Pathways towards ferroelectricity in hafnia

Abstract

The question of whether one can systematically identify (previously unknown) ferroelectric phases of a given material is addressed, taking hafnia (HfO2) as an example. Low free energy phases at various pressures and temperatures are identified using a first-principles based structure search algorithm. Ferroelectric phases are then recognized by exploiting group theoretical principles for the symmetry-allowed displacive transitions between non-polar and polar phases. Two orthorhombic polar phases occurring in space groups P ca21 and P mn21 are singled out as the most viable ferroelectric phases of hafnia, as they display low free energies (relative to known non-polar phases), and substantial switchable spontaneous electric polarization. These results provide an explanation for the recently observed surprising ferroelectric behavior of hafnia, and reveal pathways for stabilizing ferroelectric phases of hafnia as well as other compounds.Commonly known structural phases of hafnia (HfO 2 ) are centrosymmetric, and thus, non-polar. Hence, recent observations of ferroelectric behavior of hafnia thin films (when doped with Si, Zr, Y, Al or Gd) [1][2][3][4][5][6][7] are rather surprising as ferroelectricity requires the presence of switchable spontaneous electrical polarization. The emergence of non-polar hafnia-as a linear high dielectric constant (or high-κ) successor to SiO 2 -for use in modern electronic devices (e.g., field-effect transistors) is now well-established [8,9]. If the origins of its unexpected ferroelectricity can be understood and appropriately harnessed, hafnia-based materials may find applications in nonvolatile memories and ferroelectric field effect transistors as well.A broader question that arises within this context, and also the one that will be addressed directly in this contribution, is whether one can systematically identify ferroelectric phases of a given material system. We show that this can indeed be accomplished and ascertained, for the example of hafnia, in two steps. First, a computationbased structure search method, e.g., the minima-hopping method [10][11][12], is used to identify low-energy phases at various pressures and temperatures. Then, ferroelectric phases are singled out by applying the group theoretical symmetry reduction principles, established by Shuvalov for ferroelectricity [13]. These principles allow for the systematic identification of all possible lower symmetry proper ferroelectric phases that can result from highersymmetry non-polar prototype (parent) phases.Using this approach, we find two ferroelectric phases of hafnia, belonging to the P ca2 1 and P mn2 1 orthorhombic space groups, which are close in free energy with the known non-polar equilibrium phases of hafnia over a wide temperature and pressure range. Figure 1(a) displays the computed equilibrium phase diagram of hafnia indicating the regimes at which the known non-polar phases are stable. This includes the low-temperature lowpressure P 2 1 /c monoclinic phase, high-pressure P bca and P nma orthorhombic p...

Ferroelectric HfO2-based materials for next-generation ferroelectric memories

“…(Note: ZrO 2 is structurally and chemically similar to HfO 2 .) In a later theoretical work, Huan et al 18 proposed that two orthorhombic phases with polar space groups of Pca2 1 and Pmn2 1 were possible to be the ferroelectric phases of HfO 2 , because their calculations showed that both Pca2 1 and Pmn2 1 phases had low free energies and small energy barriers for polarization switching. More recently, Sang et al 19 provided supportive evidence for the existence of the Pca2 1 phase as the structural origin of ferroelectricity in Gd:HfO 2 thin films using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) in combination with position averaged convergent beam electron diffraction (PACBED (Figs.…”

Ferroelectricity in Rare-Earth Modified Hafnia Thin Films Deposited by Sequential Pulsed Laser Deposition

“…[3][4][5][6][7][8][9][10] Ferroelectric phenomenon in these doped-HfO 2 films deposited by various deposition techniques such as atomic layer deposition, [5][6][7][8][9][10] chemical solution deposition, 11 and sputtering 12 was mainly explained by the existence of noncentrosymmetric orthorhombic phase (space group of Pca2 1 ). 5,6,12 The dopant incorporation into monoclinic HfO 2 matrix results in a transformation to tetragonal/cubic phase with the appearance of an intermediate metastable orthorhombic (Pca2 1 ) phase.…”

Layered structures of organic/inorganic hybrid halide perovskites

“…This is one of several feedback mechanisms and techniques that are employed in the minima-hopping method. This method has been successfully used for materials of various classes, including inorganic, [45][46][47][48] organic, 49 and inorganic-organic hybrid compounds. 50-52…”

“…[45][46][47][48] In this expression, F vib (T ) is the entropic contribution to F (T ) from the lattice vibrations. This term can be estimated by the lattice dynamics approach within the harmonic approximation from the calculated phonon density of states g(ω) as 60-62…”