Uncertainties in the permittivity of thin films extracted from measurements with near field microwave microscopy calibrated by an image charge model

Abstract

The microwave microscope is a device which utilises near fields to characterise material properties of samples on length scales smaller than the operating wavelength. The errors associated with extracting the permittivity of a high permittivity thin film on a low permittivity substrate from measurements using such a device are found to be of the order of 25% when using a widely used image charge model of the tip-sample interaction. The uncertainties arise from the model-based extraction of the permittivity from the raw frequency shift data, and in the current case are shown to come from the assumption in the model that the tip of the microwave probe can be modelled as a sphere. The raw data from the microscope contain random uncertainties of the order of 1% and reveal variations in the properties of the thin film with sub-wavelength resolution demonstrating the microwave microscope as a sub-wavelength characterisation technique for thin films.

Measurement of the permittivity and loss of high-loss materials using a Near-Field Scanning Microwave Microscope

“…Two main types of Near-Field Scanning Microwave Microscope (NSMM) [1] are described in the literature: Instruments that are based on the perturbation of the resonance of a cavity that is coupled to a probe tip [2][3] [4][5] [6] [7] [8], and instruments that are modified Atomic Force Microscopes (AFMs). AFM-based instruments [9][10] [11] [12][13] use a Vector Network Analyser (VNA) to measure reflection coefficient data at a reference plane at a tip attached to an AFM cantilever.…”

Statistical Description of Inhomogeneous Samples by Scanning Microwave Microscopy

“…Such configuration is inspired by the seminal work of Wei, et al [20] and employed in [1], [14], [16]. The SMM used here is based on one reported elsewhere [21], adapted for highthroughput.…”

“…Analysis of the six individual calibrations compared with their mean showed a maximum-to-minimum variation of 25% in the gradient term and 14% in the intercept term, with no systematic trend between data sets. Calibrations of the resonator were performed with a set of standard samples detailed in [21], [26], [27]. All were characterized in a split post resonator [21], [26], except the quartz and LaAlO3 for which standard values were assumed [27].…”

“…Calibrations of the resonator were performed with a set of standard samples detailed in [21], [26], [27]. All were characterized in a split post resonator [21], [26], except the quartz and LaAlO3 for which standard values were assumed [27]. The temperature variations in the laboratory during experimental runs were monitored to be of the order of ±1 0 C. The coefficient of thermal expansion of copper is 17 ppm -1 [28].…”

“…In all that follows, the data shown are from magnitude and phase measurements of 21 S taken after a full two-port calibration. The coupling was much weaker than for the oneport measurements in order to make 21 ≤ −20 dB.…”