are mainly two kinds of packaging solder joint form prediction methods in the prior art: one method is to obtain the final form of the BGA solder ball after soldering by first establishing a packaging model using the finite element method, setting corresponding material parameters, dividing the grid and setting the boundary conditions for solving. However, this method generally takes a long time to solve, and requires a certain foundation in finite element modeling and simulation. Differences in the finite element model will also limit the accuracy of the results. The other method is to obtain the actual product data through experimental testing. This method requires a large amount of time and materials, which will greatly increase the labor cost and material cost, and is not conducive to improving work efficiency.

[0005] In summary, how to provide a BGA packaging solder joint form prediction method with high work efficiency and strong universality is a problem that needs to be solved at the moment. SUMMARY

[0006] The present application provides a BGA packaging solder joint form prediction method based on deep learning, which can improve the simulation accuracy and improve the work efficiency.

[0007] The BGA packaging solder joint form prediction method based on deep learning provided by the present application comprises the following steps:

[0008] S1: Taking the solder ball initial diameter, solder resist thickness and pad size as key parameters, a finite element model is simplified and established by replacing the volume of the solder ball after welding with an equal-volume cylinder volume to simulate the height value and width value of the solder ball after welding under the corresponding size;

[0009] S2: The height value and width value obtained by simulation are trained by using a deep learning method, and an optimal network model is trained; and the final height value and width value of the solder joint under a certain solder ball initial diameter, solder resist thickness and pad size are obtained by using the optimal network model.

[0010] Further, the method for simplifying and establishing the finite element model in S1 is as follows:

[0011] S11: Before welding, the initial solder ball is a spherical body one, the radius of the spherical body one is R1, and the initial volume of the solder ball, i.e. the volume of the spherical body one, is V1 = 4 / 3 * π * R1 3 ;

[0012] S12: After welding, the solder ball forms an irregular spherical body part and a cylindrical body part; the irregular spherical body part is spherical body two, the volume of the spherical body two is V3, and the cylindrical body part is cylindrical body one, the volume of the cylindrical body one is V2;

[0013] V1 = V2 + V3;

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

[0015] S13: The volume V2 of the cylindrical body one is simplified, the spherical body two is represented as a cylindrical body two, and the volume of the cylindrical body two is defined as V4, then V4 = V1 - V2;

[0016] S14: The radius R3 of the cylindrical body two is set to be equal to the pad radius R2, and the height of the cylindrical body two is h2, then V4 is π * R3 2 *h2;

[0017] It can be obtained that: π * R3 2 *h2 = 4 / 3 * π * R1 3 - π * R2 2 *h1;

[0018] Therefore, the height h2 of the corresponding finite element model cylindrical body two under the corresponding solder ball initial diameter, solder resist thickness and pad size can be obtained.

[0019] Further, in S2, when deep learning is performed, a full connection neural network (Full Connected Neural Networks, FCNN) is selected for model training, which is expressed by the formula:

[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 between the network prediction value and the actual value; M is the number of data used each time the network parameters are updated during training; k is one of the M sets of data; 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 minimum, the prediction of the network model reaches the optimal value, which can be expressed as follows:

[0027]

[0028] Furthermore, the objective function L(θ) is minimized and the parameter values ​​are 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 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 parameters after network update; η represents the learning rate; β is a constant; represents the derivative of L(θ); represents the derivative with respect to θ.

[0031] Further, the adaptive learning rate of each parameter is calculated by using Adam, which is expressed by a formula as follows:

[0032] m t = beta1 * m t-1 + (1-beta1) * g t

[0033]

[0034] Wherein, mt and vt represent the first matrix and the second matrix estimation of the gradient respectively; g t represents the gradient of the loss function at t time.

[0035] Further, mt and vt are calculated and corrected, which is expressed by a formula as follows:

[0036]

[0037] Wherein, beta1 and beta2 are close to 1.

[0038] Further, the parameters are updated by using the corrected mt and vt, which is expressed by a formula as follows:

[0039]

[0040] Wherein, the default value of epsilon is 10 18 .

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

[0042] 1、The present application simplifies the simulation model on finite element modeling, replaces the volume of the soldering finished solder ball with an equal-volume cylinder, considers the surface tension and gravity of the solder ball in the simulation, and the final solder ball shape obtained by the simulation method has high consistency with the measured data, and the simulation precision can reach 98%.

[0043] 2、The present application processes the solder ball size data obtained by finite element simulation according to a deep learning algorithm, and finally trains a model which can quickly and accurately predict the final size of the solder ball under a certain initial diameter of the solder ball, pad size and solder resist thickness, greatly improves the work efficiency, and can be used by personnel without relevant finite element simulation and data processing professional knowledge, greatly improves the universality and simplifies the operation difficulty. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a schematic view of an initial solder ball according to an embodiment of the present application;

[0045] Figure 2 is a schematic view of a soldered solder ball according to an embodiment of the present application;

[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 predicted 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 the network training provided by an embodiment of the present invention;

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

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

[0052] In the following, reference will be made to the Figures 1-7 Describe the embodiment of the present invention. 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, their detailed description will not be repeated.

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clear, the following Figures 1-7 It should be understood that the specific embodiments described herein are only used to illustrate 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: Using the initial diameter of the solder ball, solder mask thickness, and pad size as key parameters, the volume of the solder ball after soldering is replaced by the volume of a cylinder of equal volume during finite element modeling to simplify the finite element model. The height and width of the solder ball after soldering are simulated to obtain the corresponding size. The method for simplifying the finite element model is as follows:

[0056] S11: If 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 portion and a cylindrical portion; let the irregular spherical portion be sphere two 2, the volume of sphere two 2 be V3, let the cylindrical portion be cylinder one 3, the volume of cylinder one 3 be V2;

[0058] Then V1 = V2 + V3;

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

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

[0061] S14: let the radius R3 of cylinder two 4 be equal to the radius R2 of the pad 5, and the height of cylinder two 4 be h2, then V4 = π * R3 2 * h2;

[0062] It can be obtained that: π * R3 2 * h2 = 4 / 3 * π * R1 3 - π * R2 2 * h1;

[0063] Therefore, the height h2 of the corresponding finite element model cylinder two 4 under the corresponding solder ball initial diameter, solder resist layer thickness and pad size can be obtained.

[0064] After the above finite element model is established, the solder ball height and width after reflow soldering can be obtained in the corresponding finite element analysis software under the conditions of considering the surface tension of the solder ball, gravity and the like, and the finite element analysis process is specifically as shown in Figure 4 As shown, the left side is cylinder two 4, and the right side is the solder ball after reflow soldering.

[0065] The following table is Table 1, and the data in the table is the measured solder ball height value under the condition that the solder ball diameter is 0.76 mm, the pad radius is 0.6 mm, and the solder resist layer thickness is constant. As can be seen from Table 1, the average height value is 0.61512 mm. At the same time, the finite element simulation height value obtained by the above finite element model analysis is 0.6167 mm, and the simulation accuracy is high compared with the measured value. It is worth noting that in the test, the height value and the width value are a group of data obtained by simultaneous measurement and simulation, and in this scheme, only the height value is taken as an example for description for the sake of simplicity.

[0066]

[0067] The following table is Table 2, and the data in the table is the measured solder ball height value under the condition that the solder ball diameter is 0.45 mm, the pad radius is 0.4 mm, and the solder resist thickness is constant. Table 1 and Table 2 are measured under the condition that the solder resist thickness is the same. As can be seen from Table 2, the average height value is 0.33644 mm. At the same time, the finite element simulation height value obtained by analyzing the above finite element model is 0.3459 mm, and the simulation value has high simulation accuracy compared with 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 simultaneous measurement and simulation. In this scheme, for the sake of simplicity, only the height value is described as an example.

[0068]

[0069] In this embodiment, the volume of the solder ball remains basically unchanged before and after welding, so when the finite element model is established, the volume of the solder ball after welding is replaced by an equal-volume cylinder (i.e. the volume of the solder resist layer + the volume of the upper ball of the solder resist layer, as shown in Figure 2 In the simulation, the surface tension and gravity of the solder ball are considered, and the final cylinder will form an incomplete spherical body. As can be seen from the two examples in Table 1 and Table 2, the final solder ball shape obtained by the simulation method has 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 resist layer and the size of the pad are used as key parameters to simplify the establishment of the finite element model, and the simulation data after the finite element analysis has small difference with the measured data, and the simulation accuracy is high. In actual production, the most commonly used material of the solder ball is SAC305, and in this scheme, the material of the solder ball is determined as an invariant.

[0070] S2: training the height value and the width value obtained by simulation by using a deep learning method, and training an optimal network model; and obtaining the final height value and the width value of the solder joint under a certain initial diameter of the solder ball, a thickness of the solder resist layer and a size of the pad by using the optimal network model.

[0071] Since the data set is in the form of a vector, when deep learning is performed, a fully connected neural network (FCNN) is selected for model training, which is expressed by the formula:

[0072] y j =σ(ω i，j x i +b j )

[0073] wherein X is the input value of the hidden layer 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 an activation function, in the actual network training process, the gradient vanishing, 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-1 layer and the n layer respectively; ω and b represent the weight and bias 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 the key factor affecting the shape change. In this embodiment, the pad window size, the substrate green oil layer thickness, and the solder ball original size are selected as the output layer of the fully connected neural network. The output layer is the shape change amount of the solder ball after the reflow soldering process, i.e., the height and width of the solder ball.

[0075] The Relu function is selected as the activation function σ:

[0076]

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

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

[0079]

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

[0081] The mean square error loss function is positive, and when the mean square error loss function value is the smallest, the prediction of the network model reaches the optimum, which can be expressed by a mathematical formula as:

[0082]

[0083] The neural network is updated in the direction of the gradient, and this process is repeated until the loss function is minimized. In backpropagation, the gradient of all parameters is calculated by the loss function, and then the network parameters (i.e. weights and biases) are adjusted using optimization algorithms to minimize the loss function and gradually approach the true value of the network's prediction.

[0084] The objective function L(θ) is minimized, and the parameter value is updated in the direction of the gradient of the objective function until the minimum value of the function is found, i.e. along the direction of the slope of the surface created by the objective function, until the valley is reached, which can be expressed as:

[0085]

[0086] where θ is θ(ω,b), i.e. θ here is a set of ω and b; θ t represents the parameter before network update; θ t+1 represents the parameter after network update; η represents the learning rate, which determines the step size taken to minimize the optimization problem; β is a constant; represents the derivative of L(θ); represents the derivative of θ.

[0087] Adam calculates the adaptive learning rate for each parameter. In addition to storing the exponentially decaying average of past squared gradients v t , Adam also retains the exponentially decaying average of past gradients m t , which can be expressed as:

[0088] m t = β1m t-1 + (1-β1)g t

[0089]

[0090] where mt and vt represent the first and second matrix estimates 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 very small, so mt and vt need to be calculated and corrected to offset these biases, which can be expressed as:

[0092]

[0093] where β1 and β2 are close to 1, and the default value of β1 is 0.9 and the default value of β2 is 0.999 in actual calculation.

[0094] The updated parameters are updated using the corrected mt and vt, which can be expressed as:

[0095]

[0096] wherein the default value of ∈ is 10 18 .

[0097] In this embodiment, a total of 200 groups of data are generated using finite element analysis software, of which 10 groups are randomly selected as the test set, and the others are used as the training set for network training. 40 groups of data are randomly selected for network updating each iteration, ensuring that the data selected each time is not exactly the same, and a total of 1500 iterations are performed. The trained neural network described above can quickly output the corresponding parameter prediction value of the solder ball shape within 2s, with an accuracy of up to 98%, saving a lot of manpower and time cost.

[0098] Figure 5 For comparison of network prediction value and actual value, line a and line c represent the actual height value and actual width value of the solder balls after reflow soldering, respectively, and b and c represent the prediction value. From the figure, it can be clearly seen that the actual value and the prediction value are well matched.

[0099] Figure 6 For the loss function error of network training, it can be seen that it has basically converged dynamically at 5000 batches.

[0100] The following is a comparison of the network prediction value and the actual value, and the line represents the actual height and width of the solder balls after reflow soldering. The points represent the prediction value. The blue line is the actual solder ball height value, the yellow line is the actual solder ball width value, the red dot is the network predicted solder ball height value, and the green dot is the network predicted solder ball width value. From the figure, it can be clearly seen that the actual value and the prediction value are well matched.

[0101] Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application. Those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the present application.

[0102] The specific embodiments of the application described above do not constitute a limitation on the scope of protection of the application. Any various other corresponding changes and modifications made in accordance with the technical concept of the present application should be included in the scope of protection of the claims of the present application.

Claims

1. A deep learning-based BGA package joint morphology prediction method, characterized in that, Comprising the following steps: S1: Taking the solder ball initial diameter, solder resist thickness and pad size as key parameters, in finite element modeling, the volume of the solder ball after welding is replaced by an equal-volume cylindrical volume to simplify the establishment of the finite element model, and the height value and width value of the solder ball after welding are simulated; the method for simplifying the establishment of the finite element model is as follows: S11: Before welding, the initial soldering ball is a sphere one (1), the radius of the sphere one (1) is R1, and the initial volume of the soldering ball is the volume of the sphere one (1) ; S12: After welding, the solder ball forms an irregular spherical part and a cylindrical part; the irregular spherical part is set as sphere two (2), the volume of sphere two (2) is V3, the cylindrical part is set as cylinder one (3), the volume of cylinder one (3) is V2; then ; where R2 is the radius of the pad (5) and hi is the thickness of the solder resist (6); S13: Simplify the volume V2 of the cylinder one (3), express the sphere two (2) as a cylinder two (4), define the volume of the cylinder two (4) as V4, then ; S14: set the radius R3 of the second cylinder (4) equal to the radius R2 of the pad (5), and the height of the second cylinder (4) as h2, then V4 is ; It can be obtained that: ; Thus, the height h2 of the corresponding finite element model cylinder two (4) under the corresponding solder ball initial diameter, solder resist thickness and pad size can be obtained; S2: The height value and width value obtained by simulation are trained by using a deep learning method, and the best network model is trained; then the final height value and width value of the solder joint under a certain solder ball initial diameter, solder resist thickness and pad size are obtained by using the best network model. 2.The deep learning-based BGA package joint profile prediction method of claim 1, wherein, In S2, when deep learning is performed, a fully connected neural network FCNN is selected for model training, which is expressed by the formula: ； where X is the input value of the hidden layer 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 and j are the number of neurons of the (n-1)th layer and the nth layer, respectively; ω and b represent the weight and bias, respectively. 3.The deep learning-based BGA package joint profile prediction method of claim 2, wherein, A Relu function is selected as the activation function σ: 。 4.The deep learning-based BGA package joint profile prediction method of claim 3, wherein, A mean square error loss function is selected to update the network parameters, and the mean square error loss function is: ； Wherein, L(θ) represents the loss function composed of the network prediction value and the actual value; M is the number of data used in each update of network parameters in the training process; k is one of the M groups of data; S θ (Y k ) is the prediction value of the network forward propagation, and S(Y k ) is the actual value corresponding to the training data. 5.The deep learning-based BGA package joint profile prediction method of claim 4, wherein, The mean square error loss function is always positive, and when the mean square error loss function value is the smallest, the prediction of the network model reaches the optimal, which is expressed by the mathematical formula: 。 6.The deep learning-based BGA package joint profile prediction method of claim 5, wherein, Minimize the objective function L(θ), update the parameter value along the direction of the gradient of the objective function, until the minimum value of the function is found, that is, along the direction of the slope of the surface created by the objective function, downward until reaching the valley, which is expressed by the formula: ； where θ is specifically θ(ω, b), i.e., θ here is a set of ω and b; θ t represents the parameters before network update; θ t+1 represents the parameters after network update; η represents the learning rate; β is a constant; represents the derivative of L(θ); represents the derivative of θ.

7. The deep learning-based BGA package joint morphology prediction method according to claim 6, characterized in that, Adam is used to calculate the adaptive learning rate of each parameter, which is expressed by the formula: ； where m t and v t denote the estimates of the first and second matrices of gradients, respectively; g t denotes the gradient of the loss function at time t.

8. The deep learning-based BGA package joint morphology prediction method according to claim 7, characterized in that, m is calculated and corrected t and v t is expressed by the formula: ； Wherein, β1 and β2 are close to 1.

9. The deep learning-based BGA package joint morphology prediction method according to claim 8, wherein, The modified m t and v t The update parameter is expressed by the formula: ； wherein, The default value for is 10 18 .

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