Paradigm Shift at the Boundary: Quantum Limits from Tunneling Barriers to Carbon Nanotubes and Computational Power

Paradigm Shift at the Boundary: Quantum Limits from Tunneling Barriers to Carbon Nanotubes and Computational Power Mehmet Keçeci Orcid: https://orcid.org/0000-0001-9937-9839 Abstract: In classical mechanics, a particle's interaction with a potential barrier is strictly deterministic, governed solely by its kinetic energy relative to the barrier height. However, quantum mechanics introduces a wave-particle duality where particles exhibit non-zero transmission probabilities even when their energy is strictly lower than the potential barrier (E < V), an phenomenon known as quantum tunneling. While this effect has historically served as a foundational proof of quantum mechanics and enabled revolutionary imaging techniques like Scanning Tunneling Microscopy (STM), modern semiconductor scaling limits have transformed this quantum behavior into a destructive mechanism. As silicon-based field-effect transistors (FETs) approach sub-2nm nodes, gate oxide and source-to-drain tunneling cause severe leakage currents and thermal dissipation issues, threatening the continuation of Moore's Law. This comprehensive review analyzes the analytical solutions of the Schrödinger equation for various potential barriers (E>V, E<V, V=∞), examines the physical limits imposed on silicon architectures, and discusses the imminent paradigm shift toward Carbon Nanotube (CNT) field-effect transistors and Quantum Computing architectures that utilize tunneling as a computational asset rather than a parasitic limitation. Keywords: Quantum Tunneling, Schrödinger Equation, Silicon Scaling Limits, Carbon Nanotubes, Quantum Annealing, Resonant Transmission.