*3.2. Ferroelectric Domain and Domain Switching*

To approve the ferroelectricity of CIPS flakes with different thicknesses, the domain distribution of the CIPS flakes was investigated in 3 nm, 9 nm, 12 nm, 21 nm, 35 nm, and 78 nm CIPS flakes by piezoresponse force microscopy (PFM). The domain evolution of the CIPS flakes was observed with height, amplitude, and phase images, as shown in Figure 2a–f. The domain size varied with the increasing thickness of the CIPS. As shown in Figure 2a–f, the size of the ferroelectric domains increases with the thickness of the CIPS flakes. Domains vary in size but are on the order of ~100 nm and ~1 μm in diameter, respectively, different from reports in the literature [7]. In our experience, it is easy to observe clear domain structures in CIPS flakes with thicknesses in the thickness range from 20 to 40 nm, as shown in Figure 2d,e. We observed the reversed piezoelectric effect in the typical amplitude-voltage "butterfly" loops by scanning the piezoresponse hysteresis loops in dual AC resonance tracking PFM (DART-PFM) mode. There are regions where the ferroelectric inversion loop disappears in the 20 nm CIPS flakes, which may be related to the paraelectric phase caused by Cu2+ segregation.

According to the above results, we chose the CIPS sample with a thickness of 20 nm to investigate the ferroelectric switching behavior. Well-defined butterfly loops of the saturated PFM amplitude and the distinct 180◦ switching of the phase signals were observed, as shown in Figure 3a,b, indicating switchable ferroelectric polarization in the CIPS flakes with different thicknesses (28 nm and 20 nm). We divided the hysteresis loops into four sections, as shown in Figure 3a–c, and observed that the direction of the polarization switching of CIPS was consistent with that of PVDF [28], showing negative piezoelectricity, which arose from the low polarization of Cu atoms in the CIPS layer [14]. We still observed abnormal butterflies and switching of the phase loops in the 25 nm and 20 nm CIPS, however, as shown in Figure 3c,d. There are the following several possible reasons for the abnormal switching loops: One, when sweeping the electric fields in the reverse sequence, the piezoelectric response curves show asymmetric shapes. This phenomenon was attributed to the existence of remnant-injected electrons. Due to the different diffusion distances in both the positive and negative electric range, the injected electrons cannot be eliminated absolutely when applying a lower electric field [29]. Two, the abnormal hysteresis loops may also relate to negative electrostriction and electrostatic signal contributions accompanied by charge injection during scanning [30]. Three, abnormal domain switching is generated due to in-plane ionic migration in CIPS [31]. Since the Cu is deficient, when applying an electric field, a few regions of the CIPS undergo a chemical phase separation into a paraelectric In4/3P2S6 phase and a ferroelectric CuInP2S6 phase [32]. Abnormal hysteresis loops may be from the local paraelectric phase of the CuInP2S6–In4/3P2S6 region due to Cu deficiency [27].

**Figure 2.** PFM images including height, amplitude, and phase image (upper three), and height curves (bottom row) of CIPS flakes with different thicknesses. (**a**) 3 nm, (**b**) 9 nm, (**c**) 12 nm, (**d**) 21 nm, (**e**) 35 nm, and (**f**) 78 nm.

To investigate the in-plane ionic migration, we carried out a relaxation test to analyze the local ionic dynamics of CIPS via electrochemical strain measurements (ESM), as shown in Figure 4 [33,34]. As schematically shown in Figure 4a, a direct-current (DC) voltage is applied on top of an AC voltage to induce a longer-range redistribution of ions in CIPS flakes during the probe. After removing the DC voltage, the ions relax back to their original equilibrium state. The local dynamics can be deduced from the time constant associated with the relaxation of ESM amplitude, as shown in Figure 4b. The DC voltage is applied on top of the AC following the profile shown in Figure 4a to induce a longer-range redistribution of Cu<sup>+</sup> ions; meanwhile, polarizing the sample over a larger scale. The faster relaxation shown in Figure 4d corresponds to the Vegard strain directly related to the ionic concentration of Cu+. While slower relaxation in Figure 4d is because of the induced electrochemical dipoles and results from the readjustment of the negative InP2S6 − in response to the redistributed Cu+. The process takes longer over a much shorter distance. This phenomenon verifies our conjecture that the IPS paraelectric phase forms in the Cuabsent region due to the Cu ion migration, with no ferroelectric polarization switching. That is, the relaxation of Cu ions is associated with the change in ferroelectric polarization

after the addition of voltage, and the longer time is related to the saturation phenomenon of polarization specific to CIPS reported in the literature.

**Figure 3.** Ferroelectric polarization switching by PFM for CIPS flakes with different thicknesses. The PFM amplitude (green) and phase (blue) hysteresis loops during the switching process for CIPS flakes with thickness of (**a**) 28 nm, (**b**) 20 nm, (**c**) 25 nm, and (**d**) another area of the sample with the thickness of 20 nm.

**Figure 4.** Relaxation dynamics in local electrochemical strain measurements of CIPS. (**a**) Illustrated DC profile applying in the relaxation measurements. (**b**,**d**) ESM amplitude-time and phase-time curves were obtained corresponding to the DC profile. (**c**) Zoomed—in relaxation curves of (**b**) were recorded after removing negative and positive DC voltage, respectively.
