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# AI-Assisted Design-on-Simulation for Life Prediction

## Definition

Many researchers have adopted the finite-element-based design-on-simulation (DoS) technology for the reliability assessment of electronic packaging. DoS technology can effectively shorten the design cycle, reduce costs, and effectively optimize the packaging structure. However, the simulation analysis results are highly dependent on the individual researcher and are usually inconsistent between them. Artificial intelligence (AI) can help researchers avoid the shortcomings of the human factor.

## 1. Introduction

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^{[8]}. With the increasing complexity of packaging structures, manufacturing reliability test vehicles, and conducting ATCT experiments have become time-consuming and very expensive processes, the design-on-experiment (DoE) methodology for packaging design is becoming infeasible. As a result of the wide adoption of finite element analysis

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^{[15]}, accelerated thermal cycling tests are reduced significantly in the semiconductor industry, and package development time and cost are reduced as well. In a 3D WLP model, Liu

^{[16]}applied the Coffin–Manson life prediction empirical model to predict the reliability life of a solder joint within an accurate range. However, the results of finite element simulations are highly dependent on the mesh size, and there is no guideline to help researchers address this issue. Therefore, Chiang et al.

^{[17]}proposed the concept of “volume-weighted averaging” to determine the local strain, especially in critical areas. Tsou

^{[18]}successfully predicted packaging reliability through finite element simulation with a fixed mesh size in the critical area of the WLP structure. However, the results of simulation analysis are highly dependent on the individual researcher, and the results are usually inconsistent between simulations. In order to overcome this problem, the present work comparatively reviews an artificial intelligence (AI) approach in which electronic packaging design using a machine learning algorithm

^{[19]}

^{[20]}. The use of machine learning for the analysis of electronic packaging reliability is the best way to obtain a reliable prediction result and meet the time-to-market demand.

## 2. Finite Element Method for WLP

^{[21]}, then the simulation is an experiment; the experimental work can be replaced by a validated simulation procedure to create a large database for AI training and obtain a small and accurate AI model for reliability life cycles prediction. Once we obtain the final AI model for a new WLP structure, developers can simply input the WLP geometries, and then the life cycle can be obtained.

**Figure 1**illustrates this procedure.

**Figure 1.**AI-assisted design-on-simulation procedure.

**Figure 2**shows the stress–strain curve for an Sn–Ag–Cu (SAC)305 solder joint. The stress–strain curve

^{[22]}, obtained by tensile testing and the Chabochee kinematic hardening model, was used to describe the tensile curves at different temperatures. Once the model is built, boundary conditions and external thermal loading are required for the WLP simulation.

**Figure 2.**Stress–strain curve for SAC solder.

**Figure 3**. The X-direction displacement on each node was fixed to zero owing to the Y-symmetry. To prevent rigid body motion, the node at the lowest point of the neutral axis, which is at the printed circuit board (PCB), has all degrees of freedom fixed. The complete finite element model and the boundary conditions are shown in

**Figure 4**. The thermal loading condition used in this research was JEDEC JESD22-A104D condition G

^{[23]}, and the temperature range was −40 °C to 125 °C. The ramp rate was fixed at 16.5 °C/min and the dwell time was 10 min. In a qualified design, its mean-cycle-to-failure (MTTF) should pass 1000 thermal cycles. After the simulation process is completed, the incremental equivalent plastic strain in the critical zone is substituted into the strain-based Coffin–Manson model

^{[24]}for reliable life cycle prediction. For a fixed temperature ramp rate, this method is as accurate as the energy-based empirical equation

^{[25]}

^{[26]}but with much less CPU time.

**Figure 3.**Symmetrical solder ball geometry.

**Figure 4.**FEM model boundary condition.

**Table 1**presents the predicted reliability life cycles of the WLP structure. The results show that the difference between the FEM-predicted life cycle and experiment result is within a small range. Therefore, experiments can be replaced by this validated FEM simulation to minimize the cost and time. Compared with the experiment approach, this validated FEM simulation procedure can provide large amounts of data within much less time and can be effectively used to generate a database for AI training.

Test Vehicle | Experimental Reliability (Cycles) |
Simulation Reliability (Cycles) |
Difference |
---|---|---|---|

TV1 | 318 | 313 | −5 |

TV2 | 1013 | 982 | −31 |

TV3 | 587 | 587 | 0 |

TV4 | 876 | 804 | 72 |

TV5 | 904 | 885 | 19 |

## 3. Machine Learning

### 3.1. Establishment of Dataset

**Figure 5**). For illustration purposes, the four most influential parameters, namely silicon chip thickness, stress buffer layer thickness, upper pad diameters, and lower pad diameters, were selected to build the AI model and predict the reliability life cycles of new WLP structures. These four design parameters were used to generate both training and testing datasets for AI machine learning algorithms.

**Table 2**and

**Table 3**show the generated training dataset obtained through FEM simulation.

**Figure 5.**WLP geometry structure.

### 3.2. ANN Model

**Figure 6**. The model consists of three layers: the input layer, where the data are provided; the hidden layer, where the input data are calculated; and the output layer, where the results are displayed

^{[27]}. As the numbers of neurons and hidden layers are increased, the ability to handle nonlinearity improves. However, these conditions may result in high computational complexity, overfitting, and poor predictive performance.

**Figure 6.**Schematic diagram of artificial neural network.

**Figure 7**.

**Figure 7.**Sigmoid activation function.

### 3.3. RNN Model

^{[28]}

^{[29]}works on the principle that the output of a particular layer is fed back to the input layer to realize a time-dependent neural network and a dynamic model. Consequently, an ANN with nodes connected in a ring shape is obtained, as shown in the left half of

**Figure 8**. The ring-shaped neural network is expanded along the “time” axis, as shown in the right half of

**Figure 8**, where the “time” step t and the hidden state st can be expressed as a function of the output from the previous (st−1) “time” steps and previous layers (xt). U, V, and W denote the shared weights in RNN models during different “time” steps. Generally, the RNN series model can be divided into four types according to the number of inputs and outputs in given “time” steps; that is, one to one (O to O), one to many (O to M), many to one (M to O), and many to many (M to M). To synchronize the input features with the output results, RNN models can be subdivided into different series models, as shown in

**Figure 9**

^{[30]}.

**Figure 8.**Schematic structure of recurrent neural network.

**Figure 9.**Different series model for RNN.

### 3.4. SVR Model

This regression method evolved from the support vector machine algorithm. It transforms data to high-dimensional feature space and adapts the ε-insensitive loss function (Equation (4)) to perform the linear regression in feature space (Equation (5)). In this regression method, the norm value of w is also minimized to avoid the overfitting problem. In other words, f(X,w), which is the function of the SVR model, will be as flat as possible. The SVR concept is illustrated in **Figure 10**. The data points outside the ε-insensitive zone are called support vectors, and two slack variables, ξi and ξ∗i, are used to record the loss of each support vector. Thus, the whole SVR problem can be seen as an optimization problem (Equation (6)).

**Figure 10.**Schematic diagram of SVR.

### 3.5. KRR Model

KRR combines ridge regression with the kernel “trick”. This model can learn a linear function in the space induced by the respective kernel and the dataset. Nonlinear functions in the original space can be used by the nonlinear kernels. The KRR algorithm also analyzes several kernels such as the RBF kernel, sigmoid kernel, and polynomial kernel to find the suitable kernel function for the WLP nonlinear dataset.

The KRR is possibly the most elementary algorithm that can be kernelized to ridge regression ^{[31]}. The classic method is used to minimize the quadratic cost, as shown in Equation (8). However, for the nonlinear dataset, the lower-dimensional feature space replaces the higher-dimensional feature space; that is, Xi→Φ(Xi). To convert lower-dimensional space to higher-dimensional space, the predictive model undergoes overfitting. Hence, to avoid overfitting, this function requires regularization.

Hence, Equation (11) is very simple and more flexible due to introducing kernel function K, λ is the regularize factor with the identity matrix I, and y is the response variable. This model can also avoid both model complexity and computational time.

### 3.6. KNN Model

The KNN model is a statistical tool for estimating the value of an unknown point based on its nearest neighbors [69]. The nearest neighbors are usually calculated as the points with the shortest distance to the unknown point [70]. Several techniques are used to measure the distance between the neighbors. Two simple techniques are used in this study: the Euclidean distance function d(x,y), provided in Equation (12), and the Manhattan distance function d(x,y), provided in Equation (13).

### 3.7. The RF Regression Model

**Figure 10**. This algorithm creates an RF by combining several decision trees built from the training dataset. The CART tree selects one feature from all of the input features as the segmentation condition according to the minimum mean square error method.

**Figure 11**). Afterward, a set of trained decision trees is created. In step 3, the RF calculates the average value of all decision tree results to obtain the final predicted value.

**Figure 11.**Schematic diagram of random forest structure.

### 3.8. Training Methodology

**Figure 12**.

**Figure 12.**Methodology flow chart.

#### 3.8.1. Data Preprocessing

#### 3.8.2. Cross-Validation

**Figure 13**). After the choice of data preprocessing method was confirmed, cross-validation was performed to avoid overfitting of the machine learning model, as shown in

**Figure 13**. The dataset was divided into 10 parts, and each part acted as either a validation or training set in different training steps. The validation sets were also used to predict the training results.

**Figure 13.**Cross-validation model diagram from Round 1 to Round 10.

#### 3.8.3. Grid Search Technique

This entry is adapted from 10.3390/ma14185342

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