Phase Field Simulation Of Topological Domain Wall Conductivity In Ferroelectric Thin Films

Ferroelectric domain is a basic component of ferroelectrics,ferroelectric domain’s formation,structure and properties are closely related to some basic properties of ferroelectrics,including Curie temperature,depolarization field,piezoelectricity etc.The formation and properties of domain structures in ferroelectric thin films are more easily affected by substrate strain,applied electric field,size effect and other factors.Some of these topological domains have excellent conductivity and anti-interference properties,so they have great potential in the field of microelectronic memory.In this paper,Bi Fe O₃（BFO）thin film and Pb Ti O₃（PTO）/Sr Ti O₃（STO）thin film are selected as research objects.Based on Landau theory and phase-field method,a phase-field model including surface effect,size effect and flexural effect is established.The conductive properties of two types of topological walls are studied by using the phase-field model.The results are in agreement with the recent experimental results.The main contents are as follows:1.Firstly,in order to restore the topological domain structure of the experiment[Advanced Materials 34,2107711（2022）],by applying a ring electric field,a converging"cross"domain structure with high conductivity and a diverging"cross"domain structure with low conductivity are constructed.The two domain structures can be reversibly switched under the action of ring electric field,which indicates that the ferroelectric domain wall memory has good fatigue resistance.The effect of temperature,strain and thickness on the performances of low-resistance states of memory are calculated.The results show that low temperature and tension strain are more conducive to maintain the stability of thin film domain structure and provide better relative conductivity.Increasing the thickness of thin film will reduce the influence of depolarization field and surface effect at the study of thin film thickness,which will increase the electrical conductivity at the cost of stability.2.Secondly,two states of skyrmion-like domain on PTO/STO bilayer in recent experimental work[Nature 603,63（2022）]are successfully simulated by phase field method.The two states are a divergence state with polarization reversal and a convergence state without polarization reversal,corresponding to low-resistance state and high-resistance state,respectively.They can be reversibly switched when the probe bias voltage is changed.In addition,for the low-resistance state,tensile strain can improve the conductivity of the divergence state of skyrmion-like domain,and reduce the interference from the high-resistance region.Reducing the thickness of PTO thin films will reduce the absolute value of the potential at the low-resistance state,but can shield more interference from the high resistance region and make the structure more stable.It is known from the principle that these effects will be similar for high-resistance state.In this paper,based on the recent experimental results,two kinds of topological domain structures are calculated and studied theoretically via Landau theory and phase field model,which not only explains the experimental results,but also gives a reasonable analysis of the domain structure conductivity in more aspects.The results are of great significance for the investigations of topological ferroelectric domains,and also provide the theoretical basis for the development of novel domain wall memory in the future.