Reference samples are commonly used for the calibration and quantification of nanoscale electrical measurements of capacitances and dielectric constants in scanning microwave microscopy (SMM) and similar techniques. However, the traceability of these calibration samples is not established. In this work, we present a detailed investigation of most possible error sources that affect the uncertainty of capacitance measurements on the reference calibration samples. We establish a comprehensive uncertainty budget leading to a combined uncertainty of 3% in relative value (uncertainty given at one standard deviation) for capacitances ranging from 0.2 fF to 10 fF. This uncertainty level can be achieved even with the use of unshielded probes. We show that the weights of uncertainty sources vary with the values and dimensions of measured capacitances. Our work offers improvements on the classical calibration methods known in SMM and suggests possible new designs of reference standards for capacitance and dielectric traceable measurements. Experimental measurements are supported by numerical calculations of capacitances to reveal further paths for even higher improvements.

The importance of high dielectric constant materials in the development of high frequency nano-electronic devices is undeniable. Their polarization properties are directly dependent on the value of their relative permittivity. We report here on the nanoscale metrological quantification of the dielectric constants of two high-κ materials, lead zirconate titanate (PZT) and lead magnesium niobate-lead titanate (PMN-PT), in the GHz range using scanning microwave microscopy (SMM). We demonstrate the importance of the capacitance calibration procedure and dimensional measurements on the weight of the combined relative uncertainties. A novel approach is proposed to correct lateral dimension measurements of micro-capacitive structures using the microwave electrical signatures, especially for rough surfaces of high-κ materials. A new analytical expression is also given for the capacitance calculations, taking into account the contribution of fringing electric fields. We determine the dielectric constant values εPZT = 445 and εPMN-PT = 641 at the frequency around 3.6 GHz, with combined relative uncertainties of 3.5% and 6.9% for PZT and PMN-PT, respectively. This work provides a general description of the metrological path for a quantified measurement of high dielectric constants with well-controlled low uncertainty levels.