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HfO2 has a high melting point, high chemical stability, and a large dielectric constant. Cubic HfO2 modifies the fluorite-type crystal structure with 4 Hf and 8 O atoms occupying the (000) and (0.25 0.25 ±0.25) sites in the fcc unit cell, respectively. Figure 2069a shows the phase transformation of HfO2 with increasing temperature.

Phase transformation of HfO2 with increasing temperature

Figure 2069a. Phase transformation of HfO2 with increasing temperature.

Table 2069a. Properties of undoped HfO2.

  Most common, stable at low
Stabilized only above 1720 °C Stabilized only above 2600 °C
Lattice parameter (Å) & unit cell volume (V, Å3)

a = 5.124, b = 5.176, c = 5.276, β = 98.94°, V = 138.28

a = 3.63; c = 5.25 a = 5.08
Monoclinic-tetragonal: 1893-1923; Tetragonal-cubic: 2973; Cubic-liquid: 3173
Density (kg/m3)
  9680 1001  
Thermal expansion coefficient (10-6 K-1)
Heat of formation (kJ mol-1)
Boiling point (K)
Mohs hardness
Space group
  P21/c P42/mnm, P42/nmc (137) Fm-3m (225)
Static dielectric constant (K)
25 20 70 30
Band gap energy (eV)
Conduction band (CB) offset on silicon substrate
Work function (eV) of some compounds with HfO2
4.8 for NbSiN, 4.9 for NbN, 4.4-4.5 for TaSiN, 4.34-4.8 for TaN, 4.75-4.8 for HfN
Effective electron masses (me/m0)
  A-B: 1.03; B-D: 1.21 M-Γ: 0.72; Γ-Z: 0.94 L-Γ: 0.86 & 0.86; Γ-X: 1.97 & 0.68
Effective hole masses (mh/m0)
  Z-Γ: 0.85; Γ-Y: 1.28 Z-A: 0.78 & 0.78; A-M: 8.26 & 8.26 Γ-X:0.32; X-W:3.04
Amorphous with oxygen vacancies      
[4] [19]    

Doping tunes the properties of materials. Certain dopants in hafnia tabilize either the cubic or tetragonal phase over the monoclinic phase at low temperatures. However, it was also found that dopants with small ionic radii easily stabilize the tetragonal phase and dopants with large ionic radii (e.g. Gd, Dy, and Er) stabilize the cubic phase better. The dielectric properties of the films are related to the degree of crystallinity, crystal structure, crystallographic orientation, as well as their stoichiometric composition.

Table 2069b. Characteristics of impurity-doped HfO2.

Impurity Factors affecting formation Space group Structure Lattice parameter (Å) & unit cell volume (Å3) Dielectric constants Applications Notes Reference
Alkaline-earth & rare-earth doped Stabilized in cubic or tetragonal phases at room temperature Increase
dramatically compared to undoped m-HfO2
Deep vacancy trapping is responsible for the decrease in the ionic conductivity at high dopant concentrations [23]
Al Al ≤ 1.4% & annealing conditions Pbc21 (29) Non-centrosymmetry Ferroelectric, piezoelectric, pyroelectric [1]
Al Al ≤ 1.4% & annealing conditions Monoclinic 20–25 Oxygen vacancies play a key role as electron trap centers. Electron trapping and de-trapping leads to resistive switching. Formation of Hf-O-Al bonding reduces the oxygen vacancy formation energy. [3, 24]
Al 2.0% ≤ Al ≤ 3.5% Tetragonal /cubic 30–35   [3]
Al Al content & annealing conditions Antiferroelectric [1]
Al Al > 4.7% Amorphous 20 ~ 25 [3]
Ce Low Ce doping Monoclinic [4]
Ce High Ce doping Cubic  [4]
Ce Ce 12.5 at. %   Tetragonal         [21]
Co Paramagnetic [14]
Co           Ferromagnetic    
Er     Monoclinic to cubic          
Eu   P21/c (14) Monoclinic a = 5.139, b = 5.186, c = 5.311, β = 99.75°, V = 139.54       [19]
Gd 23.1 ~ 31.6 [5]
Gd Lower Gd contents P21/c (14) Monoclinic with occurrence of orthorhombic phase at the phase boundary [6]
Gd Gd at 10 ~ 20% Fm-3m (225) Cubic [6, 11]
Gd Gd > ~15 % P42/nmc (137) Tetragonal Oxygen vacancy formation energy for doped HfO2 is ~ 3 eV lower than un-doped one. [6, 26]
Gd Pbc21 (29) Non-centrosymmetric, orthorhombic Ferroelectric TiN top electrode enhances ferroelectric properties [6]
Ge Ge at 5 %   Tetragonal         [25]
Dy Cubic/ tetragonal [7, 8]
Hf             The hydrophobicity is changed into hydrophilicity [27]
La 8% La Cubic 38  
    Orthorhombic     Ferroelectric   [53]
Mn Mn at 10 ~ 20% Cubic Ferromagnetic
and half-metallic
Si Si content & annealing conditions Monoclinic Monoclinic phase is obtained if the film is not capped [1, 28]
Si Metastable tetragonal 30 Antiferroelectric   [20]
Si Cubic 30 [20]
Si Si at 4 mol.% Pbc21 (29) Orthorhombic  Ferroelectric Monoclinic phase is inhibited and orthorhombic phase is obtained if crystallization occurs under mechanical encapsulation [2, 9, 28]
Sc Cubic/ tetragonal [7, 8]
Ti           Optical and protective coatings or
optoelectronic devices
Ti ions serve as deep electron traps [22, 54]
Y Y < at. % at 1500 ° Monoclinic [17, 18]
Y Y at 10 ~ 20% Cubic a = 5.06 [12, 13]
Y Pbc21 (29) Orthorhombic

10 and 13 mol% YO1.5, quenched

Metastable tetragonal [15, 16]
Zr Simple Binary ZrO2 and HfO2 Orthorhombic Ferroelectric [29]

In the XRD and electron diffraction analyses, assuming that x % of Hf is randomly substituted by atom A, the structure factor Fhkl of the (hkl) reflection is then given by

        structure factor Fhkl of the (hkl) reflection --------- [2069]

        fA, fHf, and fO -- The atomic scattering factors of A, Hf, and O, respectively.

In about 2001, the choice of high-k dielectric oxides narrowed to HfO2, but the problems of making HfO2 into an applicable electronic material for CMOS appeared very difficult. Table 2069c shows the summary of 2003 Roadmap, listing the node, gate length, equivalent oxide thickness of high power (CPU) and low standby power devices (mobile), gate oxide material, and gate electrode material.

Table 2069c. Summary of 2003 Roadmap.

ASIC 1/2 pitch
Physical gate
Tox hi power
Tox lo power
Gate oxide
HfOx; Si, N
Gate metal
Poly Si
Metal gate, e.g. TaSiNx

Figure 2069b shows the theoretical low energy loss spectrum of EELS simulated from HfO2 film, indicating its electronic structure. The peak at 16.4 eV represents the valence plasmons excitation, while the peak at 26 eV corresponds to O 2s to Hf 5d excitations.

Theoretical low energy loss spectrum of EELS simulated from HfO2 film

Figure 2069b. Theoretical low energy loss spectrum of EELS simulated from HfO2 film.

The Hf4f7/2 peak at the binding energy between 16.4 and 17.0 eV (attributed to O–Hf–O bonding states) in XPS shown in Figure 2069c indicates the stoichiometric formation of HfO2. On the other hand, the binding energy of 29.8 eV is assigned to the 5p3/2 levels of HfO2 (not shown). Table 2069d lists the positions of the peaks of the Hf4f7/2 core-level in XPS spectra taken from different crystal structures.

XPS of HfO2

Figure 2069c. XPS of HfO2.

Table 2069d. Positions of the peaks of the Hf 4f7/2 core-level in XPS spectra taken from different HfO2 crystal structures and films.
HfO2 crystal structure/film/bond Hf 4f7/2(eV) Reference

Monoclinic + orthorhombic

18.0 - 18.5 [30]
Monoclinic 16.4 - 16.7 [35-36]
Cubic 17.8 - 18.1 [31-34]
Thick films (e.g. 26.5 nm) 16.8 [44]
Thin films (e.g. 0.6 and 5 nm) Very much scattered (17.06 - 18.3) [35-43]
Alumina addition Increase the binding energy [47-49]
Yttrium addition ~18.1 [50]
Formation of hafnium silicate Induces a shift toward higher binding energies, e.g. 17.4-18.3 [45-46]
Hf–O–N bond 16.4 [51, 52]
Hf–N bond 15.3–15.8 [51, 52]





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