  Electrochemical biosensors and the related concept of redox detection at
nanogap electrodes are increasingly explored for ultra-sensitive detection of
biomolecules. While experimental demonstrations have been encouraging, the
associated design and optimization of electrode geometry, beyond the simple
one-dimensional architectures, is inherently challenging from multiple aspects
related to numerical complexity. Here we develop a facile simulation scheme to
address this challenge using well established electronic circuit analysis
techniques that are available as open source-ware. Based on this approach, we
show that electrode geometry, especially nano-structured redox electrodes on a
planar surface, has interesting implications on the detection limits and
settling time of electrochemical biosensors. The methodology we developed and
the insights obtained could be useful for electrode optimization for a wide
variety of problems ranging from biosensors to electrochemical storage.
