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Zhang et al. Microstructures 2023;3:2023046  https://dx.doi.org/10.20517/microstructures.2023.57  Page 7 of 11

               Table 1. Local switching properties of the three types of domain structures
                Type        V i-SSPFM  (V)       V i-map  (V)      V c-SSPFM  (V)       V c-map  (V)
                Type 1      -0.6                 -1.28             7.1                  7
                Type 2      -3.55                -3.5              13.77                14
                Type 3      -0.95                1.5               11.9                 11.5







































                Figure  3.  Type 3 domain structure. (A) Topography of type 3 domain structure. (B) The corresponding OOP phase signal. (C) The
                optical image of type 3 domain. (D) IP phase signal measured at a tip-sample orientation of 0. The IP polarization variants are denoted
                on each domain. (E) The binarized version of (D). (F) IP phase signal measured at a tip-sample orientation of 90. (G) The binarized
                version of (F). (H) The reconstructed three-dimensional polarization vectors for type 3 domain.

               and the SSPFM mappings, respectively. V c-SSPFM  and V c-map  are coercive fields extracted from the averaged
               SSPFM curve and the SSPFM mappings, respectively, where V  = (|V | + |V |)/2. From the imprint
                                                                               p
                                                                          c
                                                                                     n
               mappings [Figure 4B, E, H], it can be seen that in all three types of domain structures, the downward
               domains consistently have a negative imprint while the upward domains have a positive imprint, which may
               be due to the alignment of the high concentration of defect dipoles, e.g., oxygen vacancies, during the DC
               switching processes. V i-map  for type 1, 2, and 3 domain structures are -1.28, -3.5, and 1.5 V, respectively. As a
               comparison, V i-SSPFM  shows a similar trend (-0.6, -3.55, and -0.95 V), and the deviation might originate from
               different sample sizes as the V i-SSPFM  is based on only 200 groups of datasets. The coercive fields, V c-SSPFM  and
               V c-map , show that a type I domain structure has the smallest coercive field, around 7 V, compared to about 14
               and 11 V for type 2 and 3 domain structures. The divergence is probably due to the different polarization
               variants in type 1, m1 and m2, in contrast to m1 and m3 in type 2 and 3 domain structures. The resultant
               vectors m1+ and m2+ or m1- and m2- are closer to the OOP direction of the electric field along the [100]
               directions than m1 and m3 pairs, which allows the electrical switching at a lower voltage. The coercive field
               of the type 3 domain is slightly smaller than that of the type 2 domain. It is possible that a larger domain size
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