Quantitative modeling of the non-monotonic sensitivity of defect-engineered graphene sensors

Defect engineering has been explored as a means to improve the performance of graphene-based gas sensors. However, sensor sensitivity often exhibits a non-monotonic relationship with defect density, presenting challenges for device optimization. In this study, we introduce a quantitative physical model aimed at describing and explaining this behavior. Graphene samples were irradiated with deuteron ions to generate a controlled range of defect densities, which were characterized using Raman spectroscopy. Sensitivity to hydrogen showed a Λ-shaped dependence on defect density, with a peak response observed at an intermediate concentration. This behavior is attributed to the competing effects of signal enhancement and structural degradation induced by defects. The proposed model expresses sensitivity as a function of two experimentally derived parameters: an activation coefficient (C_n) and a degradation coefficient (γ_n). These parameters provide physical insight into the underlying sensing mechanism.