Stability Of Polarization Vortex Domain Structure In Ferroelectric Nanothin Films Based On Phase Field Model

In recent years,it has been discovered in some special artificial thin films and low-dimensional ferroelectric nanostructures that electric dipoles can continuously rotate to form different types of polarization vortex domain structures.These polarization vortex structures are expected to become important candidates for high-density data storages and low-power microelectronic devices in the post-moore law period due to their novel characteristics,such as rotational chirality,strange negative capacitance,and terahertz band modulation characteristics.They also have potential application prospects in emerging fields,such as5G/6G microwave dielectric and terahertz optoelectronic devices.With the expansion of the application range of nano-ferroelectric materials,the working environment of nano-ferroelectric devices is also more complex,and it is inevitable to be disturbed by some external factors,such as mechanical and electrical loads.This would affect the service performance and stability of the ferroelectric device,and challenge the functional design of devices.Therefore,it is of great scientific and engineering significance to study the stability of the polarization vortex.The phase field method is a powerful mathematical tool for simulating and studying the microstructure evolution of materials and the coupling of multiple physical fields.In this dissertation,a phase field model was established to study the instability behavior of the polarization vortex domain structure in low-dimensional ferroelectric materials under external mechanical and electrical loads.The effects of ambient temperature,model size and shape on the stability of polarization vortex were analyzed.The main research are introduced as follows.（1）The formation and evolution of polarization vortex in PbTiO₃ nanofilms were studied.It was proposed to use the polarization curl value at the core of the vortex to characterize the polarization vortex intensity.The influences of the model size,temperature,mechanical stress and curled electric field on the polarization vortex intensity were quantitatively analyzed.The results showed that the polarization vortex intensity is an important tool for analyzing the formation and evolution of polarization vortex and evaluating its stability.（2）The instability of the single vortex polarization structure in the PbTiO₃ nanofilm under mechanical and electrical loads was investigated.It was proposed that the vortex instability energy barrier is used to analyze the stability of the polarization vortex under different loads.The results showed that the polarization vortex structure has the strongest resistance to the tensile stress,followed by the compressive stress,but the weakest to the curled electric field.The relative secant slope of the critical tensile stress curve,the relative secant slope of the critical compressive stress curve and the relative secant slope of the critical curled electric field curve were introduced as the evaluation indicators.The temperature sensitivity of vortex stability was quantitatively analyzed in different load conditions.It was found that the temperature sensitivity is the strongest for the curled electric field,followed by for the tensile stress,but the weakest for the compressive stress.（3）The effects of nanofilm size and temperature on the stability of polarization vortex structure under uniaxial tensile or compressive stress were studied.Within the studied size and temperature range,the smaller the nanofilm size,the more stable the vortex structure in tensile stress.However,in compressive stress,the stability of the vortex structure first increases and then decreases with increasing nanofilm size,so the nanofilm has a peak size.In addition,it was observed that the instability type of the polarization vortex is related to the nanofilm size and temperature.There are three types of instability:αtype,β1 type andβ2 type.Finally,the relationship between the peak size and the type of vortex instability was revealed.These are very important for design of promising nano-ferroelectric devices as high density memories.（4）The effect of the width-length ratio of nanofilm on the stability of polarization vortex structure under uniaxial tensile or compressive stress was studied.It was found that under compressive stress,the smaller the width-length ratio of the nanofilm,the better the stability of the polarization vortex structure.Under tensile stress,however,the stability of the polarization vortex structure decreases firstly,then increases but finally decreases with the decrease of the width-length ratio.This may provide the possibility for a novel ferroelectric memory device based on polarization vortex to improve its performance while maintaining storage density.