Quantitative imaging of dielectric permittivity and tunability with a   near-field scanning microwave microscope
  We describe the use of a near-field scanning microwave microscope to image the permittivity and tunability of bulk and thin film dielectric samples on a length scale of about 1 micron. The microscope is sensitive to the linear permittivity, as well as to nonlinear dielectric terms, which can be measured as a function of an applied electric field. We introduce a versatile finite element model for the system, which allows quantitative results to be obtained. We demonstrate use of the microscope at 7.2 GHz with a 370 nm thick barium strontium titanate thin film on a lanthanum aluminate substrate. This technique is nondestructive and has broadband (0.1-50 GHz) capability. The sensitivity of the microscope to changes in relative permittivity is 2 at permittivity = 500, while the nonlinear dielectric tunability sensitivity is 10^-3 cm/kV. 
D. E. Steinhauer, C. P. Vlahacos, F. C. Wellstood, Steven M. Anlage,   C. Canedy, R. Ramesh, A. Stanishevsky and J. Melngailis