A bimetallic Ag/Cu/black-phosphorus/franckeite surface plasmon resonance biosensor for label-free detection of carcinoembryonic antigen (CEA): A transfer-matrix design study

We report the design, transfer-matrix optimization and a fairly exhaustive numerical characterization of a bimetallic silver/copper plasmonic biosensor coated with monolayer black phosphorus (BP) and a thin franckeite overlayer, arranged on a calcium-fluoride (CaF 2 ) prism in the Kretschmann attenuated total reflection geometry, and intended for the label-free detection of carcinoembryonic antigen (CEA) at a working wavelength of 633 nm. Throughout, the metal permittivities are taken from the single, standard Johnson and Christy data set, a deliberate choice whose importance we return to repeatedly: with those constants silver has a plasmonic quality factor Q = −Re(ε)/Im(ε) ≈ 36, roughly four times that of copper (Q ≈ 8.5), so the low-loss advantage of silver that drives the whole design is genuine rather than an artifact of an optimistic input. The optimized six-layer stack CaF 2 /Ag(28 nm)/Cu(7 nm)/BP(0.53 nm)/franckeite(1.8 nm)/sensing reaches near-perfect critical coupling, with a reflectance minimum of about 6 × 10 −6 ; the thin copper film behaves as a phase-matching buffer that lets the silver film meet an impedance condition it cannot satisfy on its own on a low-index prism. Over a deliberately realistic bulk-index window (n s = 1.330–1.334) the device shows an angular sensitivity S ≈ 320 °RIU −1 , a resonance width FWHM ≈ 8.3° and a figure of merit FoM ≈ 39 RIU −1 . Against an equally optimized copper-only reference at the same metal budget, the bilayer raises the figure of merit by about one half, narrows the dip by roughly a tenth and lifts the sensitivity by about a third. A phase analysis shows that, close to critical coupling, the phase sensitivity exceeds 3 × 10 4 °RIU −1 , which translates into a bulk-index resolution near 3 × 10 −6 RIU. We are explicit about what the low-index prism costs (a broad, near-grazing resonance that caps the figure of merit) and about the gap between a bulk-index resolution and a clinically meaningful CEA concentration, which only a surface-binding model can bridge.