Explicit and locally one-dimensional finite-difference time-domain methods incorporated with memristor

Abstract

The analyses and applications of memristor have attracted much interest recently due to its widespread potentials in nanoelectronics as memory devices, computer logics and other nanoscale devices. Circuit analyses and simulations involving memristor have been relied mainly on its SPICE model, while full-wave electromagnetic (EM) modeling of memristor is still generally lacking. The finite-difference time-domain (FDTD) method is a flexible full-wave method that has been widely used and adopted in many EM problems, including EM analysis of circuits with lumped elements such as resistors, capacitors and inductors. Hereby, the explicit and locally one-dimensional (LOD) FDTD methods incorporated with memristor are proposed, whereby the update equations are derived based on Maxwell's equations along with the physical model of memristor given by Hewlett-Packard (HP) lab. According to the physical model, memristor is considered as variable resistor with its resistance (memristance) varying with electric charge. Memristance is also defined as the derivative of magnetic flux with respect to electric charge. In the FDTD update equations, the memristance is updated along with Maxwell's equations based on the dopant width of memristor device. Numerical results on the accuracy, efficiency and stability of the explicit FDTD method are given. The simulation results obtained from the explicit FDTD method is found to be in good agreement with those obtained from SPICE model in Advanced Design System (ADS). In addition to explicit FDTD method, the LOD-FDTD method incorporated with memristor is also proposed to circumvent the Courant-Friedrich-Lewy (CFL) stability criterion. To further enhance the computational efficiency, the fundamental LOD (FLOD) FDTD method is implemented, which achieves higher efficiency and simplicity with matrix-operator-free right-hand sides (RHS). The implicit update equations are judiciously formulated in two procedures using modified splitting matrices for memristor-incorporated FLOD-FDTD method. Numerical results are provided to demonstrate the stability of the method for time step larger than CFL limit, as well as trade-off between efficiency and accuracy.