Quantitative analysis of effective height of probes in microwave impedance microscopy

A quantitative approach is used to determine an effective height of probe beyond which the capacitance contribution is not significant in microwave impedance microscopy (MIM). We compare the effective height for three different modes of measurement, i.e., capacitance C(l) (l is the tip-sample distance), derivative of capacitance (C′(l)), and second derivative of capacitance (C″(l)). We discuss the effects of tip geometry and sample properties such as relative permittivity and sample height on the effective height with examples and analyze the implication on the spatial resolution of MIM. Finally, our results are verified by microwave impedance microscopy (MIM) measurement.