A substitution method for nanoscale capacitance calibration using scanning microwave microscopy

This paper presents a calibration method and an uncertainty budget for capacitance measurements performed on micrometric size capacitors at microwave frequencies and nanometric resolution using a scanning microwave microscopy (SMM). The method applies the classical one-port vector network analyzer calibration for SMM using three known capacitance standards. These standards are established from a commercial calibration kit placed close to the microcapacitors in order to be calibrated. The calibration kit is composed of a large number of Metal-Oxide-Semiconductor (MOS) microcapacitors with capacitance values C ranging from 0.1 fF to 8.6 fF. Diligent selection criteria were established for the choice of the three capacitors. Their capacitance values were calculated from the AFM measured values of the area of the top electrodes and the dielectric thickness and considering the contribution of fringing fields. The combined type uncertainty on these calculated values amounts between 5% and 14% in relative value (uncertainty given at one standard deviation). The comparison between the capacitance values measured on calibration kit capacitors using the calibrated SMM and the calculated values show a good agreement for capacitances higher than 0.8 fF within uncertainties varying between 6% and 9%. For smaller capacitances, most of the observed deviations are not significant at two standard deviations. The uncertainties are mostly dominated by dimensional measurements and less importantly by unwanted capacitance effects. Based on these results, capacitances of two sets of microcapacitors were calibrated. The combined uncertainties vary from 14% to 7% for capacitances ranging from 0.1 fF to 3.1 fF respectively. The permittivity values of the dielectric layer of the two samples have been determined. They are found equal to 4.0 and 4.1 with a standard uncertainty of 0.6 and correlate with the expected value of 3.9.