The Reliability of Microalloyed Sn-Ag-Cu Solder Interconnections Under Cyclic Thermal and Mechanical Shock Loading

In this study, the performance of three microalloyed Sn-Ag-Cu solder interconnection compositions (Sn-3.1Ag-0.52Cu, Sn-3.0Ag-0.52Cu-0.24Bi, and Sn-1.1Ag-0.52Cu-0.1Ni) was compared under mechanical shock loading (JESD22-B111 standard) and cyclic thermal loading (40 ± 125°C, 42 min cycle) conditions. In the drop tests, the component boards with the low-silver nickel-containing composition (Sn-Ag-Cu-Ni) showed the highest average number of drops-to-failure, while those with the bismuth-containing alloy (Sn-Ag-Cu-Bi) showed the lowest. Results of the thermal cycling tests showed that boards with Sn-Ag-Cu-Bi interconnections performed the best, while those with Sn-Ag-Cu-Ni performed the worst. Sn-Ag-Cu was placed in the middle in both tests. In this paper, we demonstrate that solder strength is an essential reliability factor and that higher strength can be beneficial for thermal cycling reliability but detrimental to drop reliability. We discuss these findings from the perspective of the microstructures and mechanical properties of the three solder interconnection compositions and, based on a comprehensive literature review, investigate how the differences in the solder compositions influence the mechanical properties of the interconnections and discuss how the differences are reflected in the failure mechanisms under both loading conditions.     

Fully Electrical Modeling of Thermoelectric Generators with Contact Thermal Resistance Under Different Operating Conditions

The Seebeck effect is used in thermoelectric generators (TEGs) to supply electronic circuits by converting the waste thermal into electrical energy. This generated electrical power is directly proportional to the temperature difference between the TEG module’s hot and cold sides. Depending on the applications, TEGs can be used either under constant temperature gradient between heat reservoirs or constant heat flow conditions. Moreover, the generated electrical power of a TEG depends not only on these operating conditions, but also on the contact thermal resistance. The influence of the contact thermal resistance on the generated electrical power have already been extensively reported in the literature. However, as reported in Park et al. (Energy Convers Manag 86:233, 2014) and Montecucco and Knox (IEEE Trans Power Electron 30:828, 2015), while designing TEG-powered circuit and systems, a TEG module is mostly modeled with a Thévenin equivalent circuit whose resistance is constant and voltage proportional to the temperature gradient applied to the TEG’s terminals. This widely used simplified electrical TEG model is inaccurate and not suitable under constant heat flow conditions or when the contact thermal resistance is considered. Moreover, it does not provide realistic behaviour corresponding to the physical phenomena taking place in a TEG. Therefore, from the circuit designer’s point of view, faithful and fully electrical TEG models under different operating conditions are needed. Such models are mainly necessary to design and evaluate the power conditioning electronic stages and the maximum power point tracking algorithms of a TEG power supply. In this study, these fully electrical models with the contact thermal resistance taken into account are presented and the analytical expressions of the Thévenin equivalent circuit parameters are provided.     

Megawatt-Scale Application of Thermoelectric Devices in Thermal Power Plants

Despite the recent investment in renewable and sustainable energy sources, over 95% of the UK’s electrical energy generation relies on the use of thermal power plants utilizing the Rankine cycle. Advanced supercritical Rankine cycle power plants typically have a steam temperature in excess of 600°C at a pressure of 290 bar and yet still have an overall efficiency below 50%, with much of this wasted energy being rejected to the environment through the condenser/cooling tower. This paper examines the opportunity for large-scale application of thermoelectric heat pumps to modify the Rankine cycle in such plants by preheating the boiler feedwater using energy recovered from the condenser system at a rate of approximately 1 MW_th per °C temperature rise. A derivation of the improved process cycle efficiency and breakeven coefficient of performance required for economic operation is presented for a typical supercritical 600-MW_e installation.     

Numerical Modeling of Passive Microwave Devices

Passive linear bilateral microwave devices principally include guided wave transmission structures, their junctions, and interconnections, as well as such complex devices as resonant cavities and planar networks. The computational methods for analyzing the behavior of this class of structures and for characterizing them for purposes of network design are brieily reviewed.     

Effect of Cyclic Thermal Loading on the Microstructure and Thermoelectric Properties of CoSb<Subscript>3</Subscript>

The effect of cyclic thermal loading on the microstructure and thermoelectric properties of CoSb₃ was investigated. The microstructures of the samples were characterized by x-ray diffractometry, scanning electron microscopy, energy dispersive x-ray spectrometry and density measurements. The electrical conductivity, the Seebeck coefficient and the thermal conductivity were measured from room temperature to 800 K. Under cyclic thermal loading, antimony partially volatilized from the surface of the sample, and the density obviously decreased. After 2000 cycles, the phase composition of the sample remained stable, and the average grain size did not change significantly. Moreover, the electrical conductivity varied only slightly, except in the low temperature region. The Seebeck coefficient decreased slightly. However, the thermal conductivity changed remarkably with increasing numbers of thermal cycles.     

Analysis of Multilayered Microelectronic Packaging Under Thermal Gradient Loading

An accurate estimation of interfacial and axial stresses in multilayered structures is important in the design process of microelectronic packaging because these stresses drive the failure modes in the package. During manufacturing, microelectronic packaging devices usually suffer from severe thermal gradients. Design engineers often simplify the thermal gradient case as an isothermal loading case by averaging the temperature of the top and bottom of the microelectronic packaging device. Such simplification usually underestimates the stress level in the devices. With the analytical model presented in this paper, the stresses in multilayered microelectronic packaging devices subjected to thermal gradient loading can easily be predicted. It is shown that ignoring the thermal gradient in the package leads to underestimation of stresses     

Thermoelectric Module Design Under a Given Thermal Input: Theory and Example

Established thermoelectric theory enables direct calculation of the power output and conversion efficiency if the temperature difference across a module is given. However, in some applications such as those using a radioisotope or solar radiation as a heat source, the thermal input remains constant while the temperature difference varies with the geometry of the thermoelectric module. In this paper, a theoretical framework for thermoelectric module design under a given thermal input is presented. It provides a convenient approach for module geometry optimization. The usefulness of the theory is demonstrated through a design study, in which an appropriate thermoelement length for a solar thermoelectric system is determined by considering conflicting requirements for a longer length to obtain a greater temperature difference and for a shorter length to produce a larger power output.     

An Introduction to System-Level,Steady-State and Transient Modeling and Optimization of High-Power-Density Thermoelectric Generator Devices Made of Segmented Thermoelectric Elements

High-power-density, segmented, thermoelectric (TE) elements have been intimately integrated into heat exchangers, eliminating many of the loss mechanisms of conventional TE assemblies, including the ceramic electrical isolation layer. Numerical models comprising simultaneously solved, nonlinear, energy balance equations have been created to simulate these novel architectures. Both steady-state and transient models have been created in a MATLAB/Simulink environment. The models predict data from experiments in various configurations and applications over a broad range of temperature, flow, and current conditions for power produced, efficiency, and a variety of other important outputs. Using the validated models, devices and systems are optimized using advanced multiparameter optimization techniques. Devices optimized for particular steady-state operating conditions can then be dynamically simulated in a transient operating model. The transient model can simulate a variety of operating conditions including automotive and truck drive cycles.     

Modeling of a Thermoelectric Generator for Thermal Energy Regeneration in Automobiles

In the field of passenger transportation a reduction of the consumption of fossil fuels has to be achieved by any measures. Advanced designs of internal combustion engine have the potential to reduce CO₂ emissions, but still suffer from low efficiencies in the range from 33% to 44%. Recuperation of waste heat can be achieved with thermoelectric generators (TEGs) that convert heat directly into electric energy, thus offering a less complicated setup as compared with thermodynamic cycle processes. During a specific driving cycle of a car, the heat currents and temperature levels of the exhaust gas are dynamic quantities. To optimize a thermoelectric recuperation system fully, various parameters have to be tested, for example, the electric and thermal conductivities of the TEG and consequently the heat absorbed and rejected from the system, the generated electrical power, and the system efficiency. A Simulink model consisting of a package for dynamic calculation of energy management in a vehicle, coupled with a model of the thermoelectric generator system placed on the exhaust system, determines the drive-cycle-dependent efficiency of the heat recovery system, thus calculating the efficiency gain of the vehicle. The simulation also shows the temperature drop at the heat exchanger along the direction of the exhaust flow and hence the variation of the voltage drop of consecutively arranged TEG modules. The connection between the temperature distribution and the optimal electrical circuitry of the TEG modules constituting the entire thermoelectric recuperation system can then be examined. The simulation results are compared with data obtained from laboratory experiments. We discuss error bars and the accuracy of the simulation results for practical thermoelectric systems embedded in cars.     

Hybrid Analytical/Numerical Coupled-Mode Modeling of Guided-Wave Devices

In this paper, a general version of coupled-mode theory for frequency-domain scattering problems in integrated optics is proposed. As a prerequisite, a physically reasonable field template is required, that typically combines modes of the optical channels in the structure with coefficient functions of in principle arbitrary coordinates. Upon 1D discretizations of these amplitude functions into finite elements, a Galerkin procedure reduces the problem to a system of linear equations in the element coefficients, where given input amplitudes are included. Smooth approximate solutions are obtained by solving the system in a least squares sense. The versatility of the approach is illustrated by means of a series of 2D examples, including a perpendicular crossing of waveguides, and a grating-assisted rectangular resonator. As an Appendix, we show that, alternatively, a similar procedure can be derived by variational means, i.e., by restricting a suitable functional representation of the full 2D/3D vectorial scattering problem (with transparent influx boundary conditions for inhomogeneous exterior) to the respective field templates.     

Two-Dimensional Static Numerical Modeling and Simulation of AlGaN/GaN HEMT

考虑AlGaN/GaN材料的自发、压电极化效应和量子效应,通过泊松方程、薛定谔方程和流体力学方程组的数值自洽求解方法,对AlGaN/GaN HEMT的二维静态模型与模拟问题进行了研究,得到了器件区域的导带图、二维电子气分布、电子温度特性、直流输出和转移特性,并对模拟结果进行了分析与讨论.     

AlGaN/GaN HEMT二维静态模型与模拟

考虑AlGaN/GaN材料的自发、压电极化效应和量子效应,通过泊松方程、薛定谔方程和流体力学方程组的数值自洽求解方法,对AlGaN/GaN HEMT的二维静态模型与模拟问题进行了研究,得到了器件区域的导带图、二维电子气分布、电子温度特性、直流输出和转移特性,并对模拟结果进行了分析与讨论.     

Numerical Modeling and Design of Thermoelectric Cooling Systems and Its Application to Manufacturing Machines

In this work the properties of thermoelectric modules (TEMs) and their behavior have been numerically modeled. Moreover, their applications very often require modeling not only of the TEM but also of the working environment and the product in which they will be working. A clear example is the fact that TEMs are very often installed with heat-dissipating elements such as fans, heat sinks, and heat exchangers; thus, the module will only work according to the heat dissipation conditions that these external sources can provide in a certain environment. In this context, analytic approaches, even though they have been proved to be useful, do not provide enough, accurate information in this regard. Therefore, numerical modeling has been identified as a powerful tool to improve detailed designs of thermoelectric solutions. This paper presents numerical simulations of a TEM in different working conditions, as well as with different commercial dissipation devices. The objective is to obtain the characteristic curve of a TEM using a valid numerical model that can be introduced into larger models of different applications. Also, the numerical model of the module and different cooling devices is provided. Both of them are compared against real tested modules, so that the deviation between them can be measured and discussed. Finally, the TEM is introduced into a manufacturing application and results are discussed to validate the model for further use.     

Thermal Modeling of a Hybrid Thermoelectric Solar Collector with a Compound Parabolic Concentrator

In this study radiant light from the sun is used by a hybrid thermoelectric (TE) solar collector and a compound parabolic concentrator (CPC) to generate electricity and thermal energy. The hybrid TE solar collector system described in this report is composed of transparent glass, an air gap, an absorber plate, TE modules, a heat sink to cool the water, and a storage tank. Incident solar radiation falls on the CPC, which directs and reflects the radiation to heat up the absorber plate, creating a temperature difference across the TE modules. The water, which absorbs heat from the hot TE modules, flows through the heat sink to release its heat. The results show that the electrical power output and the conversion efficiency depend on the temperature difference between the hot and cold sides of the TE modules. A maximum power output of 1.03 W and a conversion efficiency of 0.6% were obtained when the temperature difference was 12°C. The thermal efficiency increased as the water flow rate increased. The maximum thermal efficiency achieved was 43.3%, corresponding to a water flow rate of 0.24 kg/s. These experimental results verify that using a TE solar collector with a CPC to produce both electrical power and thermal energy seems to be feasible. The thermal model and calculation method can be applied for performance prediction.     

Compact Empirical Modeling of Nonlinear Dynamic Thermal Effects in Electron Devices

An original empirical approach to deal with nonlinear dynamic thermal effects in electron devices is proposed. The new technology-independent approach is very compact and easy to implement in computer-aided design tools. Therefore, it can be easily coupled with electrical device models in order to obtain accurate electrothermal models that are suitable for nonconstant-envelope RF applications (e.g., pulsed radar). Model equations and identification procedures are derived in this paper. Validation results and comparison with simplified models are also presented both for a simulated field-effect transistor device, as well as for a real heterojunction bipolar transistor device.      

D2-FBGA热循环载荷下的结构参数优化

利用动态机械分析仪(DMA),测定环氧模塑封材料(EMC)的粘弹性数据;经过数据拟合处理,得到有限元仿真所需的相关参数.将D2-FBGA中芯片厚度、粘结剂厚度、部分EMC厚度及基板厚度作为优化参数,选用正交实验设计,建立了这四个参数的正交表;并用MSC、 Marc,计算了D2-FBGA在热循环载荷下的热应力分布.通过统计软件stata,建立了最大等效应力与上述参数的关系的回归方程;分析了各个结构参数对器件最大等效应力的影响程度;使用单纯形法,得出一组最优结构参数及对应的最大等效应力值.结果表明:通过优化,器件的最大等效应力从(90.58 MPa)下降到66.84 MPa,优化效果明显.     

Efficiency Study of a Commercial Thermoelectric Power Generator (TEG) Under Thermal Cycling

Thermoelectric generators (TEGs) make use of the Seebeck effect in semiconductors for the direct conversion of heat to electrical energy. The possible use of a device consisting of numerous TEG modules for waste heat recovery from an internal combustion (IC) engine could considerably help worldwide efforts towards energy saving. However, commercially available TEGs operate at temperatures much lower than the actual operating temperature range in the exhaust pipe of an automobile, which could cause structural failure of the thermoelectric elements. Furthermore, continuous thermal cycling could lead to reduced efficiency and lifetime of the TEG. In this work we investigate the long-term performance and stability of a commercially available TEG under temperature and power cycling. The module was subjected to sequential hot-side heating (at 200°C) and cooling for long times (3000 h) in order to measure changes in the TEG’s performance. A reduction in Seebeck coefficient and an increase in resistivity were observed. Alternating-current (AC) impedance measurements and scanning electron microscope (SEM) observations were performed on the module, and results are presented and discussed.     

Preparation of Bi0.5Sb1.5Te3 Thermoelectric Materials by Pulse-Current Sintering Under Cyclic Uniaxial Pressure

The effects of applying cyclic uniaxial pressure during the pulse-current sintering process on the crystal alignment and thermoelectric properties of p-type Bi_0.5Sb_1.5Te₃ were investigated. Sintering was performed at 673 K using pulse-current heating under 70 MPa or 100 MPa of cyclic uniaxial pressure. x-Ray diffraction patterns and electron backscattered diffraction analyses showed that application of the cyclic uniaxial pressure enhanced crystal grain orientation. The texture consisted of flattened crystal grains stacked in the thickness direction of the sintered materials. The hexagonal c-plane strongly tended to align in the direction perpendicular to the uniaxial pressure. Owing to the crystal alignment, the Hall mobility in the direction perpendicular to the uniaxial pressure became larger than that of equivalent samples prepared with a constant uniaxial pressure. As a result of the increase in Hall mobility, the resistivity of the material was decreased while the equivalent Seebeck coefficient was maintained and the power factor was improved.