Structure of 3 at.% and 9 at.% Si-doped HfO2 from combined refinement of X-ray and neutron diffraction patterns

Abstract

a b s t r a c tThe crystal structure of 3 at.% and 9 at.% Si-doped HfO 2 powder was determined through refinements using X-ray and neutron diffraction patterns. The lattice parameters, atomic positions, dopant occupancy, and the second phase fraction were determined with high precision using a combined full pattern fitting via the Rietveld method. The results show that both 3 at.% and 9 at.% Si-doped HfO 2 powder exhibit the monoclinic crystal structure with P 1 2 1 /c 1 space group. Through the combined refinement, the crystal structure parameters, especially for the positions and occupancies of the lighter atoms, were more precisely determined compared to independent X-ray diffraction refinement. Although the ionic radius of Si 4þ is smaller than Hf 4þ , with increasing Si occupancy, the unit cell volume slightly increases; possible mechanisms for this effect are discussed. Moreover, the refined results provide evidence of the existence of a non-equilibrium phase of Hf x Si 1Àx O 2 . The second phase (SiO 2 ) fraction is determined as 0.17 at.% for 3 at.% Si-doped HfO 2 powders and 1.7 at.% for 9 at.% Si-doped HfO 2 powders.

Compensation Charge Control and Modeling for Reproducing Negative Capacitance Effect of Hafnia Ferroelectric Thin Films

“…Here, p is electric dipole moment, ε r is the relative dielectric constant and is set to 25, and r is the distance from the center of electric dipole moment to a fixed point and is set to 4.3 Å, considering the well-known lattice constant of HfO 2 (50 Å). [40,41] N grain is the number of the grains present in the thin film, N molecule is the number of switchable molecules present in the grain, and PDF(t) is the probability density function set to the normal distribution formula that represents the polarization switching in a multi-domain ferroelectric. In the single-domain ferroelectric thin film, when a domain nucleus is formed inside the ferroelectric thin film without the nucleation of an additional domain, it grows horizontally, and eventually changes the polarization direction for the entire domain.…”

Crystal structure of monoclinic hafnia (HfO2) revisited with synchrotron X-ray, neutron diffraction and first-principles calculations

“…Later, Haines et al (1997) performed an ND study on HfO 2 synthesized by quenching the sample from 800 C and 20 GPa, and reported a cotunnite structure. On the other hand, the ND technique has been applied for studying the structure of 3 and 9 at% Si-doped HfO 2 by Zhao et al (2015). The ND method was used along with XRD and molecular dynamics simulations to characterize two structurally disordered forms of hafnia, i.e.…”