（001）离子表面局部接触电势差的解析方法：对Kelvin探针力显微镜的启示
Analytical Approach to the Local Contact Potential Difference on (001) Ionic Surfaces: Implications for Kelvin Probe Force Microscopy
摘要：
建立了非接触式原子力显微镜（nc-AFM）针尖与离子晶体（001）表面之间的静电力的解析模型。该模型是能够占的局部接触电势差（CPD），而纳米原子力显微镜的开尔文探针力显微镜（KPFM）实验观察到的原子对比度。为了证明这种短程静电力的存在，本文首先导出了离子晶体表面的马德隆势。推导出的力的表达式可以分为两个主要的贡献：第一个代表尖端顶点的微观结构和尖端，离子晶体和反电极之间形成的电容器之间的耦合;第二个术语描述了Madelung表面电位对尖端的介观部分的影响，独立于其微观结构。这些短程静电力在10微微牛顿的范围内。当明确考虑晶体极化，偏置电压施加在尖端上，以补偿局部CPD，即取消短程静电力的解析表达式，推导。补偿后的CPD具有Madelung表面势的横向周期性。然而，强烈依赖于尖端的几何形状，施加的调制电压以及尖端样品的距离，这甚至可能导致高估的真实表面电位，使得定量KPFM测量的本地CPD非常困难。
英文摘要：
An analytical model of the electrostatic force between the tip of a non-contact Atomic Force Microscope (nc-AFM) and the (001) surface of an ionic crystal is reported. The model is able to account for the atomic contrast of the local contact potential difference (CPD) observed while nc-AFM-based Kelvin Probe Force Microscopy (KPFM) experiments. With the goal in mind to put in evidence this short-range electrostatic force, the Madelung potential arising at the surface of the ionic crystal is primarily derived. The expression of the force which is deduced can be split into two major contributions: the first stands for the coupling between the microscopic structure of the tip apex and the capacitor formed between the tip, the ionic crystal and the counter-electrode; the second term depicts the influence of the Madelung surface potential on the mesoscopic part of the tip, independently from its microscopic structure. These short-range electrostatic forces are in the range of ten pico-Newtons. When explicitly considering the crystal polarization, an analytical expression of the bias voltage to be applied on the tip to compensate for the local CPD, i.e. to cancel the short-range electrostatic force, is derived. The compensated CPD has the lateral periodicity of the Madelung surface potential. However, the strong dependence on the tip geometry, the applied modulation voltage as well as the tip-sample distance, which can even lead to an overestimation of the real surface potential, makes quantitative KPFM measurements of the local CPD extremely difficult.
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