Shot Noise Sets the Limit of Quantification in Electrochemical Measurements

Abstract Detection of single molecules, particles, and rapid redox events is a challenge of electrochemical investigations and requires either an amplification strategy or significant averaging in order to boost the electrochemical current above the noise level. We consider the minimum number of electrons required to reach the limit of quantification in these electrochemical measurements. A survey of the literature indicates that the state-of-the-art limit in current detection for different types of measurements (e.g., voltammetry, single-molecule redox cycling, ion channel recordings of single molecules, metal nanoparticle collision, phase nucleation, etc.) is independent of the nature of the measurement and increases linearly with reciprocal response time, Δt-1, over ∼5 orders of magnitude (from ∼10 to ∼106 s-1). We demonstrate that the practical limit of quantification requires cumulative measurement of ∼2,100 electrons during Δt, and is determined by statistics of counting electrons, i.e., the shot noise in the current.