{'fraction_non_alphanumeric': 0.0189873417721519, 'fraction_numerical': 0.0045207956600361665, 'mean_word_length': 5.184357541899441, '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}}
Pre-Breakdown Currents Due to Filamentary Thermal Breakdown in Polyimide Films

Pre-breakdown currents in polyimide (PI) films were measured under the application of dc ramp voltage (30 V/s) and the breakdown mechanism is discussed on the basis of the results. A steep current increase was observed from about 10-3 before the breakdown and was ascribed to a thermal runway which results in a filamentary thermal breakdown path. An analytical solution of the pre-breakdown current was obtained on the basis of this filamentary thermal breakdown with a constant filamentary path; it deviated from the experimental data, suggesting a decrease in the effective radius of the filamentary path with time. A numerical calculation of the pre-breakdown current has been carried out for the filamentary thermal breakdown with a temperature distribution in the filament. The calculated pre-breakdown current agrees well with experimental results, and the effective radius of the filament also decreases as observed. From these results, we conclude that filamentary thermal breakdown occurs in PI at high temperatures.