A Time Scaling Theory for Multi-Layer Electronic Systems

Abstract: For six decades, Moore's geometric scaling drove progress in semiconductors. That industry compact no longer holds: returns from pure dimensional shrinking have flattened, leading-edge design budgets exceed one billion dollars per chip, and cost-per-transistor at the most advanced nodes is no longer falling. This perspective argues for a successor scaling principle — τ scaling —that adopts time itself, rather than transistor area, as the primary metric of progress, applying a single characteristic time constant τ as the unifying optimization target across twelve orders of magnitude, from a switching transistor to a data-center workload. Two production-scale demonstrations are presented. On a mobile SoC, LogicFolding — a methodology that partitions digital, analog, and memory circuits across vertically stacked active tiers — delivers a 55% step-wise increase in transistor density and a 41% power-efficiency gain at a fixed device node. On AI systems, a co-designed stack comprising the memory-semantic Unified Bus fabric, near-packaged Hi-ONE optical I/O, and edge-to-surface 3D Folding projects more than 100× growth in hardware integration by 2035.The deeper claim is methodological: τ scaling is the first scaling principle since Dennard to establish a shared optimization target across the entire computing stack.