{'fraction_non_alphanumeric': 0.026262626262626262, 'fraction_numerical': 0.0030303030303030303, 'mean_word_length': 5.6066666666666665, '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}}
Modeling and analyzing vertical interconnections

Continual interest in miniaturization is driving electronic packaging toward three-dimensional (3-D) structures and system integration. Utilization of a third dimension allows designers much more freedom, but at the same time it leads to an increase in the complexity of signal routing. High-density of components and interconnection increases the need for electromagnetic (EM) modeling. This paper focuses on EM modeling and the analysis of vertical interconnection in a stacked 3-D package. Solder-plated polymer balls are used in vertical interconnection between interposers and laser-drilled vias through the interposers. High-frequency responses of the vertical interconnections were studied with 3-D full-wave software. Based on the EM analysis, we propose equivalent circuit models for vertical connections, which were verified with measurements. In addition, an impedance-matching technique in vertical interconnection is discussed.