First-principles study on doping and phase stability of HfO
2
Choong-Ki Lee,
1
Eunae Cho,
1
Hyo-Sug Lee,
2
Cheol Seong Hwang,
3
and Seungwu Han
1,
*
1
Department of Physics, Ewha Womans University, Seoul 120-750, Korea
2
Samsung Advanced Institute of Technology, Suwon 400-600, Korea
3
Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University,
Seoul 151-742, Korea
Received 11 March 2008; published 3 July 2008
Based on density functional methods, relative stabilities between monoclinic, tetragonal, and cubic phases of
HfO
2
with cation dopants or oxygen vacancies are investigated. It is found that dopants such as Si, Ge, Sn, P,
Al or Ti with ionic radii smaller than Hf stabilize the tetragonal phase but destabilize the cubic phase. In
contrast, larger dopants such as Y, Gd or Sc favor the cubic phase. The ionized oxygen vacancies compensating
trivalent dopants greatly stabilize both cubic and tetragonal phases. Microscopic explanations on the results are
also given. The metastable phase favored by each dopant is in good agreement with experimental data. Our
results can serve as a useful guide in selecting dopants to stabilize a specific phase.
DOI: 10.1103/PhysRevB.78.012102 PACS numbers: 71.15.Nc, 74.62.Dh, 85.40.Ry
The continuous downscaling of complementary metal-
oxide semiconductor CMOS devices with performance en-
hancement has been enabled by reducing the thickness of
gate insulators. As the thickness of SiO
2
, the traditional gate
dielectric, is reduced to a few nanometers, leakage currents
due to the quantum tunneling have increased greatly. The
introduction of an insulator with a dielectric constant k
higher than for SiO
2
can solve the leakage problem as it
allows for increasing the physical thickness of the gate insu-
lator. Among various oxides explored to date, hafnia HfO
2
and its family materials are considered to be the most prom-
ising as a high-k gate oxide since they satisfy various tech-
nical requirements.
There are several polymorphs in HfO
2
such as monoclinic
m, tetragonal t or cubic c phases see Fig. 1. The ortho-
rhombic phase is also observed at high pressure conditions.
1
While m-HfO
2
is stable at ambient conditions, the material
undergoes a phase transition to the tetragonal phase at 2000
K and to the cubic phase at 2900 K. The calculated dielectric
constants vary widely from phase to phase, and the average
dielectric constants are much higher for cubic and tetragonal
phases.
2,3
Thin films of HfO
2
typical thickness of 5 nm
deposited in CMOS devices are usually amorphous due to
the low growth temperature 300 °C and they crystallize
into the monoclinic phase upon annealing at temperatures
above 700 ° C. The two structures are similar in local bond-
ing configurations and have dielectric constants significantly
lower than those of cubic or tetragonal phases.
4
This suggests
that the dielectric constant of the HfO
2
thin film can be in-
creased without changing materials if the relative stability
among polymorphs can be controlled in a way to make a
high-temperature phase to be most stable at growth condi-
tions. Recently, a series of experiments have demonstrated
that such a phase control can be achieved by cation doping.
For example, the doping with Si,
5
Al Refs. 6 and 7 or Zr
Ref. 8 atoms leads to thin films with a significant portion of
t-HfO
2
. It was also observed that c-HfO
2
is stabilized by
using Y,
9–11
Gd,
12
Sc Ref. 13 or Dy Ref. 13 dopants.
Despite the accumulating data on the phase control of HfO
2
based on the doping method, the microscopic origin has not
been elaborated much although the mechanism would be
similar to the case of ZrO
2
Ref. 14 in some parts. In addi-
tion, theoretical studies are very rare.
15
In this Brief Report, we theoretically investigate the effect
of dopants on the relative stability between m-, t- and
c-HfO
2
. We employ first-principles methods based on the
density functional theory. For the computation of total ener-
gies and structural optimizations, we use VASP.
16
Supercells
including 96 atomic sites are used for all structures. These
supercells are obtained by expanding structures in Fig. 1
twice along each axis. The energy cutoff for the plane-wave
basis is chosen to be 500 eV and k-points are sampled on
2 2 2 uniform grids. Gaussian broadening is used with a
width of 0.05 eV to smear the density of states. The
exchange-correlation interactions between electrons are de-
scribed by the generalized gradient approximation GGA
Ref. 17 and projector-augmented wave PAW potentials
are used for the description of ion-electron interactions.
18
The atomic positions and cell parameters are relaxed until
the atomic forces and stress tensors are reduced to within
0.02 eV/Å and 1 kbar, respectively. The optimized structural
parameters are given in Table I, and the agreements with
other work and experimental data are within 2%.
As a dopant, we choose Si, P, Ge,Al, Y, Ti, Zr, Gd, and
Sc, and replace one of Hf atoms with the dopant. All Hf
sites are equivalent. This corresponds to a doping concen-
tration of 3.125%. In addition, we also consider oxygen va-
cancies since they are introduced to compensate trivalent
dopants such asAl, Y, Gd or Sc. As the vacancy site loses
electrons in this case, the doubly ionized vacancy V
O
2+
, as
well as the neutral one V
O
0
, is studied.
(a) (b) (c)
Hf O
FIG. 1. Color online The structure of HfO
2
in a monoclinic,
b cubic, and c tetragonal phases.
PHYSICAL REVIEW B 78, 012102 2008
1098-0121/2008/781/0121024 ©2008 The American Physical Society 012102-1