Numerical characterization of electrochemical transport in three-dimensional rhombic zero-depth pores

Three-dimensional (3D) rhombic zero-depth pores present a promising solution to the challenges associated with the requirement for ultrathin membranes in DNA sequencing. This study provides a comprehensive numerical analysis of 3D rhombic zero-depth pores formed at the intersection of triangular microchannels using finite element modeling. The model was validated with a mean absolute error of 2.75% between numerical and experimental results. We identified a critical channel length, beyond which pore conductance varies linearly with the diameter, vertex angle, and electrolyte concentration. We derived a mathematical correlation that provides a predictive framework for non-destructive pore size estimation without microscopy. As the vertex angle increases and the pore geometry approaches that of a 2D pore, its conductance converges toward the electrolyte conductivity. We also analyzed the electric field distribution, which influences signal amplitude and particle dwell time. Results showed maximum field intensity at the mid-plane origin along the Y-axis, with higher values at larger vertex angles and smaller pore diameters. Notably, the strongest electric fields occurred at the mid-points of the mid-plane sides, which we defined as critical points. We also derived equations that can determine the maximum electric field and effective length of the pore based on the applied voltage and the pore's geometrical properties. This study represents a significant advance in understanding zero-depth pores for future sensing and sequencing applications.