The origin of ferroelectricity in Hf1−xZrxO2: A computational investigation and a surface energy model

Abstract

The structural, thermal, and dielectric properties of the ferroelectric phase of HfO2, ZrO2 and Hf0.5Zr0.5O2 (HZO) are investigated with carefully validated density functional computations.We find, that the free bulk energy of the ferroelectric orthorhombic Pca21 phase is unfavorable compared to the monoclinic P21/c and the orthorhombic Pbca phase for all investigated stoichiometries in the HfχZr1-χO2 system. To explain the existence of the ferroelectric phase in nanoscale thin films we explore the Gibbs / Helmholtz free energies as a function of stress and film strain and find them unlikely to become minimal in HZO films for technological relevant conditions. To assess the contribution of surface energy to the phase stability we parameterize a model, interpolating between existing data, and find the Helmholtz free energy of ferroelectric grains minimal for a range of size and stoichiometry. From the model we predict undoped HfO2 to be ferroelectric for a grain size of about 4 nm and epitaxial HZO below 5 nm.Furthermore we calculate the strength of an applied electric field necessary to cause the

Ferroelectric HfO2-based materials for next-generation ferroelectric memories

“…By comparing the Helmholtz free energies of various HfO 2 (and Hf 0:5 Zr 0:5 O 2 ) phases, it was found that the o-phase became the lowest-in-energy for HfO 2 when the grain size was 3-5 nm (8-16 nm for Hf 0:5 Zr 0:5 O 2 Þ. 37 On the other hand, experimentally, Yurchuk et al 36 first reported that in Si: HfO 2 thin films, as the film thickness increased from 9 nm to 27 nm, the P r dropped from 24 C/cm 2 to 3.5 C/cm 2 . The similar inverse relation between P r and film thickness was also found in undoped HfO 2 38 and Hf 0:5 Zr 0:5 O 2 solid solution films.…”

“…37 In their work, Materlik et al 37 built the Helmholtz free energy model, which contain both an ab initio computed part for total energy and entropy, and a phenomenological part for the surface energy. By comparing the Helmholtz free energies of various HfO 2 (and Hf 0:5 Zr 0:5 O 2 ) phases, it was found that the o-phase became the lowest-in-energy for HfO 2 when the grain size was 3-5 nm (8-16 nm for Hf 0:5 Zr 0:5 O 2 Þ.…”

“…In this connection, anisotropic stresses are required for the phase transition from tetragonal to orthorhombic, i.e., a compressive stress within the aob plane and a tensile stress along the c-axis exerted on the t-phase. There are many factors reported hitherto to be responsible for causing the anisotropic stresses and thus stabilizing the ferroelectric o-phase during the film growth, such as doping, 4,5,[23][24][25][26][27][28][29][30][31][32][33][34][35] surface energy effect, [36][37][38] island coalescence, 39 thermal expansion mismatch, 17 capping layer effect, 4,38 and formation of oxygen vacancies. 40 The following of this section will discuss each of these factors in order.…”

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

“…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.…”

“…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.…”