Electric force microscopy of semiconductors: theory of cantilever frequency fluctuations and noncontact friction.

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.

Charge carrier dynamics and interactions in electric force microscopy.

In electric force microscopy, a charged atomic force microscope tip in vacuum senses a fluctuating electrical force generated by the sample. Such measurements can in principle probe electrical noise generated by moving charge carriers in an organic semiconductor. We present a theory of cantilever frequency fluctuations in electric force microscopy, driven by coupled charge carrier dynamics and dielectric fluctuations. The connection between observable frequency fluctuations in electric force microscopy and the Casimir-Lifshitz force is described. This classical electrodynamic calculation is based on Maxwell's equations coupled to diffusive carrier transport. The effects of carrier transport and inter-carrier interactions on the spectrum of cantilever frequency noise are elucidated. We find that a simplified model of freely diffusing carriers can overestimate cantilever frequency noise by several orders of magnitude because of the neglect of interactions. Electric force microscopy measurements on an organic field effect transistor are reported and qualitatively interpreted in terms of the suppression of electrical noise from charge carriers by Coulomb interactions.

Dielectric fluctuations over polymer films detected using an atomic force microscope.

We present a systematic study of the frequency noise experienced by a charged atomic force microscope cantilever due to thermal dielectric fluctuations in a thin-film sample of poly(vinyl acetate). Here, the tip of the commercial atomic force microscope cantilever oscillates in the conventional direction, normal to the surface of the film, complementing our previous studies of dielectric fluctuations carried out using an ultrasensitive custom-fabricated cantilever oscillating parallel to the film surface. We show that frequency noise induced by mechanical vibrations can be distinguished from frequency noise resulting from thermal dielectric fluctuations by the dependence on applied voltage and tip-sample separation, allowing molecular information to be unambiguously extracted. A linear response theory for cantilever frequency noise over a molecular material correctly reproduces the observed dependences on frequency, voltage, and tip-sample separation. The technique is shown to measure primarily fluctuations in the electric field gradient over the surface, which in these measurements are generated by orientational relaxation of polar polymer segments.