Nonlinear relaxational polarization of Al2O3 and HfO2

In order to increase the capacitance density and to minimize leakage currents, high permittivity metal oxides will probably replace silicon oxide in integrated circuits. But the capacitance-voltage curve of metal oxides turns out to be nonlinear and they display a dispersion of the capacitance-frequency behavior. By employing an asymmetric double well potential model with a distribution of distances between the wells resulting from the amorphous structure of the oxides both effects can be interpreted. Between the wells protons fluctuate by tunneling at low temperatures and by thermal activation at higher temperatures.