The application of an efficient rectangular finite element to the modeling of nonlinear electrothermal memory switching structures

Memory switching devices depend upon Joule heating to cause a thermally induced transition from a low to a high conductive state. The electric field and the temperature field are coupled because the electrical conductivity is a function of the temperature and the heat generated is a consequence of the current flow. The electrical conductivity also depends upon the electric field. When the thermal and electric material properties depend upon the temperature, the coupled field equations become nonlinear. The electric field is assumed to be quasi-static and the temperature field is transient.;The finite element method, employing the Newton-Raphson iteration scheme, was applied to solve the fully coupled nonlinear electric and temperature field equations. The computation was very intensive for the nonlinear and coupled problem. A four-node rectangular element that could be integrated exactly has been developed to reduce the computation time. In comparison with the models using four-node isoparametric element, models using four-node rectangular element were numerically solved three times faster with the same degree of accuracy.;A numerical model has been developed to simulate the switching process of an n...