Analytical and Numerical Modelling of Electron Transmission Probability Through Quantum Tunnelling Barriers in Nanoscale Diodes


Authors : Pratham Dungrani

Volume/Issue : Volume 10 - 2025, Issue 11 - November

Google Scholar : https://tinyurl.com/56dv8m8e

Scribd : https://tinyurl.com/4x8j6v88

DOI : https://doi.org/10.38124/ijisrt/25nov007

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Abstract : Quantum tunnelling becomes critical in nanoelectronic devices as dimensions approach or fall below the electron mean free path, wherein the classical transport models are no longer sufficient to describe carrier behavior. Accordingly, transmission of electrons across barriers is analyzed in nanodiodes within this paper using three main approaches: the Schrödinger Equation Method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Transfer Matrix Method. These methods have been applied to various tunneling situations involving barriers of different height and width, as well as semiconductor material interfaces representative of state-of-the-art device architectures in capturing the wavelike nature of electron transport typical at nanometric scales. A comparison is carried out in regard to the accuracy, efficiency of computation, and physical insights gained through each approach. Strengths and weaknesses of the above-mentioned techniques will be considered in view a variety of barrier profiles and device structures. Calculations based on self-consistent potentials in Si and GaAs hetero-structures exhibit strong exponential behavior of the tunneling current and barrier parameters. Consistency between methods appears only under the following special conditions of barrier variation. These results are discussed in relation to the emerging importance of a new class of tunneling-based devices: MIMs, RTDs, and TFETs, all promising for next-generation electronic and optoelectronic systems. These findings provide a conceptual and practical basis for the understanding and designing of nanoscale devices where tunneling is a dominant transport mechanism, adding an important comprehensive perspective to quantum transport modeling in nanoelectronics.

Keywords : Quantum Tunneling, Nanoelectronics, Schrödinger Equation, WKB Approximation, Transfer Matrix Method, Tunneling Probabilities, Metal–Insulator–Metal Diodes, Resonant Tunneling Diodes, Tunneling Field-Effect Transistors, Electron Transmission, Potential Barriers, Nanoscale Devices, Computational Efficiency, Silicon, Gallium Arsenide, Self-Consistent Potential Profiles, Quantum Mechanics in Nanoelectronics, Device Modeling, Barrier Height, Barrier Width, Material Interfaces, Numerical Simulations.

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  • Further Reading
  1. Agrawal, A., & Tiwari, R. (2021). Comparative study of analytical and numerical tunneling models for nanoscale devices. arXiv preprint arXiv:2109.11865. https://doi.org/10.48550/arXiv.2109.11865
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  3. Bagwell, P. F. (1990). Suppression of the Josephson current through a narrow, mesoscopic semiconductor channel by a single impurity. Physical Review B, 41(2), 10354–10357. https://doi.org/10.1103/PhysRevB.41.10354
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Quantum tunnelling becomes critical in nanoelectronic devices as dimensions approach or fall below the electron mean free path, wherein the classical transport models are no longer sufficient to describe carrier behavior. Accordingly, transmission of electrons across barriers is analyzed in nanodiodes within this paper using three main approaches: the Schrödinger Equation Method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Transfer Matrix Method. These methods have been applied to various tunneling situations involving barriers of different height and width, as well as semiconductor material interfaces representative of state-of-the-art device architectures in capturing the wavelike nature of electron transport typical at nanometric scales. A comparison is carried out in regard to the accuracy, efficiency of computation, and physical insights gained through each approach. Strengths and weaknesses of the above-mentioned techniques will be considered in view a variety of barrier profiles and device structures. Calculations based on self-consistent potentials in Si and GaAs hetero-structures exhibit strong exponential behavior of the tunneling current and barrier parameters. Consistency between methods appears only under the following special conditions of barrier variation. These results are discussed in relation to the emerging importance of a new class of tunneling-based devices: MIMs, RTDs, and TFETs, all promising for next-generation electronic and optoelectronic systems. These findings provide a conceptual and practical basis for the understanding and designing of nanoscale devices where tunneling is a dominant transport mechanism, adding an important comprehensive perspective to quantum transport modeling in nanoelectronics.

Keywords : Quantum Tunneling, Nanoelectronics, Schrödinger Equation, WKB Approximation, Transfer Matrix Method, Tunneling Probabilities, Metal–Insulator–Metal Diodes, Resonant Tunneling Diodes, Tunneling Field-Effect Transistors, Electron Transmission, Potential Barriers, Nanoscale Devices, Computational Efficiency, Silicon, Gallium Arsenide, Self-Consistent Potential Profiles, Quantum Mechanics in Nanoelectronics, Device Modeling, Barrier Height, Barrier Width, Material Interfaces, Numerical Simulations.

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