A direct comparison of 2D versus 3D diffusion analysis at nanowire electrodes: A finite element analysis and experimental study

Abstract

In electroanalysis, the benefits accrued by miniaturisation are a key driver in sensor development. Finite element simulations of electrochemical processes occurring at ultramicro- and nano-electrodes are used to provide key insight into experimental design in relation to diffusion profiles and expected currents. The most commonly used method, the diffusion domain approach (DDA) offers a means of reducing a three dimensional design to two dimensions to ease computational demands. However, the DDA approach can be limited when using basic assumptions which can be incorrect, for example that all electrodes in an array are equivalent. Consequently, to get a more realistic view of molecular diffusion to nanoelectrodes, it is necessary to undertake simulations in 3D. In this work, two and three dimensional models of electrodes comprising of (i) single nanowires, (ii) arrays of nanowires and (iii) interdigitated arrays of nanowires operating in generator-collector mode, were undertaken and compared to experimental results obtained from fabricated devices. The 3D simulations predicted a higher extracted current for a single nanowires and diffusionally independent nanowire arrays when compared to 2D simulations since, unlike the 2D model, they take into account molecular diffusion to and from nanowire termini. These current differences were observed to increase with increasing electrode width and decrease with electrode length. When the nanowire arrays were diffusionally overlapped, they behaved as an electrode of larger width, and the divergence between both models increased further. By contrast, using interdigitated nanowire arrays in generator-collector mode, the differences between extracted current values obtained using the 2D and 3D models were significantly lower. Simulations indicated however, that a higher collection efficiency was predicted by the 2D model when compared to the 3D model. Electrochemical experiments were undertaken to confirm the simulation study and demonstrated that the extracted currents from 3D simulations more closely mapped onto experimentally measured currents.