Atomic scale effects of zirconium and hafnium incorporation at a model silicon/silicate interface by first principles calculations

Abstract

First principles calculations aimed at quantifying the effects of zirconium and hafnium incorporation at a model silicon/silicate interface have been performed. The tetrahedral bonding character of silicates allows useful comparisons as well as important new distinctions to be drawn with the familiar Si/SiO/sub 2/ system. The calculated energy cost of forming (Zr,Hf)-Si bonds suggests that SiO/sub 2/-like bonding is energetically favored over silicide-like bonding at the Si interface. The calculations also suggest that the volume strain associated with Zr or Hf incorporation may lead to increased stress, both in the bulk oxide and in the interfacial transition region.

Full text

Page 1

14 IEEE ELECTRON DEVICE LETTERS, VOL. 22, NO. 1, JANUARY 2001
Atomic Scale Effects of Zirconium and Hafnium
Incorporation at a Model Silicon/Silicate Interface by
First Principles Calculations
Atsushi Kawamoto, Student Member, IEEE, John Jameson, Peter Griffin, Kyeongjae Cho, and
Robert Dutton, Fellow, IEEE
Abstract—First principles calculations aimed at quantifying
the effects of zirconium and hafnium incorporation at a model
silicon/silicate interface have been performed. The tetrahedral
bonding character of silicates allows useful comparisons as well
as important new distinctions to be drawn with the familiar
Si/SiO?system. The calculated energy cost of forming (Zr, Hf)-Si
bonds suggests that SiO?-like bonding is energetically favored
over silicide-like bonding at the Si interface. The calculations
also suggest that the volume strain associated with Zr or Hf
incorporation may lead to increased stress, both in the bulk oxide
and in the interfacial transition region.
IndexTerms—Computeraidedengineering,dielectricmaterials,
semiconductor device modeling, semiconductor materials.
I. INTRODUCTION
D
scaling challenge for sub-100 nm CMOS technology [1]. For
any proposed material, achieving a high quality interface with
silicon (Si) is essential. Zirconium (Zr) and hafnium (Hf)
silicates are high-
dielectrics which are thermally stable in
direct contact with Si [2]. Silicates are attractive because they
are incremental modifications of SiO . New understanding
can be built upon the existing Si/SiO knowledge base. Since
silicates contain a mixture of Si, oxygen (O), and Zr or Hf,
the interface bonding structure is of interest, including the
possibility that silicide-like bonds are formed. Since Zr–O
bonds are longer than Si–O bonds, Zr incorporation may lead
to stress. Results of a first principles study aimed at quantifying
these effects are presented.
EVELOPING an alternative high-
replace silicon dioxide (SiO ) has emerged as a key
gate dielectric to
II. COMPUTATIONAL EXPERIMENTS
Two studies were performed, one aimed at understanding
bulk silicates, the other focusing on the Si/silicate interface.
Manuscript received June 26, 2000. This work was supported by the Na-
tional Science Foundation (Graduate Research Fellowship and the DesCartes
program), Stanford Graduate Fellowship program, and by the Semiconductor
Research Corporation. The review of this letter was arranged by Editor D.
Dumin.
A. Kawamoto, P. Griffin, and R. Dutton are with Electrical Engineering and
Center for Integrated Systems, Stanford University, Stanford, CA 94305 USA
(e-mail kawamoto@stanford.edu).
J. Jameson is with Applied Physics, Stanford University, Stanford, CA94305
USA.
K. Cho is with Mechanical Engineering, Stanford University, Stanford, CA
94305 USA.
Publisher Item Identifier S 0741-3106(01)00684-X.
The computations are based on density functional theory within
the local density approximation (DFT-LDA), the first princi-
ples method-of-choice in condensed matter physics [3]–[5].
DFT-LDA has been widely applied to study the Si/SiO
interface [6]–[9].
The amount of Zr or Hf incorporation in experimental
silicate films is relatively low ( 10 atomic %). Experimental
results suggest that the bulk film may be thought of as a
“doped” form of SiO
[2]. Consequently, in the first study,
the silicate was modeled by replacing a single Si atom in
crystalline SiO ( -quartz), which led to approximately 11%
Zr or Hf concentration in the unit cell in terms of overall atomic
composition, or equivalently 50% Zr or Hf in terms of cation
ratio. Due to the computational cost of DFT-LDA, it is standard
practice to use periodic crystals to model oxides, even though
SiO is experimentally amorphous. The Zr initially forms Zr–O
bonds of length 1.62 Å, corresponding to the Si–O bond length
in
-quartz. This should be compared to Zr–O bonds in other
materials, such as the silicate zircon, ZrSiO
Å) [10]. The expected longer lengths of (Zr, Hf)–O bonds
generated stress in the model silicate. The atomic positions
and lattice vectors were then relaxed toward the total energy
minimum under DFT-LDA. The relaxation resulted in Zr–O
bond lengths of 1.94 Å and Hf–O bond lengths of 1.96 Å, rep-
resenting 24.8% and 25.6% volume expansions for the Zr and
Hf silicate models, respectively. Such volume expansions may
lead to localized strain near regions of Zr or Hf incorporation.
While this study only considers SiO -like tetrahedral bonding
arrangements, Zr atoms can have higher oxygen coordinations.
For example, in ZrSiO , Zr atoms are coordinated by four
first nearest neighbor oxygens and by four additional second
nearest neighbor oxygens. It seems reasonable to expect that
the additional volume required to accommodate more oxygen
bonds would lead to greater strain.
An interface model was next formed by attaching
SiO to Si(001) so as to minimize lattice mismatch. The re-
sultingmodel is similarto those of previous studies[6], [8]. The
lateraldimensionscorrespondtotheSilatticeconstant(5.43Å),
while the vertical dimension contains seven Si layers ( 8 Å)
and eight monolayers of oxide ( 8.5 Å). The model cell size
corresponds to the computational limits of a high performance
workstation. An oxygen bridge was formed to eliminate inter-
face states due to unsaturated bonds. All atoms were relaxed
(2.15 Å–2.29
-quartz
0741–3106/01$10.00 © 2001 IEEE

Page 2

KAWAMOTO et al.: ZIRCONIUM AND HAFNIUM INCORPORATION15
Fig. 1.
SiO
extremities are saturated with hydrogen atoms. (b) and (c) Relaxed structures
for model Si/silicate interface with Zr incorporation 1 layer (Zr model) and
three layers (Zr model) above the interface. Note that Zr-Si and Zr-O bonds
are substantially longer than the corresponding Si-Si and Si-O bonds.
(a) Reference Si/SiO interface model formed by attaching ?-quartz
to Si(001). Large atoms are silicon, small atoms are oxygen. The
except for the bottom three layers of Si, which were fixed1.
The lattice vectors were also held fixed. The boundary condi-
tions were intended to model a thin film atop a thick substrate.
Fig. 1(a) shows the resulting structure, which serves as the ref-
erence for an interface without Zr or Hf incorporation.
Four additional calculations were performed in which Zr or
Hf replaced a Si atom one or three layers away from the in-
terface. The atomic positions were again relaxed. The resulting
structures for Zr incorporation are shown in Fig. 1(b) and (c),
referred to as Zr and Zr models. The corresponding struc-
turesforHfweresimilar.Thesmallsizeofthecellpreventedre-
placing the boundary Si atom two layers away, since symmetry
would have artificially prevented lateral relaxation.
III. RESULTS AND DISCUSSION
The total energy of the Zr model ( 9135.93 eV) was 0.61
eV less than that of the Zr model. The total energy of the Hf
model ( 7937.29 eV) was 0.56 eV less than that of the Hf
model. The substantial energy differences suggest that Zr and
Hf are more likely to be found in a bulk-like environment, tetra-
hedrally bonded to four oxygens, rather than at the interface
forming two bonds each to O and Si. In other words, SiO -like
bondingisenergeticallyfavoredoversilicide-likebondingatthe
interface. This may help to explain recent experimental obser-
vations that a thin layer of SiO inevitably forms at Si/silicate
interfaces fabricated under various processing conditions [11].
1All calculations employed ultrasoft pseudopotentials, a plane wave basis
cutoff energy of 25 Ryd, and a 2 ? 2 ? 1 Monkhorst-Pack grid for k-point
sampling. Atoms were relaxed until the RMS force on free atoms was less than
0.05 eV/A
This energy difference is attributed in part to the added cost
of forming silicide-like bonds at the interface. Simple bond
counting shows that the Zr
model contains two Zr–Si and
two Si–O bonds more than the Zr model, while the Zr model
containstwoSi–SiandtwoZr–ObondsmorethantheZr model.
The Zr–Si bonds of the Zr model (2.66 Å) were measured to
be 13 to 15% longer than the corresponding Si–Si bonds of the
Zr model (2.31–2.36 Å), indicating weaker bond formation.
The Zr–O bonds of the Zr model (1.91–1.94 Å) were 17–21%
longer than the Si–O bonds of the Zr model (1.60–1.63 Å).
Similarly, the Hf–Si bonds of the Hf model (2.61 Å) were 11
to 13% longer than the corresponding Si–Si bonds of the Hf
model (2.32–2.36 Å), while the Hf–O bonds of the Hf model
(1.95–1.97Å)were20to23%longerthantheSi–Obondsofthe
Hf model (1.60–1.63 Å). Evidently, the cost of forming Zr–Si
and Hf–Si bonds in the Zr and Hf models more than offsets
the cost of forming Zr–O and Hf–O bonds in the Zr and Hf
models. This may be explained in part by the observation that
the Zr–Si and Hf–Si bonds form at the interface, where they are
constrained bytherigid Si substrate. The Zr–O and Hf–Obonds
form in the bulk oxide, where greater relaxation is possible.
Oxygen is known to form flexible bonds between neighboring
tetrahedral units, so that local distortions can be accommodated
withlittle energycost [6].
The calculated energy differences depend on the chosen
structural model. In particular, the present Si/SiO interface
model contains only the Si
oxide”) at the oxygen bridge. Previous first principles studies
have considered alternative models, which also include the
Si
and Sistates in the transition region, leading to a
different density of Si–Si bonds at the interface [6], [9]. It
seems reasonable to expect that interfacial incorporation of Zr
or Hf would become even more costly for lower suboxidation
states (e.g., Si
), due to the increased density of Si–Si bonds
and of Zr–Si or Hf–Si bonds that would result.
The limited size of the model cell may have artificially con-
strained relaxation near the Zr atom. To test this, two additional
models
times larger in the lateral directions than the Zr
and Zr models were formed (Zr ’ and Zr ’ models). Because
these were considerably more expensive to relax, only the Zr
modelswere studied.Theincreasedflexibilityforrelaxationled
to a smaller energy difference of 0.43 eV between the Zr ’ and
Zr ’ models. The additional relaxation was concentrated near
the Zr atom. However, the substantial change in the energy dif-
ference raises the possibility that even the value obtained with
the larger cells is still not well converged with respect to the cell
size. Hence, the 0.43 eV can only be considered as an upper
bound, and it is possible that a larger model cell would lead to
an even smaller energy difference.
Electronic structure analysis also revealed that silicide-like
bonding in the Zr and Hf models produced interface states
with deep energy levels within the Si bandgap. Zr introduces a
state 0.24 eV below the conduction band of Si, while Hf intro-
duces a state 0.11 eV below. These estimates are only approxi-
mate since the LDA approximation underestimates the bandgap
[3]. As commonly done, this work assumes that the underesti-
mation is constant for all models considered, so that deep level
energies can be referenced to the conduction band edge. There
partial oxidation state (“sub-

Page 3

16IEEE ELECTRON DEVICE LETTERS, VOL. 22, NO. 1, JANUARY 2001
Fig. 2.
Fig. 1. Tetrahedra associated with bulk Si (bottom), the Si
states at the oxygen bridge (middle), and bulk oxide (top) are indicated.
Tetrahedral volumes of local bonding units for the interface models in
partial oxidation
are well-known corrections that achieve greater accuracy at the
costofincreasedcomputation[12].FortheZr andHf models,
theZrandHfstatesweresweptoutoftheSibandgap.Thesecal-
culationswereonlyperformedforthesmallermodels(lateraldi-
mensionsof5.43Å),aslimitedworkstationresourcesprevented
sampling the band structure for the larger models.
While there is some uncertainty in excited state energies,
DFT-LDA is known to be very accurate for ground state
structural properties. To characterize the local strain induced
by Zr, the volumes of tetrahedral bonding units were measured.
Fig. 2(a) shows that for the reference Si/SiO model, the Si
suboxide state accommodates the structural transition from
bulk Si to bulk oxide. Oxide reliability models have considered
this region to be especially vulnerable to electrical stress, since
oxidation-induced strain is largely localized at the interface
[13]. The tetrahedron associated with Zr near the interface in
Fig. 2(b) (Zr model) is 45% larger than the corresponding
volume in the reference model, suggesting that the transition
region may become increasingly strained when Zr is incorpo-
rated. For the Hf model the difference is 48%. Similarly, the
tetrahedron associated with Zr in the bulk oxide in Fig. 2(c)
(Zr model) is 70% larger than the corresponding volume in the
reference model. For the Hf model the difference is 78%. It is
expected that in an amorphous silicate film, the large volume
strains predicted by the present crystalline models would be
more easily accommodated, particularly in the bulk oxide.
The long-range disorder characterizing amorphous films could
provide greater freedom for relaxation near regions of Zr or Hf
incorporation via the flexible oxygen bonds.
IV. CONCLUSION
First principles calculations have been performed to quantify
the atomic scale effects of Zr and Hf incorporation at a model
Si/silicate interface. The calculated energy cost of forming (Zr,
Hf)–Si bonds suggests that an abrupt SiO -like layer is likely
to form between the bulk silicate and the Si substrate. Con-
trolling the extent of such interfacial oxide formation is critical
to avoid degrading the achievable capacitance of the dielectric
stack. More detailed energetics of the oxide layer formation and
possible ways to engineer the interface to avoid such growth de-
serve further study.
ACKNOWLEDGMENT
The authors thank S. Tang of Texas Instruments for helpful
discussions.
REFERENCES
[1] P. Packan, “Pushing the limits,”Science, vol. 285, pp. 2079–2081,1999.
[2] G. Wilk, R. Wallace, and J. Anthony, “Hafnium and zirconium silicates
foradvancedgatedielectrics,”J.Appl.Phys.,vol.87,pp.484–492,2000.
[3] A. Kawamoto, J. Jameson, K. Cho, and R. Dutton, “Challenges for
atomic scale modeling in alternative gate stack engineering,” IEEE
Trans. Electron Devices, Comput. Electron.: Spec. Issue on New
Challenges and Directions, vol. 47, pp. 1787–1794, Oct. 2000.
[4] M. Payne, M. Teter, D. Allan, T. Arias, and J. Joannopoulos, “Iterative
minimization techniques for ab initio total-energy calculations: Molec-
ular dynamics and conjugate gradients,” Rev. Mod. Phys., vol. 64, pp.
1045–1097, 1992.
[5] CASTEP (Cambridge Serial Total Energy Package) 4.0 is commercially
licensed through MSI (Molecular Simulations Inc.).
[6] R. Buczko, S. Pennycook, and S. Pantelides, “Bonding arrangements
at the Si–SiO and SiC–SiO interfaces and a possible origin of their
contrasting properties,” Phys. Rev. Lett., vol. 84, pp. 943–946, 2000.
[7] A. Pasquarello, M. Hybertsen, and R. Car, “Structurally relaxed models
of the Si(001)–SiO interface,” Appl. Phys. Lett., vol. 68, pp. 625–627,
1996.
[8] C. Kaneta et al., “Structure and electronic property of Si(100)/SiO in-
terface,” Microelectron. Eng., vol. 48, pp. 117–120, 1999.
[9] A. Pasquarello and M. Hybertsen et al., “Model interface between sil-
icon and disordered SiO ,” in Physics and Chemistry of SiO and the
Si–SiO Interface,H.Massoudetal.,Eds.
trochem. Soc., 2000, pp. 271–282.
[10] R. Wyckoff, Crystal Structures, 2nd ed.
4, pp. 157–158.
[11] Attendees of Materials Research Soc. Workship on high-k dielectrics,
private communication, June 1–2, 2000.
[12] S. Louie, “Quasiparticle theory of electron excitations in solids,” in
Quantum Theory of Real Materials, J. Chelikowsky and S. Louie,
Eds.Boston, MA: Kluwer, 1996, pp. 83–99.
[13] T. YangandK.Saraswat,“Effectofphysical stressonthe degradationof
thin SiO films under electrical stress,” IEEE Trans. Electron Devices,
vol. 47, pp. 746–755, Apr. 2000.
Toronto,ON,Canada:Elec-
New York: Wiley, 1968, vol.