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Zhang et al. Microstructures 2023;3:2023010 https://dx.doi.org/10.20517/microstructures.2022.39 Page 3 of 12

[31]
approximation (GGA) method as implemented in the Vienna ab initio simulation package (VASP) [32,33] . A
plane wave cutoff of 450 eV was set in our calculations. K-point samplings of 5 × 3 × 2 were used. DFT-
D3(BJ) level [34,35] was used in our calculations to take into consideration of the van der Waal forces. Atomic
-1
relaxation was performed until the force on each atom was smaller than 0.001 eV Å , and the total energy
change was less than 10 eV. The space group of CuInP S and In P S are Cc and P2 /c, respectively. The
-6
1
4/3 2 6
2 6
unit cell CuInP S contains 4 Cu, 4 In, 8 P and 24 S atoms, while the In P S contains 8 In, 12 P and 36 S
4/3 2 6
2 6
atoms. The calculated lattice parameters are listed in Supplementary Table 1, which are consistent with
previously reported experimental values [36,37] .
Scanning probe microscopy
Piezoresponse force microscopy (PFM) and conductive-atomic force microscopy (c-AFM) measurements
were performed using a commercial atomic force microscope (Asylum Research MFP-3D) with Pt/Ir-
coated Si cantilever tips (radius of ~25 nm). The spring constant is in the range of ~0.5-9.5 N/m. The out-
of-plane (OP) phase and amplitude images were acquired using the dual-frequency resonance tracking
piezoresponse force microscopy (DART-PFM) mode with an ac voltage (V = 2 V). The conductive Si
ac
cantilever was excited with an ac voltage of 2 V at the tip-sample contact resonant frequency of ~350 kHz.
The switching spectroscopy PFM (SS-PFM) was performed to obtain the hysteresis loops to characterize the
local ferroelectricity. In c-AFM measurement, the voltage was applied to the conducting Au bottom
electrode, which was continuously swept and simultaneously read the current. In contact resonance atomic
force microscopy (CR-AFM) measurement, the NCL Pt-coated tips with k ≈ 48 N/m were used. The contact
force between the cantilever and the sample was ~25 µN. More calculation details of Young’s modulus are
presented in the Supplementary Information.

Raman measurement
Raman spectra were collected using a micro-Raman system with a Horiba iHR550 spectrometer and a 100X
objective (Olympus, NA = 0.95). A 633 nm Helium-Neon Laser (Newport) was used to excite the Raman
scattering and the laser power was low enough to avoid excessive heating of the sample. Raman
measurements were performed under a microscope in backscattering configuration with linear polarized
excitation and unpolarized detection.

Nanoindentation measurement
The nanoindentation experiments were performed using a commercial nanoindenter (G200 Keysight),
which has load and displacement resolutions of 50 nN and 0.01 nm, respectively. The indentation tests were
conducted normal to the (001) plane at room temperature with a Berkovich indenter. Calibration was
performed using fused silica with a modulus of 72.1 GPa. The sample was fixed to the silicon wafer by the
commercially provided mounting glue. Then the glue and sample were cured for at least 24 h.

RESULTS AND DISCUSSION
The CIPS-IPS crystal has millimeter-sized lateral dimension and a thickness of ~tens micrometers, as shown
in Figure 1A. The crystal is transparent and flexible. For the subsequent structural characterization, thin
flakes of CIPS-IPS were prepared by mechanical exfoliation, as shown in the bottom panel of Figure 1A.
Figure 1B shows the crystal structure of IPS, CIPS and CIPS-IPS heterostructure. IPS is non-polar due to a
lack of Cu ions. To confirm that this sample is indeed a two-phase coexisted CIPS-IPS crystal, we compare
the Raman spectrum with that of CIPS crystal, as shown in Figure 1C. Two peaks appear at ~255 and
~270 cm in CIPS-IPS, which is different from that of pure CIPS. Therefore, the Cu-deficient CIPS crystal
-1
exhibits a local chemical phase separation, presenting both a Cu-free paraelectric IPS phase and a
ferroelectric CIPS phase. Figure 1D shows the topography of CIPS-IPS, which displays a labyrinth-like
distribution. The corresponding elemental mappings confirmed the non-uniform distribution of Cu