Bi-directional homogenization equivalent modeling for the prediction of thermo-mechanical properties of a multi-layered printed circuit board (PCB)

Abstract

Warpage of multi-layered printed circuit boards (PCB) during the reflow process is a serious problem which affects the reliability of solder ball connections between the PCB and the mounted semi-conductor packages in electronic devices. It is essential to predict the warpage of the PCB accurately; however, the complicated copper patterns in multi-layered PCBs render a full modeling analysis impossible due to the excessive computing time required. To overcome this problem, we have developed analytical equations of three Cu patterns (line, square, and grid) for the application of thermo-mechanical properties simply by equivalent modeling of Cu patterns. In the proposed equations, the effect of thermo-viscoelastic properties as well as the influence of surrounding layers such as woven glass fabric/BT (bismaleimide triazine), composite laminate (BT core), and photoimageable solder resist (PSR) were considered. To verify the developed equations, vibration tests based on the wave propagation approach were performed at various temperatures. Good agreement was observed between the equivalent model and the experimental results.

Model updating for the simulation of surface strains on printed circuit boards considering parameter uncertainty

“…Since printed circuit boards consist of several different materials with complex and thin structures, it is very challenging to build up a detailed model. Especially the copper traces are too complex to be modeled efficiently [13]. Therefore, a homogenization approach is usually applied to incorporate the material properties of the laminate material and the copper traces in a simplified model [14].…”

Developing Reprocessable shape memory thermosetting resins with high thermal resistance and strength through building a crosslinked network based on bismaleimide and epoxy resins

“…Epoxy resin is the most representative type of thermosetting resins and occupies about 70% of the whole market of thermosetting resins, 23 so SMPs based on epoxy resin have attracted great interest, 17,22,[24][25][26] however, these SMPs generally have low heat resistance and insufficient mechanical strength. 18,[20][21][22]24,[27][28][29][30][31] Bismaleimide resin is a typical kind of heat resistant thermosetting resins, and has been applied in many industries including aerospace, 32 insulating materials, 33,34 printed circuit boards, [35][36][37] etc. However, up-to-date, only two reprocessable shape memory resins based on bismaleimide resin (BA1, BA2) were reported in SCI database, 7 which were prepared through copolymerizing bismaleimide with new diallyl compounds containing dynamic ester bonds.…”

“…Bismaleimide resin is a typical kind of heat resistant thermosetting resins, and has been applied in many industries including aerospace, 32 insulating materials, 33,34 printed circuit boards, 35–37 etc. However, up‐to‐date, only two reprocessable shape memory resins based on bismaleimide resin (BA1, BA2) were reported in SCI database, 7 which were prepared through copolymerizing bismaleimide with new diallyl compounds containing dynamic ester bonds.…”

Dual-function thermoelastic cloak based on coordinate transformation theory

“…Temperature rise and unevenly distributed stress on the substrate are often the main reasons of damage. In the field of high-speed PCBs 30 or chips 31 , heat concentration 32,33 and the excitation of elastic waves 34,35 have attracted much attention. Syvret et al 36 analyzed the possible breaking of thermal invisibility caused by coupling effect, illustrating the shortcomings of existing single function cloaks in a coupled field.…”