# Optimization of Bifurcated Switching by Enhanced Synthetic Antiferromagnetic Layer
## 2 Results and Discussion
### MRAM Device Performance  
In our MRAM array, the MTJ cell was inserted between two metal lines in the back-end-of-line (BEOL) process as shown in Figure 2a. A brief flow of processes such as  
Figure 1: (**a**) Structure of the p-MTJ stack. (**b**) Major hysteresis loops of p-MTJs measured by MOKE. (**c**) Minor loops of p-MTJs. (**d**) Typical spectra as a function of magnetic field at RF frequency of 45 GHz. (**e**) Resonance field dependence of RF frequency. (**f**) FMR linewidth dependence of RF frequency. photolithography, etching, chemical mechanical polishing, etc., is shown in Figure 2a. Voltages were applied across the MTJ cell to obtain various electrical properties, such as resistance state, critical switching voltage, and so on. The R-H curves of 180 MTJ cells were measured at room temperature, and 15 cells were selected in Figure 2b for a clear look. The free layer switched its moment after the applied magnetic field exceeded its coercive field (\(H_{\mathrm{C}}\)) while the read voltage was continuously applied. There are similar sharp switching curves compared to MOKE curves, but the value of inline \(H_{\mathrm{C}}\) is significantly higher than that of offline \(H_{\mathrm{C}}\) due to its considerably smaller cell size, which lacks domain-wall assisted flipping. The distribution of \(H_{\mathrm{C}}\) extracted from 180 samples is shown in Figure 2c, where the \(H_{\mathrm{C}}\) switching either from AP state to P state or from P state to AP state shows perfect concentricity. When it came to electrical switching, the critical switching voltage was measured by gradually increasing the applied voltage with a pulse width of 20 ns. The switching voltage distribution for two directions (i.e., from AP mode to P mode and from P mode to AP mode) is shown in Figure 2d. Good uniformity is observed, and there is no obvious tail piece. Compared to the mean value of the switching voltage, about 35% overdrive is needed to achieve a satisfactory write-error rate according to the limited write times. To fully realize STT-MRAMs for memory applications, it is critical to demonstrate robustness in terms of write-error rate (WER). About 100 MTJ cells were written repeatedly 10,000 times to test the MRAM write-error rate and determine the write voltage. Even though the MTJ array showed good uniformity in limited samples, the failure behavior became more dominant with increasing cycling time. For each die, the WER curve was smooth, and the dependence of the WER on the amplitude of the voltage pulse did not show an abnormal switching characteristic (back-hopping) of the junctions. However, bifurcated switching appeared in the cumulative curve when the order of magnitude reached \(10^{-2}\), as shown in Figure 2f; this is also called the balloon effect. Unlike back-hopping, bifurcated switching can be overcome by increasing the program voltage to maintain a satisfactory  
Figure 2: (**a**) A brief flow of the MRAM chip BEOL process. The insert is the TEM of MTJ cell in MRAM. (**b**) The R-H curves of the 15 selected MTJ cells. (**c**) The distribution of the switching field from AP to P and from P to AP. (**d**) The distribution of the switching voltage from AP to P and from P to AP (the step of switching voltage is 0.03 V). (**e**) The write-error rate of 100 MTJ cells with increasing write voltage (each cell was retested 10,000 times). (**f**) The write error of MTJ array with increasing write voltage. write-error rate. However, increasing the voltage leads to an increase in the probability of breaking the barrier layer and causing permanent hard faults. According to the WER curve, the overdrive of write voltage reached above 50%, which is much higher than the result according to the mean value and the coefficient of variation. For the perpendicular MTJ cell, the WER can be derived based on the Fokker-Planck theory [32, 33].