Ferri-ionic coupling in CuInP2S6 nanoflakes: Polarization states and controllable negative capacitance

We consider nanoflakes of van der Waals ferrielectric <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:msub><a:mrow><a:mi>Cu</a:mi><a:mi>In</a:mi><a:mi mathvariant="normal">P</a:mi></a:mrow><a:mn>2</a:mn></a:msub><a:msub><a:mrow><a:mrow><a:mi mathvariant="normal">S</a:mi></a:mrow></a:mrow><a:mn>6</a:mn></a:msub></a:math> covered by an ionic surface charge and reveal the appearance of polar states with a relatively large polarization of approximately 5 µC/<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><f:msup><f:mi>cm</f:mi><f:mn>2</f:mn></f:msup></f:math> and stored free charge of around 10 µC/<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><i:msup><i:mi>cm</i:mi><i:mn>2</i:mn></i:msup></i:math>, which can mimic “midgap” states associated with a surface-field-induced transfer of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><l:mi>Cu</l:mi></l:math> and/or <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><o:mi>In</o:mi></o:math> ions in the van der Waals gap. The change in the ionic screening degree and mismatch strains induce a broad range of the transitions between paraelectric phase, antiferroelectric, ferrielectric, and ferri-ionic states in <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><r:msub><r:mrow><r:mi>Cu</r:mi><r:mi>In</r:mi><r:mi mathvariant="normal">P</r:mi></r:mrow><r:mn>2</r:mn></r:msub><r:msub><r:mrow><r:mrow><r:mi mathvariant="normal">S</r:mi></r:mrow></r:mrow><r:mn>6</r:mn></r:msub></r:math> nanoflakes. The states’ stability and/or metastability is determined by the minimum of the system free energy consisting of electrostatic energy, elastic energy, and a Landau-type four-well potential of the ferrielectric dipole polarization. The possibility of governing the transitions by strain and ionic screening can be useful for controlling the tunneling barrier in thin-film devices based on <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><w:msub><w:mrow><w:mi>Cu</w:mi><w:mi>In</w:mi><w:mi mathvariant="normal">P</w:mi></w:mrow><w:mn>2</w:mn></w:msub><w:msub><w:mrow><w:mrow><w:mi mathvariant="normal">S</w:mi></w:mrow></w:mrow><w:mn>6</w:mn></w:msub></w:math> nanoflakes. Additionally, we predict that the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><bb:msub><bb:mrow><bb:mi>Cu</bb:mi><bb:mi>In</bb:mi><bb:mi mathvariant="normal">P</bb:mi></bb:mrow><bb:mn>2</bb:mn></bb:msub><bb:msub><bb:mrow><bb:mrow><bb:mi mathvariant="normal">S</bb:mi></bb:mrow></bb:mrow><bb:mn>6</bb:mn></bb:msub></bb:math> nanoflakes reveal features of the controllable negative capacitance effect, which make them attractive for advanced electronic devices, such as nanocapacitors and gate oxide nanomaterials with reduced heat generation.