Towards Unification of Conservation Laws, Circuit Theory and Semiconductor Physics: A First-Principles Theory for Semiconductor Behaviors

Abstract

Transistors are core component across all domains of electrical and electronic engineering (EEE), such as data centers,^1,2 electrified transportation,^3,4 robotics,⁵ renewables^6,7 and grid applications,^8-10 etc. Transistors’ switching behavior governs energy loss, carbon emissions, cooling demand, water use, lifetime, material use and cost etc. throughout EEE. Despite near a century since the transistor’s invention,^11,12 the understanding of transistor switching remains fragmented: switching is treated as a black box relying on observed waveforms, cannot be explained using physical laws alone, and is not integrated into circuit theory. This forms one of the most critical barriers to recognizing the true physical boundaries, prohibiting more sustainable solutions. For example, the conventional E_on prediction model, derived from the conventional switching analysis, exhibits significant prediction errors (ranging from 34.41% to 80.05%). Here we present a unified first-principles paradigm to explain the switching phenomena. Using this paradigm, we revealed the physical origins and mechanisms of switching-ON phenomena across scenarios, and derived the proposed E_on prediction model, with error ranging from 0.88% to 11.60%, achieving a 17-fold average improvement. These results demonstrate the unprecedented power of the proposed paradigm: textbook-level foundations are established, transforming the fundamental understanding of transistor switching from empirical to first-principles analysis, and simultaneously stimulating follow-up research and applications for sustainable development across disciplines including materials science,^13,14 semiconductor physics,^15,16 device engineering,^17,18 packaging,^19,20 reliability,^21,22 thermal management,^2,23 power electronics,^24,25 and even sustainability sciences,^2,26,27 standards,²⁸ economics,²⁹ policy^30,31 and education.^32,33