Factors Favoring Ferroelectricity in Hafnia: A First-Principles Computational Study

Abstract

The surprising ferroelectricity displayed by hafnia thin films has been attributed to a metastable polar orthorhombic (Pca2 1 ) phase. Nevertheless, the conditions under which this (or another competing) ferroelectric phase may be stabilized remain unresolved. It has been hypothesized that a variety of factors, including strain, grain size, electric field, impurities and dopants, may contribute to the observed ferroelectricity. Here, we use first-principles computations to examine the influence of mechanical and electrical boundary conditions (i.e., strain and electric field) on the relative stability of a variety of relevant nonpolar and polar phases of hafnia. We find that although strain or electric field, independently, do not lead to a ferroelectric phase, the combined influence of in-plane equibiaxial deformation and electric field results in the emergence of the polar Pca2 1 structure as the equilibrium phase. The results provide insights for better controlling the ferroelectric characteristics of hafnia thin films by adjusting the growth conditions and electrical history.

Effect of Annealing Ferroelectric HfO2 Thin Films: In Situ, High Temperature X‐Ray Diffraction

“…Materlik et al calculated the free energy of various phases with varying strain, and the free energy of the t-phase or the o-phase decreases with decreasing tensile strain compared to that of the m-phase. [26] These previous studies strongly suggest that a decrease in the m-phase fraction is expected when the tensile stress in doped HfO 2 thin films is released during the heating phase of in situ XRD. [26] These previous studies strongly suggest that a decrease in the m-phase fraction is expected when the tensile stress in doped HfO 2 thin films is released during the heating phase of in situ XRD.…”

“…[63] Instead, the Pmn2 1 polar o-phase was energetically more favorable compared to the experimentally observed Pca2 1 o-phase. [23] Thus, Batra et al [26] suggested that various factors including compressive strain and electric field need to be combined to stabilize the Pca2 1 o-phase. [23] Thus, Batra et al [26] suggested that various factors including compressive strain and electric field need to be combined to stabilize the Pca2 1 o-phase.…”

“…[23] In the latter study, it was confirmed that the o-phase can be stabilized within the nuclei formed during the atomic layer deposition (ALD) process, but the interface/grain boundary effect is not sufficient to stabilize the o-phase within the final grain size after annealing. [23,24] Stress in thin films was also suggested as a possible origin, [1,25,26] and Shiraishi et al experimentally proved that the polymorphism of Hf 0.5 Zr 0.5 O 2 thin films is strongly affected by the thermal expansion coefficient (TEC) of the used substrate. [23,24] Stress in thin films was also suggested as a possible origin, [1,25,26] and Shiraishi et al experimentally proved that the polymorphism of Hf 0.5 Zr 0.5 O 2 thin films is strongly affected by the thermal expansion coefficient (TEC) of the used substrate.…”

Prediction of new metastable $$\hbox {HfO}_{2}$$ HfO 2 phases: toward understanding ferro- and antiferroelectric films

“…This discovery is of great interest to the semiconductor industry and has led to intensive experimental [3][4][5][6][7][8][9][10][11][12][13][14] and theoretical [9,[15][16][17][18][19][20][21][22] research, because these materials are believed to avoid the problems typical for the traditional ferroelectric materials (such as lead zirconate titanate) during integration into microelectronic devices. However, precise identification of the phase(s) in these films is problematic due to experimental limitations such as the broadness of the thin-film diffraction spectra, unknown film texture and strain fields, and possible presence of multiple phases within a single film.…”

“…The free energy change that may lead to formation of a metastable structure can be due to a combination of finite-temperature (primarily vibrational entropy) effects, finite-size (surface) effects, strain, and "doping" (alloying). These aspects have recently been discussed from a theoretical perspective [19][20][21][22]45]; in particular, changes in the relative free energy of several HfO 2 , ZrO 2 , and HfZrO 4 phases have been estimated by Materlik et al [19], who reported that within a wide range of experimentally reasonable conditions and for film thicknesses in 9nm…30 nm range the vibrational entropy, surface, and strain contributions are well within <∼180 meV/f.u. The changes due to intentional "doping" (alloying) need be evaluated on a case-by-case basis but can be expected to be <<∼ 50 meV/f.u.…”