  This paper introduces a novel unified framework for calculating the first
arrival position (FAP) density in diffusion-based molecular communication (MC)
systems with fully-absorbing receivers, applicable to any spatial dimension or
receiver shape. We validate the effectiveness of our proposed method by
presenting two concrete examples from the MC literature: the 2D line receiver
and 3D spherical receiver. Our approach successfully reproduces existing
results on FAP density and further enhances the original formula for the 2D
line receiver by accommodating arbitrary drift directions. The proposed
framework offers a comprehensive and versatile solution for determining FAP
density in diffusive MC channels with fully-absorbing receivers, paving the way
for more robust and efficient system designs.
