Residual Thermal Strain Distribution Measurement of Underfills in Flip Chip Electronic Packages by an Inverse Approach Based on the Sampling Moiré Method

Abstract

Residual deformation evaluation of underfill (UF) materials in flip chips is crucial to improve the reliability of electronic packages. In this study, we propose to evaluate the residual thermal strain distributions using an inverse method based on the sampling moiré technique. Even if a grid pattern is fabricated on the specimen at room temperature, the residual strain distributions at an arbitrary temperature relative to the specimen formation temperature can be successfully calculated. The residual strain distributions relative to the free contraction state at an arbitrary temperature can also be measured when the coefficient of thermal expansion is available. A thermal chamber for flip chips was designed under a laser scanning microscope. Using the proposed method, the normal, shear and principal internal strain distributions and deformation characteristics of two kinds of UFs in flip chips were investigated relative to 150 °C. The strains of the UF with low glass transition temperature (UF-A) concentrate near the die material, especially at the die corner, while the strain concentration of the underfill with high glass transition temperature (UF-B) mainly occurs at the die corner and the buffer layer. The maximum principal strain of UF-A is greater than that of UF-B around the die corner. The residual maximum principal strain distributions relative to the free contraction state at 25 °C were compared with the simulation results by the finite element method. The residual strain distribution trends from experiments are consistent with those from simulations.

Identification of thermomechanical parameters based on the virtual fields method combined with the sampling moiré method

“…Generally, the cubic spline interpolation was implemented to generate the phase-shifting moiré fringes. [24] Furthermore, the moiré phase can be calculated from the phase-shifting method using a discrete Fourier transform (DFT) algorithm [31] :…”

“…In the SM method, the grating is downsampled with sampling pitch p s , and then moiré patterns are generated by cubic spline interpolation. [24] Taking a one-dimensional SM method as an example, owing to the lack of sufficient grayscale information near the specimen edges, overinterpolation will occur, which results in a large phase error (see Figure 5). Figure 5a indicates that because of equally spaced sampling, the interpolated values of the moiré patterns near the specimen edges exceeded the original range of the grey value.…”

“…Generally, the cubic spline interpolation was implemented to generate the phase‐shifting moiré fringes. [ 24 ] Furthermore, the moiré phase can be calculated from the phase‐shifting method using a discrete Fourier transform (DFT) algorithm [ 31 ] : The relationship between the phase difference and displacement fields between a deformed state and an initial state can be represented by [ 31 ] where represents the moiré phase after deformation, represents the moiré phase of the initial state, and u x and u y represent the displacement fields in the x and y directions, respectively.…”

“…In recent years, the sampling moiré (SM) method has rapidly developed as a new moiré technique and has been widely applied in deformation measurements at the macro-and micro-scales. [24][25][26][27][28] Compared with MI, the SM method does not require highdensity diffraction gratings and can achieve high-precision measurements using low-frequency gratings. Moreover, the fabrication procedure for gratings in the SM method is simpler, more efficient and low-cost, especially for heat-resistant gratings.…”

Measurement of microscopic strain distributions of CFRP laminates with fiber discontinuities by sampling moiré method

“…The DIC method is simple but weak against noise because the deformation carrier is speckled, which is difficult to extract from random noise. In contrast, ESPI has high deformation sensitivity but requires strong anti-vibration measures [30] aside from the costs.…”