This work aims to elucidate the underlying physical mechanisms of quantum tunneling in one-dimensional complex potential barrier systems. By integrating the analytical scattering matrix (S-matrix) formalism with tight-binding numerical simulations using the Kwant package, we systematically investigate the influence of barrier geometry and configuration on the electron transmission spectrum. The theoretical analysis establishes the systematic advantages of the S-matrix approach over the conventional wave-function elimination method for treating cascaded systems. This formalism is then employed to derive and generalize a Fabry-Pérot-like resonant tunneling law for multi-barrier structures, which is governed jointly by intra- and inter-barrier interference. Numerical simulations for various configurations, including rectangular, trapezoidal, parabolic, and periodic multiple barriers, reveal that a single barrier with a complex geometry can be effectively analyzed by discretizing it into multiple rectangular segments. For multi-barrier systems, the transmission properties are dominated by both intra – and inter-barrier interference. Unlike in the single-barrier case, this leads to the formation of sharp transmission peaks even for incident electron energies within the classically forbidden region. Furthermore, an increase in the number of barriers significantly enhances the overall impediment to electron transmission, while the added complexity of the barrier configuration affords greater control over the tunneling process. This study deepens the understanding of electron tunneling and quantum coherence in complex potential landscapes, providing theoretical support for the design of functional quantum devices based on the resonant tunneling effect.
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Luo, J., He, J. (2024) Research on Multi-Configuration Barrier Quantum Tunneling and Fabry-Pérot-like Interference Phenomenon Based on Kwant. Scientific Research Bulletin, 1(6), 14-35.