Bypassing the Memory Wall: A Unified Quantum-Ballistic Paradigm for Sub-5nm VLSI Interconnects

As semiconductor scaling approaches the 2nm regime, classical copper (Cu) interconnects experience a catastrophic failure known as the “Wire Wall,” characterized by Anderson Localization and exponential resistance growth. This paper presents a unified solution to the “Memory Wall” by transitioning from diffusive drift to ballistic waveguiding. We derive a unified mathematical model addressing Latency (τ ) and Energy (E) via the Bose-Ramanujan Mahalanobis (BRM) framework, demonstrating a 4080x reduction in power density and the mathematical elimination of length-dependent latency.