Impact of Voltage Polarity on Time-Dependent Dielectric Breakdown of 1-nm MgO-Based STT-MRAM With Self-Heating Correction

Time-dependent dielectric breakdown (TDDB) lifetime of ultrathin (1 nm) MgO in spin-transfer torque magnetoresistive random access memory (STT-MRAM) devices has recently been shown to be driven by factors other than voltage alone. This study focuses on the specific role of asymmetry in the current flow for different polarity pulsing modes of voltage stress on the TDDB lifetime of 1-nm MgO. Numerical analysis, based on a 3-D heat-diffusion equation and spintronic simulations, has been performed to characterize the temperature rise in the devices for precise correction of self-heating to obtain a correct interpretation of MgO TDDB. It is shown that the different lifetimes for the positive and negative modes can be attributed to different temperature increases arising from self-heating. While the positive and negative modes displayed a non-Arrhenius behavior, the bipolar mode showed an Arrhenius trend in which we observed a unique bimodal behavior of TDDB activation energy ( ${E}_{\text {a}}$ ) as a function of stress voltage in the ultrathin MgO stack. We discuss the role of additional driving forces, such as current, self-heating, charge trapping, and interface strain governing the breakdown mechanism along with the voltage effect.


Impact of Voltage Polarity on Time-Dependent
Dielectric Breakdown of 1-nm MgO-Based STT-MRAM With Self-Heating Correction

I. INTRODUCTION
S PIN-TRANSFER torque magnetoresistive random access memory (STT-MRAM) has shown great potential as a replacement for SRAM cache due to its low latency [1] and for embedded Flash due to its high endurance, retention, and favorable form factor [2]. The principle behind the operation of STT-MRAM is the reversible flipping of magnetic spins in the free layer (FL) relative to magnetization in the reference layer (RL) using current density in a range of 5-7 MA/cm 2 . The parallel (P) and antiparallel (AP) magnetization configurations correspond to low (R P ) and high (R AP ) resistance states, respectively.
Several studies on time-dependent dielectric breakdown (TDDB) in ultrathin MgO layer have shown that it can be described by the ξ -model [3], [4], [5], 1/ξ model [5], [6], [7], [8], [9], or the power law model [8], [9], [10], [11], with latest studies showing that the power law model is the most appropriate [12], [13]. Solutions to improve the endurance of STT-MRAM have also been studied with regard to the impact of process integration and fabrication impact, accounting for the effects of process steps such as etching, encapsulation, and annealing [9], [10], [11], [14], [15]. Further solutions to improve STT-MRAM endurance include increasing the write efficiency [16] and enhancing the thermal stability [17]. It is increasingly evident that the MgO breakdown is driven by multiple mechanisms [18], [19]. Despite the above studies conducted by various groups, the explicit role of voltage, current, and temperature in the defect generation process is still unknown. It has been reported that self-heating has a severe impact on device endurance by accelerating breakdown [6], [9], [10]. In our study, with the use of 3-D numerical simulations, the role of self-heating and its dependence on operating conditions have been quantified. Subsequently, self-heating correction (SHC) has been appropriately done during the analysis of the stress test results.
The tunnel magnetoresistance (TMR) of industrial-grade magnetic tunnel junction (MTJ) is ∼50%-100% at typical TDDB voltage conditions; as such, there is a large asymmetry in the switching current inherent to the device operation. This complicates the TDDB analysis resulting in a need to look This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ beyond traditional MgO breakdown mechanisms reported thus far [20]. This study is aimed at understanding the breakdown mechanism by testing TDDB with different pulse voltage magnitude and polarity, device area, and temperature. We find that the differences in TDDB for the positive and negative modes are mainly caused by self-heating. The TDDB of the positive and negative modes is non-Arrhenius, unlike the Arrhenius trend for the bipolar mode. Bipolar TDDB activation energy (E a ) is shown to have a bimodal behavior. The effects of current, self-heating, charge trapping, and interface strain on MgO breakdown are discussed and a hypothesis for the breakdown model is proposed.

II. TEST STRUCTURE AND ELECTRICAL CHARACTERIZATION
The MTJ stack was deposited using magnetron sputtering on 300-mm Si wafers. FL and RL are CoFeB-based ferromagnets and the RL is pinned with synthetic antiferromagnet (SAF) layers. The MTJ devices studied were cylindrical with nominal diameters of target critical dimension (TCD), TCD −15% and TCD +15%. All three diameters were between 50 and 100 nm. Pulsed voltage TDDB tests with a 200-ns pulsewidth were used to measure MgO endurance for bit cell arrays comprising 256 devices per set for positive, negative, and bipolar modes. Positive polarity is defined as a current flow from RL to FL, as shown in Fig. 1(a). MTJ devices are set to the AP and P states for positive and negative voltages, respectively. Typical resistance-voltage (R-V ) characteristics are shown in Fig. 1(b), and note that R AP at high positive voltage is ∼50%-100% larger than R P .

A. Calibration of STT-MRAM Device Performance
The measured resistance-hysteresis (R-H ) curves to determine the current level and resistance of the devices at various voltages are shown in Fig. 1(c). Even at high bias, R P state values remain relatively constant, while R AP decreases significantly with increasing voltage. The extracted TMR = (R AP -R P )/R P × 100% is plotted in Fig. 1(d). The value of TMR decreases by around 60% at ±750 mV with reference to the zero-field value. Fig. 1(e) shows the R-H loop measured for V = 10 mV at T = 25 • C, 85 • C, and 125 • C. Note the reduction in TMR by 20% with increasing temperature from 25 • C to 125 • C [see Fig. 1(f)]. These TMR dependencies suggest that the extent of asymmetry in the tunneling current for different pulsing modes depends heavily on stress voltage and internal temperature, which in turn affects the TDDB lifetime of these devices and makes them sensitive to the polarity of the voltage used.

B. 3-D Self-Heating Simulation
To quantify the internal temperature rise due to self-heating, the 3-D heat-diffusion equation (1) has been solved along with the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation [21] using the finite-element method Here, ο (Kgm −3 ) is the material density, c (Jkg −1 K −1 ) is the specific heat capacity, and k (Wm −1 K −1 ) is the thermal conductivity, with values shown in Table I. V is the volume, and I 2 R is the rate of heat generation due to current I and resistance R of the MTJ. The associated current and resistance have been calculated from the dynamics of the FL of MTJ by self-consistently solving the LLGS equation. A constant voltage pulse of 0.94 V was applied for 5 μs, which was enough to reach the steady-state temperature of the device [5], [6], [10], [18], [22], [23], [24]. Within this framework, mass density, thermal conductivity, and specific heat capacity of all the layers were considered. The outer boundary of the encapsulation of the stack was kept fixed at 298 K. It may be noted that even though the encapsulation and electrode are not shown in the thermal distribution, the full device comprising electrode, stacked layers, and encapsulation were considered in the heat simulation study.
The spatial distribution of temperature [see Fig. 1(e)] of the entire STT-MRAM stack shows that the highest temperature rise is in the MgO layer. The obtained temperature rise in the MgO layer of the devices is shown in Fig. 1(f) and (g) under positive and negative stressing modes, respectively. As expected, the temperature in the MgO layer is higher by 20-50 K for the negative stressing mode due to the lower resistance of the R P state.
To validate the self-heating simulation, T sim was compared with experimentally extracted internal temperature rise (T exp ) using (2) from [22], where P is the dissipated power and φ th is the thermal resistance and is a constant fitting parameter that heavily depends on the local material stack environment surrounding the MgO layer. Note that the electrical resistance R MTJ is experimentally measured and, as such, inherently considers the nonlinear changes in R MTJ under different stress voltages and ambient temperature conditions. When the trends of decreasing TMR with increasing stress voltage and ambient temperature from Fig. 1(c) and (d) are accounted for, the estimates of T exp match very well with T sim , with an error of ∼1%. Note that φ th , here, is a fitting parameter with values  Table II. Smaller CD devices have higher φ th as they have smaller cross-sectional area contacts with the top and bottom electrodes to dissipate heat. The significant deviation in positive mode φ th is likely due to varying dependencies of R AP on voltage for different device sizes Considering the high current density (∼6-10 MA/cm 2 ) used in our accelerated cycling test, the effects of self-heating must be considered prior to quantitative comparison of the temperature-dependent breakdown data. It is to be noted that for STT-MRAM devices that even under typical operating conditions which involve tunneling current densities of ∼3-5 MA/cm 2 , self-heating plays a prominent role and needs to be accounted for. This contrasts with logic and other nonvolatile memory devices where the self-heating effects under nominal operating conditions are minimal. The self-heating simulations, coupled with spintronic simulations performed in this work, provide further insight into self-heating with due consideration of switching dynamics of the MTJs. Breakdown distribution is assumed to follow the Weibull trend [9], [10], [11], [18], [19]. We observed that the negative stress always yields a lower lifetime than that of the positive stress for any combination of voltage and temperature, and the difference in the extrapolated MTTF (using the power law extrapolation model) [12], [13] can be up to three to four orders of magnitude [see Fig. 2(b)]. Devices in the negative stress mode experience a higher current density due to lowresistance R P state, leading to shorter MTTF. Note that the positive and negative MTTFs converge at higher temperatures and voltages due to reduced TMR.

D. TDDB Dependence on Current Density
Given the high nominal current density-low voltage operating regime of STT-MRAM, it is necessary to determine whether the breakdown is mainly current-driven. The trend of MTTF versus current density for the positive and negative modes shown in Fig. 2(c) reveals the contrary. For the same current density, the MTTF for the negative mode can be a few orders higher than the positive mode. This suggests that neither current nor voltage alone is responsible for breakdown, and both current and voltage have a collective role to play, which will be discussed later in Section III-G.

E. Lowest Lifetime for Bipolar Stress
Based on the trends above, it may be logical to assume that the bipolar mode will have an MTTF in between the positive and negative modes. However, this is not the case. As shown in Fig. 2(d) and (e), MTTF for the bipolar mode is always the lowest across all device areas, voltages, and temperatures. This shorter lifetime for bipolar stress is discussed in further detail in the subsequent sections.

F. Weibull Slope Comparison for Different Stress Modes
As shown in Fig. 2(f) and (g), we notice that at all temperatures and voltages, the Weibull slope (β) is much higher for the bipolar mode, compared to that of both positive and negative stresses. Moreover, the value of β remains unchanged for the positive and negative modes, suggesting that they have the same mechanism of degradation. The higher value of β for the bipolar mode (β bipolar ) could be attributed to higher defect generation efficiency (α) according to the percolation model [25], where β and α are linearly correlated. The value of α may be empirically estimated from the downward slope of the resistance-time degradation trend during endurance tests of the devices in the bipolar mode, closer to the breakdown transient [see Fig. 2(h)]. The higher value of α bipolar ∼2.7, compared to α positive ∼0.1 and α negative ∼0.3, agrees with higher β bipolar . Another noteworthy trend is the consistently increasing β with stress voltage and T , again due to an enhancement in α caused by higher trap-assisted tunneling current [21] and thermal stress in the dielectric. Fig. 3(a) shows the Arrhenius plot of MTTF in MgO for the positive, negative, and bipolar modes in a device of TCD diameter, where k B is Boltzmann's constant. The Arrhenius plot can be corrected for self-heating by translating the Arrhenius plots along the x-axis for each mode by T from Fig. 1(f) and (g), as shown in Fig. 3(b). The bipolar mode was corrected with T from the negative mode as that represents the worst case scenario temperature rise under bipolar stress. After SHC, the Arrhenius plots of the positive and negative modes clearly depict the same trend, suggesting that they share the same underlying breakdown mechanism. However, the Arrhenius plot trend for the bipolar stressing still significantly deviates from both the positive and negative modes, indicating the presence of an additional mechanism that causes degradation of the MgO.

G. Non-Arrhenius Trend of MgO Breakdown
Another important observation from Fig. 3(b) is the highly non-Arrhenius behavior for the positive and negative modes of stressing, while the bipolar data show a clear Arrhenius trend. The non-Arrhenius behavior of the positive and negative modes could be due to the unidirectional stressing and charge trapping [4], [26] as well as the complex non-Arrhenius dependence of charge transport mechanisms such as inelastic trap-assisted tunneling. As for the bipolar mode of stressing, the convoluted effect of multiple possible phenomena, including charge trapping at both interfaces, mechanical strain induced by compressive-tensile strain changes in the MgO-CoFeB interface, as well as voltage, current, and temperature results in a "pseudo-Arrhenius" trend. Based on the model proposed by Wu et al. [27] for SiO 2 and HfO 2 which also display non-Arrhenius dependence of time-to-breakdown, the generation of oxygen vacancies at the MgO-CoFeB interface through Mg-O bond breaking via multiple electron-induced coherent vibrational excitations could be the origin for the non-Arrhenius trend for the positive and negative modes.
The bipolar mode TDDB E a with and without SHC is plotted with voltage in Fig. 3(c). It is clearly seen that E a decreases with voltage and has a bimodal behavior with different sensitivity to voltage. Similar E a trends have been reported in SiO 2 dielectrics [28], [29], [30], [31], but there has been no clear explanation provided to the best of our knowledge. Considering the conducting nature of 1-nm MgObased STT-MRAM devices, there could be multiple combined effects contributing to the E a trend such as current, selfheating, charge trapping [4], [26], and interface strain along with the voltage effect. Noman et al. [32] reported electron trapping-induced filament formation in TiO 2 -based resistive devices contributing to percolation path formation. With the large applied current density in our MgO devices, electron trapping could take place at preexisting oxygen vacancies, the presence of boron oxide or lattice mismatches at the CoFeB-MgO interface [4], [21] that can lead to strong localized fields. The trapped electrons result in greater current flow in the local region, which further induces more electron trapping. This process speeds up to create structural changes that lead to the formation of a breakdown percolation path when the localized field, current, and temperature reach a threshold value. The bimodal trend of E a could also be driven by the formation of defects [33] and/or voltage-induced CoFeB-MgO interface strain [34] through the breaking of Mg-O bonds. In addition, the bimodal trend of E a could be due to multiple breakdown pathways as reported in [30] and [35].

H. Power Law Model for MgO Breakdown
The power law model has been proposed by Wu et al. [36] to describe breakdown processes that are both field and currentdriven. The power exponent from the power law model fitting [see Fig. 3(d)] is represented as a function of temperature in Fig. 3(e). The monotonic reduction in the power exponent with temperature for all three stress modes is an additional confirmation of the validity of the power law, which is recommended for current and field co-induced breakdown [37]. The power exponent trend against temperature is a signature of the physical breakdown mechanism. Referring to Fig. 3(e), after SHC, the positive and negative modes' power exponent trends match well as indicated by the dotted line, hence implying that they share the same signature. However, the bipolar power exponent trend deviates significantly from the other two modes after SHC, which indicates a different breakdown mechanism. These suggest that the main difference between the positive and negative breakdown is due to self-heating, while the bipolar breakdown is driven by a fundamentally different process.

I. Physical Mechanism of MgO Breakdown
We propose a schematic illustrating the breakdown mechanism as shown in Fig. 3(f) with "U" denoting the defects of the unipolar positive and negative modes and "B" denoting the bipolar modes defects. It is evident that breakdown cannot (e) Trend of power-law exponent versus temperature for positive (UNI+), negative (UNI−), and bipolar (BIP) modes with and without SHC for TCD −15% diameter devices. (f) Sequence of defect generation in the MTJ for positive, negative, and bipolar modes. The numbers inside the circles represent order of locations where defects are generated. "1a" and "1b" imply equally probable locations for the first defect to be generated. The red arrows denote the directional evolution of percolation.
be described by "current only" or "voltage only." The fieldfree Mg-O bond energy of 2.0-4.4 eV as obtained from experimental and DFT studies [18], [20], [22], [38], [39] is significantly higher than the maximum ballistic electron energy of 0.94 eV. The breakdown process in the 1-nm MgO layer could proceed in two stages: 1) current-assisted defect generation at the interface and 2) field-assisted defect generation in the bulk.
In the positive and negative modes, the first defect is generated at the MgO-CoFeB anode interface through multiple electron-induced coherent vibrational excitations of the Mg-O bond due to trapped charges and high charge fluence (U1). These interfacial defects reduce E a for bulk defects to be created in their vicinity (U2). The bulk defects trigger the final defect (U3) at the other MgO-CoFeB interface to be generated in its vicinity, again due to lower E a caused by lattice relaxation.
In the bipolar mode, both MgO-CoFeB interfaces are equally susceptible to nucleate the percolation path. Charge trapping and defect generation probability are high at both interfaces (B1a/B1b). The trapped charges and/or nucleation of defects at both interfaces drastically reduce E a for MgO bulk defect generation (B2) resulting in easier percolation. Hence, MTTF for the bipolar mode is much smaller than that of the unipolar modes. Considering that 1-nm MgO is 4-6 monolayer thick, it is expected that the percolation path comprises only around three defects.

IV. CONCLUSION
A holistic comparison of TDDB lifetime trends in STT-MRAM devices is presented considering three different types of pulse stressing modes and SHC with varying device area and temperature. After SHC, it was shown that positive and negative modes have similar TDDB trends, implying that they share the same breakdown mechanism. The bipolar TDDB trends deviate significantly. Bipolar TDDB E a versus stress voltage trend was observed to have a bimodal behavior that could be due to charge trapping, interface strain, or model mixing. Our results support a degradation model driven by both current and field, leading to a fluence-field co-assisted breakdown mechanism, which complicates the physics of failure for the commonly used bipolar pulse condition. Analysis of Mg-O breakdown via atomic force microscopy or in situ transmission electron microscopy could reveal more insights into the structural changes and strain effects. Further density functional theory calculations of the defect energetics, charge trapping, and breakdown transients are required to unveil the fundamental physics of breakdown in ultrathin MgO stacks.

ACKNOWLEDGMENT
The authors would like to acknowledge Everspin Technologies, 1 Chandler, AZ, USA, for their technical expertise in the fabrication of the devices used in this work.