Modelling and design tools were developed in the frame of HYMAGINE to cover both the fundamental and design aspects of the project.

Concerning the fundamental aspects, we developed a code allowing to calculate both the transport properties and the magnetization dynamics in systems of complex geometry wherein the current can be expected to be non-uniform for geometrical reasons or because of magnetic inhomogeneities.

To address this issue, a code was developed using a finite element solver allowing us to solve the equations of spin-dependent diffusive transport in any 2D and 3D geometries. Charge current vector, spin current tensor, spatial distribution of spin accumulation, in-plane and out-of-plane spin-transfer-torque can be calculated at any point of the structure. As an illustration, the spin-dependent transport through a 2D nanoconstriction is illustrated below. The system consists in a magnetic Co/Cu/Co nanoconstriction sandwiched between two Cu electrodes (Fig.1).

Fig.1: system under investigation: A 2D nanoconstriction sandwiched between two thick Cu electrodes. The color code shows the electrostatic potential across the system. The arrows show the charge current flow.

Very interestingly, it was discovered in this study that the spin-current has a very different behaviour than the charge current. While the charge current converges towards the constriction and then diverges away from the constriction as expected, the spin-current exhibits vortices on both sides of the constriction in antiparallel magnetic configuration. This is due to an extremely high spin accumulation appearing in the constriction in this geometry (see Fig.2). This unexpected phenomenon was interpreted on the basis of these simulations.

Fig.2: Representation of the charge current and y-spin-current through the constriction showing spin-current vortices on both sides of the nanoconstriction. In this geometry and magnetic configuration, a very high spin accumulation exists in the constriction.

This simulation tool was used to investigate spin-dependent transport in various spintronic systems including magnetoresistive heads for hard disk drives and MRAM. The data provided by these simulations can serve as input in micromagnetic simulations including spin-transfer torque.

At a different level, a full set of design tools was developed within HYMAGINE in order to enable us to design complex hybrid CMOS/MTJ circuits. These tools are now in particular used by our start-up company eVaderis.

Tools were developed both for full-custom/analog (Fig.3) and digital design (Fig.9).

Fig.3 : Sequence of steps required for full-custom/analog design of electronic circuits

Full-custom design is used for the design of relatively simple circuits. The design is realized at the device level. No standard cells are used. The electrical analog behavior of the circuit is simulated. The technology and devices information are provided by the manufacturer within a Process Design Kit (PDK).
Within HYMAGINE, an accurate SPICE model of MTJs written by field, spin-transfer-torque and with or without thermal assistance was developed. It was written in C language and compiled for the electrical simulator SPECTRE of CADENCE. An example of calculated response in the case of an STT-MRAM cell is shown in Fig.4.

Fig.4: Example of calculated response of a STT-MRAM cell submitted to a pulse of write current. Calculation performed with SPINTEC SPICE simulator.

The SPICE model was further improved to take into account the thermal fluctuations of the storage layer magnetization and thereby be able to simulate the stochasticity of the switching as illustrated in Fig.5

Fig.5: Example of SPICE simulations taking into account the thermal fluctuations of the storage layer magnetization and showing their impact on the stochasticity of the switching.

The next step that we developed were tools for the layout and verification of the circuits. This was carried out in collaboration between SPINTEC and CMP (Centre Multi-Projets).
For that a standard pCell of the MTJ was developed to ease the layout drawing as illustrated in Fig.6. This allows Design Rules Checking (DRC), extraction and Layout versus Schematic (LVS)

Fig.6: p-cell representing a STT-MRAM cell and example of implementation in a layout.

As an example, these tools were used to design a FPGA comprising non-volatile Magnetic Look-up Tables using the Thermally Assisted MRAM technology as illustrated in Fig.7. This device was built and tested and its full functionality was demonstrated (Fig.8).

Fig.7: Layout of a non-volatile magnetic Look-Up Table designed, built and tested within HYMAGINE

Fig.8: Experimental demonstration of the reconfiguration of the magnetic LUT of Fig.7 . The function « 0010 » is initially stored in the DRAM configuration memory. The function « 0110 » is then written in the MRAM memory. The DRAM memory is then refreshed. The new function is checked

For the design of more complex digital circuits, it is not possible to describe each element at the individual cell level. The functionality of the circuit is described by a hardware description language (VHDL, Verilog). Digital simulations are performed on events in contrast to the previous analog description. The synthesis of the circuit is performed by using elementary standard cells. The layout of the circuits is automatically generated. A process Design Kit is provided by the manufacturer. The design flow is then illustrated in Fig.9.
Within HYMAGINE, all the tools require for these digital designs of complex circuits were developed and are now being used by eVaderis.
An example of microcontroller developed by using these tools is shown in Fig.10.

Fig.9: Design flow for the design of complex digital circuits

Fig.10 : Example of layout of microcontroller developed using SPINTEC design tools.

Publications associated with WP3 :

Finite Element Modeling of Charge- and Spin-Currents in Magnetoresistive Pillars With Current Crowding Effects
Strelkov, N., Vedyayev, A., Gusakova, D., Buda-Prejbeanu, L.D., Chshiev, M., Amara, S., Vaysset, A., Dieny, B.
Magnetics Letters, IEEE, 1, 3000304 (2010).https://www.spintec.fr/IMG/pdf/finit…

Spin-current vortices in current-perpendicular-to-plane nanoconstricted spin valves
Strelkov, N., A. Vedyaev, N. Ryzhanova, D. Gusakova, L.D. Buda-Prejbeanu, M. Chshiev, S. Amara, N. de Mestier, C. Baraduc and B. Dieny
Physical Review B 84 (2011) 024416 http://dx.doi.org/10.1103/PhysRevB….

Diffusive model of current-in-plane-tunneling in double magnetic tunnel junctions
Clement, P.-Y., C. Ducruet, C. Baraduc, M. Chshiev and B. Dieny
Applied Physics Letters 100 (2012) 262404

Magnetostatics of synthetic ferrimagnet elements
Fruchart, O. and B. Dieny
Journal of Magnetism and Magnetic Materials 324 (2012) 365

Macrospin model of precessional spin transfer torque switching in planar magnetic tunnel junctions with perpendicular polarizer
Mejdoubi, A., B. Lacoste, G. Prenat and B. Dieny
Applied Physics Letters 102 (2013) 152413http://dx.doi.org/10.1063/1.4802720

A hybrid magnetic/complementary metal oxide semiconductor process design kit for the design of low-power non-volatile logic circuits
Di Pendina, G., G. Prenat, B. Dieny and K. Torki
Journal of Applied Physics 111 (2012) 07E350http://dx.doi.org/10.1063/1.3680013

A compact model of precessional spin-transfer switching for MTJ with a perpendicular polarizer
Mejdoubi, A., G. Prenat and B. Dieny
Proceedings of the 28th International Conference on Microelectronics (2012) 225

SPICE modelling of precessional spin transfer switching in MRAM cells with a perpendicular polarizer
Mejdoubi, A., G. Prenat and B. Dieny
Proceedings of the International Semiconductor Conference Dresden-Grenoble (2012) 179

Compact model of a three-terminal MRAM device based on spin-orbit torque switching
Jabeur, K., G. Prenat, G. di Pendina, L.D. Buda-Prejbeanu, I.L. Prejbeanu and B. Dieny
Proceedings of the International Semiconductor Conference Dresden-Grenoble (2013)

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