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Wang2006-Solid-Solid-Interfaces.pdf
Current Opinion in Solid State and Materials Science 10 (2006) 26–32
Theoretical studies of solid–solid interfaces
S.Q. Wang *, H.Q. Ye
1
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences,
72 Wenhua Road, Shenyang 110016, PR China
Received 23 December 2005
Abstract
We review recent progresses in the theoretical studies on the structural, cohesive, mechanic and thermodynamic aspects of interfaces
in solids. The technological developments for these studies are reviewed at first. In the next, we summarize the new achievements in the
studies on the cohesive and structural properties of metal/metal, ceramic/metal and semiconductor interfaces by ab initio computations
and molecular dynamics simulations. Then, the recent progresses in theoretical studies on the mechanics and thermodynamics of solid
interfaces are discussed. Finally, an outlook for the future directions in the research field is proposed.
Ó 2006 Elsevier Ltd. All rights reserved.
PACS: 68.35.p; 05.70.Np; 68.35.Md; 68.35.Ct; 71.15.Dx
Keywords: Solid/solid interfaces; Interface cohesion; Interface mechanics/thermodynamics; Computation and simulation
1. Introduction
Interface is one of the commonest microstructures in
solids. It plays critical role in various physical and chemical
properties, such as in mechanics, electrics, and carrier
transportation, of a material. Many important properties
of materials in technological applications are strongly
affected or even determined by the presence of interfaces.
The physical and chemical properties of a material may
be modified or changed significantly around the interface.
The importance of interfaces can never be overstated to
material researches. With technical advances both in theoretically and experimentally, interface science is becoming a
new branch in materials research [1]. The goal of interface
science is to facilitate material manufacture of technological importance by optimizing the material’s properties
based on a comprehensive understanding of the micro-
*
Corresponding author. Tel.: +86 24 23971842; fax: +86 24 23891320.
E-mail addresses: [email protected] (S.Q. Wang), [email protected]
(H.Q. Ye).
1
Tel.: +86 24 23971836; fax: +86 24 23891320.
1359-0286/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cossms.2006.06.001
structure of the interface and its influence on material performances. The capability to precisely engineer interface is
becoming increasingly indispensable in the development of
new materials.
Interface is a kind of buried structures in material, which
imposes more difficulties to investigate than other aspects
of material’s properties. Experimentally, the interface
structure is studied by transmission electron microscopy,
high-resolution transmission electron microscopy, electron
energy loss spectroscopy, and grazing incidence X-ray scattering [2], etc. The combination of highly-developed computer technique with computational molecular and
quantum theories has made theoretical investigation as
an important way in the studies of solid interfaces today.
Actually, ab initio calculation and atomistic simulation
are even the only choice for exploring many aspects of
the solid interface behaviors. The structure, cohesion, and
thermodynamics of solid interfaces are the areas of
research with most interests. There had been a few review
articles on interface problems. Sinnott and Dickey
reviewed the progresses in ceramic/metal interface structures and their relationship to atomic- and meso-scale
properties [3], Renaud reviewed the experimental studies
S.Q. Wang, H.Q. Ye / Current Opinion in Solid State and Materials Science 10 (2006) 26–32
on oxide surface and metal/oxides interfaces by grazing
incidence X-ray scattering [2], Ernst summarized the early
works on metal/oxide interfaces [4], Rühle reviewed the
application of electron microscopy to the study of ceramic/metal interfaces [5], Stoneham and Harding discussed
the challenges in computer simulation of interfaces [6]. In
this paper, we review the recent research achievements
and method developments in the field of theoretical investigation of solid interfaces in the last few years. Special
attentions are focused on those theoretical works for the
relationship of atomistic and electronic structures to interface properties.
This article is organized as follows. The recent technological developments in interface study are discussed in
the following section. Then we summarize the recent progresses in structure and cohesion of solid interfaces. Investigations in mechanical and thermodynamic aspects of
interface are reviewed in Section 4. At last, we sum up
our discussion and highlight the prospects for the future
development in the field.
2. The recent technological developments in interface study
In view of the structural characteristics of solid interface, the common tools for theoretical investigation of
the problem are the electronic calculation based on quantum mechanics theory and the atomistic simulation by
molecular dynamics (MD) algorithm. The recent advance
of density functional theory (DFT) has greatly benefited
researcher for ab initio first-principles studies of solid materials. The first-principles calculation is superior to classically empirical methods in its strict theory and
parameter-free realization. The ab initio calculation generally involves heavily computational task and thus is quite
time-consuming. It is limited only to small systems. Therefore, many technical problems have to be solved for
first-principles investigation of a real interface structure.
Molecular dynamics simulation uses empirical potential
for inter-atomic interaction. It enables one to study a system as large as over million atoms. In general, the empirical
potential function can be obtained by fitting the measured
data of material’s bulk properties from experiments.
However, the experimental information for heterogeneous
interface is quite scare. For this reason, how to describe
the interactions among the atoms across the interface is a
difficult problem to the studies of solid interfaces.
Significant progresses have been made for creating the
interatomic potentials of heterogeneous interface in recent
years. The simplest solution is to use the same potential
form as bulk material by only modifying the parameters
in the potential function. The embedded atom method
(EAM) potentials of Ag/Ni and Cu/Ni interfaces [7], the
pair potential of Cu/Al2O3 interface [8,9] were built in this
way. A more general mechanism for generating the pair
potential of heterogeneous interface was proposed by
Long et al. [10]. In their realization, the curve of adhesive
energy of the two hetero-phases with a simple interface
27
configuration is obtained from ab initio calculation firstly.
Then, the interfacial pair potentials are established by fitting the energy curve using a Mobius inversion method.
The generated potentials can be conveniently used in
large-scale molecular dynamics simulation. The advantages of their method are that the potential has a concise formula and is easy in generation and application. But the
condition in the potential’s transferability has to be
improved. Another exciting progress in potential function
method is the reactive force field (ReaxFF) approach
[11,12]. The ReaxFF method is superior to other empirical
potential methods in that it enables one do accurate simulation for a chemical reaction including the charge transfer
during the procedure. The parameters in ReaxFF are
obtained only from ab initio calculation and are fully
transferable, which provides the most convenience for an
interface study. Initial successes had been achieved using
ReaxFF in the investigations for the nonwetting–wetting
transition of Al/a-Al2O3 interface [13], and the kinetic friction simulation of Al/Al and a-Al2O3/a-Al2O3 interfaces
[14].
The lattice parameters of two heterogeneous phases can
not be perfectly matched. The resulted interface is either
incoherent or semicoherent. The local coherent regions
are separated by misfit dislocations to relax the lattice misfit. Hence, a rather large supercell is necessary for full
description of a real interface structure. To enable firstprinciples calculation, several approximations have to be
made. The reported ab initio works on heterogeneous
interfaces are mostly restricted to those interfaces with
the small lattice mismatch of a few percentages between
the two phases, thus far. It is observed from the experiments for the formation of nonreactive interface in pseudomorphous epitaxial growth that the epitaxial film matches
the lattice dimensions of the substrate when the film thickness is thin enough. Thus, if the interface is formed by two
small lattice-mismatched phases of the same crystalline
symmetry and along the same axial direction, it is the usual
way to build a coherent interface by matching the interfacial lattice dimension of the softer phase to the harder
phase in building the supercell for ab initio calculation
[15–18]. When the interface is formed by two phases with
different crystalline symmetries or along different axial
directions, it is essential to rotate the two sub-lattices for
a best structure match across the interface [19]. A better
solution for the problem of large interfacial lattice mismatch was proposed by Wang and Smith [20]. They suggested that the lateral lattice dimensions of the supercell
for the interface model should be optimized to minimize
the interfacial free energy. In this way, the calculated work
of interface separation with a small supercell will approach,
in accuracy, that of a larger one [20]. The lateral strain
along the interface is an important factor to affect the accuracy of theoretical result. It is strongly recommended to
estimate its influence for large lattice mismatch interfaces,
especially before making quantitative comparison between
two different interfaces [21].
28
S.Q. Wang, H.Q. Ye / Current Opinion in Solid State and Materials Science 10 (2006) 26–32
Theoretically, the intensity of interface cohesion is generally given by the work of adhesion Wad from ab initio
calculation, which is defined by
tot
tot
W ad ¼ Etot
ð1:1Þ
A þ E B E A=B =S:
where Etot
A=B is the total ab initio energy of the supercell with
an interface constructed by slabs of phases A and B in the
tot
middle and vacuum regions at its two ends. Etot
A and E B are
the total energy of full-relaxed, isolated A and B slabs,
respectively [22]. The typical supercell configuration of
interface structure in ab initio calculation is presented in
Fig. 1. The theoretical result of Wad is useful in that its value is comparable with the adhesion energy measurement
by wetting experiment [5]. In general, the larger Wad, the
stronger cohesion the interface is. However, it is known
that Wad is not able to uniquely determine the strength
of a heterogeneous interface system. The question for comparing the interfacial strength with the strength of its constituent materials should be explored by imposing loads
that lead to fracture of the system. When an interface is
formed between two heterogeneous phases, some charge
transference from the bulk regions of the two phases to
the interface occurs [15,17,22,23]. The more charge transference, the stronger the interface is adhered. But, too
much charge transference to the interface may cause charge
deficiency in the bulk regions near the interface and hence
weaken the bonding cohesion in the region. There are three
ways of structure failure for a heterogeneous interface system as shown in Fig. 2. Although it is possible of some
charge decrement near the interface in the harder phase,
structure failure does not likely occur at this side of the
interface system. If the interface is not well adhered, the
failure point will be at the interface (A point). For an
over-adhered interface, the failure point is at B, which is
a few angstrom distance from the interface in the softer
phase. The failure of a perfect adhered interface system will
occur inside the softer phase far away from the interface.
A B
C
softer phase
harder phase
interface
Fig. 2. The structure failure modes of heterogeneous interface system.
Because the energy is always higher for a homogeneous
interface without impurity segregation, the failure point
should be at the interface in this case generally. It is seen
that the structure failure or fracture analysis is essential
for a comprehensive evaluation of the cohesion of an interface system. Several pioneering theoretical works have been
done along this direction [24,25].
The technical development of epitaxial film growth
greatly facilitates researchers to fabricate interfaces for various purposes. The interfacial atomic structure of heterogeneous phases can be controlled through the growth
condition in epitaxial experiments. In the aspect of theoretical investigation, the relationship between interfacial
structure stability and environmental thermodynamic condition has also arisen as a main interest in recent years. The
technique of film growth thermodynamics study from
ab initio calculation has been developed [26–30]. In these
studies, the Gibbs free energy of the system and the chemical potentials of the composite phases are obtained at 0 K
and zero pressure by first-principles calculation firstly.
Then, the Gibbs free energy at a finite temperature T is calculated through the thermodynamic relationships from
these ab initio results [27,29,30]. In this way, the dependences of the interfacial energy and structure stability to
temperature and the partial pressure of the component element in the interface formation can be studied theoretically. The technique provides a theoretical tool for
designing and controlling the interface structure of solids.
3. Interface cohesion and structure
Vacuum
In this section we review the recent progresses in theoretical studies of the cohesion and structure for various solid/
solid interfaces.
Phase A
3.1. Metal/metal interfaces
Interface
Phase B
Vacuum
Fig. 1. Model of heterogeneous interface.
The interfaces composed by metal/metal phases commonly exist in physical, chemical and engineering applications, such as contacts for electronic circuits, anti-corrosion
protection coating, and multilayered magnetic devices, etc.
Alkali metal/transition metals composite is very important
in catalysis reaction. In view of the bonding property in
metals and the system dimension involved, molecular
dynamics simulation using empirical interatomic potentials
is the common choice in these investigations. The embedded atom model (EAM) potential [31] is used for simulation of metal systems in general.
S.Q. Wang, H.Q. Ye / Current Opinion in Solid State and Materials Science 10 (2006) 26–32
Liu et al. studied the interfacial energies and atomic
structures of various Ag/Ni and Cu/Ni interfaces by MD
simulation using EAM potentials [7]. The pair interaction
function across the interface is fitted by the dilute-limit
heats of solution of the alloys. Their results show that
the interfacial energies fall in the same order as that of
the surface energies in these systems, while for the interfaces matched in different crystal direction the interfacial
energy is proportional to the degree of lattice misfit. Lee
et al. investigated the depositing growth of Ni film on
Al(0 0 1) substrate by MD simulation [32]. Ni–Al intermixing was observed at the interface. They found that the Ni/
Al interface structure strongly depends on the substrate
temperature and the adatom incident energy. Spisak and
Hafner studied the problem of interface stabilization by
adding Ti interlayers in Fe/Al films [33]. Fe/Al film is used
for fabricating magnetic tunnel junctions. Due to inter-diffusion between Al and Fe, a well-shaped Fe/Al interface is
hard to achieve. They found that Ti deposition on Al surface will increase the stiffness of the interface and block Fe
diffusion into Al substrate. But, the effect decreases with
temperature increment. Besides, many of the works on
metal/metal interfaces are involved to investigate the
mechanic or thermodynamic aspects, and are going to be
discussed in detail in Section 4.
3.2. Ceramic/metal interfaces
Ceramic coatings on metals are used in many engineering fields for their stable mechanical properties at high temperature and good resistance to wear, erosion and
oxidation of ceramic materials. Understanding of the structure and adhesion properties of the interface between coat-
29
ing ceramic and metal is critical in the application. The
usual coating ceramics are basically the refractory ceramics, including metal oxides, metal nitrides, metal carbides
and metal silicides etc. Many investigations have been done
both experimentally and theoretically on ceramic/metal
interfaces so far. A brief list of the theoretical works in last
few years is presented in Table 1.
The general conclusions from these studies can be
drawn: (1) the interface adhesion of metal with the metalloid-terminated ceramics is stronger for the polar interfaces; (2) the atom of the metal locates on the top
metalloid atom of the ceramics has the strongest adhesion
for those nonpolar interfaces; (3) the ab initio analysis of
film growth thermodynamics can be used to control the
film growth condition for a specific terminate type of the
ceramic surface.
3.3. Interfaces of semiconductor materials
The steadily tendency of dimension decrement in the
microelectronics industry has led to the urgent demand
for seeking exceedingly new materials to replace the traditional ones in the fabrication of advanced devices. With
the logical devices in integrated circuit unit approaching atomic dimension, the behaviors and properties of
the microstructures in the device are going to play a key
role in the device performance. Therefore, the knowledge for the structure, cohesion and properties of the
interfaces between metal/semiconductor, semiconductor/
semiconductor or semiconductor/insulator in these devices
becomes essential to the design and fabrication of them.
The high-k gate dielectrics are the basic materials for
advanced CMOS transistors and have attracted many
Table 1
Theoretical works on ceramic/metal interfaces in last few years
Class
Interface
Property
Method
Oxides
Al(1 1 1)/a-Al2O3(0 0 0 1) [13]
Al(1 1 1)/a-Al2O3(0 0 0 1) [28]
Cu(1 1 1)/a-Al2O3(0 0 0 1) [8,9,29]
Rh(0 0 1)/Mg(0 0 1) [34]
Pd(1 1 1)/ZnO{0 0 0 1} [21]
Cu(0 0 1)/MgO(0 0 1) [35]
Ni(1 1 1)/a-Al2O3(0 0 0 1) [29]
Nb(1 1 1)/Al2O3(0 0 0 1) [27,26]
Ag(1 1 1)/a-Al2O3(0 0 0 1) [28]
Adhesion,
Adhesion,
Structure
Adhesion,
Adhesion,
Adhesion,
Adhesion,
Adhesion,
Adhesion,
structure
structure
structure
growth thermodynamics
growth thermodynamics
growth thermodynamics
MD
DFT
MD
DFT
DFT
DFT
DFT
DFT
DFT
Nitrides
Ti(1 1 0)/TiN(1 1 1) [22]
Al(0 0 1)/TiN(0 0 1) [15]
Al(1 1 1)/TiN(1 1 1) [23]
Al(1 1 1)/TiN(1 1 1) [25]
Adhesion, bonding
Adhesion
Adhesion, growth thermodynamics
Fracture, segregation
DFT
DFT
DFT
DFT
Carbides
Al(0 0 1)/TiC(0 0 1) [15,17]
Fe(1 1 0)/ZrC(1 0 0) [19]
Ti(1 1 0)/TiC(1 1 1) [36]
Al(0 0 1)/TiC(0 0 1) [37]
Al(0 0 1)/TiC(0 0 1) [18]
Adhesion
Structure, bonding, adhesion
Adhesion, structure
Adhesion, segregation
Lattice mismatch
DFT
DFT
DFT
DFT
DFT
Silicides
Fe(1 0 0)/MoSi2(0 0 1) [38]
Fe(1 1 0)/MoSi2(1 1 0) [38]
Adhesion, structure
Adhesion, structure
DFT
DFT
wetting
growth thermodynamics
30
S.Q. Wang, H.Q. Ye / Current Opinion in Solid State and Materials Science 10 (2006) 26–32
research interests recently. Peacock and Robertson studied
the bonding, energies, and band offsets of Si–ZrO2 and
HfO2 interfaces by DFT calculation [39]. The general
bonding rules for Si and ionic oxides interfaces are proposed in the study. Their result shows that the oxygen-terminated interface is favored for devices from band
structure consideration. Puthenkovilakam et al. made a
comparative investigation for ZrO2/Si and ZrSiO4/Si interfaces [40]. They got the conclusion that ZrSiO4/Si interface
is superior over the ZrO2/Si one in electronic properties
and is a suitable candidate for replacing the common
SiO2 as a gate insulator in silicon-based field effect transistors. Först et al. studied the formation of Zr/Si interface by
deposition growth through first-principles calculations [41].
They found that it is hard to obtain a flat Zr/Si interface
due to the island-style growth of Zr on silicon surface.
Recently, Dong et al. investigated the atomic structure,
band offset and the optimal condition of epitaxial growth
of ZrO2/Si interface by DFT calculation [42]. Their work
shows that the band offset is quite sensitive to the interface
structure and the interface structure can be atomic-level
controlled by altering the chemical environment during epitaxial growth. They suggested the possibility of epitaxial
growth of ZrO2 on Si for gate dielectric application. The
interface between high-k oxide LaAlO3 and silicon was theoretically studied by Först et al. [43]. The phase diagram of
the interface stability was drawn as a function of oxygen
and Al chemical potentials. Their result gives a negative
answer for using LaAlO3 as an epitaxial gate dielectrics.
Pourtois et al. studied the origin of work function shifts
for the gate/dielectric interfaces [44]. Kirichenko et al. studied the silicon interstitials at Si/SiO2 interface by DFT calculation [45]. Watanabe et al. investigated the growth of
amorphous SiO2 on Si surface by large-scale MD simulation [46]. It is expected that more works will be done on
the high-k gate materials in the near future for its urgent
importance in microelectronic industry.
In the aim for developing new electronic devices, such as
blue–green emitters, spin-transistors, nonvolatile memory
cells, and solar cell etc., the interfaces of transitional metal
silicides with silicon [47], NiMnSb/GaAs [48], ZnSe/GaAs
[16] and crystalline-Si/amorphous-Si [49] were studied by
ab initio calculations, respectively. In an attempt for understanding the effects of misfit dislocations to interface adhesion, large-scale ab initio calculation of Si/Cu interface was
accomplished [20].
4. Mechanics and thermodynamics of the interfaces
in solids
The mechanics and thermodynamics of the interfaces in
solid are important aspects in the material’s application.
Friction and plastic deformation involve the relative movement of the grains at two sides of the interface. Fracture
and structure failure frequently occur at the interface.
The role played by the interface in the melting transition,
and how to control or alter the behavior of materials near
the melting point by interface structure are among the
interesting questions attracted many researchers.
First-principles calculations are recently used to predict
the strength of a system with solid interface. Qi and Hector
studied the mechanical strength of aluminum/diamond
interfaces by applying a series of tensile strain vertical to
the interface up to fracture [24]. They summarized three
stages for the interface fracture: elastic stretching, incipient
de-cohesion and jump to separation. Liu et al. investigated
the effect of hydrogen on Al/TiN interface by DFT calculation. Different fracture modes were found for the interfaces with and without hydrogen contamination [25].
The investigations on dislocation and sliding along
interface involve large system size and are usually studied
by MD simulation. Dmitriev et al. studied the lattice
mismatch and dislocation patterns of Cu(1 1 1)/aAl2O3(0 0 0 1) interface by simple pair interfacial potential
and MD simulation [8,9]. Maheswaran et al. studied the
lattice mismatch and misfit dislocation by combining
high-resolution transmission electron microscopy and
MD simulation [50]. Spearot et al. simulated the nucleation
of dislocations at R5 (3 1 0) bicrystal interface in Al under
uniaxial tensile deformation. A disclination dipole model
was proposed for explaining the emission of dislocation
loops from the bicrystal interface [51]. Stankovic et al.
studied the problem of dry sliding friction at the commensurate interfaces between two metals by nonequilibrium
MD simulation using the generic embedded atom model
[52]. The sliding frictions of Ni/Zr [53], Al/Al and aAl2O3/a-Al2O3 [14], and Cu/Cu [54] were also investigated,
respectively, by other researchers.
The thermodynamic property of interfaces is significantly different from the bulk areas of material. In early theoretical works, Nguyen et al. simulated the thermal
structure disorder and melting of the interfaces in aluminum. No interface premelting was found in their study
[55]. Zhao et al. did large-scale MD simulation for the melting behavior of B2 NiAl interface on parallel computer. A
mechanism of cluster-induced structural disorder and melting transition at the interface of NiAl alloy was proposed
[56,57]. To verify the puzzle whether there is interface premelting or not in solids, Zhao et al. studied a series of the
symmetrical tilt boundaries (STB) in copper. They found
that the high-energy STBs generally undergo interface premelting before the bulk melts, but this phenomenon was not
observed in low-energy STBs [58]. The recent study by
Huang et al. showed that the surface melting temperature
of semiconductor can be changed by a microscopic coating
with another different lattice-matched semiconductor phase
[59]. The work presented a typical example for the interfacecontrolled thermodynamics of materials.
5. Conclusions and future direction
It is seen from the developments of the field in last few
years that the theoretical studies of solid interfaces present
growing importance and capability to solve problems in
S.Q. Wang, H.Q. Ye / Current Opinion in Solid State and Materials Science 10 (2006) 26–32
materials science in both aspects of theory and application.
With the decrement in the microstructures of advanced
materials to nano- and atomic scales, the interface will play
the more important role in materials’ behaviors, and thus
become a prior problem for consideration. For example,
the area of interface occupies several to several tens percentage of the total volume in nano-alloys. Different from
traditional materials, the mechanical properties of nanoalloys are largely determined by the interfaces inside them.
In modern microelectronic industry, the device size is
approaching a few nanometers. Quantum transportation
and interface contact are becoming the major concerns in
designing microelectronic circuits and devices.
We expect the following three aspects for the future
developments in theoretical studies of solid interfaces.
Firstly, more attention will be paid on the kinetic and
dynamic behaviors of solid interfaces. Theoretical understanding of these properties is essential for better material
applications. The modern computation and simulation
techniques are being made it as a convenient choice to
study these problems theoretically. Secondly, more theoretical works on the structural and physical properties of the
interfaces in microelectronic devices are expected. The formation condition of a specific interface structure will also
be an important topic in these studies. Thirdly, the
mechanical properties of interface and how to improve
the material’s performance by modifying its interfacial
structures are going to be the two preferential problems
in the theoretical studies of bulk nano-materials.
Acknowledgments
The authors would like to acknowledge the financial support of this work by the Special Funds for the Major State
Basic Research Projects of China (No. G2000067104). This
work was also partially supported by the National Natural
Science Foundation of China (No. 50472085).
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