Accurately reproducing the measured scattering matrix of black carbon (BC) through numerical simulations remains a challenge. Researchers have developed various morphological models of BC and computed their scattering matrices in attempts to replicate experimental measurements. However, prior simulation endeavors frequently encountered issues such as significant discrepancies with observational data, implausible particle shapes, or unsuitable computational parameters. In this study, we developed a fractal-based overlapping and necking model to represent the morphology of bare BC particles. We computed the scattering matrices for both individual particles and particle population using these models and compared the results with the previously reported measurements. Our findings revealed that the overlapping model reproduces the measured scattering matrix elements more accurately, whereas the necking model fails to achieve similar consistency. At a wavelength of 532 nm, the overlapping model yields F 22(pi)/F 11(pi) ranging from 0.80 to 0.99 for single particles and from 0.86 to 0.99 for particle population, both of which are much closer to the experimental observations than those of the necking model. In contrast, only a small subset of results from the necking model falls within the measured range. The overlapping model outperforms the necking model in reproducing the scattering matrix and should be preferred for representing bare BC particles. The established understanding provides useful guidance for retrieving microphysical parameters of BC from polarization features and for diminishing the uncertainties associated with its radiative forcing estimates.