A theory for the image production mechanism of scanning nonlinear dielectric microscopy and its application to the quantitative evaluation of linear and nonlinear dielectric properties of ferroelectric and piezoelectric materials

A theory for scanning nonlinear dielectric microscopy (SNDM) and its application to the quantitative evaluation of the linear and nonlinear dielectric constants of dielectric materials are described. First, a general theorem for the capacitance variation under an applied electric field is derived and a capacitance variation susceptibility S_nl, which is a very useful parameter for the quantitative measurement of nonlinear dielectric constants, is defined. This S_nl is independent of the tip radius, and therefore the sensitivity of the SNDM probe does not change, even if a tip with a smaller radius is selected to obtain a finer resolution. Using the theoretical results and the data taken by SNDM, the quantitative linear and nonlinear dielectric properties of several dielectric materials were successfully determined. From the calculation of a one-dimensional image of a 180° c-c domain boundary, it is demonstrated that the SNDM has an atomic scale resolution.