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Zhang et al. Microstructures 2023;3:2023010 https://dx.doi.org/10.20517/microstructures.2022.39 Page 7 of 12

where k and k are the contact stiffness and the spring constant of the cantilever, respectively. γ is the
*
lever
relative position of the tip at the end of the cantilever. The values of flexural resonance wavenumber x L can
n
[41]
be calculated with the nth order resonant frequency f of the tip-sample system :
n

Therefore, the cantilever parameter c L for each mode can be obtained directly from the free resonance
B
frequencies f . Because the normalized contact stiffness of the first and second modes k /k should be the
0
*
lever
n
same, the relative tip position γ can be determined by the intersection of the two modes k /k -γ curves
*
lever
*
plotted from Equation (4), as shown in Figure 2H. On this basis, the reduced modulus E of the sample can
s
be calculated from the normalized contact stiffness k /k as:
*
lever
where E is the reduced modulus of reference material, and can be obtained from Equation (2). k /k and
*
*
lever
s
ref
k /k are the normalized contact stiffness of sample and reference material, respectively. Then, the elastic
*
lever
ref
modulus E of the sample can be calculated from the reduced modulus E using Equation (2).
*
s
s
Combined with the Equations (2 and 4-6), the elastic modulus of CIPS-IPS was calculated and the results
are listed in Table 1. It is worth noting that the Poisson’s ratio used in the actual calculation comes from the
result obtained from the conversion of the elastic coefficient calculated by DFT. The Poisson’s ratio of CIPS
is -0.044 (the value of the reference is -0.060 ), and the Poisson’s ratio of IPS is 0.107, as shown in Table 1.
[43]
The elastic modulus of CIPS phase is 27.42 ± 0.05 GPa, which is slightly smaller than that of IPS phase,
which is 27.51 ± 0.04 GPa. The moduli obtained by the CR-AFM measurement of both CIPS and IPS are
larger than the Young’s modulus result of 22.20 ± 0.48 GPa from the nanoindentation measurement. This
may be induced by the fractures or the effect of dislocations during the indenting process. Through the
results of the continuous stiffness method [Supplementary Figure 5], we can find that the modulus gradually
decreases with the increase of the indentation depth, which confirms the effect of fracture in reducing the
measured modulus value of nanoindentation measurement.
In order to confirm the difference in the elastic modulus of the two phases, we used density functional
theory (DFT) to accurately calculate the elastic matrices of the CIPS phase and the IPS phase (The crystal
structure parameters of CIPS and IPS are listed in Supplementary Table 1), and the results are shown in
Table 2. From the table, we can find that the modulus of IPS is larger than that of CIPS, with a difference of
nearly 1.23 GPa, which is consistent with our experimental results.

To further study the ferroelectric property of CIPS-IPS, the flakes were obtained by mechanical exfoliation
and then transferred to Au-coated silicon. Figure 3A shows the topography, which indicates the thickness is
around 176.2 nm. The corresponding phase image is shown in Figure 3B, and the enlarged amplitude and
phase signals of blue-boxed region are shown in Figure 3D and E, respectively. The vanish of amplitude
signal indicates the region of non-ferroelectric IPS phase. In contrast, there are two opposite polarization
states in the CIPS phase, such as the yellow domain (point P1) and the black domain (point P2). There are
three phase state distribution characteristics, in which the intermediate contrast is from non-polarized IPS.