Analytical Modeling of Thermomagnetic Effects on the Dynamic Transport of Minority Carriers in an n⁺-p-p⁺ Silicon Solar Cell under Modulated Illumination

This work develops an analytical model for the dynamic transport of minority electrons in the base of an n？-p-p？ silicon solar cell subjected to a transverse static magnetic field at different temperatures and to modulated polychromatic illumination. The continuity equation is solved in the harmonic regime by accounting for optical generation, bulk and interface recombination, and the thermomagnetic dependence of the diffusion coefficient. The frequency response is described through the complex diffusion length, the complex minority-carrier density, and the complex photocurrent. At 300 K, the zero-field diffusion coefficient is 34.90 cm²/s, whereas the thresholds corresponding to 1% and 10% reductions in Dn are 0.745 T and 2.469 T, respectively. For a carrier lifetime of 1 μs, the characteristic frequency fc is 159.15 kHz. At this frequency, the diffusion-length magnitude is 84.1% of its quasi-static value and its phase is ？22.5？. However, the change in internal transport is not transmitted proportionally to the photocurrent: at 300 K and f = f_c, a 1% reduction in D_n at 0.745 T produces only a 0.0858% attenuation of the photocurrent, whereas the 1% electrical threshold is reached near 2.61 T. Increasing temperature reduces mobility and shifts the magnetic thresholds toward higher fields. The indicators C_TM, S_B and I_TM respectively characterize the normalized magnetic response, define the electrical thresholds and isolate the thermomagnetic interaction relative to 300 K.