Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA.
J Chem Phys. 2013 Nov 14;139(18):184702. doi: 10.1063/1.4828862.
An electric force microscope employs a charged atomic force microscope probe in vacuum to measure fluctuating electric forces above the sample surface generated by dynamics of molecules and charge carriers. We present a theoretical description of two observables in electric force microscopy of a semiconductor: the spectral density of cantilever frequency fluctuations (jitter), which are associated with low-frequency dynamics in the sample, and the coefficient of noncontact friction, induced by higher-frequency motions. The treatment is classical-mechanical, based on linear response theory and classical electrodynamics of diffusing charges in a dielectric continuum. Calculations of frequency jitter explain the absence of contributions from carrier dynamics to previous measurements of an organic field effect transistor. Calculations of noncontact friction predict decreasing friction with increasing carrier density through the suppression of carrier density fluctuations by intercarrier Coulomb interactions. The predicted carrier density dependence of the friction coefficient is consistent with measurements of the dopant density dependence of noncontact friction over Si. Our calculations predict that in contrast to the measurement of cantilever frequency jitter, a noncontact friction measurement over an organic semiconductor could show appreciable contributions from charge carriers.
静电力显微镜采用真空环境下带电荷的原子力显微镜探针，以测量样品表面上方由分子和电荷载流子动力学产生的波动静电力。我们提出了半导体静电力显微镜中两个可观测量的理论描述：与样品中低频动力学相关的悬臂梁频率波动（抖动）的谱密度，以及由更高频运动引起的非接触摩擦系数。这种处理是基于扩散电荷在介电连续体中的线性响应理论和经典电动力学的经典力学方法。频率抖动的计算解释了先前对有机场效应晶体管的测量中没有来自载流子动力学的贡献。非接触摩擦的计算预测，随着载流子密度的增加，载流子密度波动受到抑制，非接触摩擦系数会减小。预测的摩擦系数与非接触摩擦对 Si 上掺杂密度的测量结果一致。我们的计算预测表明，与悬臂梁频率抖动的测量相比，在有机半导体上进行非接触摩擦测量可能会显示出电荷载流子的可观贡献。
