We present what is, to our knowledge, the first experimental demonstration of dielectric constant measurement and quantification of supported lipid bilayers in electrolyte solutions with nanoscale spatial resolution. The dielectric constant was quantitatively reconstructed with finite element calculations by combining thickness information and local polarization forces which were measured using an electrostatic force microscope adapted to work in a liquid environment. Measurements of submicrometric dipalmitoylphosphatidylcholine lipid bilayer patches gave dielectric constants of ε(r) ~ 3, which are higher than the values typically reported for the hydrophobic part of lipid membranes (ε(r) ~ 2) and suggest a large contribution of the polar headgroup region to the dielectric response of the lipid bilayer. This work opens apparently new possibilities in the study of biomembrane electrostatics and other bioelectric phenomena.

Quantitative measurement of the low-frequency dielectric constants of thick insulators at the nanoscale is demonstrated utilizing ac electrostatic force microscopy combined with finite-element calculations based on a truncated cone with hemispherical apex probe geometry. The method is validated on muscovite mica, borosilicate glass, poly(ethylene naphthalate), and poly(methyl methacrylate). The dielectric constants obtained are essentially given by a nanometric volume located at the dielectric-air interface below the tip, independently of the substrate thickness, provided this is on the hundred micrometer-length scale, or larger.

We present a procedure for calibrated complex impedance measurements and dielectric quantification with scanning microwave microscopy. The calibration procedure works in situ directly on the substrate with the specimen of interest and does not require any specific calibration sample. In the workflow tip-sample approach curves are used to extract calibrated complex impedance values and to convert measured S11 reflection signals into sample capacitance and resistance images. The dielectric constant of thin dielectric SiO2 films were determined from the capacitance images and approach curves using appropriate electrical tip-sample models and the εr value extracted at f = 19.81 GHz is in good agreement with the nominal value of εr ∼ 4. The capacitive and resistive material properties of a doped Si semiconductor sample were studied at different doping densities and tip-sample bias voltages. Following a simple serial model the capacitance-voltage spectroscopy curves are clearly related to the semiconductor depletion zone while the resistivity is rising with falling dopant density from 20 Ω to 20 kΩ. The proposed procedure of calibrated complex impedance measurements is simple and fast and the accuracy of the results is not affected by varying stray capacitances. It works for nanoscale samples on either fully dielectric or highly conductive substrates at frequencies between 1 and 20 GHz.

We present a systematic analysis of the effects that the microscopic parts of electrostatic force microscopy probes (the cone and cantilever) have on the electrostatic interaction between the tip apex and thick insulating substrates (thickness > 100 μm). We discuss how these effects can influence the measurement and quantification of the local dielectric constant of the substrates. We propose and experimentally validate a general methodology that takes into account the influence of the cone and the cantilever, thus enabling us to obtain very accurate values of the dielectric constants of thick insulators.