Phase selection during calcium silicide formation for layered and powder growth

Article abstract of DOI:10.1016/j.jallcom.2011.01.112

Phase selection during Ca silicide formation was discussed using the chemical potential and the effective heat of formation (ΔH′) models. The compositional analyses of Ca silicides were experimentally carried out in detail for both the layered and powder

Full text of DOI:10.1016/j.jallcom.2011.01.112

Journal of Alloys and Compounds 509 (2011) 4583–4587
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Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jallcom
Phase selection during calcium silicide formation for layered and powder growth
a
b
c
a,c,∗
Cuilian Wen , Akihiko Kato , Tomomi Nonomura , Hirokazu Tatsuoka
a
Graduate School of Science and Technology, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, Shizuoka 432-8011, Japan
FDK Corporation, 2281 Washizu, Kosai 431-0495, Japan
Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, Shizuoka, 432-8561, Japan
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Phase selection during Ca silicide formation was discussed using the chemical potential and the effective
heat of formation (ꢀH ) models. The compositional analyses of Ca silicides were experimentally carried
Received 13 November 2010
Received in revised form 17 January 2011
Accepted 18 January 2011
Available online 22 January 2011
ꢀ
out in detail for both the layered and powder growth process. Based on the calculation, the Ca2Si phase
ꢀ
has the largest negative ꢀH and is the first phase to form in the Ca–Si system. In addition, the total
energy consideration consisting of the formation energy of each phase and interfacial energy between
two adjoining phases is proposed to explain the experimental results of phase selection in the Ca silicide
formation.
Keywords:
Interfaces
Growth from vapor
Calcium compounds
Semiconducting silicon compounds
©
2011 Elsevier B.V. All rights reserved.
1
. Introduction
These rules heavily rely on phase diagram information such as the
lowest eutectic, stability and diffusion species, but do not directly
use thermodynamic data. Some metal–silicons, such as the Cr–Si,
Co–Si and Ni–Si systems have been extensively discussed [11–13].
However, there are few reports on the phase selection during the
silicide formation of the Ca–Si system. Ca silicide powders and films
Recently, semiconducting silicides have attracted much atten-
tion as environmentally conscious materials, which consist of
non-toxic and abundant materials. The solid phase interaction
between thin metal films and silicon has been widely studied
because of the importance of silicides as interconnects and contacts
in silicon devices.
The phase formation and transformation of multi-component
compound systems have been intensively discussed based on ther-
modynamic considerations [1–8]. For the case of phase formation
and phase stability, thermodynamic descriptions were developed
using thermodynamic models for Cr–Sn–Ti [1] and Al–Zn–Mg–Si
have been grown on Si or Si/Mg Si powders or substrates by heat
2
diffusion treatments [14–18], however, it is still difficult to grow
high quality single phase Ca silicide. There are multiple silicide
phases, such as CaSi , CaSi, Ca5Si3 and Ca Si that exist in the Ca–Si
2
2
system, which could lead to the simultaneous formation during its
growth [14–17]. Among them, Ca Si and Ca5Si have been reported
2
3
to have a semiconducting behavior [14,15,19]. It is important to
understand the elemental chemical potential gradients and effec-
tive heat of formation (EHF) as certain driving forces for diffusion in
the Ca–Si system, in addition to the concentration controlled phase
selection.
[
2]. The chemical potentials consideration was made for the growth
of gold-seeded III–V semiconductor nanowires [3]. On the other
hand, for the case of growth phase evolution, the preferable phase
formation or phase selection was investigated under the consider-
ation of thermodynamics for Mg–Sn–Si and Mg–Sn–Si–Ca [4] and
Fe–Co [5]. The phase transformation or the solidification pathways
was investigated for from anantase to rutile [6], Mg–Pd nanoparti-
cles [7] and Mg–Zn–Y–Zr alloys [8].
For considering the silicide growth, there has been considerable
interest in formulating rules for predicting the first silicide phase
which forms as well as the sequence of subsequent phases [9–11].
Experimentally, Ca-silicide formations were reported in Refs.
[16,19], which reported for the layered growth, the Ca Si and CaSi
2
interface was formed while the Ca5Si3 phase was not significantly
formed. On the other hand, for powder growth, the Ca5Si3 single
phase powders were grown. However, a detailed compositional
analysis has not been carried out.
In this study, the compositional analysis of Ca-silicides was
made for both the layered and powder growth processes. In addi-
tion, the phase selection during the Ca silicide formation was
discussed based on the chemical potential and the effective heat of
∗ Corresponding author at: Faculty of Engineering, Shizuoka University, 3-5-1
Johoku, Naka-ku, Hamamatsu, Shizuoka 432-8561, Japan. Tel.: +81 53 478 1099;
fax: +81 53 478 1099.
ꢀ
formation (ꢀH ) models associated with the additional interfacial
energy to explain the experimental Ca silicide layered and powder
growth processes.
E-mail address: tehtats@ipc.shizuoka.ac.jp (H. Tatsuoka).
0
925-8388/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2011.01.112

4
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C. Wen et al. / Journal of Alloys and Compounds 509 (2011) 4583–4587
domains compared to the Ca5Si3 phase, which suggests that the
Ca5Si single-phase formation window is narrower than that of the
3
other phases.
o
The heats of formation (ꢀH ) of the Ca silicide phase is cal-
culated from the potential energies shown in Fig. 1 according the
formula shown below:
ꢁCamSin = mꢁCa + nꢁSi − ꢀGCamSin
(3)
Assuming the equilibrium condition, ꢀGCamSin = 0, ꢁCamSin is the
chemical potential for m × ꢁ + n × ꢁ in the CamSin phases. From
Ca
Si
Fig. 1, it is calculated as −1.44, −1.34, −4.84 and −1.70 eV for CaSi ,
2
CaSi, Ca5Si3 and Ca Si, respectively. The heat of formation energy
2
for 1 mol is obtained as:
ꢀ
Ho = NA × ꢁCamSi
(4)
where NA is the Avogadro constant of 6.02 × 1023 mol . The
−1
Fig. 1. The calculated two-dimensional chemical potential diagram of CaSi2, CaSi,
calculated heat of formation energy for each phase is listed in
Table 1. In addition, most available phase equilibriums and thermo-
dynamic data for the Ca–Si system have been collected and critically
evaluated by Heyrman et al. [21]. Some ꢀH calculated from the
literature [22–24] is also shown in the table, which is in excellent
agreement with our calculated results.
Ca5Si3 and Ca2Si phases for the Ca–Si system. The origins of each chemical potential
bulk
bulk
are set to the bulk ones, ꢁCa and ꢁSi
.
o
2.
Experimental
As the first step in the silicide layer growth, Mg2Si layers were grown on Si
substrates prior to the Ca2Si growth. The Mg source and Si substrates were placed
in a loosely sealed quartz container, which was loaded into a vacuum chamber.
The container was then heated and the temperature was maintained at 370 C. The
The driving force for a process to take place is given by the
change in the Gibbs free energy:
◦
growth procedure of the Ca2Si layer is basically the same as the Mg2Si growth, except
for the growth temperature and growth time. The Ca2Si layers were grown by the
heat treatment of Mg2Si/Si (1 1 1) substrates at 600 C in Ca vapor for 3 h [16].
ꢀG = ꢀH − TꢀS
(5)
◦
where ꢀH is the change in enthalpy (or heat of formation) during
the reaction at temperature T and ꢀS is the change in entropy.
For the solid state interactions, ꢀS ≈ 0 and ꢀG is thus approxi-
mated by the change in ꢀH during the reaction. However, the first
formed phase is not only determined by the lowest heat of forma-
tion, but also by the concentration of atoms at the growth interface
available to participate in the reaction. The effective concentration
differs from the physical concentration at the growth interface and
cannot be directly calculated [12,25–27]. The effective heat of for-
The Ca5Si3 powders were synthesized by exposure of the Si powder to Ca fluxes.
The Ca source and Si powder were first placed in a loosely sealed glass container,
and then the container was loaded into a vacuum chamber. The container was then
◦
heated and the temperature was maintained at 750 C for 12 h [19].
The structural properties of the resultant layers and powders were characterized
by scanning electron microscopy (SEM) measurements. In addition, the composi-
tional analysis was completed using energy dispersive X-ray spectroscopy (EDS).
The two-dimensional chemical potential diagram of the CaSi2, CaSi, Ca5Si3 and
Ca2Si phases for the Ca–Si system was calculated by a first principles scheme based
on the local density functional theory. It was postulated that the CamSin phase is
grown under thermodynamically equilibrium conditions which is characterized by
the chemical potentials of the constituent elements, ꢁCa and ꢁSi. The following
expression should be satisfied:
ꢀ
mation (ꢀH ) of the Ca silicide phases is calculated as a function
of the concentration, and is given by the Ca–Si phase diagram in
ꢀ
Fig. 2. A general definition of the ꢀH is given in Ref. [11]. It is clear
ꢁ
CamSin ≤ mꢁCa + nꢁSi
(1)
ꢀ
that all the phases have a negative ꢀH and thus the release of the
where ꢁCamSin is the chemical potential of CamSin per one chemical formula. Fur-
thermore, if no segregation in CamSin occurred, the following conditions should be
added:
energy from the system occurs when the concentrations of Ca and
Si match that of the composition of a particular compound. In order
to determine the phase that will be formed, it is necessary to know
the effective concentration of the elements at the growth interface.
Generally, the intermixing at the interface during the solid phase
reaction is expected to take place at the concentration of the lowest
temperature eutectic of the binary system. In the case of the Ca-Si
system, this occurs at a composition of 3.5 at% Si as shown in Fig. 2.
A rule for the first phase formation can thus be formulated which
state the following: the first silicide compound to form during the
metal–silicon interaction is the congruent phase with the most neg-
bulk
bulk
ꢁ
CamSin = mꢁCa + nꢁSi − ꢀGCamSin
,
ꢀGCamSin > 0,
(
2)
bulk
bulk
ꢁ
Ca < ꢁCa
,
ꢁSi < ꢁSi
,
where ꢁCa and ꢁ bS iu lk are the chemical potentials of bulk Ca and Si crystals, respec-
bulk
tively, and ꢀGCamSin is the heat of formation. The ꢁCamSin , ꢁCa and ꢁ bS iu lk values were
obtained by first principles total energy calculations (the entropy contributions was
neglected). Our total energy calculation scheme is described in Ref. [20].
bulk
3
. Results and discussion
ꢀ
ative ꢀH at the concentration of the lowest temperature eutectic of
ꢀ
The two-dimensional chemical potential diagram for Ca silicide
the binary system [11]. The value of ꢀH has been calculated for the
phases is shown in Fig. 1. The stable domain of each stoichiomet-
ric phase is defined by a line, because the sum of the chemical
potentials of the different components weighted by the appropriate
stoichiometric coefficient is equal to the Gibbs energy of formation
of the phase. The points of intersection of the two lines identify the
two-phase equilibriums. The planes, defined by the intersection of
the corresponding lines, represent the corresponding phase’s coex-
isting field. It is noted that the stable domain of the single-phase
only existed in the line of no planes with the other lines, called
the single-phase line. It was found that all of the binary phases
mentioned here have a certain stable domain as shown by the
single-phase lines in the figure. In addition, it is noted that the
CaSi , CaSi, and Ca Si have relatively larger stable single-phase
Ca–Si system at the lowest melting eutectic composition in Table 1.
o
It is shown that CaSi has the largest negative ꢀH of −15.6 kcal/g
atom. However, at the lowest temperature eutectic point (3.5 at%
Si), the limiting element is Si, and the Ca Si phase has the largest
2
ꢀ
negative ꢀH of −1.4 kcal/g atom. Thus, it is expected that Ca Si is
2
to be the first phase to form in the Ca–Si system.
During the normal Ca silicide formation, the effective concen-
tration at the growth interface is controlled by the lowest eutectic.
At this concentration, according to the EHF model, it can be seen
ꢀ
that Ca Si has the largest negative ꢀH and is expected to form
2
first as shown in Fig. 2. For thin Ca on thick silicon, all the Ca will be
consumed to form Ca Si, and the effective concentration moves to
2
the right side of the EHF diagram. According to the theory, Ca5Si3
2
2

C. Wen et al. / Journal of Alloys and Compounds 509 (2011) 4583–4587
4585
Table 1
o
ꢀ
Heats of formation (ꢀH ) and the effective heat of formation (ꢀH ) calculated for the lowest-melting eutectic composition for the Ca–Si system.
◦
ꢀ
◦
◦
◦
Phase
Composition
ꢀH
Limiting element
ꢀH (kcal/g at.)
ꢀH [14] (kcal/g at.)
ꢀH [15] (kcal/g at.)
ꢀH [16] (kcal/g at.)
(
kcal/g mol)
(kcal/g at.)
Lowest eutectic = Ca0.965Si0.035
CaSi2
CaSi
Ca5Si3
Ca2Si
Ca0.333Si0.667
Ca0.500Si0.500
Ca0.625Si0.375
Ca0.667Si0.333
−33.4
−31.1
−11.1
−15.6
−14.0
−13.1
Si
Si
Si
Si
−0.6
−1.1
−1.3
−1.4
−12.0
−18.0
–
−16.7
−9.0
−11.9
−13.2
−13.4
−12.0
−14.4
–
−16.7
−111.8
−39.2
ꢀ
formation should lead to the largest negative ꢀH until the effec-
tive concentration is about 65 at% Ca is reached. After complete
transformation of Ca Si to Ca5Si , the effective Ca concentration
by an external stress, because of the formation of CaSi2 phase with
trigonal–rhombohedral stacking sequence structure, as reported
previously [16]. On the other hand, Ca Si layers were successfully
2
3
2
at the growth interface further decreases to a concentration of less
than about 55 at% Ca, thus the CaSi formation is thermodynamically
favored. While after reaching 35 at% Ca, CaSi2 formation is favored.
To examine the phase selection during the Ca silicide formation
for the layered growth experimentally, selection of the substrate
material is important to obtain the Ca-silicide layered structure.
For the growth of Ca-silicide layers directly on Si substrates, the
resultant Ca-silicides were easily removed from the Si substrates
grown on Mg Si/Si substrates [16]. Thus, the Mg Si/Si substrates
were employed for the Ca-silicide layered growth.
2
2
Fig. 3 shows the cross-sectional SEM micrograph and the cor-
responding EDS analysis for the Ca Si/CaSi interface made by the
2
Ca-silicide layered growth. It is found that no evidence of the for-
mation of the Ca5Si3 phase is observed between the Ca Si and CaSi
2
layers.
As shown in Figs. 1 and 2, Ca5S3 is one of stable phases, though
the Ca5Si single-phase formation window is narrower than that of
3
the other phases. However, the un-formation of the Ca5Si3 phase
cannot be explained by the formation energy of each material.
In fact, it is possible to grow the Ca5Si3 phase as shown in
Fig. 4, which shows the SEM micrograph and the correspond-
ing EDS analysis for the particles of the resulting powders. The
powders are confirmed to be Ca5Si3 by the XRD spectrum in Ref.
[
19]. The morphology and the EDS analysis showed powder size of
about ∼200 ␮m and the compositionally homogeneous compound
is formed through the powders.
Even though the Ca5Si3 phase has a narrower growth window
as shown in Figs. 1 and 2, if the appropriate Ca and Si concentra-
tion ratio and the growth condition could be preferably chosen,
the Ca5Si3 single-phase compound can be successfully obtained,
as expected for the second nucleation phase in the EHF considera-
tion. For the powder growth, when the powder size is smaller, the
boundary condition is not fixed, and the composition of any part
of the powder can be maintained at the same composition, and the
composition of the powder is determined by the growth conditions.
On the other hand, not only Ca Si, but also the CaSi phase
2
was grown, and formation of the Ca5Si3 phase was skipped dur-
ing the experiment. The EHF consideration does not explain this
phenomenon, but might be explained as follows. For the layered
growth, the boundary conditions are always fixed, for example,
the Ca-silicide phases are formed between the Si substrate and
the deposited Ca. This growth condition causes the formation of
a layered structure with a distinct compositional gradient from the
substrate to the layer surface. The domains or substrates with 100%
Si always exist on one side of the reaction region. It is considered
that the Si rich silicide phases are formed when the Ca flux through
the silicide layers to Si layers (substrate) decreases. It would also
be possible that the second lowest eutectic affects the silicide for-
mation in the Si-rich region.
As already mentioned, the formation energy consideration can-
not explain the formation of the Ca Si/CaSi structure. The total
2
energy consideration consisting of the formation energy of each
phase and interfacial energy between two adjoining phases is pro-
posed to explain the formation of the structure. As shown in Fig. 3,
the Ca Si/CaSi interface is formed, while no formation of the Ca5Si3
2
phase is observed for the layered growth. The structure is schemat-
ically illustrated in Fig. 5(a).
ꢀ
Fig. 2. The effective heat of formation (ꢀH ) and phase diagram [28] for the Ca–Si
Assuming that a part of the Ca Si/CaSi interface region is trans-
2
system. Each triangle in the effective heat of formation diagram represents the
energy released as a function of the concentration during the formation of a par-
ticular calcium silicide phase.
formed into the Ca5Si3 phase, a Ca5Si3 layer with a thickness of
c = 1.46 nm (the largest lattice constant) between the Ca Si and CaSi
2

4
586
C. Wen et al. / Journal of Alloys and Compounds 509 (2011) 4583–4587
◦
Fig. 3. The cross-sectional SEM micrograph and the corresponding EDS analysis for the resulting layers grown at 600 C for 3 h.
regions is formed, as shown in Fig. 5(b). The phase transformation
reaction is shown as:
shown in the Fig. 5 table. The A1 and C1 layers are not listed, because
the internal energy is not changed for the cases whether or not
Ca5Si3 is formed.
2
Ca Si + CaSi → Ca5Si .
(6)
2
3
The sum of the internal energy deduced from the heat of for-
−
8
mation energy in each region, A2, C2 and B1, are −8.95 × 10
,
The number of Ca and Si atoms should be equal for both
cases shown in Fig. 5(a) and (b). Thus, the amounts of the sub-
−
8
−7
−3.55 × 10
and −1.28 × 10 kcal, respectively. Comparing the
−
7
internal energy for (a) E
(
= −1.25 × 10
kcal with that for
stances in each region should be nA2 (mol) = 2 × nB1(mol) and nC2
A2 + C2
−
7
b) EB1 = −1.28 × 10 kcal, the case (b) Ca Si/Ca5Si /CaSi structure
(
mol) = nB1(mol). Assuming the interface area of the layers is a unit
2
3
2
is more thermodynamically favored than the case (a) Ca Si/CaSi
area, namely, 1 cm , the calculated amounts of the substances are
2
◦
Fig. 4. SEM micrograph and the corresponding EDS analysis for the particles of the resulting powders grown at 750 C for 12 h.

C. Wen et al. / Journal of Alloys and Compounds 509 (2011) 4583–4587
4587
formed between the Ca Si and CaSi phases. On the other hand, the
2
single Ca5Si3 phase was formed during powder growth, and the
stoichiometry distribution of the Ca5Si3 is homogeneous through-
out the powders. In the calculation, the Ca Si phase has the largest
2
ꢀ
negative ꢀH with the value of −1.4 kcal/g atom at the lowest tem-
perature eutectic point (3.5 at% Si) and the first phase to form in
the Ca–Si system. The proposed phase selection model including
the potential energy and the additional interfacial energy success-
fully explains the experimental results, in which the Ca5Si3 phase
would not form between the Ca Si and CaSi layers.
2
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9
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−8
2
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7
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8
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= −8.93 × 10 kcal. The result suggests that the for-
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. Conclusions
Phase selection during calcium silicide formation was discussed
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