First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide

Abstract

Crystalline structures, zone-center phonon modes, and the related dielectric response of the three low-pressure phases of HfO2 have been investigated in density-functional theory using ultrasoft pseudopotentials and a plane-wave basis. The structures of low-pressure HfO2 polymorphs are carefully studied with both the local-density approximation (LDA) and the generalized gradient approximation (GGA). The fully relaxed structures obtained with either exchange-correlation scheme agree reasonably well with experiment, although LDA yields better overall agreement. After calculating the Born effective charge tensors and the force-constant matrices by finite-difference methods, the lattice dielectric susceptibility tensors for the three HfO2 phases are computed by decomposing the tensors into the contributions from individual infrared-active phonon modes.PACS numbers: 77.84.Bw Hafnia (HfO 2 ) is technologically important because of its extraordinary high bulk modulus, high melting point, and high chemical stability, as well as its high neutron absorption cross section. HfO 2 resembles its twin oxide, zirconia (ZrO 2 ), in many physical and chemical properties. The resemblance is attributable to the structural similarity between the two oxides, which can in turn be explained by the chemical similarity of Hf and Zr, which have similar atomic and ionic radii (i.e., ionic radii for Hf 4+ and Zr 4+ of 0.78 and 0.79Å, respectively [1]) as a result of the so-called lanthanide contraction. Under ambient pressure, both oxides are monoclinic (m, space group P 2 1 /c) at low temperature, and transform to a tetragonal structure (t, space group P 4 2 /nmc) and then to a cubic structure (c, space group F m3m) as the temperature increases, as illustrated in Fig. 1.High-K metal-oxide dielectrics have recently been the focus of substantial ongoing efforts directed toward finding a replacement for SiO 2 as the gate dielectric in complementary metal-oxide-semiconductor (CMOS) devices. HfO 2 , ZrO 2 and their SiO 2 mixtures show promise for this purpose [2,3]. Thus, a systematic theoretical investigation of the structural and dielectric properties of these dielectrics, in both bulk and thin-film form, is clearly desirable. As a first step in this direction, we have, in a previous paper [4], investigated the bulk structures and lattice dielectric response of ZrO 2 polymorphs. We found that the dielectric responses vary dramatically with the crystal phase. Specifically, we found that the monoclinic phase has a strongly anisotropic lattice dielectric tensor and a rather small orientationally-averaged dielectric constant owing to the fact that the mode effective charges associated with the softest modes are relatively weak.This report presents the corresponding work on HfO 2

Novel high-κ dielectrics for next-generation electronic devices screened by automated ab initio calculations

“…More importantly, the doped phases possessed increased dielectric constants, as predicted by theory. 28 Therefore, we reasonably expect that c-BeO can be stabilized by doping or strain and will exhibit physical properties similar to the present calculations. Except for c-BeO, we could not find any outstanding high-κ dielectrics with either E g or κ larger than those of the HfO 2 thin films currently used in CPU or DRAM (E g~6 .0 eV and κ~20-25; see t-HfO 2 in Figure 4).…”

Study of interfacial reactions and phase stabilization of mixed Sc, Dy, Hf high-k oxides by attenuated total reflectance infrared spectroscopy

“…The amorphicity or crystalline phase strongly affects the permittivities which are achieved. The thermodynamically stable crystal structure of HfO 2 at room temperature is monoclinic and is characterized by a k $ 16 [4]. Tetragonal and cubic high temperature phases on the other hand show much higher permittivities (k $ 70 and 29 respectively [4]).…”

“…The thermodynamically stable crystal structure of HfO 2 at room temperature is monoclinic and is characterized by a k $ 16 [4]. Tetragonal and cubic high temperature phases on the other hand show much higher permittivities (k $ 70 and 29 respectively [4]). These phases have been shown to be stabilized by doping HfO 2 with lanthanides [5][6][7][8].…”

Chemical Descriptors of Yttria-Stabilized Zirconia at Low Defect Concentration: An ab Initio Study

“…and NCP pseudopotentials [18][19][20]23 . The frequency of the phonon at the W-point is more sensitive to numerical approximations, and for instance, varies from i18 cm -1 to i65 cm -1 as the FFT grid scale is increased from x1.5 to x2.5.…”

“…Previous calculations of the phonon spectrum using the generalised gradient approximation (GGA) to density functional theory (DFT) report an imaginary mode [18][19][20][21] of frequency i195cm -1 at the X-point of the first Brillouin zone corresponding to the low-temperature instability of the cubic phase 20 . The eigenvector of this mode involves displacements of oxygen anions along the ⟨1 0 0⟩ direction breaking the cubic symmetry which, upon full relaxation of the cell and internal coordinates, results in the observed tetragonal phase 22 .…”