Reconstruction of Transistor Amplification Principle and Engineering Implementation Based on Status-Relational Entropy (SRE) Dynamics

Nanoscale IC manufacturing faces a critical bottleneck: the stochastic drifting of transistor amplification coefficients (beta) and reference voltages (VT) caused by thermal fluctuations. Traditional engineering relies on redundant on-chip feedback loops to suppress these drifts, incurring severe power and area overheads. This paper eliminates these redundancies by reconstructing transistor physics through a discrete informational statistics framework derived from SRE Dynamics (doi.org). Macroscopic currents are modeled as the absolute convergence of micro-causal Bernoulli trials governed by the Law of Large Numbers. By mapping thermal and processing deviations onto a single dimensionless topological scale ratio (eta), engineers can program the physical base layout geometry (L) to pin single-carrier traversal probabilities. Telemetry and Silvaco TCAD data confirm this method locks current gain, confining thermal drift to under 0.45%/C across 25C to 125C without active or passive compensation circuitry, providing a mask-ready layout blueprint for ultra-precision, low-power microelectronics.