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[Audio] Good day! This is Jiangyu Li, from the Department of Materials Science and Engineering, Southern University of Science and Technology, in Shenzhen, China. The title of my presentation is Flexoelectric Engineering of Two-Dimensional Materials, Structures, and Devices..

[Audio] As we know, in crystallography there are 32 point groups, among them 21 are non-central symmetric, 20 are piezoelectric, and 10 are polar. So in order to induce polarization by strain, central symmetry must be broken..

[Audio] We can also break central symmetry locally by strain gradient, and thus induce polarization in any crystals regardless of their symmetries. This is the concept of flexoelectricity..

[Audio] The idea was first proposed by former soviet physicists, though in the first a couple of decades it was mainly studies from theoretical point of view..

[Audio] In early 2000s, Wenhua Ma and Eric Cross published a series of paper reporting experimental observation of flexoelectric effect, and the field started to get hot..

[Audio] The defining feature of flexoelectricity is smaller is stronger, as strain gradient scales with length inversely. That is why a lot of effort was devoted to the nanomaterials and structures..

[Audio] In the last a few years, my group has focused on suspended two-dimensional membrane, which provided an ideal platform to study flexoelectrcity..

[Audio] We started from general theoretical framework, from which the governing equations can be derived for flexoelectricity. You can refer to our 2020 JMPS paper for more information.

[Audio] We then developed a von Karman plate theory for flexoelectricity in suspended membrane, taking into account large deflection and strong nonlinearity. As you see from the governing equation, if the flexoelectric coefficient f is zero, then classical von Karman plate theory is recovered. More details can be found in our 2024 JMPS paper..

[Audio] Both bending of plate and flexoelectricity require C1 continuity, and we adopt Conforming BCIZ plate elements to satisfy this requirement in our finite element simulaiton.

[Audio] We also use piezoresponse force microscopy for experimental validation..

[Audio] We first look at 12nm thick MoS2 suspended on silicon substrate with microfabricated hole. Simulation predict higher piezoresponse arising from flexoelectricity around the boundary of the hole, which is confirmed by PFM measurement..

[Audio] If we increase the force applied to the suspended membrane, then the contrast in piezoresponse become smaller, which is also consistent with our PFM mapping.

[Audio] For thicker MoS2 membrane, the contrast is reversed, with higher piezoresponse in the center. This is also confirmed by the PFM experiment..

[Audio] Another implication of flexoelectricity, as evident from the governing equation, is that the Young's modulus of suspended membrane is stiffen by flexoelectric effect.

[Audio] This can be verified by AFM nanoindentation experiment. But deriving Young's modulus from nanoindentation force-displacement curve is challenging, especially for different thickness under which bending and stretching make different contribution..

[Audio] We develop a machine learning neural network for this purpose, using finite element simulation data for training, after which the Young's modulus, pretention and thickness of the suspended membrane can be derived from experimental force-displacement curve..

[Audio] To verify this, we have made a number of freestanding PZT film with a range of thickness, the thinnest one has just 7 unit cells..

[Audio] We discovered strong size effect in the Young's modulus of PZT. It increase substantially at a few nanometers thickness due to flexoelectric effect, higher than bulk value. From such increase we can also estimate the flexoelectric coefficient, which agrees well with the values reported in Cross papers. More details can be found in our 2024 Advanced Materials paper..

[Audio] Another implication is that flexoelectric effect results in an effective electric field, which can switched polarization in two-dimensional ferroelectric materials such as CIPS, as we reported in our 2022 Science Advances paper. But can we really use it for device application?.

[Audio] The answer is yes, and we have use that to engineer bulk photovoltaic effect in CIPS. Bending align the CIPS polarization, resulting in higher photocurrent, as we schematically show here..

[Audio] We made a structure with CIPS suspended on microfabricated hole, and observe that both piezoreponse and photocurrent increase in the suspended region compared to the one supported by the substrate. And that enhancement comes from strain gradient in the suspended region, a signature of flexoelectricity..

[Audio] We also show that both the piezoresponse and photocurrent can be actively modulated by AFM tip force, the there is a linear variation between photocurrent and strain gradient..

[Audio] We have made a photodetector based on CIPS and graphene electrodes, and observe that photocurrent shows sinusoidal variation with the angles of light polarization. This confirms the bulk photovoltaic nature of photocurrent. More details can be found in our 2024 Nano Letters paper..

[Audio] The previous device was based on two-dimensional ferroelectric. But we can also induce polarization in two-dimensional semiconductors, such as MoS2, with which we can combine the ferroelectric gate and semiconducting channel into one, which can be modulated by mechanical force. We call this new device concept mechanically gated transistor, similar to piezo channel found in biology that won Nobel Prize a few years ago..

[Audio] As we have already discussed, suspended MoS2 can be bent, resulting in strain gradient and flexoelectric polarization.

[Audio] We then make a two terminal device using suspended MoS2, which can be turned on and off by mechanical force, with on/off ratio differing by 3 orders of magnitude. In contrast, the device made with MoS2 supported on the substrate does not show switching behavior..

[Audio] We have also confirmed by scanning microwave microscopy the underlying mechanism of the device, that carrier concentration is enhanced by 3 order of magnitude by strain gradient..

[Audio] In conclusion, we have demonstrated that Polarization can be conveniently induced in suspended membrane for otherwise non-existing electromechanical coupling; Young's modulus of suspended membrane become size dependent, and can be substantially enhanced by flexoelectricity; Mechanically modulated devices have also demonstrated. Thanks for all your attention..