Three-species drift-diffusion models for memristors

Clément Jourdana (1) , Ansgar Jüngel (2) , Nicola Zamponi (2)

1 EDP - Equations aux Dérivées Partielles
2 Institute for Analysis and Scientific Computing [Wien]

A system of drift-diffusion equations for the electron, hole, and oxygene vacancy densities in a semiconductor, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann boundary conditions. This system describes the dynamics of charge carriers in a memristor device. Memristors can be seen as nonlinear resistors with memory, mimicking the conductance response of biological synapses. In the fast-relaxation limit, the system reduces to a drift-diffusion system for the oxygene vacancy density and electric potential, which is often used in neuromorphic applications. The following results are proved: the global existence of weak solutions to the full system in any space dimension; the uniform-in-time boundedness of the solutions to the full system and the fast-relaxation limit in two space dimensions; the global existence and weak-strong uniqueness analysis of the reduced system. Numerical experiments in one space dimension illustrate the behavior of the solutions and reproduce hysteresis effects in the current-voltage characteristics.

Domaines: Equations aux dérivées partielles [math.AP]

Clément Jourdana, Ansgar Jüngel, Nicola Zamponi. Three-species drift-diffusion models for memristors. Mathematical Models and Methods in Applied Sciences, 2023, 33 (10), pp.2113-2156. ⟨10.1142/S0218202523500501⟩. ⟨hal-03639406⟩