Electrostatic Gaussian Transistor for Real-Time Probabilistic Inference

Gaussian distribution functions underpin a wide range of probabilistic computing models, yet their faithful and tunable implementation at the hardware level remains a fundamental challenge. Conventional approaches based on anti-ambipolar transistors rely on heterojunctions formed from dissimilar semiconducting materials, introducing intrinsic asymmetries in carrier mobility, interface quality, and band alignment that prevent accurate mirroring of symmetric Gaussian curves. Here we report a single-material, single-channel split-gate Gaussian-mirroring transistor (SC-GMT) that generates symmetric, Gaussian-shaped transfer curves through reversal voltage biasing. By independently modulating carrier concentrations via split-gate control, the device achieves tunable amplitude, mean, and standard deviation with >99.99% coefficient of determination to ideal Gaussian distributions. To demonstrate practical utility, we integrate the SC-GMT into a custom-built printed circuit board with digital-to-analog control and real-time current sensing. Using this platform, we implement a hardware Gaussian Naive Bayes (GNB) classifier capable of distinguishing deepfake and authentic voices with 82% accuracy. Moreover, the transistor's drain current scales with the product of two gate voltages, enabling quadratic-order analog multiplication critical for probabilistic models and attention-based architectures.