Theory of scanning nonlinear dielectric microscopy and application to quantitative evaluation

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. A general theorem for the capacitance variation under an applied electric field is derived and a capacitance variation susceptibility S_n1 is defined. The results show that the sensitivity of the SNDM probe does not change, even if a tip with a smaller radius is selected to obtain a finer resolution and that SNDM has an atomic scale 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.