Nanoscale mapping of electric polarizability in a heterogeneous dielectric material with surface irregularities is of scientific and technical significance, but remains challenging. Here, we present an approach based on intermodulation electrostatic force microscopy (EFM) in conjunction with finite element computation for precise and high-resolution mapping of polarizability in dielectric materials. Instead of using electrostatic force in conventional quantitative EFM approaches, the force gradient is acquired to achieve an unprecedented spatial resolution. In the meantime, the finite element model is applied to eliminate the interference from the heterogeneity and surface irregularity of the sample. This approach directly reveals the high polarization ability of the amorphous region in a ferroelectric, semi-crystalline polymer with significant surface roughness, i.e. poly (vinylidene fluoride-co-chlorotrifluoroethylene), in which the result is consistent with the predicted data in the latest research. This work presenting a quantitative approach to nanoscale mapping of electric polarizability with unprecedented spatial resolution may help to reveal the complex property-structure correlation in heterogeneous dielectric materials.

具有表面不规则性的异质介电材料中电极化率的纳米级映射具有科学和技术意义，但仍然具有挑战性。在这里，我们提出了一种基于互调静电力显微镜 (EFM) 并结合有限元计算的方法，用于精确和高分辨率地映射介电材料的极化率。不是在传统的定量 EFM 方法中使用静电力，而是通过获取力梯度来实现前所未有的空间分辨率。同时，应用有限元模型消除样品的不均匀性和表面不规则性的干扰。这种方法直接揭示了铁电体中非晶区的高极化能力，具有显着表面粗糙度的半结晶聚合物，即聚（偏二氟乙烯-共-三氟氯乙烯），其结果与最新研究中的预测数据一致。这项工作提出了一种具有前所未有的空间分辨率的纳米级极化映射定量方法，可能有助于揭示异质介电材料中复杂的特性-结构相关性。