Lagrangian and Impedance-Spectroscopy Treatments of Electric Force Microscopy
Lagrangian and Impedance-Spectroscopy Treatments of Electric Force Microscopy
复制标题
电力显微镜的拉格朗日和阻抗谱处理
DOI：
10.1103/physrevapplied.11.064020
复制
发表时间：
2019
影响因子：
4.6
通讯作者：
Marohn, John A.
中科院分区：
文献类型：
--
作者：
Dwyer, Ryan P.;Harrell, Lee E.;Marohn, John A.
扫描探针显微镜通常超出简单的地形成像，以研究电力和样品的性质，最广泛使用的实验是调频开尔文探针力显微镜。然而，通常用于解释这种调频实验的方程依赖于两个隐藏的假设。第一个假设是尖端电荷与悬臂运动同相振荡以保持尖端电压恒定。第二个假设是针尖-样品相互作用的任何变化都是缓慢发生的。从机电模型的悬臂梁-样品相互作用，我们使用拉格朗日力学推导出耦合的运动方程的悬臂梁的位置和电荷。我们用微扰理论解析求解这些方程，为了验证，用数值方法求解。这种通用方法严格描述了扫描探针实验，即使在违反快速尖端充电和缓慢变化的样本属性的通常假设的情况下也是如此。我们开发了一个马格努斯展开近似，以说明如何突然变化的尖端样品相互作用引起的悬臂梁的振幅和相位的突然变化。我们发现，无反馈的时间分辨电力显微镜不能唯一地确定亚周期光电容动力学。然后，我们使用一阶微扰理论悬臂频率偏移和耗散的样品阻抗，即使当尖端电荷振荡与悬臂运动的相位。类似于电化学中阻抗谱的处理，我们应用这种近似来确定悬臂梁频率偏移和耗散的任意样品阻抗在本地介电谱和宽带本地介电谱实验。我们开发的通用方法为严格建模广泛的电扫描探针显微镜实验中悬臂位置和电荷的耦合运动提供了一条前进的道路，其中传统方程的隐藏假设被违反或不适用。
Scanning probe microscopy is often extended beyond simple topographic imaging to study electrical forces and sample properties, with the most widely used experiment being frequency-modulated Kelvin probe force microscopy. The equations commonly used to interpret this frequency-modulated experiment, however, rely on two hidden assumptions. The first assumption is that the tip charge oscillates in phase with the cantilever motion to keep the tip voltage constant. The second assumption is that any changes in the tip-sample interaction happen slowly. Starting from an electromechanical model of the cantilever-sample interaction, we use Lagrangian mechanics to derive coupled equations of motion for the cantilever position and charge. We solve these equations analytically using perturbation theory, and, for verification, numerically. This general approach rigorously describes scanned probe experiments even in the case when the usual assumptions of fast tip charging and slowly changing samples properties are violated. We develop a Magnus-expansion approximation to illustrate how abrupt changes in the tip-sample interaction cause abrupt changes in the cantilever amplitude and phase. We show that feedback-free time-resolved electric force microscopy cannot uniquely determine subcycle photocapacitance dynamics. We then use first-order perturbation theory to relate cantilever frequency shift and dissipation to the sample impedance even when the tip charge oscillates out of phase with the cantilever motion. Analogous to the treatment of impedance spectroscopy in electrochemistry, we apply this approximation to determine the cantilever frequency shift and dissipation for an arbitrary sample impedance in both local dielectric spectroscopy and broadband local dielectric spectroscopy experiments. The general approaches that we develop provide a path forward for rigorously modeling the coupled motion of the cantilever position and charge in the wide range of electrical scanned probe microscopy experiments where the hidden assumptions of the conventional equations are violated or inapplicable.
登录
查看更多内容
DOI：
--
发表时间：
2016
期刊：
影响因子：
--
作者：
Z. Schumacher;Andreas Spielhofer;Y. Miyahara;P. Grutter
通讯作者：
P. Grutter
通过耗散静电力调制进行开尔文探针力显微镜
DOI：
--
发表时间：
2015
期刊：
影响因子：
--
作者：
Y. Miyahara;J. Topple;Z. Schumacher;P. Grutter
通讯作者：
P. Grutter
通过扫描力显微镜成像的局部电耗散
影响因子：
4
作者：
W. Denk;D. Pohl
通讯作者：
D. Pohl
影响因子：
13.6
作者：
Dwyer RP;Nathan SR;Marohn JA
通讯作者：
Marohn JA
探测纳米尺度的离子输运：玻璃电解质的时域静电力谱
DOI：
--
发表时间：
2004
期刊：
影响因子：
--
作者：
A. Schirmeisen;A. Taskiran;H. Fuchs;B. Roling;S. Murugavel;H. Bracht;F. Natrup
通讯作者：
F. Natrup