Modeling pyramidal silicon nanopores with effective ion transport

Abstract

While the electrical models of the membrane-based solid-state nanopores have been well established, silicon-based pyramidal nanopores cannot apply these models due to two distinctive features. One is its 35.3° half cone angle, which brings additional resistance to the moving ions inside the nanopore. The other is its rectangular entrance, which makes calculating the access conductance challenging. Here, we proposed and validated an effective transport model (ETM) for silicon-based pyramidal nanopores by introducing effective conductivity. The impact of half cone angle can be described equivalently using a reduced diffusion coefficient (effective diffusion coefficient). Because the decrease of diffusion coefficient results in a smaller conductivity, effective conductivity is used for the calculation of bulk conductance in ETM. In the classical model, intrinsic conductivity is used. We used the top-down fabrication method for generating the pyramidal silicon nanopores to test the proposed model. We found that the ETM can predict the conductance more accurately compared with the classical model. We also found that the ETM is applicable when the ratio of excess ion concentration and bulk ion concentration is smaller than 0.2. At last, it is proved that ETM can estimate the tip size of pyramidal silicon nanopore. We believe the effective transport model would provide an improved method for evaluating the pyramidal silicon nanopores.

Ion Current Rectification and Long-Range Interference in Conical Silicon Micropores

“…In our analysis we exclude the charge on the planar membrane outside the pore, effectively neglecting an edge EDL conductance G s base and G s tip as depicted in Figure a. Other authors have noted that this region on the outside of the pore can contribute to both the Ohmic conductance , and the current rectification , for thin pores with R b / L ≤ 1. The charge on the outside of the membrane not only increases the edge conductance as noted by , but surprisingly can also induce excess ICR .…”

“…Here the reference pressure P 0 = 1 atm. For K + and Cl – we use equal diffusion coefficients D = 1 nm 2 ns –1 , which is somewhat smaller than the bulk diffusion constant at 20 °C and 0.1 M. , Such a discrepancy between channel and bulk diffusion constants has been noted in ref .…”

“…However, to describe our experiments, either theory would need to be extended as the membranes thickness here is similar to the radius of the pores, and the theory therefore has to account for the electric edge resistance which is comparable to the pore resistance. There is a variety of theories available in the literature accounting for Ohmic edge resistance, ,,− , the most commonly used one by Hall, which we reproduce here. In this work we will find that edge resistances do not only alter Ohmic conductance but also significantly alter rectification.…”

“…For application purposes regarding larger scale porous membranes, a low electric resistance of the channel is desirable to mitigate Ohmic losses. Two intuitive ways to construct a channel with low resistance are by making (i) larger openings or (ii) shorter channels. , Considering the accumulation/depletion mechanism described above, recent theoretical work predicts that ICR can also occur in wide channels without overlapping electric double layers, as long as a substantial part of the ionic current is due to surface conductance. ,− In fact, ICR in mesoscopic channels and chemically modified micrometer-sized systems have recently been observed. ,, For thin membranes with short channels, on the other hand, it has become clear that the applied potential partially drops outside the channel rather than fully over the channel itself. ,− These extended entrance effects give rise to an edge, or access, resistance and become relevant for the behavior of a fluidic pore with a channel length of the order of the diameter, which can either positively contribute to ICR or interfere destructively in arrays of pores. − As of now however, such pore–pore interactions are still poorly understood.…”

Editorial for ‘focus collection in memory of Prof Mark A Reed’

“…M Weber, a former member, contributed a series of articles on the theoretical and experimental studies of dielectrophoretic capture and detection of microbial cells [9,10], W Guan, a former member, wrote an article on modeling study of pyramidal silicon nanopores which can be an effective analytical tool for ion transport [11], Y Jung, also a former member, wrote an article on vertically aligned twodimensional (2D) molybdenum disulfide (MoS 2 ) layers for gas sensors [12]. And, M S Strano, a collaborator with Mark Reed, contributed an article on 2D hexagonal boron nitride (hBN) for quantum emission [13].…”