Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy

Abstract

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.

Coaxial tips for a scanning microwave microscope and its calibration with dielectric references

“…This can be done using e.g. capacitive, resistive, or inductive standards [7,8] or different dopant densities [9].…”

3D Imaging and Quantitative Subsurface Dielectric Constant Measurement Using Peak Force Kelvin Probe Force Microscopy

“…The first methods typically operate in the contact mode, incorporating microwave signals. They include the so-called scanning microwave microscopy (SMM) [33,34] and scanning microwave impedance microscopy (sMIM). [35] Despite their importance for the measurement of dielectric constants in the radio-frequency range, these methods still suffer from the drawbacks associated with contact mode operation.…”

Nanometrology

“…We are therefore happy that, in this Special Issue, we can present papers from various fields, coming from both academia and metrology institutes. This includes the aspects of traceability for analytical techniques, in particular X-ray-based techniques [ 5 ], electrical SPM [ 6 , 7 ], quantitative data processing [ 8 ], tools for estimation related to data processing [ 9 ] and exploring novel routes for quantitative measurements [ 10 ]. We hope that this will provide a nice example of many different flavors of today’s nanometrology.…”