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Experimental and Numerical Investigation of Electromigration Behavior of Printed Silver Wire Under High Current Density 大电流密度下印刷银线电迁移行为的实验与数值研究
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-09-02 DOI: 10.1115/1.4055469
Haibin Zhang, Quanshe Sun, Zhidan Sun, Yebo Lu
The electromigration (EM) damage is becoming a severe problem in the printed flexible electronics as the printed circuits are fabricated thinner and thinner due to the development of printing technology. In this work, the EM behavior of printed silver wires was investigated by EM experiments and numerical simulations. The EM tests showed that voids are generated in the cathode area and hillocks are formed in the anode area for a wire with a small length. However, with the increase of wire length, hillocks tend to occur on the two sides of the silver wire middle part. The results of numerical simulations based on the atomic flux divergence (AFD) method revealed that the formation of the hillocks on the printed wire is caused by not only the mechanism of electron wind, but also the strong temperature gradient along the wire length and width direction. Also, it can be concluded that the temperature gradient induced by Joule heating plays a more important role than electron wind in the atomic migration of the printed silver wire subjected to a high current density. The influence of the printed silver wire size on the EM behavior was also analyzed by numerical simulation, and the results demonstrated that the printed silver wires with a larger length and a smaller width-to-thickness ratio are more likely to develop hillocks on the two sides of silver wire middle part while subjected to a high current density.
随着印刷技术的发展,印刷电路越来越薄,电迁移损伤已成为印刷柔性电子器件中一个严重的问题。本文通过电磁实验和数值模拟研究了印刷银线的电磁行为。电磁测试结果表明,对于较短的导线,在阴极区产生了空洞,在阳极区形成了小丘。但随着银丝长度的增加,银丝中间部分两侧容易出现小丘。基于原子通量散度(AFD)方法的数值模拟结果表明,印刷导线上丘状结构的形成除了受电子风机制的影响外,还受沿导线长度和宽度方向的强温度梯度的影响。在高电流密度下,焦耳加热引起的温度梯度比电子风对印刷银线的原子迁移起着更重要的作用。通过数值模拟分析了印刷银线尺寸对电磁行为的影响,结果表明,在高电流密度下,印刷银线长度越大、宽厚比越小,银线中部两侧越容易出现小丘。
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引用次数: 0
Shear and Fatigue Properties of Lead-Free Solder Joints: Modeling and Microstructure Analysis 无铅焊点的剪切和疲劳性能:建模和微观结构分析
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-08-24 DOI: 10.1115/1.4055318
Xin Wei, M. Belhadi, S. Hamasha, Ali Alahmer, R. Zhao, B. Prorok, N. Sakib
The reliability of SAC-based solder alloys has been extensively investigated after the prohibition of lead in the electronics industry owing to their toxicity. Low-temperature solder (LTS) alloys have recently received considerable attention because of their low cost and reduced defects in complex assemblies. The shear and fatigue properties of individual solder joints were tested using an Instron micromechanical testing system in this research. Two novel solder alloys (Sn-58Bi-0.5Sb-0.15Ni and Sn-42Bi) with low melting temperatures were examined and compared with Sn-3.5Ag and Sn-3.0Ag-0.8Cu-3.0Bi. The surface finish was electroless nickel-immersion gold (ENIG) during the test. Shear testing was conducted at three strain rates, and the shear strength of each solder alloy was measured. A constant strain rate was used for the cyclic fatigue experiments. The fatigue life of each alloy was determined for various stress amplitudes. The failure mechanism in shear and fatigue tests were characterized using scanning electron microscopy/energy-dispersive spectroscopy (SEM/EDS). The results revealed that Sn-3.0Ag-0.8Cu-3.0Bi had superior shear and fatigue properties compared to other alloys, but was more susceptible to brittle failure. The shear strain rate affected the failure modes of Sn-3.0Ag-0.8Cu-3.0Bi, Sn-58Bi-0.5Sb-0.15Ni, and Sn-42Bi; however, Sn-3.5Ag was found to be insensitive. Several failure modes were detected for Sn-3.5Ag in both shear strength and fatigue tests.
在电子工业中禁用铅后,由于其毒性,sac基焊料合金的可靠性得到了广泛的研究。低温焊料(LTS)合金因其低成本和减少复杂组件中的缺陷而受到广泛关注。采用Instron微力学测试系统对单个焊点的剪切和疲劳性能进行了测试。研究了两种新型低温钎料合金Sn-58Bi-0.5Sb-0.15Ni和Sn-42Bi,并与Sn-3.5Ag和Sn-3.0Ag-0.8Cu-3.0Bi进行了比较。在测试过程中,表面光洁度为化学镀镍浸金(ENIG)。在三种应变速率下进行了剪切试验,并测量了每种焊料合金的剪切强度。采用恒应变速率进行循环疲劳试验。测定了各合金在不同应力幅值下的疲劳寿命。利用扫描电镜/能谱分析(SEM/EDS)对剪切和疲劳试验中的破坏机理进行了表征。结果表明:Sn-3.0Ag-0.8Cu-3.0Bi合金具有较好的剪切性能和疲劳性能,但更易发生脆性破坏;剪切应变速率影响Sn-3.0Ag-0.8Cu-3.0Bi、Sn-58Bi-0.5Sb-0.15Ni和Sn-42Bi的破坏模式;而Sn-3.5Ag则不敏感。Sn-3.5Ag在抗剪强度和疲劳试验中检测到多种破坏模式。
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引用次数: 13
An Automatic Fem-bem Coupling Method for Elastic-plastic Problems of Multiscale Structures in Electronic Packaging 电子封装中多尺度结构弹塑性问题的Fem-bem自动耦合方法
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-08-01 DOI: 10.1115/1.4055125
F. Qin, Qi He, Yanpeng Gong, Chuantao Hou, Hao Cheng, Tong An, Yanwei Dai, Pei Chen
We introduce a coupled finite and boundary element method for elastic-plastic analysis over multiscale electronic packaging structures. Based on the FE-BE coupling algorithm, an automatic implementation procedure for the coupling of the Abaqus with a self-written elastic BE code is introduced for elastic problems. In the mixed FEM-BEM model, the effective stiffness and effective forces at the interfacial boundary are evaluated by the self-written BE code. Then, the obtained effective stiffness and effective forces are assembled to the global FE formulations by using the user subroutine (UEL) in Abaqus. Numerical simulation of structures with plastic deformation, stress concentration, etc. is carried out by using FEM theory. The boundary element method is used for linear elastic domains with large-scale structure. The proposed method offers several key improvements compared with current analysis methods available for multi-scale electronic packaging structures. The benefits are: (i) the powerful pre- and post-processing of ABAQUS; (ii) the higher accuracy of the solution; (iii) the computational cost and time can be reduced by using the scheme; and (iv) solving systems with infinite extension by using the BEM as a supplement. Furthermore, we demonstrate the ability of the proposed approach to handle multiscale structures in electronic packaging problems.
我们介绍了一种用于多尺度电子封装结构弹塑性分析的有限元和边界元耦合方法。基于FE-BE耦合算法,针对弹性问题,介绍了一种自动实现Abaqus与自写弹性BE码耦合的过程。在混合FEM-BEM模型中,界面边界处的有效刚度和有效力通过自行编写的BE程序进行评估。然后,使用Abaqus中的用户子程序(UEL)将获得的有效刚度和有效力组装到全局有限元公式中。利用有限元理论对具有塑性变形、应力集中等情况的结构进行了数值模拟。边界元法适用于具有大型结构的线弹性域。与目前可用于多尺度电子封装结构的分析方法相比,所提出的方法提供了几个关键改进。其优点是:(i)ABAQUS强大的预处理和后处理功能;(ii)解的精度越高;(iii)通过使用该方案可以减少计算成本和时间;以及(iv)通过使用边界元作为补充来求解具有无限可拓性的系统。此外,我们还证明了所提出的方法处理电子封装问题中的多尺度结构的能力。
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引用次数: 1
Development and Validation of a Transient Heat Transfer Model for Evaluating Thermal Management Solutions for Packaging Next-Generation Smart City Infrastructure Devices 用于评估下一代智能城市基础设施设备封装热管理解决方案的瞬态传热模型的开发和验证
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-07-26 DOI: 10.1115/1.4055094
Shuv Dey, Luis Diego Monge Jimenez, J. M. Brown, Y. Joshi
Outdoor digital displays have become increasingly popular and common for smart city applications, and more recently provides a concealment solution and integration point for outdoor communications devices meant to be attached to buildings, streetlamps, or traffic poles. Given the larger energy requirements for powering next generation 5G cellular networks, these devices create unique difficulties in developing and evaluating thermal management solutions. The present study develops and validates the extreme condition transient (ECT) climate model using a CFD/HT numerical model, to evaluate diurnal thermal responses from a representative 5G small cell devices. The model is validated for local conditions present in Atlanta, GA for two unique days. The thermal response from the ECT climate model is presented alongside three real case study locations, Miami, FL, New York City, NY, and Phoenix, AZ.
户外数字显示器在智能城市应用中越来越受欢迎和普遍,最近为连接到建筑物、路灯或交通杆的户外通信设备提供了隐藏解决方案和集成点。鉴于为下一代5G蜂窝网络供电的能源需求更大,这些设备在开发和评估热管理解决方案方面带来了独特的困难。本研究使用CFD/HT数值模型开发并验证了极端条件瞬态(ECT)气候模型,以评估具有代表性的5G小电池设备的昼夜热响应。该模型针对佐治亚州亚特兰大的当地条件进行了为期两天的验证。ECT气候模型的热响应与佛罗里达州迈阿密、纽约市和亚利桑那州凤凰城三个真实案例研究地点一起呈现。
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引用次数: 2
Accelerated Solder Interconnect Testing Under Electromigratory and Mechanical Strain Conditions 电迁移和机械应变条件下的加速焊料互连测试
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-07-18 DOI: 10.1115/1.4055024
Mahsa Montazeri, Whit Vinson, D. Huitink
In this work, a novel testing system has been employed to facilitate the estimation of the reliability of solder interconnects under the combined influence of EM and mechanical strain. The system subjects solder interconnects to high current density, elevated ambient temperature, and a constant tensile stress while recording the change in electrical resistance and change in length of the solder over time. The solder samples were created using two copper wires connected by a eutectic Pb/Sn solder ball to imitate flip-chip or BGA packaging interconnects, allowing for controlled testing conditions in order to demonstrate the combined effects of a mechanical load and EM on the lifetime of a solder joint. A significant reduction in lifetime was observed for samples which endured the coupled accelerating factors. Comparing the experimental results of different current densities at different stress levels provided a new outlook on the nature of coupled failure acceleration in solders. This novel test methodology can inform model generation for better anticipating the failure rate of solder interconnects which naturally experience multiple stress inputs during their lifetime.
在这项工作中,采用了一种新的测试系统来方便地估计焊接互连在电磁和机械应变共同影响下的可靠性。该系统将焊料互连置于高电流密度、升高的环境温度和恒定的拉伸应力下,同时记录电阻的变化和焊料长度随时间的变化。焊料样品是用两根铜线通过共晶Pb/Sn焊料球连接而成,以模拟倒装芯片或BGA封装互连,允许控制测试条件,以证明机械负载和EM对焊点寿命的综合影响。寿命的显著减少被观察到的样品经受耦合加速因素。比较不同电流密度下不同应力水平下的实验结果,为研究焊料中耦合破坏加速的性质提供了新的视角。这种新颖的测试方法可以为模型生成提供信息,以便更好地预测焊料互连的故障率,焊料互连在其使用寿命期间自然会经历多次应力输入。
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引用次数: 2
Performance Analysis of Corrosion Resistant Electroless Nickel-Plated Impinging CNC Manufactured Liquid Cooling Cold Plate 耐腐蚀化学镀镍冲击数控制造液冷冷板的性能分析
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-07-13 DOI: 10.1115/1.4054972
Vahideh Radmard, Ahmad R. Gharaibeh, Mohammad I. Tradat, C. H. Hoang, Yaman M. Manaserh, K. Nemati, Scott N. Schiffres, B. Sammakia
More than ever before, data centers must deploy robust thermal solutions to adequately host the high-density and high-performance computing that is in high demand. The newer generation of central processing units (CPUs) and graphics processing units (GPUs) has substantially higher thermal power densities than previous generations. In recent years, more data centers rely on liquid cooling for the high-heat processors inside the servers and air cooling for the remaining low-heat Information Technology Equipment (ITE). This hybrid cooling approach creates a smaller and more efficient data center. The deployment of direct-to-chip cold plate liquid cooling is one of mainstream approaches to providing concentrated cooling to targeted processors. In the current study, a processor level experimental setup was developed to evaluate the cooling performance of a novel Computer Numerical Control (CNC) machined nickel-plated impinging cold plate on a 1 in x 1 in mock heater that represents a functional processing unit. The pressure drop and thermal resistance performance curves of the electroless nickel-plated cold plate are compared to those of a pure copper cold plate. A temperature uniformity analysis is done using CFD and compared to the actual test data. Lastly, the CNC machined pure copper one is compared to other reported cold plates to demonstrate its superiority of the design with respect to the cooling performance.
数据中心比以往任何时候都更需要部署强大的热解决方案,以充分承载高密度和高性能的计算需求。新一代的中央处理单元(CPU)和图形处理单元(GPU)具有比前几代高得多的热功率密度。近年来,越来越多的数据中心对服务器内的高温处理器采用液体冷却,对剩余的低热信息技术设备(ITE)采用空气冷却。这种混合冷却方法创建了一个更小、更高效的数据中心。直接到芯片冷板液体冷却的部署是为目标处理器提供集中冷却的主流方法之一。在当前的研究中,开发了一个处理器级实验装置,以评估新型计算机数控(CNC)加工的镀镍冲击冷板在1英寸x 1英寸模拟加热器上的冷却性能,该加热器代表一个功能处理单元。将化学镀镍冷板与纯铜冷板的压降和热阻性能曲线进行了比较。使用CFD进行温度均匀性分析,并与实际测试数据进行比较。最后,将数控加工的纯铜冷板与其他报道的冷板进行了比较,以证明其在冷却性能方面的设计优势。
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引用次数: 0
The Discussion About the Identification of the Anand Model Parameters and Two Alternative Identification Methods 关于阿南德模型参数辨识及两种辨识方法的讨论
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-06-16 DOI: 10.1115/1.4054821
Yuqian Xu, Qiwen Zeng, Yuexing Wang, Mingyong Wu, Xiangyu Chen, Gang Chen
The Anand model is a unified viscoplastic model which is widely employed to describe the solder material deformation. The parameters in the Anand model for a certain material are usually identified by using the classical method based on two algebraic equations derived from the original differential equation of the Anand model. However, the second algebraic equation describing the relationship between the stress and inelastic strain is obtained with some terms about the unsteady value of internal variable neglected. But the effects induced by the omission of some unsteady terms on the effectiveness of classical method are not researched comprehensively. Therefore, in this paper, the effects of the omitted terms on the accuracy of the classical method are discussed. The inelastic deformation for the material which the second algebraic equation can not describe due to the omission of unsteady terms is presented. The precondition for obtaining accurate results from the second algebraic equation is given out. Two criteria used to judge the effectiveness of the second algebraic equation are derived. To reduce the error related to the second algebraic equation of the classical method for some materials, two alternative identification methods are proposed. By combining the step of solving differential equation and genetic algorithm, the parameters in the Anand model originally identified by the second algebraic equation are determined in the process of the two proposed methods. The effectiveness of the two alternative methods is presented by identifying the material Anand parameters where the classical method can not be applied.
Anand模型是一个统一的粘塑性模型,广泛用于描述焊接材料的变形。对于某种材料,Anand模型中的参数通常是通过使用基于从Anand模型的原始微分方程导出的两个代数方程的经典方法来识别的。然而,在忽略了关于内变量非定常值的一些项的情况下,得到了描述应力和非弹性应变之间关系的第二个代数方程。但是,一些非定常项的遗漏对经典方法有效性的影响并没有得到全面的研究。因此,本文讨论了省略项对经典方法精度的影响。给出了由于省略了非定常项,第二代数方程无法描述的材料的非弹性变形。给出了从第二代数方程中获得精确结果的前提条件。导出了判断第二代数方程有效性的两个准则。为了减少某些材料的经典方法的第二代数方程的误差,提出了两种可供选择的识别方法。通过将求解微分方程的步骤与遗传算法相结合,在两种方法的过程中确定了由第二代数方程识别的Anand模型中的参数。在经典方法无法应用的情况下,通过识别材料Anand参数,证明了两种替代方法的有效性。
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引用次数: 1
Experimental and Numerical Investigations of Intermittence for Electronic Connectors Subjected to Mechanical Shocks 电子连接器在机械冲击下间歇性的实验和数值研究
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-06-16 DOI: 10.1115/1.4054822
T. Huang, K. Liao
A phenomenon of the intermittence is a critical issue for electronic joints of components installed in such as a mobile carrier. In this study, a finite element analysis of DDR4 connector is utilized to assess the dynamic responses of terminal pairs embedded in the polymeric housing subjected to various mechanical shock conditions. Two approaches, respectively based on the contact normal force and relative displacement between the contacting terminal and the associated gold finger, are proposed to investigate the presence of intermittence. The intermittence of the critical terminal pair under various shock conditions along the normal and longitudinal direction of the terminal is found to be strongly related to the contact loss. Under the shock conditions along the transverse direction of the terminal, a threshold of the relative displacement between two reference points is set to effectively and accurately assess the occurrence of intermittence. The elastic/elastic-plastic multi-scale rough surface (MSRS) model adopted to directly estimate the contact resistance history of the terminal pair is further attempted. Relatively low contact resistance of the terminal pair under the condition denoting pass can be observed. On the other hand, a sudden rise of the contact resistance of the terminal pair under the condition referring to fail is demonstrated based on the MSRS model although dramatic underestimations of the contact resistance are given when the contact normal force is rather low.
对于安装在诸如移动载波等电子元件上的电子接头来说,间歇性现象是一个关键问题。在本研究中,利用DDR4连接器的有限元分析来评估嵌入在聚合物外壳中的终端对在各种机械冲击条件下的动态响应。提出了两种方法,分别基于接触法向力和接触终端与相关金手指之间的相对位移,来研究间歇性的存在。在各种冲击条件下,临界端子对沿法向和纵向的间断与接触损耗密切相关。在终端横向冲击条件下,设置两个参考点之间相对位移的阈值,有效准确地评估间歇性的发生。进一步尝试采用弹性/弹塑性多尺度粗糙表面(MSRS)模型直接估计端子对的接触电阻历史。在表示通的条件下,可以观察到端子对的接触电阻相对较低。另一方面,尽管在接触法向力较低时接触电阻被严重低估,但基于MSRS模型证明了在失效条件下端子对的接触电阻会突然上升。
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引用次数: 0
Viscoelastic Influence On the Board Level Assessment of Wafer Level Packages Under Drop Impact and Under Thermal Cycling 粘弹性对跌落冲击和热循环下晶圆级封装板级评估的影响
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-06-13 DOI: 10.1115/1.4054784
Abel Misrak, Rabin Bhandari, D. Agonafer
Structural components such as printed circuit boards (PCBs) are critical in the thermomechanical reliability assessment of electronic packages. Previous studies have shown that geometric parameters such as thickness and mechanical properties like elastic modulus of PCBs have direct influence on the reliability of electronic packages. Elastic material properties of PCBs are commonly characterized using equipment such as tensile testers and used in computational studies. However, in certain applications viscoelastic material properties are important. Viscoelastic influence on materials is evident when one exceeds the glass transition temperature of materials. Operating conditions or manufacturing conditions such as lamination and soldering may expose components to temperatures that exceed the glass transition temperatures. Knowing the viscoelastic behavior of the different components of electronic packages is important in order to perform accurate reliability assessment and design components such as printed circuit boards (PCBs) that will remain dimensionally stable after the manufacturing process. Previous researchers have used creep and stress relaxation test data to obtain the Prony series terms that represent the viscoelastic behavior and perform analysis. Others have used dynamic mechanical analysis in order to obtain frequency domain master curves that were converted to time domain before obtaining the Prony series terms. In this paper, nonlinear solvers were used on frequency domain master curve results from dynamic mechanical analysis to obtain Prony series terms and perform finite element analysis on the impact of adding viscoelastic properties when performing reliability assessment. The computational study results were used to perform comparative assessment to understand the impact of including viscoelastic behavior in reliability analysis under thermal cycling and drop testing for Wafer Level Chip Scale Packages.
结构部件如印刷电路板(pcb)在电子封装的热机械可靠性评估中是至关重要的。以往的研究表明,pcb的厚度等几何参数和弹性模量等力学性能对电子封装的可靠性有直接影响。多氯联苯的弹性材料特性通常使用诸如拉力测试仪之类的设备进行表征,并用于计算研究。然而,在某些应用中,粘弹性材料的性能是重要的。当超过材料的玻璃化转变温度时,粘弹性对材料的影响是明显的。操作条件或制造条件,如层压和焊接,可能使组件暴露在超过玻璃化转变温度的温度下。了解电子封装不同组件的粘弹性行为对于执行准确的可靠性评估和设计组件(如印刷电路板(pcb))非常重要,这些组件在制造过程中保持尺寸稳定。以前的研究人员已经使用蠕变和应力松弛试验数据来获得代表粘弹性行为的proony系列项并进行分析。其他人则使用动态力学分析来获得频域主曲线,在获得普罗尼级数项之前将其转换为时域。本文采用非线性求解方法对动力力学分析得到的频域主曲线结果进行求解,得到proony级数项,并对可靠性评估时加入粘弹性特性的影响进行有限元分析。计算研究结果用于进行比较评估,以了解在热循环和跌落测试下对晶圆级芯片规模封装的可靠性分析中包含粘弹性行为的影响。
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引用次数: 0
Hybrid Monte Carlo-Diffusion Studies of Modeling Self-Heating in Ballistic-Diffusive Regime for GaN HEMTs 氮化镓hemt弹道扩散自热模型的混合蒙特卡罗扩散研究
IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2022-06-01 DOI: 10.1115/1.4054698
Han-Ling Li, Yang Shen, Y. Hua, S. Sobolev, B. Cao
Exact assessment of self-heating is of great importance to the thermal management of electronic devices, especially when completely considering the cross-scale heat conduction process. The existing simulation methods are either based on convectional Fourier's law or limited to small system sizes, making it difficult to deal with non-continuum thermal transport efficiently. In this paper, a hybrid phonon Monte Carlo-diffusion method is adopted to predict device temperature in ballistic-diffusive regime. Heat conduction around the heat generation region and boundaries are simulated by phonon Monte Carlo (MC) method, while the other domain is by Fourier's law. The temperature of the hybrid method is higher than that of Fourier's law owing to phonon ballistic transport, and the calculation efficiency of the hybrid method is remarkably improved compared with phonon MC simulation. Furthermore, the simulation results indicate that the way of modeling self-heating has a remarkable impact on phonon transport. The junction temperature of the heat source (HS) scheme can be larger than that of the heat flux (HF) scheme, which is opposite to the result under Fourier's law. In the HS scheme, the enhanced phonon-boundary scattering counteracts the broadening of the heat source, leading to a stronger ballistic effect and higher temperatures. The conclusion is verified by a one-dimensional analytical model. This work has opened up an opportunity for the fast and extensive thermal simulations of cross-scale heat transfer in electronic devices and highlighted the influence of heating schemes.
准确评估自热对电子器件的热管理具有重要意义,特别是在全面考虑跨尺度导热过程的情况下。现有的模拟方法要么基于对流傅立叶定律,要么局限于小系统尺寸,难以有效处理非连续热输运问题。本文采用混合声子蒙特卡罗-扩散方法预测了弹道扩散状态下的器件温度。用声子蒙特卡罗(MC)方法模拟了热生成区域和边界周围的热传导,另一个区域用傅立叶定律模拟。由于声子的弹道输运,混合方法的温度高于傅立叶定律的温度,与声子MC模拟相比,混合方法的计算效率得到了显著提高。此外,模拟结果表明,自加热的建模方式对声子输运有显著的影响。热源(HS)格式的结温可以大于热流通量(HF)格式的结温,这与傅里叶定律的结果相反。在HS方案中,声子边界散射的增强抵消了热源的展宽,导致更强的弹道效应和更高的温度。通过一维解析模型验证了这一结论。这项工作为电子设备中跨尺度传热的快速和广泛的热模拟提供了机会,并突出了加热方案的影响。
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引用次数: 3
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Journal of Electronic Packaging
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