Numerical Analysis and Innovative Simulation Techniques for Designing Advanced MRAM

Abstract

Scaling spin-transfer torque magnetoresistive random access memory (STT-MRAM)to sub-20 nm dimensions poses major challenges for thermal stability, switching reliability, and energy efficiency. As devices shrink, the macro-spin approximation breaks down, requiring a rigorous treatment of non-uniform magnetization dynamics and transport phenomena. This thesis presents a computational framework for modeling and optimizing ultra-scaled, multi-layered magnetoresistive random access memory (MRAM) devices. First, a three-dimensional micromagnetic solver based on finite element method(FEM) is developed. To address the computationally expensive demagnetization field in complex geometries, a hybrid finite element-boundary element method (FE-BEM) is used. Numerical stiffness from the exchange interaction is handled by a tangent-plane time integration scheme, which reformulates the nonlinear Landau–Lifshitz–Gilbert equation as a linear saddle-point problem. This approach is benchmarked against adaptive higher-order backward differentiation formula (BDF) and implicit-explicit(IMEX) methods, demonstrating superior stability and efficiency for the stiff dynamics of ultra-scaled magnetic elements. Central to this work is the extension of the micromagnetic framework to include a coupled spin and charge drift-diffusion formalism. Unlike standard models that assume continuity of spin currents, this work derives and implements specialized boundary conditions. These are used to rigorously describe spin filtering across magnesium oxide(MgO) tunnel barriers and spin dephasing at metallic interfaces. Furthermore, a novel numerical approach for interlayer exchange coupling (IEC) is introduced. This leverages an interface-mapping algorithm to efficiently simulate synthetic antiferromagnet (SAF)without the prohibitive computational cost of volumetric meshing of angstrom-scale spacers. Applying this unified solver reveals that reliability issues in ultra-scaled devices, such as back-hopping, are deterministic consequences of the inter-segment torque hierarchy within composite free layers. They are not stochastic thermal effects. Crucially, this thesis demonstrates that by engineering the relative tunnel barrier polarizations and free layer geometry, this instability can be either suppressed for reliable binary switching or deliberately exploited. This allows realization of multi-level cell (MLC) capable of storing multiple bits per physical cell through distinct intermediate magnetization configurations. Additionally, double-spin torque magnetic tunnel junction (ds-MTJ) architectures are investigated. In these, the cooperation between giant magnetoresistance (GMR) and tunneling magnetoresistance (TMR) torques enables sub-nanosecond switching. When IEC is introduced in advanced multi-layer stacks, it emerges as a unifying design parameter. Specific coupling windows govern the stability of the SAF-enhanced reference layer. Hybrid free layers with metallic spacers exploit the spacer material’s spin-flip length to enhance switching speed. The joint optimization of spacer material and thickness determines write efficiency.