Charge Transport Systems with Fermi-Dirac Statistics for Memristors

Area of Science:

• Semiconductor Physics
• Mathematical Modeling
• Materials Science

Background:

• Memristive devices are crucial for semiconductor technology.
• Understanding charge carrier dynamics is essential for device performance.
• Existing models require rigorous mathematical analysis for complex systems.

Purpose of the Study:

• To analyze an instationary drift-diffusion system for electron, hole, and oxygen vacancy densities.
• To prove the global existence of weak solutions for these densities coupled with the Poisson equation.
• To establish bounds on densities under realistic physical conditions.

Main Methods:

• Analysis of a coupled drift-diffusion and Poisson system.
• Application of Fermi-Dirac and Blakemore statistics.
• Utilizing free energy inequality and iteration arguments.
• Estimations of the Fermi-Dirac integral.

Main Results:

• Global existence of weak solutions proved for the system in up to three space dimensions.
• Densities are shown to be bounded under a physically realistic elliptic regularity condition.
• The mathematical framework supports the modeling of charge carrier dynamics in memristors.

Conclusions:

• The study provides a rigorous mathematical foundation for memristive device modeling.
• The findings contribute to the theoretical understanding of charge transport in semiconductors.
• This work validates the use of the developed model for simulating memristor behavior.