Barrier interface condition is critical for spin-polarized tunneling and spin-transfer torque switching in CoFeB∣MgO∣CoFeB-based magnetic tunnel junctions. The differential tunnel conductance contains information on CoFeB’s magnetic properties at tunnel interfaces. Experimentally, we find to follow a “cross-normalization” relationship between the parallel and antiparallel alignments. This we show originates from the leading order spin-flip scatter terms related to CoFeB interface magnetic properties such as its exchange-stiffness. By connecting the observable slopes to electrode-specific spin-flip scatter rates, we obtain an efficient measurement for mass-screening of junctions for interface magnetic differences. This provides valuable information for device and fabrication process optimization.
We describe an observation, and a method brought forth by related understanding for quick screening of magnetic tunnel junctions (MTJs). We characterize the bias-dependent differential conductance of an MTJ with a normalized conductance-bias slope. This quantity is related to electrode-specific magnetic properties, such as exchange-stiffness at tunnel interfaces. This characterization can be done quickly on a large number of devices, making it useful for feedback in materials and process optimization for technology development.
An MTJ’s conductance increases with bias, which is due to inelastic magnetic processes,1–5 inelastic electronic processes such as interface charge traps,6–9 and density of state effects.10 To the leading-order well below ∼1 V, at ambient temperature, and for technology interests, we focus on the nearly universal bias-dependent magnetoresistance (MR),1 dominated by tunnel electron’s spin-flip scattering,1,4,5 which reflects electrode’s interface-specific magnetic excitation.
MTJs reported are of CoFeB∣MgO∣CoFeB type with perpendicular magnetic anisotropy (PMA),11,12 using thin film stacks similar to Refs. 13 and 14. Films are with a ∼1.7 nm thick CoFeB free-layer (F), and a synthetic antiferromagnetic (SAF) reference layer (R), sputter deposited at ambient temperature, followed by a vacuum anneal around 300-400C for 1h prior to fabrication. Device diameter ranges from 15 to beyond 50 nm as estimated from resistance, and selectively calibrated via scanning electron microscopy. Tunnel magnetoresistance is of the order ∼100%. The resistance-area product (RA, or rA) ranges from ∼5 to 30 Ω μm2.
Fig. 1(a) shows the current-voltage (IV) characteristics of one such device11,15–17 at ambient temperature. It has a parallel state resistance of Rp ≈ 19 kΩ, and an MR ∼ 82 %. Curvatures in IV reflect a bias-dependent differential conductance . The hysteresis is due to spin-transfer-torque (STT) switching. The up-branch represents sweep with increasing voltage from the negative starting point in the parallel (P) state (in black). The down-branch for decreasing voltage sweep, starting from the antiparallel (AP) state (in red). represent the differential conductance dI/dV for the AP,P state (red, black curves, below switching thresholds, in Fig. 1(a)). The low-bias conductance for mV are designated as gap0 and gp0.
For MTJs with high-quality, high conductance tunnel barrier, electronic trap-state’s effect on for V is weak,18 as is band-structure effects.19 The leading order V dependence of is electron spin-flip scattering with creation of magnons.1,3–5,20,21 Such spin-flip magnon scattering opens up otherwise forbidden tunnel-channels, increasing the total tunnel conductance.
Focusing on an MTJ in its P or AP state, or “0” and “1” states in memory technology language, we write the low voltage conductance with a term representing the electron tunnel current’s access to the oppositely spin-polarized initial and final states. A spin-flip scatter rate factor, is introduced, with α = (p, ap) representing corresponding IV-branches. Using g(p,ap)0 for the bias-independent elastic tunnel conductance, we have
IV in Fig. 1(a) is converted into the form of
where V > 0 corresponds to an STT “write-one” or W1 direction, or for electrons streaming from F to R layer, and V < 0 for the “write-zero”, or W0 direction. are shown in Fig. 1(b). Both branches are truncated beyond their respective STT switching threshold. These measured s have subtle features, whose details vary from device to device. Those relate to resonant inelastic signals similar to tunnel spectroscopy,2 which is not the focus in this study. With limited voltage step size and a massive amount of devices, and with materials variation, we concentrate on the coarse-limit general behavior, i.e. the average slope of vs V. This slope is robust, around 0.5 to 0.9 1/V, depending on the specifics of junction film stack.
Our observations are, for such average slopes, there is an approximate symmetry in ± voltage directions. The P and AP branches also have similar . For this particular junction, one may write , sharing a single slope value for MTJs with nearly symmetric electrode interfaces at MgO.
In the rest of this paper, we derive a model that naturally explains the origin of this observation. The model is developed with interface-specific parameters. We show that the model results are consistent with data shown in Fig. 1 in a symmetric electrode limit. The model results presented is however more general, and can be used for less symmetric devices.
To facilitate discussions below, and make explicit the upstream vs downstream tunnel electrode’s parameters, we encode the bias voltage’s polarity into the subscripts of the Γs. We write to represent the magnetic state of the MTJ, and the bias direction an STT switching directs. For example, a Γ0W1 describes a “0-write-to-1” case, with junction in the P-state (μ = 0), and a bias direction for electrons to tunnel from F to R layer (i.e. for STT switching directing it into AP, or ν = 1, state). The four combinations in μWν scripts describe the four slopes obtained from experiment such as in Fig. 1(b). Once coded into subscripts this way, for , with V ≥ 0 and ημWν > 0.
Next we examine the ημWν slopes of across samples of varying junction size and rA, but with otherwise symmetric CoFeB∣MgO∣CoFeB interfaces. Fig. 2 shows data from five wafers with different rA values. The slope of deduced from measurement using Eq. 2 are linearly fit and plotted, from wafer-level junction screening data. Each point in the figure is the average from several hundred devices of sizes in the range of 10 to 90 nm for Fig. 2(a). The rA axis represent different wafers, with each wafer having a well defined mean-value rA. The wafer with the lowest rA (of about 4 Ωμm2) is least reliable due to limited yield, resulting in fewer junctions available for data averaging.
For rA > 5 Ωμm2, the shows no significant rA dependence trend beyond data noise. Similarly, when analyzed as a function of junction size in Fig. 2(b), no systematic size dependence of is visible either to the leading order.
To understand the observations above in terms of spin-flip scattering, we revisit a spin-dependent tunneling model. Following the assumptions in Refs. 1, 8, 22, and 23, we have the spin sub-band differential electrical conductance of elastic channels between the reference (R) and free (F) electrodes separated by a tunnel barrier:
where and are spin indices of the R and F tunnel electrodes, respectively. A rotation between F and R moments of angle θ gives , and . θ = 0 is the P state. θ = π, the AP. are the spin-channel specific electron conductance.
We assume a R and F electrode ‘separatability’ so that where the Ωs are the electrode’s interface spin-subband density of states in their own spin-quantization direction at the Fermi-surface,22,24,25 while the factor f represents the spin-independent pre-factor in the tunnel state summation.1,22 For simplicity we set f = 1 and let Ωs absorb this amplitude coefficient f, without loss of generality for parameterization.
We define an interface-specific phenomenological spin-flip scattering rate factor
From left to right, the first subscript position A=(R,F) indicates the spin-flip scattering action is occurring with magnon excitation in the R or F layer. The second subscript B=(U,D) describes the direction of tunnel electrons, with (U,D) representing the upstream and downstream electrodes, respectively. The third and fourth subscripts describe the direction of spin-flip, with (du) for minority-to-majority band electron scattering, and (ud) for majority-to-minority.
Assume these ΓABpq-factors are the only ones with bias-V dependence in conductance. Treat them as the leading order correction to the elastic tunnel expressions Eq. 3 (i.e. Eq. 2-3 in Ref. 23). Follow Refs. 8, 22, and 23, we derive the sub-band electrode- and spin-specific conductance expressed as g(R,F)(u,d) = dI(R,F)(u,d)/dV. The by Eq. 3 including the spin-flip scattering rate factor now reads:
The sub-band differential conductance expressions are therefore:
The presence of the ΓABpqs in Eq. 6 through necessitates the distinction in Eq. 5–6 of upstream vs downstream electrons. Eq. 5–6 as written above are explicitly coded for the direction of electrons tunnel from reference into the free-layer, corresponding to a spin-torque-driven AP-to-P switching direction, or, a “write-0” direction. For the opposite voltage bias direction, a substitution of subscripts in the form of for the ΓABpqs in Eq. 5 and Eq. 6 is taken.
Summing up the terms in Eq. 6 for either R or F electrodes (the R- and F-electrode’s sums should and do give the same result, as dictated by charge neutrality), one has the total junction differential conductance as , which gives the parallel and antiparallel charge conductance as and . To the leading order of the Γs, for the two configurations of corresponding to , and the two possible bias direction of , this gives the configuration-specific MTJ conductance of as
The subscripts for gμWν means “in state μ and in the bias direction for Writing to state ν”, same as the definition for ΓμWν described earlier.
Assume a leading order linear voltage dependence of ΓABpq = ηABpqV, and write the experimentally observed normalized conductance from Eq. 2 as
For both Γ and η, the triple-character subscript μWν refers to experimentally measured values as defined by Eq. 2 and Eq. 8. This is different from Γs with quad-character subscripts such as those defined in Eq. 7 and which represent the interface electrode and scatter-direction specific materials quantities. They are deduced and not directly measured. With these definitions we may now write, to the leading order and with V > 0:
Further, write the interface tunnel density-of-states Ωs in a form of spin-polarization as
which in the high spin-polarization limit (for large tunnel magnetoresistance or TMR) assumes a leading-order approximate form as
where a, b > 0 describes asymmetry between F and R electrodes, and ϵ → 0+ is for leading-order large TMR expansion. These in the limit of high TMR (ϵ → 0) and low temperature T ≪ Tc when minority-to-majority spin-flip scatter dominates, or ΓABdu ≫ ΓABud,26,27 one has
Eqs. 9 and 12 are the main results in terms of modeling in this work. They relate the observable conductance slopes ημWν to interface-specific spin-flip scatter rate’s energy-dependence slopes described by ηABpq. Such interface-specific spin-flip scatter rates can further be related to exchange-stiffness values governing magnon excitation spectra, in the form of ηABpq ∝ 1/Aex where Aex is the relevant interface’s exchange energy.1
One may, for nearly symmetric barrier interfaces with CoFeB, assume a ∼ b which would further simplify Eq. 12. However, whether the up- and down-stream spin-flip rate coefficients η(R,F)(U,D)du in Eq. 9 are similar is not clear. If the upstream spin-flip scattering process is much reduced from that of the downstream, one would have η(R,F)Udu ≪ η(R,F)Ddu, and thus η0Wν ∼ η1Wν/2 for symmetric electrodes. If on the other hand, the up- and down-stream spin-flip scattering rates are similar, then one would have η0Wν ∼ η1Wν. The conductance expressions from Ref. 1 in their low temperature limit for symmetric electrodes would result in η0Wν ∼ η1Wν.
Experimental data for nearly symmetric interfaces from Fig. 1–2 indicate , consistent with a nearly symmetric up- and down-stream spin-flip scattering coefficient, i.e. η(R,F)Udu ∼ η(R,F)Ddu. This implication however is not necessarily unique, as a significantly reduced interface magnetic ordering temperature could also cause the reverse-scattering terms (ud) in Eq. 9 to become more significant, thus making the ημWν values more symmetric for P- or AP-state (μ = 0, 1).
A challenge for such interface modeling has always been that there are more parameters than measurements to confine them within reason. The value of this line of analysis therefore lies less in its ability to determine in absolute terms these interface-related η values, but in relating changes in observed ημWν to materials modification of a specific tunnel junction structure. This enables identification of changes of corresponding interface properties.
For example, the noticeable rise of η1Wν for low rA devices shown in Fig. 2(a) likely indicates a low-RA interface degradation to CoFeB structure’s magnetic exchange energy, as the spin-flip scatter coefficient is expected to be inversely proportional to the magnetic exchange energy η(F,R)Ddu ∝ 1/Aex,(F,R).1
The device-to-device variation of η0Wν is significantly larger than that of η1Wν as shown in Fig. 2. This trend is observed repeatedly on many sample wafers. The exact cause of this difference is not yet definitively known. It may reflect a different exchange energy and anisotropy environment the interface magnetic moments experience under magnetically parallel (0Wν) and antiparallel (1Wν) configurations. Alternatively, sensitivity of η0Wν to TMR according to Eq. 12 may make η0Wν more susceptible to spin-inactive shunts – present possibly due to edge-damage or other non-ideal barrier structures.
In summary, from an MTJ’s bias dependent slope of conductance , electrode-specific spin-flip scattering can be parameterized. An MTJ’s is experimentally shown to have the empirical form of Eq. 1–2. The slopes are shown to relate to individual electrode-MgO interface’s spin-flip scattering factors Γ(R,F)(U,D)(du,ud) as defined in Eq. 4. With these electrode-specific parameters, one can associate the four quadrants of observed slopes of as shown in Figs. 1–2 with corresponding electrode- and current flow-specific parameters as described by Eq. 12. This association allows for electrode interface specific identification of materials behaviors, thus assisting materials evaluation and optimization during technology development.
Work done with the MRAM group at IBM T. J. Watson Research Center supported in part by partnership with Samsung Electronics.