Compact Modeling of 2D Field-Effect Biosensors

Francisco Pasadas¹, Tarek El Grour², Enrique G. Marin¹, Alberto Medina-Rull¹, Alejandro Toral-Lopez¹, Juan Cuesta-Lopez¹, Francisco G. Ruiz¹, Lassaad El Mir² and Andrés Godoy¹

Compact Modeling of Two-Dimensional Field-Effect Biosensors.

Sensors 2023, 23, 1840.

DOI: 10.3390/s23041840

1 Pervasive Electronics Advanced Research Laboratory (PEARL), Departamento de Electrónica y Tecnología de Computadores, Universidad de Granada,18071 Granada, Spain
2 Laboratory of Physics of Materials and Nanomaterials Applied at Environment (LaPhyMNE) LR05ES14, Faculty of Sciences of Gabes, Gabes University, Erriadh City, Zrig, 6072 Gabes, Tunisia

Abstract: A compact model able to predict the electrical read-out of field-effect biosensors based on two-dimensional (2D) semiconductors is introduced. It comprises the analytical description of the electrostatics including the charge density in the 2D semiconductor, the site-binding modeling of the barrier oxide surface charge, and the Stern layer plus an ion-permeable membrane, all coupled with the carrier transport inside the biosensor and solved by making use of the Donnan potential inside the ion-permeable membrane formed by charged macromolecules. This electrostatics and transport description account for the main surface-related physical and chemical processes that impact the biosensor electrical performance, including the transport along the low-dimensional channel in the diffusive regime, electrolyte screening, and the impact of biological charges. The model is implemented in Verilog-A and can be employed on standard circuit design tools. The theoretical predictions obtained with the model are validated against measurements of a MoS2 field-effect biosensor for streptavidin detection, showing excellent agreement in all operation regimes and leading the way for the circuit-level simulation of biosensors based on 2D semiconductors

FIG: Schematic of a two-dimensional field-effect biosensor. A sketch of the position-dependent potential is also shown, highlighting the surface charge density at the 2D channel (σ2D), at the oxide-electrolyte interface (σ0), and at the membrane-diffuse regions of the electrolyte (σmd). The latter comprises a charge-free layer (Stern layer) and an ion-permeable membrane due to the presence of charged macromolecules, with a diffusion layer located between the barrier oxide surface and the bulk electrolyte. The potential difference from the electrolyte bulk to the barrier oxide surface, ψ0, encompasses two contributions originating from a potential drop (ψ0 − ψm) across the Stern layer extending between the outer Helmholtz plane (OHP) and the barrier oxide surface, and a potential drop across the ion-permeable membrane layer formed by charged macromolecules and the diffuse layer (ψm)

Funding: This work is funded by the Spanish Government MCIN/AEI/10.13039/501100011033 through the projects PID2020-116518GB-I00 and TED2021-129769B-I00 (MCIU/AEI/FEDER-UE); and by FEDER/Junta de Andalucía-Consejería de Transformacion Económica, Industria, Conocimiento y Universidades through the projects P20_00633 and A-TIC-646-UGR20. F. Pasadas acknowledges funding from PAIDI 2020 and the European Social Fund Operational Programme 2014–2020 no. 20804. A. Medina-Rull acknowledges the support of the MCIN/AEI/PTA grant, with reference PTA2020- 018250-I. J. Cuesta-Lopez acknowledges the FPU program FPU019/05132, and A. Toral-Lopez the support of Plan Propio of Universidad de Granada.

Data Availability Statement: The Verilog-A model for 2D EIS BioFETs is available from the corresponding author (fpasadas@ugr.es) upon reasonable request.