Ta/CoFeB/MgO analysis for low power nanomagnetic devices

The increasing demand of processing power of modern computing systems moved the attention to develop solutions to mitigate the impact of the so called memory-wall.¹ In this scenario, technologies that can combine storage and logic capabilities are becoming very attracting. Perpendicular Nano Magnetic Logic (pNML) is one of the promising beyond CMOS technologies listed in the International Roadmap for Devices and Systems (IRDS 2017)² capable of providing both these features. pNML is a technology in which the information, encoded in non-volatile magnetic states, is elaborated and transmitted exploiting the magnetic dipole coupling between adjacent elements. The materials employed are characterized by a strong perpendicular magnetic anisotropy. Among the domain wall-based technologies, pNML is the most mature, providing a functional complete set of logic gates, memory and logic capabilities. In recent years, the correct operation of logic gates,³ devices such as full adder,^4,5 multiplexer⁶ and memory elements⁷ have been experimentally demonstrated. In addition, the fabrication process offers monolithic 3D integration.^3,8

The propagation of information requires the superposition of the coupling field from neighboring magnets and an external out-of-plane magnetic field. These two contributions enable the magnetization reversal. The applied clocking field varies periodically in both positive and negative direction to allow both stable magnetization states to propagate. Finally, to define the propagation direction and enhance its efficiency a weak spot in the material is artificially generated. Such zone is called artificial nucleation center (ANC) and can be defined with a local Focused Ion Beam (FIB) irradiation with Ga⁺ ions during the fabrication process.⁹ Other mechanisms for propagation are possible involving local currents, in place of global magnetic fields for magnetization reversal.^10,11

The first experimental realizations of pNML devices were obtained on Co\Pt multilayer films.^4,5,7,9 The film structure composed of many repetitions of Co\Pt bilayers makes it possible to reach a strong coupling between neighboring elements. In addition, the stack characteristics can be locally tuned by means of ion irradiation techniques to generate ANCs for controlled domain wall (DW) nucleation.⁹ The main limitation of this configuration is the required clocking field to obtain a correct propagation of information that showed values above 50 mT with quasi-static fields.⁴ The intensity of the external magnetic field impacts heavily on the energy budget of the circuit. The overall power consumption depends almost exclusively on the required clocking field and on the efficiency of the generation circuit. A forecast on the power dissipation of an on-chip clocking scheme sandwiched in a soft-magnetic cladding showed that the maximum required amplitude should fall below 20 mT.^12,13 In the literature, other thin film configurations with strong perpendicular anisotropy have been presented and studied for spintronic devices. Co\Ni thin films showed to be promising due to the perpendicular anisotropy and the possibility to locally tailor their characteristics via ion beam irradiation.^13,14 Another promising solution is represented by the CoFeB\MgO stacks. They show a strong magnetic anisotropy and fast magnetic dynamics. Moreover, the perpendicular anisotropy, arising at the ferromagnet-oxide interface, can be finely tuned during the fabrication and modulated with electric fields.^15,16 They received great attention for the excellent compatibility with magnetic tunnel junction in which they are used both as free and reference layer.^17–19 These stacks have also been integrated with CMOS technology to realize high speed magnetic memories.^20–22 CoFeB\MgO stacks have the potential to be also a good candidate for the development of low power nanomagnetic logic devices. In this paper, a Ta₂\CoFeB₁\MgO₂\Ta₃ stack, with alloy composition Co₂₀Fe₆₀B₂₀, is investigated. The presented study examines in depth its applicability for nanomagnetic logic both at the experimental and simulation level. In section II, the experimental setup and experimental measurements are presented. In section III, the micromagnetic simulation are described and the main outcomes are presented, with particular attention to the layout topology of the logic gates. Finally, section IV concludes the paper summarizing the results and presenting future perspectives for the presented structures.

Nanomagnetic structures made from Ta\CoFeB\MgO thin films with perpendicular magnetic anisotropy are fabricated and subsequently characterized, assessing their eligibility for advanced pNML concepts. The individual layers (thicknesses given in nanometer) are deposited onto silicon (100) substrates, featuring an oxide layer of ≈ 50 nm thickness, via confocal rf-magnetron sputtering (base pressure < 2×10^-7 mbar). The power density applied to the 2-inch targets is constant for all materials (0.5 W cm⁻²). The same holds for the working pressure (4 µbar ≈ 3 mTorr), except for the MgO, which is sputtered from a compound target at 2 µbar (≈ 1.5 mTorr). After the deposition, the samples are annealed for 10 min at 550 K in a nitrogen atmosphere to set the PMA to the desired ≈ 5×10⁵ J m⁻³. The magnetic properties (also the simulation parameter) of the used Ta₂\CoFeB₁\MgO₂\Ta₃ stack are derived from vibrating sample magnetometer measurements (K_u is calculated via the area method) and cross-checked via broadband ferromagnetic resonance spectroscopy.

To realize the desired test structures, a sample with the same stack configuration is further processed. First, focused ion beam (FIB) lithography (using PMMA as a positive E-beam resist) is used to define the structure layouts. The deposition of a 5 nm thick Ti layer is then combined with a lift-off process to create the necessary hard mask for the subsequent Ar⁺ ion-beam milling step, which removes all material but the earlier defined layouts. The on-chip field coils are realized in the last step via conventional optical contact lithography together with the deposition of a Cu metal layer (≈ 750 nm) and a second lift-off process. An overview of the final design is depicted in figure 1. The test-structures (400 nm wide wires for DW-velocity, and 1 µm wide disks for coercivity measurements) are analyzed statically as well as in the time domain via stroboscopic Wide-field Kerr-microscopy (WMOKE), synchronizing magnetic field pulses in the ns-range with the image acquisition of a high dynamic range sCMOS camera. Ultra short magnetic field pulses are generated via on-chip coils with a single winding, as illustrated in figure 1. To reach pulse widths down to the single digit ns-range, a low-side switch in combination with a fast gate diver is used to discharge a capacitance through the on-chip coils. The gate driver is thereby addressed by an Agilent 81112A Pulse Generator.

The coercivity of single domain magnets is in contrast to films domianted by the nucleation field, H_c ≈ H_nuc presuming that the domain wall (DW) depinning fields are much lower (H_depin ≪ H_nuc). It is furthermore important to differentiate between coercivities measured at quasi-static fields from those measured at short time scales of microseconds and below. The magnetization reversal process of single-domain magnets is comprised of two phases. Following the initial DW nucleation, at a point of lowered anisotropy, the DW must propagate through the entire structure to complete the reversal. For this propagation to happen, the DW, however, must first overcome the anisotropy gradient at the nucleation site and depin. It is therefore, important to differentiate and consider both the nucleation as well as the propagation time separately (t_switch ≈ t_nuc + t_prop). The timescales for the nucleation process are governed by the Arrhenius-Néel law, from which the so-called Sharrock formalism can be derived. It describes the external field necessary to switch a single domain magnet with at least 50 % probability within a certain time. This threshold mark is defined as

with H_s0 as the switching field at 0 K, f₀ as the attempt frequency (≈ 1×10⁹ Hz) and E₀ = K_uV as the energy barrier without field equal to the product of anisotropy and volume.²³ 

For the quasi-static case, the switching field distribution (SFD) is calculated from a data-set of 1600 nano-disks resulting in a mean coercivity of H_c, mean = (8.67±0.06) mT, and a narrow FWHM SFD of only σ_FWHM = (2.87±0.10) mT. This is a significant reduction in the absolute as well as relative SFD even compared to the recently evaluated low anisotropy Co\Ni multilayers.¹³ The most plausible explanation for this is the amorphous structure of CoFeB layers annealed at low temperatures.

Figure 2 displays the time evolution of H_sw for timescales ranging from the quasi-static case down to the single-digit ns-range according to the guidelines in Ref. 12. H_sw is determined for 80 nano-disks with the FWHM of the SFDs displayed as error bars. The obligatory fit, according to the Sharrock formula, shows good agreement with the collected data down to timescales below 100 ns. Here, several effects start to affect the measurements. For very short pulses, the time is not sufficient to propagate the DW through the entire magnet, leading to detection errors within the optical readout system. This, however, can be resolved by applying a ms-range field pulse with a low amplitude (≈ 3 mT) after every nucleation pulse. However, below 50 ns, we propose another mechanism leading to a measured deviation from the Arrhenius behavior. Depending on the properties of the nucleation site, the timescales might be too short for the domains to stabilize, resulting in a back-flip of the magnetization. This behavior, however, should be very sensitive to constructive bias fields, as the additional energy helps to stabilize the nucleated domains. The inlet of figure 2 displays the measured coercivities depending on the applied bias field. H_sw is thereby corrected by the amplitudes of the bias field. As proposed, the measured coercivities are reduced significantly even for small bias fields, after which a plateau is formed, indicating the inhibition of possible back-flipping events.

The time-dependent nucleation probability follows an Arrhenius model at least down to pulse widths of ≈ 20 ns. A fit, according to the Sharrock formalism shows good agreement, with the fitting parameters converging to H_s0 = (38.23±1.50) mT and $E0=kBT28.57±kBT2.2$⁠. Considering the relatively high anisotropy of the film (K_eff ≈ 1.3×10⁵ J m⁻³), these are very encouraging results, rivaling those of heavily optimized Co\Ni multilayers.¹³ 

Nucleation is only one part of the reversal process. Equally relevant is the rapid expansion and propagation of the DW through the magnet. Similar to electronic circuits, the slowest path determines the maximum operating frequency. Hence it is possible to estimate upper limits for the clocking frequencies f_clk for the used feature size, given the design and DW velocity v_DW. DW motion can, roughly speaking, be separated into two distinct domains. At low fields, DW depinning heavily depends on thermal activations, thus resulting in a slow probabilistic creep motion. However, this motion is no longer affected by pining and depinning events at high fields, leading to flow like motion, with v_DW linearly depending on H. For applications, the creep regime is generally considered irrelevant, due to thelow velocities ≪ 1 m s⁻¹.

In order to assess the DW velocities of the Ta\CoFeB\MgO thin film, DWs were propagated through 400 nm wide nano-wires (example depicted in figure 1) by bursts of 25 ns long field pulses with varying amplitudes. First of all, very short pulse widths were chosen to limit random nucleation events inside the nanowires and second, to mimic typical clock-cycle lengths. The number of bursts was adjusted between 1 and 10 to keep the mean DW-displacement above ≈ 1 µm to reliably identify the displacements. The actual velocities can then be calculated from the pulse-width dependent DW displacements.

Figure 3 depicts the measured DW-velocity distributions for fields up to 28 mT as box plots. The depinning field in these nanowires at quasi-static fields is in the range of 0.3 mT. However, reliable measurements in the creep regime are extremely difficult considering pulse widths below 1 µs. Data can be gathered starting at ≈ 7 mT. The measurements show a clear initial increase in DW-velocity, plateauing between 13 mT and 22 mT, before increasing again from 22 mT on-wards. The observed plateau may result from the decreasing velocities above the Walker-breakdown.²⁴ The Walker-breakdown, calculated to occur below 1 mT for this material system, is masked by the creep motion. The second velocity increase above 22 mT, could mark the onset of flow motion. However, the wide distribution of the collected data suggests some form of intermediate flow in which large pinning sites still dominate. Reliable data for higher fields could not be collected due to the increasing amount of random nucleation events. For possible applications, the relevance of very high fields is, of course, also limited. Considering clock fields around 20 mT and a feature size of l_max =400 nm as simulated below, it is possible to estimate clock frequencies around 20 MHz. For a scaled architecture (feature sizes < 100 nm) frequencies in range of a few hundred MHz seem feasible, even considering to further optimization regarding DW mobility.

The data from the experiments showed low coercivity and high perpendicular magnetic magnetic anisotropy, comparable with the one obtained with Co\Ni multilayer stacks. This makes Ta\CoFeB\MgO films very appealing for logic applications. We investigate two layout topologies through micromagnetic simulations, which are performed with the GPU accelerated software package mumax3.²⁵ The aim is to identify what layout configuration fits the needs for the development of a new family of logic gates based on Ta\CoFeB\MgO nanomagnets. The idea is to develop a robust and regular structure that can implement NAND/NOR functions according to a global or a local bias field.

The first topology consider co-planar inputs and output, whereas in the second structure the inputs are moved to another physical layer (figure 4f). Figure 4a illustrates schematically the 3D-stacked layout, with all the dimensions involved. These dimensions are valid also for the co-planar layout with the difference that the inputs are on the side of the output (wide as the gap size), separated by the inter-magnet space y-space. The magnetic properties of the stack are taken from the measured samples. The saturation magnetization is M_s = 8.3×10⁵ A m⁻¹ and the uniaxial anisotropy constant K_u = 5.6×10⁵ J m⁻³. The exchange constant A = 20×10^-12 J m⁻¹ is taken from the literature.²⁶ The discretization of the sample is 2.5 nm×2.5 nm×0.5 nm. A variation of 5% of the anisotropy constant was applied over the whole film. The damping constant of the CoFeB\MgO film was taken from the literature²⁶ and it is equal to α = 0.015.

In the 3D layout, the two inputs are co-planar and parallel on layer 2 (L2), separated by a small gap. They partially overlap the output magnet lying on layer 1 (L1). In this study, the gap size is 50 nm. The output magnet is located on the first layer (L1), centered on the gap. Every input magnet has the following dimensions: width = 100 nm, depth = 400 nm and thickness = 1 nm. The stray field reaching the output magnet has been analyzed for different vertical distances (10 nm, 15 nm, 20 nm, 25 nm, 40 nm). Figure 4b shows the z-component varying the vertical space among the layers (L1 and L2) when both inputs are magnetized to the logic 0. In this configuration, the inputs are anti-ferromagnetically coupled to the output. The dashed line shows the position of the 50 nm gap, where the soft PMA spot should be defined. It is possible to observe that a vertical separation of 15 nm and 20 nm provide the best trade-off in term of coupling strength and field homogeneity at the center, in correspondence of the gap. Indeed, the coupling reaches 6.4 mT with 15 nm separation and 4.8 mT with 20 nm distance. For the 20 nm vertical distances, the out-of-plane component of the stray field over the output magnet is displayed in figure 4h. For the sake of clarity the position of the output is indicated by a black box. The yellow area identifies the region with a stronger out-of-plane field. Figure 4g illustrates the z-component when the inputs are anti-parallel. For the 20 nm distance the out-of-plane field reaching the gap is almost canceled out. Therefore, the final magnetization of the output is determined only by the bias field and the sign of the global field.

Similarly, we investigated the topology with co-planar inputs and output with horizontal spaces: 10 nm, 20 nm, 40 nm. The out-of-plane components, reported in figure 4d, shows that the coupling reaches a maximum value of 6.6 mT and 4.8 mT for 10 nm and 20 nm respectively. However, even if the coupling appears strong enough also for these configurations, the planar layout cannot be successfully adopted for performing logic operations. The z-component is stronger on the edges weaker at the center, where the nucleation center is supposed to be located. This can favor the domain wall nucleation from edges instead of starting from the center of the output magnet. The in-plane component for the three distances is reported in figure 4e. It is possible to identify the position of the two inputs, starting in correspondence of the peaks. When the horizontal distance is below 10 nm (figure 4e) the in-plane component of the inputs combined with the strong z-component on the edges may initiate the magnetization reversal. The dashed line in figure 4.d-e show the size and position of the 50 nm gap.

Therefore, the 3D-stacked layout appears more promising in term of field distribution and feasibility of the fabrication process. In the pNML technology, the logic computation is achieved by the superposition of the dipole coupling of adjacent nanomagnets and the global out-of-plane field. Here, in addition to that a bias field is introduced. The bias field can be locally generated by a third input magnet located under the output or globally generated by adding a bias to the clocking field. The bias field defines the logic function implemented by each gate, whereas the global clocking field starts the computing phase. The bias field acts as a third input and can program all the gates (global bias) at once, or every gate independently (local bias) in the logic architecture to operate as NAND/NOR gate. The global bias field can be seen as a virtual input, since it will not be physically present in the design, but it defines the logic function of every gate. Table I summarizes the truth table of the logic gate. It is possible to observe that it virtually operates as a majority with only two physical inputs. The sign of the bias field determines the logic function implemented.

In this paper, we have investigated the Ta₂\CoFeB₁\MgO₂\Ta₃ stack from the perspective of developing a new family of perpendicular magnetic logic devices. The low coercivity, below 10 mT and high perpendicular magnetic anisotropy make the material very appealing for memory and logic applications with low energy computing capabilities. The measurements exhibit faster domain wall motion and narrower FWHM SDF if compared to Co\Pt and Co\Ni films. Our simulation results show that a vertical separation ranging between 15 and 20 nm provides enough coupling for implementing two inputs NAND/NOR gates. Moreover, we demonstrated that the 3D-stacked layout is preferable in order to reach the maximum coupling strength at the center of the output magnet. The proposed solution makes it possible to design NAND/NOR gate with only two physical inputs (global bias) or to individually control the logic function of each gate by a third additional input.

The data that support the findings of this study are available from the corresponding author upon reasonable request.