Modelling the capacitance of multi-layer conductor-facing interdigitated electrode structures

Interdigitated electrode structures have applications in a myriad of fields and have become attractive for in-line electrochemical detection in lab-on-a-chip microsystems. Analytical models can replace complex and expensive numerical simulations to determine the capacitance of interdigitated electrode structures in cases where simple geometries can be assumed. Closed-form analytical expressions derived from Schwarz–Christoffel conformal mappings were used to determine the capacitance of multi-layer interdigitated electrode structures with an additional parallel continuous electrode. The partial capacitance approach was reformulated to find the capacitance of multi-layer structures with non-monotonically changing permittivities. The analytical model was found to be in close agreement with finite-element simulations. The model is used for optimization of an insulated transducer for sensitive detection of surface processes.