DIFFUSION COEFFICIENT, CHARGE-CARRIER DENSITY, PHOTOCURRENT AND PHOTOVOLTAGE OF A PARALLEL VERTICAL-JUNCTION POLYCRYSTALLINE SILICON SOLAR CELL: COUPLED EFFECTS OF FREQUENCY, GRAIN BOUNDARIES AND GRAIN SIZE

In this work, we present a theoretical study of the combined effect of the modulation frequency (ω), the grain-boundary recombination velocity (Sg) and the grain size (g) on the fundamental transport parameters of a parallel vertical-junction polycrystalline silicon solar cell, namely the effective diffusion coefficient, the minority-carrier density, the photocurrent and the photovoltage. Solving the three-dimensional continuity equation by decomposition into a double Fourier series yields the expressions of these four quantities. Bode and Nyquist diagrams are used to analyse their behaviour. The main result of this work is the identification of a high-frequency convergence regime (beyond ω ≈ 10⁶ rad/s), not previously reported in the literature on polycrystalline solar cells, in which all transport quantities converge toward values set by Sg and g. In this regime the dynamic diffusion length becomes too short for the carriers to reach the grain boundaries before the field reverses, opening the way to dynamic-regime operation as a strategy for partially circumventing microstructural limitations. A second, equally original result emerges from the direct comparison of the short-circuit photocurrent, the open-circuit voltage and the effective diffusion coefficient for the same set of microstructures: whereas D_eff varies by a factor greater than 10 depending on grain-boundary quality, Jsc varies by a factor smaller than 1.25 over the same range. This differential sensitivity reveals that the short-circuit current is a far less discriminating indicator of microstructural quality than base transport or the photogenerated voltage — an observation not formulated in this form in earlier studies of this type of structure.