Self-consistent drift-diffusion modelling of photoinduced halide segregation in wide-bandgap perovskite solar cells

Wide-bandgap mixed-halide perovskites for tandem solar cells undergo photoinduced halide segregation (the Hoke effect): under illumination the halides demix into iodide-rich, low-bandgap domains that pin the open-circuit voltage. We solve Poisson's equation with the electron, hole and mobile-ion continuity equations while the local band gap follows a segregation order parameter. After validation against analytical benchmarks and an independent solver, an imposed iodide-rich region lowers the open-circuit voltage by 48 mV and the efficiency by 1.7 percentage points at a 0.15 eV photoluminescence red-shift, and by 127 mV and 6.8 percentage points at 0.30 eV, at almost unchanged short-circuit current; the voltage penalty per unit red-shift lies between 0.27 and 0.49 depending on the band-offset partition. Segregation also reduces the impedance arc and alters the hysteresis. When the order parameter is driven by the local photocarrier density through a phenomenological closure, the amplitude, time constant and threshold of segregation are model inputs, whereas its spatial organisation is an output: a reversible low-gap region forms on the illuminated side of the absorber behind a mesh-converged front, grows with light intensity and bias, and is suppressed at short circuit. Its formation, location and reversibility survive five alternative driving laws, a halide back-diffusion length and band-gap-coupled absorption, whereas the sharpness of the front and of the intensity threshold are specific to the reference law. The magnitude of the resulting loss (here 29 mV and 2.9 percentage points) is set by the chosen parameters and requires experimental calibration. The solver is openly available.