A simple analytical model, based on reaction-diffusion theory, is developed to predict the trade-off between average response (settling) time (ts) and minimum detectable concentration (?0) for nanobiosensors and nanochemical sensors. The model predicts a scaling relationship ?0tsMD ? kD, where MD and kD are dimensionality dependent constants for one, two, and three dimensional nanosensors. We explore the performance limits of nanosensors using this analytical model and support its conclusions using detailed numerical simulation. Our results have obvious and significant implications for analyte density and response time reported in the literature and for design consideration of nanobiosensors and nanochemical sensors.
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