Theoretical Study Of The Size Effect Of PbTiO₃ On Its Charge Separation Ability

The demand for compact,precise devices is growing as a result of the globaleconomy’s rapid expansion and the improvement of science and technology.The particle size effect has emerged as a fresh area of study in recent years.The size effect refers to the fact that when the scale of a particle is smaller than its corresponding physical properties（such as wavelength of de Broglie）,the periodic interface of the particle is broken and exhibits some new properties,such as sound,light,electricity,magnetism,heat,etc.Currently,various ferroelectric nanostructures,such as ultrathin films,can be prepared in a controlled manner at the atomic scale,since significant mechanical property changes relative to the bulk form of the material can be observed as its characteristic dimensions approach the nanoscale.As the size of the material approaches the 2D limit,it makes certain material properties with size dependence become more significant.Since its discovery,perovskite-type materials have attracted wide attention from researchers all over the world,ABO₃-type ferroelectrics are the most studied multifunctional perovskite materials.This ferroelectric oxide has many superior properties,We found that,when the particle thickness of perovskite ferroelectrics changes,size effects occur,including dielectric constants,spontaneous polarization and Curie temperature decreases.PbTiO₃（PTO）is a ferroelectric oxide with a typical ABO₃-type perovskite structure.However,the majority of prior research has concentrated on the PTO material preparation process,making the correlation between heteroatom doping and the piezoelectric effect superior.The internal mechanisms of performance and the size effect of redesigned interfaces are also of interest,which will lead to more new experimental phenomena being observed.In nanoferroelectrics,work has been done to analyse in depth the critical dimensions of its measurements,but this is still a challenging topic in this field.There is no theoretical study for its intrinsic mechanism,interfacial size effect,etc.Therefore,it is of great importance to use theoretical calculations to investigate the mechanism on the size effect of nanoparticles.In this work,first-principles methods were used to investigate the crystal geometry,electronic structure,electrical characteristic,and surface charge transfer of monolayer as well as multilayer PTO in order to understand the origin of significant size effect.According to the reference and experimental analysis,we selected six crystal planes of PTO,such as 001,010,100,102,111 and 110,and model them separately.The thickness of different crystal planes of PTO was superimposed.By calculating the energy band diagram of different crystal planes and different thicknesses,only the 110crystal plane has a considerable size effect in contrast to other crystal planes,and its energy gap is correlated with the thickness of its layers,according to our research.The energy gap consistently shrinks as size and thickness grow.The findings demonstrate that PTO can change from a semiconductor to a metal due to the size effect.It is found that when the exposed face is O atom,the energy gap decreases monotonically with increasing thickness.The exposure of O atoms causes the surface polarized charge（Bound charge）caused by spontaneous polarization to generate a depolarization field,which will be partially shielded by the shielding charge below the surface,and the shielding part will enhance the charge separation ability when it reaches a constant value in a certain size range.The introduction of Si O₂ into the surface dielectric layer can enhance the internal electric field of ferroelectric and reduce the shielding of the depolarization field,thus further improving the charge separation ability.We have captured the process of rapid changes in surface electron density through a surface charge injection mechanism.It can also be seen from the electron density that as the number of layers increases,the surface electron density becomes smaller,and the electron density in model bottom becomes larger and more concentrated.Our study explains the relatively clear and well-defined crystal plane that contains the size effect,and provide a theoretical premise for the application of two-dimensional PTO crystals in charge separation mechanism,as well as for exploring the interface interaction and size effect of other ABO₃ perovskite semiconductor materials.