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Zeroth-Order Molecular Kinetics for Linear Symmetric Weight Updates in Neuromorphic Memristors
Why most analog memory devices update their conductance nonlinearly and asymmetrically, and how a molecular memristor avoids it. In oxide filaments, phase-change cells, ferroelectrics and electrochemical synapses the switching steps (ion drift, melt-quench, domain nucleation, charge injection) speed up or saturate as the device fills, so equal pulses give unequal conductance steps. In a ruthenium azo-aromatic complex film, short low-amplitude pulses drive a two-step transition: a fast electron transfer between neighbouring molecules followed by a slow, kinetically limited counterion relaxation that makes the new state non-volatile. Because each pulse converts a constant fraction of the film, the transition follows zeroth-order kinetics, with the same activation energy at every level, and conductance changes linearly and symmetrically over about 16,500 levels spanning four orders of magnitude. A model built from Marcus electron-transfer rates, electrostatic screening along the film thickness and nucleation-limited switching in each layer reproduces this, and shows that linearity needs a slow nucleation rate, small pulse amplitudes, a large coupling ratio between the two states and clean electrode interfaces.