Characterization of Non-linear Polymer Properties to Predict Process Induced Warpage and Residual Stress of Electronic Packages

Nonlinear thermo-mechanical properties of advanced polymers are crucial to accurate prediction of the process induced warpage and residual stress of electronics packages. The Fiber Bragg grating (FBG) sensor based method is advanced and implemented to determine temperature and time dependent nonlinear properties. The FBG sensor is embedded in the center of the cylindrical specimen, which deforms together with the specimen. The strains of the specimen at different loading conditions are monitored by the FBG sensor. Two main sources of the warpage are considered: curing induced warpage and coefficient of thermal expansion (CTE) mismatch induced warpage. The effective chemical shrinkage and the equilibrium modulus are needed for the curing induced warpage prediction. Considering various polymeric materials used in microelectronic packages, unique curing setups and procedures are developed for elastomers (extremely low modulus, medium viscosity, room temperature curing), underfill materials (medium modulus, low viscosity, high temperature curing), and epoxy molding compound (EMC: high modulus, high viscosity, high temperature pressure curing), most notably, (1) zero-constraint mold for elastomers; (2) a two-stage curing procedure for underfill materials and (3) an air-cylinder based novel setup for EMC. For the CTE mismatch induced warpage, the temperature dependent CTE and the comprehensive viscoelastic properties are measured. The cured cylindrical specimen with a FBG sensor embedded in the center is further used for viscoelastic property measurements. A uni-axial compressive loading is applied to the specimen to measure the time dependent Young’s modulus. The test is repeated from room temperature to the reflow temperature to capture the time-temperature dependent Young’s modulus. A separate high pressure system is developed for the bulk modulus measurement. The time temperature dependent bulk modulus is measured at the same temperatures as the Young’s modulus. The master curve of the Young’s modulus and bulk modulus of the EMC is created and a single set of the shift factors is determined from the time temperature superposition. The supplementary experiments are conducted to verify the validity of the assumptions associated with the linear viscoelasticity. The measured time-temperature dependent properties are further verified by a shadow moiré and Twyman/Green test.

Assessing the influence of abiotic factors and leaf-level properties on the stability of growing-season canopy greenness in a deciduous forest

Maps depicting spatial pattern in the stability of summer greenness could advance understanding of how forest ecosystems will respond to global changes such as a longer growing season. Declining summer greenness, or “greendown”, is spectrally related to declining near-infrared reflectance and is observed in most remote sensing time series to begin shortly after peak greenness at the end of spring and extend until the beginning of leaf coloration in autumn,. Understanding spatial patterns in the strength of greendown has recently become possible with the advancement of Landsat phenology products, which show that greendown patterns vary at scales appropriate for linking these patterns to proposed environmental forcing factors. This study tested two non-mutually exclusive hypotheses for how leaf measurements and environmental factors correlate with greendown and decreasing NIR reflectance across sites. At the landscape scale, we used linear regression to test the effects of maximum greenness, elevation, slope, aspect, solar irradiance and canopy rugosity on greendown. Secondly, we used leaf chemical traits and reflectance observations to test the effect of nitrogen availability and intrinsic water use efficiency on leaf-level greendown, and landscape-level greendown measured from Landsat. The study was conducted using Quercus alba canopies across 21 sites of an eastern deciduous forest in North America between June and August 2014. Our linear model explained greendown variance with an R2=0.47 with maximum greenness as the greatest model effect. Subsequent models excluding one model effect revealed elevation and aspect were the two topographic factors that explained the greatest amount of greendown variance. Regression results also demonstrated important interactions between all three variables, with the greatest interaction showing that aspect had greater influence on greendown at sites with steeper slopes. Leaf-level reflectance was correlated with foliar δ13C (proxy for intrinsic water use efficiency), but foliar δ13C did not translate into correlations with landscape-level variation in greendown from Landsat. Therefore, we conclude that Landsat greendown is primarily indicative of landscape position, with a small effect of canopy structure, and no measureable effect of leaf reflectance. With this understanding of Landsat greendown we can better explain the effects of landscape factors on vegetation reflectance and perhaps on phenology, which would be very useful for studying phenology in the context of global climate change

Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems

We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method successively extracts information from the previous hierarchical residual to the current hierarchical term at a finer hierarchical scale. As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of finitely many hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.