TY - JOUR

T1 - A method of recursive images to obtain the potential, the electric field and capacitance in multi-layer interdigitated electrode (IDE) sensors

AU - Dias, C. J.

AU - Igreja, R.

N1 - sem pdf conforme despacho.
Portuguese Foundation for Science and Technology -UID/CTM/50025/2013

PY - 2017/4/1

Y1 - 2017/4/1

N2 - InterDigitated electrodes (IDE) have been widely used in chemical and biosensors showing huge potential. Nevertheless, calculation of electric field, electric potential, charge and capacitance remain difficult in many cases, in particular when the IDE are embedded in multilayered structures. On these cases time consuming Finite Element Methods (FEM) are still needed to compute its electric properties. In this work a method of Recursive Images is presented to find the electric potential, field and capacitance in multilayered IDE sensors. This method starts with the analytical equations for these quantities, obtained from the conformal mapping of the IDE with a semi-infinite layer. Then, using the method of images, while considering the lower interface containing the electrode as an electric line source, we find the solution for an interface between two dielectrics. After that, through a recursive application of the method of images, at the upper and the lower interfaces, one establishes the overall solution for a 1-finite layer IDE sensor. In addition, resorting to a similar reasoning as for the 1-finite layer algorithm, the method is extended to deal with IDEs of 2- and 3-finite layers in a way that can be easily generalized to an n-finite layer IDE sensor. Furthermore, the capacitance of the IDE sensors is also calculated using the Method of Recursive Images. Three simulations are performed of IDE sensors of 1, 2 and 3 finite layers and their results compared and discussed with those using the FEM. It was found that the Method of Recursive Images gives accurate results, when the dielectric constant of the substrate is large relative to that of the first layer, while still giving excellent results, for a dielectric constant of the substrate of a lower value.

AB - InterDigitated electrodes (IDE) have been widely used in chemical and biosensors showing huge potential. Nevertheless, calculation of electric field, electric potential, charge and capacitance remain difficult in many cases, in particular when the IDE are embedded in multilayered structures. On these cases time consuming Finite Element Methods (FEM) are still needed to compute its electric properties. In this work a method of Recursive Images is presented to find the electric potential, field and capacitance in multilayered IDE sensors. This method starts with the analytical equations for these quantities, obtained from the conformal mapping of the IDE with a semi-infinite layer. Then, using the method of images, while considering the lower interface containing the electrode as an electric line source, we find the solution for an interface between two dielectrics. After that, through a recursive application of the method of images, at the upper and the lower interfaces, one establishes the overall solution for a 1-finite layer IDE sensor. In addition, resorting to a similar reasoning as for the 1-finite layer algorithm, the method is extended to deal with IDEs of 2- and 3-finite layers in a way that can be easily generalized to an n-finite layer IDE sensor. Furthermore, the capacitance of the IDE sensors is also calculated using the Method of Recursive Images. Three simulations are performed of IDE sensors of 1, 2 and 3 finite layers and their results compared and discussed with those using the FEM. It was found that the Method of Recursive Images gives accurate results, when the dielectric constant of the substrate is large relative to that of the first layer, while still giving excellent results, for a dielectric constant of the substrate of a lower value.

KW - Capacitive sensors

KW - Interdigitated electrodes

KW - Method of images

KW - Recursive images

KW - Sensor modelling

UR - http://www.scopus.com/inward/record.url?scp=85012085324&partnerID=8YFLogxK

U2 - 10.1016/j.sna.2017.01.021

DO - 10.1016/j.sna.2017.01.021

M3 - Article

AN - SCOPUS:85012085324

VL - 256

SP - 95

EP - 106

JO - Sensors and Actuators A: Physical

JF - Sensors and Actuators A: Physical

SN - 0924-4247

ER -