Leon Xu

A simulation-based multi-objective design optimization of electronic packages under thermal cycling and bending

In this study, a simulation-based multi-objective design optimization methodology was developed for improving electronic packaging reliability. It was demonstrated using a generic model of an electronic package on a printed wiring board. The objective for the optimization was to improve the reliability of solder joints under both thermal cycling and bending by optimizing a group of design parameters. A parametric finite element model was developed using ANSYS for both load conditions. To improve the numerical efficiency of the optimization, a multi-quadric response surface method was implemented to approximate the response of finite element simulations for each loading condition. Subsequently, the multi-objective optimization of solder joint reliability was implemented using a Minmax principle on all response surfaces and a differential evolution algorithm as optimal search engine, which is capable of finding global minimum when local minima exist. Our study demonstrated that the reliability of the solder joints is significantly improved for this given generic model of electronic package. The proposed methodology can be effectively used in improving the reliability of electronic packages.

Optimal Parameter Selection for Electronic Packaging Using Sequential Computer Simulations

Optimal parameter selection is a crucial step in improving the quality of electronic packaging processes. Traditional approaches usually start with a set of physical experiments and then employ Design of Experiment (DOE) based response surface methodology (RSM) to find the parameter settings that will optimize a desired system response. Nowadays deterministic computer simulations such as Finite Element Analysis (FEA) are often used to replace physical experiments when evaluating a system response, e.g., the stress level in an electronic packaging. However, FEA simulations are usually computationally expensive due to their inherent complexity. In order to find the optimal parameters, it is not practical to use FEA simulations to calculate system responses over a large number of parameter combinations. Nor will it be effective to blindly use DOE-based response surface methodology to analyze the deterministic FEA outputs. In this paper, we will utilize a spatial statistical method (i.e., the Kriging model) for analyzing deterministic FEA outputs from an electronic packaging process. We suggest a sequential method when using the Kriging model to search for the optimal parameter values that minimize the stress level in the electronic packaging. Compared with the traditional RSM, our sequential parameter selection method entertains several advantages: it can remarkably reduce the total number of FEA simulations required for optimization, it makes the optimal solution insensitive to the choice of the initial simulation setting, and it can also depict the response surface and the associated uncertainty over the entire parameter space.

Numerical studies of the mechanical response of solder joint to drop/impact load

The geometry of the solder ball is one of several factors which have significant effects on the reliability of interconnects of electronic packages. Intensive studies of the thermo-mechanical reliability of BGA packages with different solder balls have been reported in recent years. Only a few studies of the geometric shape effect on the reliability of solder joints under drop loading conditions could be found in the literature. Because of the different failure modes and failure mechanisms, the geometric shape effects on the reliability of solder joints could be very different under thermo-mechanical loading condition and drop loading condition. In this paper, the effects of the solder ball geometry on the reliability under drop loading conditions are systematically studied with numerical simulations. The solder ball shape is predicted by using the Surface Evolver software. The solder ball geometry is parameterized with solder volume, diameter, height, and pad size. The variation of stresses on the solder joint/pad interface with solder volume and pad diameter is obtained from numerical simulations. The effect of the solder ball geometric parameters on the drop damage is discussed.

A novel response surface method for design optimization of electronic packages

The response surface method has been widely used in practical engineering design optimization problems, where the optimal searches are based on the response surfaces mimicking the physical processes or models. Sometimes the response surface method is the only practical option to be able to perform design optimization, such as simulation-based design optimization when the simulations are usually computationally expensive. In conventional approaches, the response surfaces are usually built up using a group of sampling points based on certain design of experiment schemes. The accuracy of the response surface depends largely on the number of sampling points and their distributions in the design space, as well as the approximation functions for the response surface. Currently there is no general method that could achieve the necessary accuracy of a response surface with the minimal expensive (or the number of sampling points). In this paper, a novel sequential response surface updating approach is proposed to improve the efficiency and the accuracy of simulation-based optimizations for electronic packages. It is a dynamic and adaptive approach, which starts with a small number of initial sampling points based on Halton sequence (also called quasi Monte Carlo method), and then refines the response surface by adding more sampling points during the optimization process. This method is demonstrated with a design optimization problem of the thermo-mechanical analyses of a ceramic chip carrier assembly. A simplified thermo-mechanical model is used to perform the interfacial stress analysis of the solder bounding. The objective of is to minimize the interfacial stress by changing the bonding compliance in the specified design space. The case study indicates that, comparing with the conventional direct methods, this approach could greatly improve the computational efficiency of optimization processes with the needed accuracy for simulation-based design optimization.

Reliability study of flexible display module by experiments

Flexible display module reliability were investigated herein with experiments, such as bending, twisting and ball drop. The pretests of all the three experiments were carried out firstly to primarily understand the flexibility and mechanical behavior of the display. Based on the pretest results, the corresponding fatigue test setup method and process were put forward. Then, the fatigue tests were executed. At last, through the failure analysis, the flexibility and reliability of the flexible display in different use cases were evaluated. Suggestions about how to use the display and improve the reliability through change the design were given also.

Optimization of a circular thin-film piezoelectric actuator lying on a clamped multilayered elastic plate

A system consisting of a circular multilayered thin-film elastic plate and a piezoelectric actuator, which is generally used for ultrasound generation in air, is studied in this paper. Effects of the electrode dimension of a circular thin-film piezoelectric actuator lying on a clamped multilayered elastic plate are discussed theoretically, while the first-order theory of asymmetrically laminated piezoelectric plates with consideration of coupled extension and flexure of the reference plane is used. Numerical results show that the deflection of the elastic plate can be optimized by adjusting the radius of the top electrode.

Research on an improved amplitude modulation method of audio directional loudspeaker

Aimed at solving the harmonic distortion problem of the DSB (Double Side Band) method which is employed in audio directional loudspeaker, an improved amplitude modulation (AM) method is investigated. According to the parametric acoustic array principle and self-demodulation theory, the theoretical self-demodulation model of the improved AM method is established, and a conclusion that the variational phase in the improved AM method hardly affects the second pressure is drawn. Furthermore, the harmonic distortion of the improved AM method is analyzed theoretically and tested by experiments, and the results show that the improved AM method has a far smaller total harmonic distortion than the DSB method when their modulation factors are equal. However, the improved AM method can only be applied reasonably when the modulation factor is small, because its total harmonic distortion is notable when the modulation factor is high.

Three-Dimensional Modeling and Simulation of a Falling Electronic Device

This article focuses on a realistic mathematical model for multiple impacts of a rigid body to a viscoelastic ground and its comparison to theoretic results. The methodology is used to study impact on an electronic device. When an electronic device drops to the floor at an uneven level, the rapid successions of impact sequence are important for their shock response to internal structure of the devices. A three-dimensional, continuous contact, computational impact model has been developed to simulate a sequence of multiple impacts of a falling rigid body with the ground. The model simulates the impact procedure explicitly and thus is capable of providing detailed information regarding impact load, impact contact surface, and the status of the body during the impact. For the purposes of model verification, we demonstrate the numerical simulation of a falling rod problem, in which the numerical results are in good agreement with the analytic solutions based on discrete contact dynamics impact models. It is indicated by the numerical experiments that simultaneous impacts occurred to multiple locations of the body and that subsequent impacts might be larger than initial ones due to different angles of impact. The differential equation-based computational model is shown to be realistic and efficient in simulating impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device.

Combined stereovision and phase shifting method: use of a visibility-modulated fringe pattern

We propose to use a visibility-modulated fringe pattern to enable real-time image acquisition in the newly proposed combined stereovision and phase shifting method for 3-D shape measurement. The combined stereovision and phase shifting method uses two cameras and one projector and can eliminate errors caused by inaccurate phase measurement, such as periodic errors due to the nonlinearity of the projectors gamma curve. In order to achieve pixel-to-pixel matching between the two cameras, we previously used two phase-shifted fringe patterns, one with fringes in the vertical direction and the other in the horizontal direction. This means that the projected fringe pattern has to be switched during the image acquisition process, which slows down the process. As a result, measurement of dynamically changing objects is difficult. In this paper, we propose to use a visibility-modulated fringe pattern to eliminate the need of the second fringe pattern. This new fringe pattern is sinusoidal in the horizontal direction as in a conventional fringe pattern, but is visibility-modulated in the vertical direction. With this new pattern, we can obtain the phase information in one direction and fringe visibility information in the other direction simultaneously for stereo matching. Since no pattern changing is necessary during the image acquisition process, the image acquisition time can be reduced to less than half of the time previously required, thus making the measurement of dynamically changing objects possible. Experimental results are presented to demonstrate the effectiveness of the proposed method.

Modeling and simulation of multiple impacts of falling rigid bodies

When an electronic device drops at an inclination angle to the floor, the rapid successions of clattering sequence are important for their shock response to circuits, displays and disk drives. This article deals with both analytical and numerical analysis of multiple impacts. A three-dimensional computational dynamics code with a continuous contact impact model has been developed to simulate the multiple impacts of a falling rigid body with the ground. Results from the computational model as well as analytic analysis from a discrete contact impact model indicate that subsequent impacts might be larger than the initial impact in some situations. The differential equation based three-dimensional model is shown to be realistic in simulating a multiple-impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device.