Mathematical Model and Its Realization of Subthreshold Internal Membrane Dynamics and Implementation in CMOS Neuromorphic Systems

ABSTRACT The ionic flow in biological neurons and electron flow in MOSFETs both exhibit nonlinear behavior, enabling transistors to mimic neuronal spiking. The transistor and capacitor networks form conductive channels analogous to ion channels , , , and , generating membrane‐like voltages and action potentials. The paper introduces mathematical modeling of a silicon neuron that incorporates membrane dynamics through an adaptation mechanism for neuromorphic compatibility. The derived modeling equations are inspired by calcium and voltage‐activated potassium conductances that allow the circuit to self‐regulate firing rates, preventing over‐excitation and enabling energy‐efficient, biologically plausible neuromorphic systems. The same is implemented in a proposed neuron circuit model that uses physical similarities between biological and silicon channels to accurately simulate action potentials and channel currents on the basis of modeling behavior. The design modulates excitatory ion currents and channel time constants, allowing the tuning of spike frequency across a wide range. The simulation results show that the neuron consumes an average power of 15.23 nW and energy efficiency 2.623 fJ/spike at a spike firing rate of 14.66 MHz, and highlight modeling to CMOS neuron implementation (45 nm GPDK, Cadence Virtuoso).