Design and optimization of an Ag/Cu–black phosphorus/Franckeite heterostructure for high-sensitivity surface plasmon resonance biosensing

Introduction Surface plasmon resonance (SPR) biosensors enable label-free, real-time detection, but simultaneously achieving strong field confinement, near-critical coupling, and a high figure of merit (FoM) remains challenging, particularly when low-loss silver must be protected from aqueous media. Methods A CaF 2 /Ag/Cu/black phosphorus (BP)/Franckeite Kretschmann heterostructure was modeled at λ = 633 nm using the frequency-domain Maxwell wave equation and the transfer matrix method under TM-polarized angular and phase interrogation. The Ag and Cu thicknesses were optimized individually and jointly, size-dependent Drude damping corrections were applied, and performance was benchmarked against a Cu-only reference with identical BP/Franckeite overlayers. Fabrication tolerance to BP layer number and Franckeite thickness was also evaluated. Results Joint optimization identified a near-critical-coupling configuration at approximately 31 nm Ag and 7 nm Cu, with a minimum reflectance of 1.1 × 10 −3 within the sensing window. Over 1.328–1.336 RIU, the sensor reached a peak angular sensitivity of 372°/RIU and a FoM of 47.0 RIU −1 at n s = 1.332, approximately 62% and 78% higher than the Cu-only reference. Phase interrogation reached 29,200°/RIU, corresponding to a minimum detectable refractive-index change of approximately 3.4 × 10 −7 RIU. The 1/e evanescent-field penetration depth was 178–201 nm. Size-dependent damping reduced the FoM by approximately 5%, and realistic 2D-layer thickness variations reduced it by no more than approximately 10%. Discussion The Ag/Cu/BP/Franckeite architecture is a promising platform for label-free biosensing, including carcinoembryonic antigen (CEA) detection, subject to experimental validation of long-term stability, surface functionalization, and thermally compensated phase readout.