Bias dependent conductance in CoFeB-MgO-CoFeB magnetic tunnel junctions as an indicator for electrode magnetic condition at barrier interfaces

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 $gV$ 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 r_A) ranges from ∼5 to 30 Ω μm².

Fig. 1(a) shows the current-voltage (IV) characteristics of one such device^11,15–17 at ambient temperature. It has a parallel state resistance of R_p ≈ 19 kΩ, and an MR ∼ 82 %. Curvatures in IV reflect a bias-dependent differential conductance $gV≜dI/dV$⁠. 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). $gap,pV$ 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 $V≤20$ mV are designated as g_ap0 and g_p0.

For MTJs with high-quality, high conductance tunnel barrier, electronic trap-state’s effect on $gV$ for $V≪1$ V is weak,¹⁸ as is band-structure effects.¹⁹ The leading order V dependence of $gV$ 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, $ΓαV$ 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. $Γp,apV$ are shown in Fig. 1(b). Both branches are truncated beyond their respective STT switching threshold. These measured $Γp,apV$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 $ΓV$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 $ΓV$⁠. For this particular junction, one may write $ΓpV≈ΓapV≈ΓV≈ηmV$⁠, sharing a single slope value $ηm$ 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 $μ,ν∈0,1$ to represent the magnetic state of the MTJ, and the bias direction an STT switching directs. For example, a Γ_0W1 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 $ΓμWνV=ημWνV$⁠, with V ≥ 0 and η_μWν > 0.

Next we examine the η_μWν slopes of $ΓμWνV$ across samples of varying junction size and r_A, but with otherwise symmetric CoFeB∣MgO∣CoFeB interfaces. Fig. 2 shows data from five wafers with different r_A values. The slope of $ΓμWνV$ 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 r_A axis represent different wafers, with each wafer having a well defined mean-value r_A. The wafer with the lowest r_A (of about 4 Ωμm²) is least reliable due to limited yield, resulting in fewer junctions available for data averaging.

For r_A > 5 Ωμm², the $ΓμWνV$ shows no significant r_A dependence trend beyond data noise. Similarly, when analyzed as a function of junction size in Fig. 2(b), no systematic size dependence of $ΓμWνV$ 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 $σR$ and $σ′F=±=u,d$ are spin indices of the R and F tunnel electrodes, respectively. A rotation between F and R moments of angle θ gives $±∣±=cosθ/2$⁠, and $±∣∓=±sinθ/2$⁠. θ = 0 is the P state. θ = π, the AP. $Gσ,σ′$ are the spin-channel specific electron conductance.

We assume a R and F electrode ‘separatability’ so that $Gσ,σ′=fΩRσΩFσ′$ 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 Γ_ABpq-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 $Gσ,σ′$ by Eq. 3 including the spin-flip scattering rate factor now reads:

The sub-band differential conductance expressions are therefore:

where we also assumed as in Refs. 8 and 22 that the sub-band density-of-state factors, now including spin-flip scatter induced coupling, are still separated by their corresponding interfaces.

The presence of the Γ_ABpqs in Eq. 6 through $Gσσ′$ 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 $Uud,Dud,Udu,Ddu→Ddu,Udu,Dud,Uud$ for the Γ_ABpqs 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 $gθ=g(R,F)u+g(R,F)d$⁠, which gives the parallel and antiparallel charge conductance as $g0$ and $gπ$⁠. To the leading order of the Γs, for the two configurations of $θ=0,π$ corresponding to $μ=0,1$⁠, and the two possible bias direction of $ν=0,1$⁠, this gives the configuration-specific MTJ conductance of $gμWνV$ as

The subscripts for g_μWν means “in state μ and in the bias direction for Writing to state ν”, same as the definition for Γ_μWν described earlier.

Assume a leading order linear voltage dependence of Γ_ABpq = η_ABpqV, and write the experimentally observed normalized conductance from Eq. 2 as

where the binary indices $μ,ν∈0,1,μ¯=NOTμ$⁠, we can then connect the measurement-derived η_μWν in Eq. 8 to the interface-specific model parameters of η_ABpq in Eq. 7.

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 ≪ T_c when minority-to-majority spin-flip scatter dominates, or Γ_ABdu ≫ Γ_ABud,^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 η_μWν to interface-specific spin-flip scatter rate’s energy-dependence slopes described by η_ABpq. Such interface-specific spin-flip scatter rates can further be related to exchange-stiffness values governing magnon excitation spectra, in the form of η_ABpq ∝ 1/A_ex where A_ex 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 η_0Wν ∼ η_1Wν/2 for symmetric electrodes. If on the other hand, the up- and down-stream spin-flip scattering rates are similar, then one would have η_0Wν ∼ η_1Wν. The conductance expressions from Ref. 1 in their low temperature limit for symmetric electrodes would result in η_0Wν ∼ η_1Wν.

Experimental data for nearly symmetric interfaces from Fig. 1–2 indicate $η0Wν≲η1Wν∼0.75−11/V$⁠, 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 η_μWν 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 η_μWν to materials modification of a specific tunnel junction structure. This enables identification of changes of corresponding interface properties.

For example, the noticeable rise of η_1Wν for low r_A 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/A_ex,(F,R).¹ 

The device-to-device variation of η_0Wν is significantly larger than that of η_1Wν 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 η_0Wν to TMR according to Eq. 12 may make η_0Wν 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 $gV$⁠, electrode-specific spin-flip scattering can be parameterized. An MTJ’s $gV$ 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 $gV$ slopes of $ημWν=dΓ/dV∣μWν$ 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.