Wagner Christian, Tautz F Stefan
Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425 Jülich, Germany. Jülich Aachen Research Alliance (JARA)-Fundamentals of Future Information Technology, 52425 Jülich, Germany.
J Phys Condens Matter. 2019 Nov 27;31(47):475901. doi: 10.1088/1361-648X/ab2d09. Epub 2019 Jun 26.
Electrostatic forces are among the most common interactions in nature and omnipresent at the nanoscale. Scanning probe methods represent a formidable approach to study these interactions locally. The lateral resolution of such images is, however, often limited as they are based on measuring the force (gradient) due to the entire tip interacting with the entire surface. Recently, we developed scanning quantum dot microscopy (SQDM), a new technique for the imaging and quantification of surface potentials which is based on the gating of a nanometer-size tip-attached quantum dot by the local surface potential and the detection of charge state changes via non-contact atomic force microscopy. Here, we present a rigorous formalism in the framework of which SQDM can be understood and interpreted quantitatively. In particular, we present a general theory of SQDM based on the classical boundary value problem of electrostatics, which is applicable to the full range of sample properties (conductive versus insulating, nanostructured versus homogeneously covered). We elaborate the general theory into a formalism suited for the quantitative analysis of images of nanostructured but predominantly flat and conductive samples.
静电力是自然界中最常见的相互作用之一，在纳米尺度上无处不在。扫描探针方法是一种在局部研究这些相互作用的强大方法。然而，此类图像的横向分辨率通常受到限制，因为它们基于测量由于整个尖端与整个表面相互作用而产生的力（梯度）。最近，我们开发了扫描量子点显微镜（SQDM），这是一种用于表面电势成像和量化的新技术，它基于局部表面电势对附着在纳米尺寸尖端上的量子点进行门控，并通过非接触原子力显微镜检测电荷状态变化。在此，我们提出一种严格的形式体系，在该体系框架内可以对SQDM进行定量理解和解释。特别是，我们基于静电学的经典边值问题提出了SQDM的一般理论，该理论适用于全范围的样品特性（导电与绝缘、纳米结构与均匀覆盖）。我们将该一般理论细化为一种适用于对纳米结构但主要是平坦且导电的样品图像进行定量分析的形式体系。
