Study of precessional switching speed control in voltage-controlled perpendicular magnetic tunnel junction

We study the characteristics of the precessional switching induced by voltage control of magnetic anisotropy (VCMA) in back-end-of-line (BEOL)-compatible perpendicular magnetic tunnel junction devices. Using micromagnetic simulation, we find three operation regimes differentiated by zero excess energy, lower boundary, zero energy barrier, and upper boundary. Experimentally, the switching speed (fs) is characterized by two phases: non-precession and acceleration. Non-precession is a thermal mediated phase, where fs cannot be deduced, while in acceleration, both the higher electric field (EF) and in-plane field (Bx) increase fs progressively. We find that the intrinsic thresholds can be retrieved by linear extrapolation of fs as a function of EF. Those thresholds and experimental results are in good agreement with the simulation. In addition, we numerically calculate the characteristic switching speed of 2γ*mz*Bx and verify it experimentally. This work provides insights into the VCMA-induced precessional switching, including detailed understandings of the switching mechanism and modeling of switching speed for reliable write duration control for practical applications.We study the characteristics of the precessional switching induced by voltage control of magnetic anisotropy (VCMA) in back-end-of-line (BEOL)-compatible perpendicular magnetic tunnel junction devices. Using micromagnetic simulation, we find three operation regimes differentiated by zero excess energy, lower boundary, zero energy barrier, and upper boundary. Experimentally, the switching speed (fs) is characterized by two phases: non-precession and acceleration. Non-precession is a thermal mediated phase, where fs cannot be deduced, while in acceleration, both the higher electric field (EF) and in-plane field (Bx) increase fs progressively. We find that the intrinsic thresholds can be retrieved by linear extrapolation of fs as a function of EF. Those thresholds and experimental results are in good agreement with the simulation. In addition, we numerically calculate the characteristic switching speed of 2γ*mz*Bx and verify it experimentally. This work provides insights into the VCMA-induced precessional sw...

Among the emerging memories, magnetic random access memory (MRAM) has great potential to be introduced as cache memories in the advanced technology nodes due to its complementary metal-oxide-semiconductor (CMOS) process compatibility and scalability. [1][2][3] Its non-volatile feature enables a reduction in the static power in comparison with dynamic RAMs. In the past decades, the spin-transfer-torque (STT) effect, as the write mechanism, has been extensively studied, and STT-based magnetic tunnel junction (MTJ) devices have achieved a reliable writing time down to few nanoseconds. 4,5 However, the required switching current is dramatically increased for gigahertz operation, causing degradation and reliability issues in the MgO tunnel barrier. 6 Magnetization switching utilizing the voltage control of magnetic anisotropy (VCMA) effect is an alternative mechanism that allows drastic reduction in energy consumption and sub-nanosecond writing of the MRAM. [7][8][9] While various origins are studied, 10-12 the electronic-based VCMA effect is commonly explained by applying an electric field (EF) that charges the oxide/ferromagnet interface and redistributes the electrons between the 3d orbitals, resulting in enhancement or weakening of the interfacial perpendicular magnetic anisotropy (iPMA). 13 By such a principle, in perpendicular MTJ (p-MTJ) devices, magnetization switching is executed by applying an EF that removes the energy barrier (E b ) between the anti-parallel (AP) and the parallel (P) states; simultaneously, an external in-plane magnetic field (Bx) induces an oscillation of the free-layer (FL) about this field direction, allowing for precessional switching control. 8,9 A successful switching relies on an accurate control of pulse duration (tP), which should match with half of the precession period. This type of EF-driven device has merits as follows: (1) the time scale of the half period usually falls in the range of sub-nanoseconds, in correspondence to ARTICLE scitation.org/journal/adv gigahertz writing, and (2) the thickness of the MgO barrier is intentionally made thicker than that of the STT-driven devices; hence, the current flowing through the device is suppressed, and the switching energy can reach the scales of femto-joules. In such a writing scheme, the switching speed (fs) varies with both EF and Bx. These three mutual-related parameters (EF, Bx, and fs) are the key parameters to achieve a successful writing process as they control the optimum switching time window with a maximized switching probability (Psw). 14,15 Therefore, fundamental understanding of the switching threshold and the parameters to control fs is crucial to enable reliable modeling for applications. In this work, we first discuss the estimation of the VCMA properties. Based on the first discussion, in the second section, we simulate and analyze the operation regimes with energy consideration and correlate them to our experimental results. Finally, we discuss the parameters that allow the numerical calculation of the switching speed for applications.
We study bottom-pinned p-MTJ stacks of [Co/Pt]-multilayerbased hard-layer/spacer/reference-layer/MgO(t)/CoFeB(1.7)/Ta (20) /Ru(50) sputter deposited on 300 mm thermally oxidized Si(100) wafers using a Canon-ANELVA EC7800 cluster tool. Numbers in parentheses are the nominal thicknesses in nanometers. The reference-layer (RL) is a CoFeB-based multilayer. Two MgO thicknesses, t = 1.4 nm and 1.1 nm, are prepared to target the resistancearea (RA) products at 1000 Ω μm 2 and 100 Ω μm 2 , respectively. Devices with high RA products are used to estimate the VCMA coefficient under direct current (DC) conditions without the disturbance of the STT effect, while a device with a lower RA product aims at fast assessment of the electrical switching properties. After deposition, the films are annealed at 400 ○ C for 30 min in vacuum under 2T out-of-plane magnetic field. Stacks are then patterned into 100 nm circular pillars using 193 nm immersion lithography and ion beam etch (IBE). Saturation magnetization of the different layers in the stack is characterized using a MicroSense vibrating sample magnetometer (VSM) on blanket 8 × 8 mm 2 samples. Electrical pulse switching experiments are carried out in a constantly applied external magnetic field (see the supplementary material for the configuration of the electrical switching setup).
To study and model the VCMA switching characteristics, fundamental parameters such as the saturation magnetization of the FL (MS,FL), the effective perpendicular magnetic anisotropy field (B k,eff ), and the EF-dependence of the perpendicular anisotropy field (dB k,eff /dEF) must be quantified. We measure the MS,FL on 8 × 8 mm 2 blanket samples, and it is 1.45 × 10 6 A/m considering the presence of a 0.7 nm magnetic dead layer (see the supplementary material for the VSM measurements). Such a dead layer thickness is comparable to the value obtained from the similar stack. 16 Next, to evaluate B k,eff and dB k,eff /dEF, we measure devices with high RA products using an out-of-plane magnetic field sweep method to obtain the switching probability distributions. Figure 1(a) shows the AP-to-P switching field distributions of 500 switching events under different DC-EF conditions. Due to the VCMA effect, the distributions are shifted accordingly. Subsequently, these distributions are fitted with a macro-spin based failure model to extract B k,eff as a fitting parameter 17,18 (see the supplementary material for the fitting equation). Figure 1 interface is electron-accumulated (-depleted) such that B k,eff is reduced (enhanced); hence, the FL is switched at weaker (stronger) fields. There is also a Rashba field that can lead to a change in PMA. 19 However, for the current perpendicular to the plane measurements, the Rashba field is not generated because the cross product of the wave vector and the electric field is zero. In addition, we observe a linear VCMA response indicating that such an effect is attributed to the depletion/accumulation effect, in contrast to the Rashba splitting which has a quadratic reaction. Since we obtain a linear dependence, B k,eff at zero bias and dB k,eff /dEF are estimated to be 80 mT and 60 mT/(V/nm), respectively. The VCMA coefficient (ξ) is then evaluated as ξ = M S,FL t FL 2 dB k,eff dEF ≅ 43.5 fJ/Vm. By linear extrapolation, B k,eff is expected to be removed at −1.3 V/nm approximately, which we define it as the characteristic electric field (EF C0 ). These parameters obtained from the experiments will be applied to the micromagnetic simulation for in-depth analyses.
In the following, we study the characteristics of the VCMA switching from both simulation and experiment and afterward correlate the results to get insights into the switching properties. In the simulation, we focus on the analyses of energy diagrams under ARTICLE scitation.org/journal/adv correspond to the three different operation regimes. In regime I, both Eex and E b are positive, and the FL cannot switch over the barrier. When increasing the EF up to regime II, Eex becomes negative, while E b remains positive. Since the EF pulse is considered as a square pulse with a negligible rise time, there is a minimum relaxation of the FL toward the equilibrium state. In the case of ideal systems, i.e., extremely low damping and without thermal disturbance, the FL has sufficient energy to switch even with a barrier present. This energy is consistent with Eex; hence, Eex = 0 defines the lower boundary of switching. If the EF is further increased up to regime III, E b is completely removed. In this regime, switching should be induced in any system, since there is no barrier to prevent switching. For instance, in the real systems, there is finite damping which causes energy dissipation. While it results in the relaxation of the FL toward the equilibrium states, the precessional switching characteristics can be properly observed. Accordingly, the upper boundary can be defined at E b = 0. In addition, we observe a linear dependence of Eex on the EF, as shown in Fig. 2(d), indicating that the switching characteristics of the FL will be varied linearly as well. This behavior will be confirmed in the observation of the following experiments. Experimentally, we investigate the VCMA switching speeds using a device with a lower RA product for faster assessment of the FL states. At this designed RA product, the STT effect has a negligible impact on the spin dynamics in the precessional switching regime, 15,21 and any switching behavior is solely induced by the VCMA effect. Furthermore, there is no noticeable difference in the fundamental properties such as coercive fields, thermal stability factors, and VCMA coefficients between the devices with lower and higher RA products. The experiments are carried out by measuring the switching probability (Psw) as a function of pulse duration (tP), with 1000 switching events per condition. We observe the oscillatory behavior in Psw, as exemplified in Fig. 3(a). Theoretically, the spin dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation, where γ is the gyromagnetic ratio (considering as 29.4 GHz/T 22 ), B eff is the effective field, and α is the damping constant. The first term on the right-hand side of Eq. (1) describes the precessional motion of the magnetization about B eff , from which the oscillating probability originates when switching is executed. In general, the precession frequency (fP) corresponds to the Larmor frequency γB eff . To systematically assess fP, we apply a periodic equation, e.g., a cosine function, to fit the first period of the probability curve. The maximum of the fitting equation is a floating value which can be greater than 100, implying that the normalized out-of-plane component of the FL does not necessarily be one to achieve 100% switching. The error is minor in the fitting, and it has a negligible impact on fP. be attributed to the thermal fluctuation effect dominating over the precessional switching characteristics. Specifically, for perpendicularly magnetized devices, B eff is expressed as Eq.
(2) to account for the VCMA effect, where Bx is the applied in-plane magnetic field and B thermal is the ambient temperature-driven thermal fluctuation field (Joule heating effect is much less pronounced in VCMA devices due to the thick MgO). When the magnitude of B eff is small, the random thermal field dominates the spin dynamics such that the precession characteristics are concealed. Such EFC can be reduced by increasing Bx because it contributes in lowering the energy barrier along its direction. Subsequently, there is an acceleration phase above EFC, where the effective field is stable against the thermal fluctuation and the oscillatory features become clear. Here, we observe that the higher EF increases fs progressively. This is explained with Fig. 2(d); since the field applied on the magnetization is proportional to the energy, fs is linearly increased with the EF. By linear extrapolation of fs to zero, the intrinsic thresholds (EF th ) without thermal agitation can be retrieved. Regarding the discussions above, we correlate the results from both simulation and experiments. The landscape of Eex is plotted as functions of EF and Bx, and the operation regimes are distinguished by the two boundaries, as shown in Fig. 3(c). The experimental data and the extrapolated EF th are attached in the same plot for comparison. We observe that EF th are in regime II. The deviation of EF th from Eex = 0 can be attributed to the finite damping in the real systems. Additionally, it can be attributed to the non-square pulse shape in the switching experiments which can induce relaxation during the pulse rising edge and falling edge (see the supplementary material for the pulse shape). Those measured datapoints situate in regime III, indicating that a certain amount of overdrive is required to overcome the thermal fluctuation. These experimental results show good agreement with the analyses of the fundamental switching mechanism.
Finally, we remark the characteristic speed which can be computed numerically. From the estimation of B k,eff and dB k,eff /dEF, it is foreseen that the PMA can be completely removed without the assistance of Bx at EF C0 . At such a condition, B eff (EF C0 ) is approximately Bx according to Eq. (2), for Bx ≫ B thermal . Accordingly, the corresponding characteristic frequency is γ

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scitation.org/journal/adv that the FL can be tilted by Bx, the effective torque applied on the FL is then scaled to mz * Bx, with mz = √ 1 − [Bx/B k,eff (0)] 2 using the macro-spin approximation. Hence, the characteristic fs is predicted as 2γ * mz * Bx. In Fig. 4, fs measured at EF C0 are in good agreement with this hypothesis. Speeds at other EFs are also demonstrated. However, since B k,eff is non-zero in those cases, B eff and fs can only be solved analytically. Nevertheless, these results demonstrate that characteristic speeds can be modeled numerically, which enables reliable prediction of the write duration for practical applications.
In summary, we investigate the VCMA properties with both simulation and experiments. From the simulation, three operation regimes are distinguished by the two boundaries: Eex = 0 and E b = 0. Experimentally, the variation of fs is studied under various EF and Bx conditions. The measured and extrapolated datapoints correspond to the second and third operation regimes, respectively, which are consistent with the fundamental switching mechanism. For the prediction of speeds, we demonstrate that the characteristic fs at EF C0 can be numerically estimated, enabling reliable control of the write duration to maximize the switching probability for practical applications.
See the supplementary material for the electrical setup for the pulse voltage controlled magnetization switching, magnetic properties of the CoFeB free-layer, and effective perpendicular magnetic anisotropy extraction. This work was supported by IMEC's Industrial Affiliation Program on MRAM devices.