Dielectric relaxation in lanthanide doped/based oxides used for high-k layers

Lanthanide doped/based oxide thin films were deposited by liquid injection metal organic chemical vapor deposition or atomic layer deposition. Frequency dispersion is often found in the capacitance-voltage measurements. After taking the extrinsic frequency dispersion into account, the frequency dependence of the dielectric constant (k-value), that is the intrinsic frequency dispersion (dielectric relaxation) has been successfully theoretically modeled. For the physical mechanism of the dielectric relaxation, it was found that the effect of grain sizes for the high-k materials' structure mainly originates from higher surface stress in smaller grain due to its higher concentration of grain boundary. Variations in the grain sizes of the samples are governed by the deposition and annealing conditions and have been estimated using a range of techniques including Scherrer analysis of the X-ray diffraction patterns. The relationship extracted between grain size and dielectric relaxation suggests that tuning properties for improved frequency dispersion can be achieved by controlling grain size, hence, the strain at the nanoscale dimensions.