PINN Monte Carlo based InGaN nanowire HEMT for the prediction model optimization using residual for breast cancer biomolecule

The objective of this work is to have a comprehensive framework integrating Poisson's equation, the Schrödinger equation, and charge transport through drift-diffusion within a ML-neural network training paradigm. The model undergoes 3000 epochs of training, using a fused loss function that incorporates data-driven losses together with physical residuals explicitly to the Poisson’s, Schrödinger’s equations, boundary conditions (BC), and normalization. This approach is meant to optimize datasets comprehensively depending on device physics to ensure convergence of total loss across varying lengths of diameter (d = 10, 15 & 20) nm, leveraging a mesh grid with (N = 100) points. Applying a Finite Element Method (FEM) combined with Physics-Informed Neural Networks Monte Carlo (PINN-MC), to the framework models InGaN nanowire High Electron Mobility Transistors (HEMTs). It effectively predicts charge density and electric potential changes prompted by breast cancer biomolecular interactions, including shifts in threshold voltage (V t ). The analysis integrates physics-based equations, countenancing accurate assessments of device performance, counting critical factors like strain and charge transport. The FEM framework adeptly simulates essential aspects such as band structures, potential profiles, quantum confinement, and electric field distributions. The resultant PINN-MC model for In 0 . 25 Ga 0 . 75 N nanowire HEMT biosensors unifies semiconductor physics encapsulated in partial differential equations with deep learning optimization techniques. This synergy results in specific and interpretable predictions amid complex quantum states, crucial for evaluating electrostatic potential, sheet carrier density, normalized drain current, limit of detection (LOD), sensitivity, signal-to-noise ratio (SNR), and optimizing device performance under varying noise levels associated with biomarker concentrations. This innovative methodology establishes a robust foundation for analysing key performance metrics, including mean detection limit (LOD), maximum sensitivity, and noise at levels of 1%, 5%, and 10%. The findings contribute significantly to advancing biosensor technology in detecting biomarkers with high precision.