{'fraction_non_alphanumeric': 0.017455391776570985, 'fraction_numerical': 0.0, 'mean_word_length': 5.4636591478696745, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A numerical method on thermal and vapor pressure effects on void growth in electronic packaging

Reliability issues associated with thermal-humidity and vapor pressure have become increasingly significant for electronic devices. With the more density of electronic packaging and the trend of lead-free material application, materials of electronic packaging will experience more harsh stress and thermal environment. Therefore, it is significant to investigate failure mechanism of materials applied in microelectronic industry. This paper mainly studies the failure of polymers induced by vapor pressure and thermal stress. During the reflow process, the moisture stored in micro-voids will vaporize and become vapor pressure which causes dilation of the voids in polymer materials. Ultimately, with the voids growing to a critical value, popcorn failure will take place. Hence, in this paper, we firstly analysis the deformation of voids which are subjected to internal vapor pressure and thermal stress simultaneously under the assumption of large deformation. And then the finite element method is applied to simulate the growth of voids under the linear elastic and non-linear model via the commercial FEM software, respectively. By comparison, we may conclude that the deformation on large deflection theory is “stiffer” than that predicted by small. Additionally, numerical results under the infinitesimal deformation assumption have a good agreement with the classical solution in linear elastic theory. Further in this paper, the increase of void volume fractions with respect to vapor pressure are obtained under small and large deformation assumption, respectively. According to the results we acquire, it is notable that the growth of void volume fractions is linearly dependent with the increase of vapor pressure under infinitesimal deformation assumption and nonlinearly dependent on the large deformation theory. Besides, the non-linear constitutive model is taken into consideration in our study. Combining the geometrical non-linearity and material non-linearity analysis, the growth of void volume fractions with respect to vapor pressure are obtained, when the hyperelastic constitutive model is incorporated, which is compared with the consequence without consideration of material non-linearity. At last, we simulate the dynamic growth of voids during the reflow process, and we can clearly see the change of voids with respect to time. This paper will present us a profound understanding of growth of micro voids from the perspective of numerical methods.