The Rayleigh law in silicon doped hafnium oxide ferroelectric thin films

A wealth of studies have confirmed that the low-field hysteresis behaviour of ferroelectric bulk ceramics and thin films can be described using Rayleigh relations, and irreversible domain wall motion across the array of pining defects has been commonly accepted as the underlying micro-mechanism. Recently, HfO2 thin films incorporated with various dopants were reported to show pronounced ferroelectricity, however, their microscopic domain structure remains unclear till now. In this work, the effects of the applied electric field amplitude, frequency and temperature on the sub-coercive polarization reversal properties were investigated for 10 nm thick Si-doped HfO2 thin films. The applicability of the Rayleigh law to ultra-thin ferroelectric films was first confirmed, indicating the existence of a multi-domain structure. Since the grain size is about 20-30 nm, a direct observation of domain walls within the grains is rather challenging and this indirect method is a feasible approach to resolve the domain structure.