Quantitative microwave impedance microscopy with effective medium approximations

T S Jones,C R Pérez,J J Santiago-Avilés

doi:10.1063/1.4976729

Abstract

Microwave impedance microscopy (MIM) is a scanning probe technique to measure local changes in tip-sample admittance. The imaginary part of the reported change is calibrated with finite element simulations and physical measurements of a standard capacitive sample, and thereafter the output ΔY is given a reference value in siemens. Simulations also provide a means of extracting sample conductivity and permittivity from admittance, a procedure verified by comparing the estimated permittivity of polytetrafluoroethlyene (PTFE) to the accepted value. Simulations published by others have investigated the tip-sample system for permittivity at a given conductivity, or conversely conductivity and a given permittivity; here we supply the full behavior for multiple values of both parameters. Finally, the well-known effective medium approximation of Bruggeman is considered as a means of estimating the volume fractions of the constituents in inhomogeneous two-phase systems. Specifically, we consider the estimation of porosity in carbide-derived carbon, a nanostructured material known for its use in energy storage devices.

Highlights

Microwave impedance microscopy (MIM), a scanning probe technique used to measure the change in admittance local to the tip, has been the subject of a number of recent studies.[1,2,3,4,5,6,7]
Many of the existing studies using MIM are somewhat qualitative in nature and the technique is used generally to measure the contrast in the tip-sample admittance across an image; some effort has been given to quantification of results and analyzing the tip-sample system in detail
The electrostatic force microscopy (EFM) approach curve method is used in the calibration of a very similar instrument, the scanning microwave microscope (SMM) of Keysight Technologies.[10]

Summary

INTRODUCTION

Microwave impedance microscopy (MIM), a scanning probe technique used to measure the change in admittance local to the tip, has been the subject of a number of recent studies.[1,2,3,4,5,6,7] The technique has been used, for example, to image the highly conductive domain walls in ferromagnetics,[2,3,4] and identify metallic and semiconducting carbon nanotubes individually and non-destructively.[6]. Wei et al have produced a Green’s theorem approach to quantify the tip-sample capacitance and verified this approach by comparison of the MIM signal with an electrostatic force microscopy (EFM) approach curve,[8] and have modeled effects of the height of the probe on the measurement.[9] The EFM approach curve method is used in the calibration of a very similar instrument, the scanning microwave microscope (SMM) of Keysight Technologies (formerly Agilent Technologies).[10] Lai et al have demonstrated a quantitative calibration scheme for MIM by imaging samples of known bulk permittivity, comparing the average output (in arbitrary units) of the instrument with finite element simulations.[7] Lai et al.[11] and Tselev et al.[4] have offered estimates of the ratio of capacitance to the signal output. We use an effective medium approximation to estimate the porosity of a nanostructured carbon material, carbide-derived carbon (CDC)

MATERIALS

SIMULATIONS

INSTRUMENT CALIBRATION

RESULTS

CONCLUSIONS