|
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.
Figure 2069a. Phase transformation of HfO2 with increasing temperature.
Table 2069a. Properties of undoped HfO2.
|
Amorphous |
|
|
|
Occurrence |
|
Most common, stable at
low
temperatures |
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 |
Polymorphism |
Monoclinic-tetragonal: 1893-1923; Tetragonal-cubic: 2973; Cubic-liquid: 3173 |
Density (kg/m3) |
|
9680 |
1001 |
|
Thermal expansion coefficient (10-6 K-1) |
|
5.8 |
|
|
Heat of formation (kJ mol-1) |
-1145.29 |
Boiling point (K) |
4700 |
Mohs hardness |
6.5 |
Space group |
|
P21/c |
P42/mnm, P42/nmc (137) |
Fm-3m (225) |
Static dielectric constant (K) |
25 |
20 |
70 |
30 |
Band gap energy (eV) |
5.8 |
|
|
|
|
1.4 |
|
|
|
|
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 |
Notes |
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 |
[10] |
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 |
|
|
|
|
|
Y |
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
--------- [2069]
where,
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.
Year |
2001 |
2003 |
2005 |
2007 |
2009 |
2012 |
2016 |
2018 |
Node |
130 |
100 |
80 |
65 |
45 |
32 |
22 |
18 |
ASIC 1/2 pitch |
150 |
107 |
80 |
65 |
45 |
32 |
25 |
18 |
Physical gate
length |
65 |
45 |
32 |
25 |
20 |
13 |
9 |
7 |
Tox hi power |
1.5 |
1.3 |
1.1 |
0.9 |
0.8 |
0.6 |
0.5 |
0.5 |
Tox lo power |
|
2.2 |
2.1 |
1.6 |
1.4 |
1.1 |
1.0 |
0.9 |
Gate oxide |
Oxynitride |
HfOx; Si, N |
LaAlO3 |
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.
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.
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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|