Modeling and Simulation of Topological Insulators, Topological Semi-Metals and Ferrimagnets for Time and Energy Efficient Switching of Magnetic Tunnel Junction
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Magnetic Tunnel Junction (MTJ) sits at the very heart of all spintronic devices with possible applications in on/off-chip memories, sensors etc. The most significant step in the operation cycle of MTJ is the switching of the magnetization direction of the free magnetic layer (write operation). Fast and energy-efficient switching of MTJ is a big challenge and has been investigated by researchers. MTJ switching is mainly of two types – spin-transfer torque based switching (STT-MTJ) and spin-orbit torque based switching (SOT-MTJ). SOT-MTJ has fewer reliability issues than STT-MTJ because of separate read and write paths. In SOT-MTJ, switching is executed by injecting spin-polarized current in the MTJ free layer. Spin-polarized current can be generated by passing charge current through heavy metals (HM) like Pt, β-W etc. Nevertheless, the charge to spin current conversion efficiency is low (3%-10%) in HMs. On the other hand, topological insulator (TI) has excellent charge current to spin current conversion efficiency (~37% in Bi2Se3, a 3D TI), far better than HMs. We proposed a simulation framework for TI/Ferromagnet (FM) heterostructures that can capture the ‘inverted’ surface electronic band structure of 3D TI and calculate the spin transport properties at TI/FM interface using non-equilibrium Green’s function (NEGF) formalism. The magnetization dynamics of the FM layer, due to the transfer of spin angular momentum, is simulated using Landau–Lifshitz–Gilbert–Slonczewski (LLGS) formalism. Finally, we evaluated the performance of three different TI/FM memory structures and showed that TI based memories are not energy efficient because of the shunting current through the FM layer. In order to solve the shunting current issue, we explored newly discovered Topological semi-metals (TM). We found that TM like Na3Bi has higher charge current to spin current conversion eﬃciency (~30%) than HMs and higher electrical conductivity (∼12.5x more) than TIs. Therefore, Na3Bi provides us a trade-oﬀ point between HM and TI as a non-magnetic spin injector. We modeled the MTJ with Na3Bi as spin injector. Our simulation showed that a CoFeB-MgO-CoFeB-Na3Bi MTJ consumes almost 10x and 728x less electrical power during iso-speed write operation compared with CoFeB-MgO-CoFeB-Pt and CoFeB-MgO-CoFeB-Bi2Se3 MTJs, respectively.
Slow switching speed due to long precession time is another major drawback of a ferromagnet (FM) based MTJ as compared with traditional CMOS technology. Ferrimagnet (FiM) can offer faster switching speed because of ‘bulk torque’ generation. Our ab-initio analysis of ferrimagnet CoTb based ferrimagnet MTJ (FMTJ) showed that a thick (~10-12nm) CoTb layer is necessary to fully utilize the advantage of bulk torque generation inside CoTb. We developed a model to simulate the FiM magnetization dynamics incorporating Dzyaloshinskii-Moriya interaction (DMI) at FiM/HM interface. Our simulation exhibited that for picosecond range switching speed, CoTb based FMTJ is ∼25 times more energy eﬃcient and more immune to thermal noise than CoFeB based MTJ. Nevertheless, FMTJ has lower TMR and higher critical switching current.Finally, we analyzed the MTJ reliability issues. The major reliability concern in an MTJ is the time-dependent dielectric breakdown (TDDB) in the thin MgO tunneling barrier layer. We simulated the lifetime of MTJ with 1nm thick MgO layer using Weibull plot analysis. We found that at an operating voltage of 0.6V and room temperature, 1% of the MTJs (in a sample of 1000 MTJs) will have 3rd soft-dielectric breakdown in the MgO layer in almost 24 years.