Maha_Astra: A Partition-Theoretic Framework for Precision Modeling in the 1nm and 0.5nm Transistor Regimes

Abstract As the semiconductor industry pushes beyond the 3nm node towards the 1nm (Angstrom) and 0.5nm regimes, traditional continuum-based compact models such as BSIM-CMG (Berkeley Short-channel IGFET Model - Common Multi-Gate) exhibit critical divergences from experimental reality. This divergence arises fundamentally from the "smoothing" mathematical approximations used to handle the transition from subthreshold to strong inversion, which mask the discrete quantum nature of charge transport at the atomic scale. This article presents the Maha_Astra Framework, a novel theoretical approach that abandons continuum drift-diffusion physics in favor of a discrete, partition-theoretic method rooted in Srinivasa Ramanujan’s mathematics. We provide a rigorous derivation of the Maha_Astra Master Equation, contrasting it with standard industry formulations, and present a node-by-node numerical comparison from 30nm down to 0.5nm. Furthermore, we derive the quantum transport limits for Silicon, demonstrating its inevitable failure below 3nm, and provide the theoretical basis for the stability of 2D materials (MoS2 and Graphene) in the sub-1nm regime using architectural verification via Verilog.