{'fraction_non_alphanumeric': 0.017316017316017316, 'fraction_numerical': 0.0, 'mean_word_length': 5.801470588235294, '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}}
Two-dimensional Analysis of Resonant Tunneling Using the Time-dependent Schrödinger Equation

Numerical solution of the time-dependent two-dimensional Schrödinger equation is used here to analyze resonant tunneling in double-barrier structures. One-dimensional simulation is shown to be insufficient even for a system with a perfect barrier, which is regarded as one-dimensional because it does not include the two-dimensional effect attributed to the effective mass difference between the barrier and well regions. The effect of barrier roughness on tunneling characteristics is also analyzed and the transmitted fraction is calculated for various systems with different structural parameters, including the roughness of the barrier. Decomposition of the fraction into transverse momentum clarifies tunneling characteristics in two dimensions, and two-dimensional calculation is shown to be necessary for accurate analysis.