Quantitative imaging of sheet resistance, permittivity, and ferroelectric critical phenomena with a near-field scanning microwave microscope

I describe the design and use of a near-field scanning microwave microscope to make quantitative measurements of sample properties, such as sheet resistance and permittivity. The system consists of a resonator contained in a coaxial cable, terminated at one end with an open-ended coaxial probe. When a sample is brought near the probe tip, the resonant frequency and quality factor are perturbed depending on the local properties of the sample. The spatial resolution depends on the diameter of the probe's center conductor, which can be in the range 1--500 mum. This versatile technique is nondestructive, and has broadband (0.1--50 GHz) capability.; Quantitative imaging of the sheet resistance of conducting thin films can be achieved through a thin-film calibration sample. To reinforce our understanding of the physical mechanisms of the measurement, I use a physical model for the system based on microwave transmission line theory. I demonstrate the technique at 7.5 GHz by imaging the sheet resistance of a variable-thickness YBa2Cu3O7-delta thin film on a sapphire substrate at room temperature.; Using a probe with a sharp, protruding center conductor held in contact with the sample, high-resolution (1 mum) imaging can be accomplished. I use a finite element calculation of the electric field near the probe tip, combined with perturbation theory, to make quantitative linear and nonlinear dielectric measurements of thin films and crystals. I demonstrate this capability by imaging the dielectric permittivity and nonlinearity of a (Ba,Sr)TiO3 thin film.; The microscope can also be used to image domains in ferroelectric crystals such as lithium niobate, barium titanate, and deuterated triglycine sulfate (DTGS). Critical phenomena can be investigated by varying the temperature of the sample. I measured the permittivity, dielectric nonlinearity, and domain relaxation time of DTGS as a function of temperature near the ferroelectric transition. For permittivity measurements, I found reasonable agreement with thermodynamic theory.