Analytical modelling of In0.25Ga0.75N nanowire HEMT utilizing FEM analysis and SRH recombination for breast cancer biomolecule

Abstract

This work establishes a finite element drift–diffusion framework that integrates polarization sheet charge boundary conditions and Shockley–Read–Hall (SRH) recombination to accurately model an InGaN nanowire HEMT biosensor. The formation of the two-dimensional electron gas (2DEG) and two-dimensional hole gas (2DHG) is a result of both spontaneous and piezoelectric polarization at the subband discontinuities of the InGaN/GaN interface. Analysis reveals that the overall effect of the 2DEG and 2DHG significantly influences the filling of quantum levels, with maximum sheet carrier charge densities of approximately 1.5 × 10⁻¹³ cm⁻² occurring at a distance of 2 nm, followed by a secondary peak around 13.5 nm. The electrostatic potential assessments indicate a notable energy band bending of − 3.0 eV at 5 nm at the heterojunction interface. The sheet density is calculated using a combination of Schrödinger–Poisson equations and quantum-corrected drift–diffusion methods, which are then integrated over the confinement region. The biosensing mechanism is effectively incorporated as a surface charge density at the gate dielectric’s top boundary, resulting in a threshold voltage shift that is influenced by quantum, electrostatic effects and the charge density profile. The coupled system comprises Poisson’s equation along with continuity equations for both holes and electrons. This setup includes drift–diffusion currents and SRH recombination, while the interface jump conditions necessitate the inclusion of polarization charges. By meticulously parameterizing material properties such as subband offsets, effective sheet carrier densities, total polarization constants, mobilities and trap lifetimes, the simulation successfully reproduces I_d–V_g characteristics, 2DEG/2DHG distributions, electrostatic effects, charge density profiles, as well as wave functions and wave probability density functions corresponding to quantum energy levels relevant to breast cancer-related biomolecular interactions. This comprehensive modelling framework lays the foundation for advancing the design and effectiveness of biosensors aimed at detecting critical biomolecular signals.