An ultrasensitive cantilever, oscillating parallel to a surface in vacuum, is used to probe weak thermal electric field gradient fluctuations over thin polymer films. We measure the power spectrum of cantilever frequency fluctuations as a function of cantilever height and voltage over polymers of various compositions and thicknesses. The data are well described by a linear-response theory that calculates stochastic electric fields arising from thermally-driven dielectric fluctuations.

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.

We present spatially resolved photovoltage spectra of a bulk heterojunction solar cell film composed of phase-separated poly(9,9'-dioctylfluorene-co-benzothiadiazole) (F8BT) and poly(9,9'-dioctylfluorene-co-bis-N,N'-(4-butylphenyl)-bis-N,N'-phenyl-1,4-phenylenediamine) (PFB) polymers prepared on ITO/PEDOT:PSS and aluminum substrates. Over both PFB- and F8BT-rich domains, the photopotential spectra were found to be proportional to a linear combination of the polymers' absorption spectra. Charge trapping in the film was studied using photopotential fluctuation spectroscopy, in which low-frequency photoinduced electrostatic potential fluctuations were measured by observing noise in the oscillation frequency of a nearby charged atomic force microscope cantilever. Over both F8BT- and PFB-rich regions, the magnitude, distance dependence, frequency dependence, and illumination wavelength dependence of the observed cantilever frequency noise are consistent with photopotential fluctuations arising from stochastic light-driven trapping and detrapping of charges in F8BT. Taken together, our findings suggest a microscopic mechanism by which intermixing of phases leads to charge trapping and thereby to suppressed open-circuit voltage and decreased efficiency in this prototypical bulk heterojunction solar cell film.

Abstract

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.