Pfannstiel Anton, Imlau Mirco, Bazzan Marco, Vittadello Laura
Department of Mathematics/Informatics/Physics, Institute of Physics, University of Osnabrück, Barbarastraße 7, 49076, Osnabrück, Germany.
Center for Cellular Nanoanalytics, University of Osnabrück, Barbarastraße 11, 49076, Osnabrück, Germany.
Sci Rep. 2024 Sep 27;14(1):22047. doi: 10.1038/s41598-024-71858-6.
Polarons play a major role in the description of optical, electrical and dielectrical properties of several ferroelectric oxides. The motion of those particles occurs by elementary hops among the material lattice sites. In order to compute macroscopic transport parameters such as charge mobility, normal (i.e. Fickian) diffusion laws are generally assumed. In this paper we show that when defect states able to trap the polarons for long times are considered, significant deviations from the normal diffusion behaviour arise. As an example of this behavior, we consider here the case of lithium niobate (LN). This can be considered as a prototypical system, having a rich landscape of interacting polaron types and for which a significant wealth of information is available in literature. Our analysis considers the case of a stoichiometric, defect-free lithium niobate containing a certain concentration of small electron polarons hopping on regular Nb sites, and compares it to the material in congruent composition, which is generally found in real-life applications and which is characterized by a large concentration of antisite Nb defects. While in the first case the charge carriers are free polarons hopping on a regular Nb sublattice, in the second case a fraction of polarons is trapped on antisite defects. Thus, in the congruent material, a range of different hopping possibilities arises, depending on the type of starting and destination sites. We develop a formalism encompassing all these microscopic processes in the framework of a switching diffusion model which can be well approximated by a mobile-immobile transport model providing explicit expressions for the polaron mobility. Finally, starting from the Marcus-Holstein's model for the polaron hopping frequency we verify by means of a Monte Carlo approach the diffusion/mobility of the different polarons species showing that, while free polarons obey the laws for normal diffusion as expected, bound polarons follow an anomalous diffusion behaviour and that in the case of the congruent crystal where mixed free and bound polaron transport is involved, our expressions indeed provide a satisfactory description.
极化子在描述几种铁电氧化物的光学、电学和介电性质方面起着重要作用。这些粒子的运动通过在材料晶格位置之间的基本跳跃来发生。为了计算诸如电荷迁移率等宏观输运参数，通常假设服从正常（即菲克）扩散定律。在本文中，我们表明，当考虑能够长时间捕获极化子的缺陷态时，会出现与正常扩散行为的显著偏差。作为这种行为的一个例子，我们在此考虑铌酸锂（LN）的情况。这可以被视为一个典型系统，具有丰富的相互作用极化子类型图景，并且在文献中有大量可用信息。我们的分析考虑了化学计量比、无缺陷的铌酸锂的情况，其中含有一定浓度的小电子极化子在规则的铌位点上跳跃，并将其与实际应用中通常发现的同成分材料进行比较，该材料的特征是存在大量的反位铌缺陷。在第一种情况下，电荷载流子是在规则铌子晶格上跳跃的自由极化子，而在第二种情况下，一部分极化子被困在反位缺陷上。因此，在同成分材料中，根据起始和目的地位点的类型会出现一系列不同的跳跃可能性。我们在一个切换扩散模型的框架内开发了一种形式体系，该模型涵盖了所有这些微观过程，并且可以通过一个移动 - 固定输运模型很好地近似，该模型为极化子迁移率提供了明确的表达式。最后，从马库斯 - 霍尔斯坦的极化子跳跃频率模型出发，我们通过蒙特卡罗方法验证了不同极化子种类的扩散/迁移率，结果表明，虽然自由极化子如预期那样服从正常扩散定律，但束缚极化子遵循反常扩散行为，并且在涉及自由和束缚极化子混合输运的同成分晶体的情况下，我们的表达式确实提供了令人满意的描述。
