Gomila G, Gramse G, Fumagalli L
Institut de Bioenginyeria de Catalunya (IBEC), C/Balidiri i Reixac 15-21, 08028 Barcelona, Spain. Departament d'Electrònica, Universitat de Barcelona, C/Martí i Franquès 1, 08028 Barcelona, Spain.
Nanotechnology. 2014 Jun 27;25(25):255702. doi: 10.1088/0957-4484/25/25/255702. Epub 2014 Jun 4.
A numerical analysis of the polarization force between a sharp conducting probe and a dielectric film of finite lateral dimensions on a metallic substrate is presented with the double objective of (i) determining the conditions under which the film can be approximated by a laterally infinite film and (ii) proposing an analytical model valid in this limit. We show that, for a given dielectric film, the critical diameter above which the film can be modeled as laterally infinite depends not only on the probe geometry, as expected, but mainly on the film thickness. In particular, for films with intermediate to large thicknesses (>100 nm), the critical diameter is nearly independent from the probe geometry and essentially depends on the film thickness and dielectric constant following a relatively simple phenomenological expression. For films that can be considered as laterally infinite, we propose a generalized analytical model valid in the thin-ultrathin limit (<20-50 nm) that reproduces the numerical calculations and the experimental data. Present results provide a general framework under which accurate quantification of electrostatic force microscopy measurements on dielectric films on metallic substrates can be achieved.
本文对尖锐导电探针与金属基底上具有有限横向尺寸的介电薄膜之间的极化力进行了数值分析，其具有双重目的：（i）确定薄膜可由横向无限大薄膜近似的条件；（ii）提出在此极限下有效的解析模型。我们表明，对于给定的介电薄膜，薄膜可被建模为横向无限大的临界直径不仅如预期的那样取决于探针几何形状，而且主要取决于薄膜厚度。特别是，对于中等厚度至大厚度（>100 nm）的薄膜，临界直径几乎与探针几何形状无关，并且基本上取决于薄膜厚度和介电常数，遵循相对简单的唯象表达式。对于可被视为横向无限大的薄膜，我们提出了一个在薄至超薄极限（<20 - 50 nm）下有效的广义解析模型，该模型再现了数值计算结果和实验数据。目前的结果提供了一个通用框架，在此框架下可以实现对金属基底上介电薄膜的静电力显微镜测量的精确量化。
