# Influence of Applied Stress on the Ferroelectricity of Thin Zr-Doped HfO\({}_{2}\) Films
## 3 Results and Discussion
### Endurance Characterization  
Furthermore, the endurance properties of HZO ferroelectric materials under the two conditions have been investigated. Figure 4 depicts the variation of P-E loops of the HZO capacitor in both the (a) stress free and (b) stressed conditions with the polarization number at an annealing temperature of 450 \({}^{\circ}\)C, respectively. The measurement of P-E curves was carried out under a constant voltage of 3 V. The cycle signal was set to a square wave signal with a frequency of 1 MHz and featured an amplitude of \(\pm\)3 V. The P-E loop results show that the capacitor varied little with the reversal of cycles under the condition of stress; however, it changed significantly in the absence of stress, showing that stress has a significant effect on the endurance properties of HZO materials. The variation of E\({}_{\text{c}}\) and P\({}_{\text{r}}\) with reversal cycles corresponding to the two stress conditions was extracted as shown in Figure 4c,d. Although the capacitive structures under the two conditions exhibit certain fatigue characteristics, the results for the stressed capacitive structures were significantly better than those for the unstressed ones. The interpolated results indicate that under stressed conditions, the P\({}_{\text{r}}\) value does not change significantly until 10\({}^{8}\) operation cycles, which is an improvement of nearly two orders of magnitude when compared to the change in P\({}_{\text{r}}\) at 10\({}^{6}\) cycles under unstressed conditions. This can be attributed to the introduction of the top electrode W, which makes the stress at the top and bottom electrodes asymmetric, and greater stress may make the defect density at the grain boundaries in the HZO material smaller, thus enhancing the endurance. Besides, according to previous studies [32,33], there is a contradictory relationship between the endurance of the material and the remnant polarization strength, which is called the polarization-endurance dilemma, i.e., the endurance properties are weakened by increasing the remnant polarization charge; however, in our stress experiments, we found that the P\({}_{\text{r}}\) of the stressed and unstressed capacitance structures are basically the same, and the stressed one is also a little larger, so the introduction of stress enhances the endurance of the material without sacrificing P\({}_{\text{r}}\), which can be a great improvement on the material properties. Figure 4: Variation between the absence of stress (**a**) and stress (**b**) for P–V curves with polarization cycles at a 450 \({}^{\circ}\)C annealing temperature. (**c**,**d**) The extracted endurance property values. The endurance measurements for HZO capacitance at different annealing temperatures were taken in order to further explore the endurance characteristics of HZO materials. In general, according to the requirement of the endurance of the memory device, the \(\mathrm{P_{r}}\) reduction of the material should be less than 10% after \(10^{9}\) to \(10^{12}\) cycles. We chose the operation cycle corresponding to the degradation of the remnant polarization to 90% of the initial polarization charge as the judgment criterion of capacitance endurance, and the extracted endurance results are shown in Figure 5. The vertical axis represents the operation cycle at each annealing temperature when \(2\mathrm{P_{r}}\) degrades to 90% of the corresponding initial value. The results show that the endurance properties of the material show a gradual weakening with the increase of the annealing temperature, where it can be seen in Figure 3c that the \(\mathrm{P_{r}}\) value for the material increases as the annealing temperature increases. The endurance will weaken according to the polarization-endurance dilemma; however, on the other hand, the effect of stress on the optimization of the endurance properties at each temperature is obvious, where the endurance with the stress condition at each temperature is significantly better than that of the endurance without the stress condition.