“ Thermodynamic and kinetic study of solid state reaction in the Cu-Si system” , R.R. Chromik,
W.K. Neils, and E.J. Cotts, Journal of Applied Physics, vol. 86, no. 8, p 4273-4281, Oct. 1999.
Thermodynamic and kinetic study of solid state reactions in the
Cu-Si system
R.R. Chromik, W.K. Neils and E.J. Cotts
Department of Physics, Binghamton University, State University of New York, Binghamton, New
York 13902-6016
Abstract
It has been shown that significant changes in the course of solid state reactions can be realized
by decreasing length scale, temperature, or by varying parent microstructures. In the case of the
formation of Cu3Si by interdiffusion of Cu and Si, previous research has shown that over a large
temperature range reaction rates are determined by the rate of grain boundary diffusion of Cu
through the growing Cu3Si phase. We have examined the effect of replacing crystalline Si with
amorphous Si (a-Si) on these solid state reactions, as well as the effect of decreasing the temperatures
and length scales of the reactions. Multilayered thin film diffusion couples of Cu and a-Si were
prepared by sputter deposition, with most average composite stoichiometries close to that of the
equilibrium phase Cu3Si. Layer thicknesses of the two materials were changed such that the
modulation (sum of the thickness of one layer of Cu and a-Si), λ, varied between 5 and 160 nm. Xray diffraction analysis and transmission electron microscopy analysis were used to identify phases
present in as prepared and reacted diffusion couples. Complete reactions to form a single phase or
mixtures of the three low temperature equilibrium silicides (Cu3Si, Cu15Si4 and Cu5Si) were observed.
Upon initial heating of samples from room temperature, heat flow signals were observed with
differential scanning calorimetry corresponding to the growth of Cu3Si. At higher temperatures (>
525 K) and in the presence of excess Cu, the more Cu rich silicides, Cu15Si4 and Cu5Si formed. Based
on differential scanning calorimetry results for samples with average stoichiometry of the phases
Cu3Si and Cu5Si, enthalpies of formation of these compounds were measured. Considering the
reaction of these phases forming from Cu and a-Si, the enthalpies were found to be –13.6±0.3 kJ/mol
for Cu3Si and –10.5±0.6 kJ/mol for Cu5Si. The growth of Cu3Si was found to obey a parabolic
growth law: x 2 = k 2 t , where x is the thickness of the growing silicide, k 2 is the temperature
dependent reaction constant, and t is the reaction time. Also, the form of the reaction constant, k 2 ,
was Arrhenius: k 2 = k$ exp(− Ea kb T ) with k b being Boltzmann’s constant and the pre-factor, k$ =
1.5x10-3 cm2/s, and activation energy, E a = 0.98 eV. These results indicate a much slower reaction to
form Cu3Si in thin film Cu/a-Si diffusion couples than indicated by previous researchers using mostly
bulk samples of Cu and crystalline Si (x-Si).
1
I. Introduction
The properties of metal silicides are of interest in a number of areas in applied science,
including catalysis, high temperature applications, and microelectronics1,2. The study of the
thermodynamics of the Cu-Si system aids in the development of a basic understanding of metalsilicon systems. Some Cu silicides, in particular Cu3Si, have shown promise as catalysts, with
clear evidence that the oxidation of silicon is catalyzed by Cu3Si3-6, and some evidence that Cu3Si
serves as an effective catalyst in other reactions7-9. In microelectronics, the use of Cu
metallization in VLSI applications depends upon the prevention of the formation of Cu
silicides1,10. When Cu is directly deposited on Si crystals, Cu3Si forms readily at moderate
temperatures11 (e.g. 470 K). To prevent the formation of silicides, a thin film diffusion barrier is
used1,10,12-13. An understanding of the kinetics and energetics of these reactions facilitates their
prevention. It has been speculated that a large driving force for the formation of Cu3Si results in
the formation of Cu3Si by transport through diffusion barriers1 although the heat of mixing of
Cu3Si has never been reported.
There have been a number of reports on the Cu-Si system that detail phase formation
sequences and reaction kinetics for bulk diffusion couples14-18, lateral diffusion couples19, and thin
film or thick film Cu on bulk crystalline Si11,20-26. There are many consistent aspects of these
previous reports. For example, it has been well documented that the first phase to form in the
system, in both bulk and thin film diffusion couples, is the orthorhombic η′′-Cu3Si phase. Also,
the growth kinetics of this phase have been characterized by five previous investigators over a
combined temperature range of 470 to 800 K15-19. All of these researchers found that the
formation of Cu3Si followed a parabolic growth law x 2 = k 2 t , where x is the thickness of the
Cu3Si layer, t is the time and k2 is the temperature dependent reaction constant. These results are
in reasonable agreement for the magnitude of the reaction constant, k2. The activation energies
observed by these investigators at temperatures below 740 K vary from 0.8 to 1.34. In the most
recent publication, Becht, et. al.15 reported an activation energy of 1.81 eV above a temperature
of 743 K, which they associated with a bulk diffusion mechanism. Table 1 summarizes the
previous studies, where the type of diffusion couple is indicated (bulk, lateral or thin film) and the
activation energy obtained for a given temperature range is shown.
This study has focused on examining the thermodynamics and kinetics of the formation of
the three low temperature Cu silicides: Cu3Si, Cu5Si and Cu15Si4 in sputtered, thin film
composites. We sought to examine the effect on solid state reactions of the different
microstructures presented by thin film Cu and amorphous Si (a-Si). Differential scanning
calorimetry (DSC)
was
used
to
Researcher
Diffusion
Temperature
Activation
monitor
the
Couple
Range (K)
Energy (eV)
growth
of
the
Cu
Hong, et. al.
Lateral
473-533
0.95±0.03
silicides in Cu/a-Si
Ward and Carroll
Bulk
523-623
1.01
thin film diffusion
Veer, et. al.
Bulk
615-795
0.81
couples.
X-ray
Becht, et. al.
Bulk
670-740
1.14
Bulk
740-920
1.81
diffraction analysis
Onishi and Muira
Bulk
683-735
1.34
was
used
to
examine the asTable I- Descriptions of the technique and results for previous investigations of the growth
prepared state of
kinetics of Cu3Si.
the
Cu/a-Si
2
multilayers and identify product phases in samples reacted in the differential scanning calorimeter.
Transmission electron microscopy was also available for imaging the thin films and obtaining
electron diffraction patterns.
II. Experimental
An examination of the Cu-Si phase diagram27, 28, shown in Fig. 1, is helpful in considering
the formation of Cu silicides at Cu/a-Si interfaces. There are three low temperature equilibrium
compounds that may form: Cu3Si (η′′), Cu15Si4 (ε) and Cu5Si (γ). The total stoichiometric range
(eight atomic percent) for these three compounds is rather narrow. The nearness in stoichiometry
of the equilibrium alloys makes an attempt to fabricate single-phase alloys more troublesome than
usual. Small errors in average stoichiometry of a composite may result in the formation of
significant amounts of secondary phases upon reaction to equilibrium.
Multilayer, thin film diffusion couples of Cu and a-Si were prepared by sputter deposition.
For this process, a sample chamber equipped with commercially available magnetron sputter guns
was evacuated to a base pressure of less than 3x 10-7 torr prior to sample preparation. To
facilitate the sputtering process, VLSI grade argon gas was flowed into the chamber. Using a
capacitance manometer for pressure measurements, the chamber pressure was set to 5 mtorr
during sample preparation. Sputtering rates were determined with calibrated quartz crystal rate
monitors. Using DC power for Cu and RF power for Si, the rates were set at 0.12 nm/s for Cu
and 0.09 nm/s for Si.
The modulation, λ (sum of the thickness of one layer of Cu and one layer of a-Si), and
stoichiometry of the Cu/a-Si multilayers were controlled by timed sequential deposition of each
material onto a NaCl substrate (5.1 cm
diameter disk). A range of stoichiometries was
used between 55 and 89 atomic percent Cu,
where some specific stoichiometries were
studied in more detail: Cu75Si25, Cu83Si17 and
Cu89Si11. For the two most Cu-rich
stoichiometries a single modulation was used
for each: 136 nm for Cu83Si17 and 196 nm for
Cu89Si11. In the case of the Cu75Si25 samples,
the modulation was varied between 5.2 and 160
nm.
To obtain freestanding films from the as
sputtered samples, the NaCl substrate was
dipped into de-ionized water. The thin film,
between 1 and 2 µm total film thickness and
containing between 14 and 200 individual
layers of Cu and a-Si (depending on λ), was
captured on filter paper and thoroughly rinsed
with de-ionized water and then semiconductor
grade acetone. The sample was then placed in
Figure 1- A sketch of the Cu-Si equilibrium phase diagram.
an oven with a dry nitrogen atmosphere set at There are three low temperature silicide phases: Cu3Si (η″),
308 K. After drying for one hour, the sample Cu15Si4 (ε), Cu5Si (γ).
was removed from the oven and cut into
3
smaller pieces for easy handling in preparation for x-ray diffraction analysis and differential
scanning calorimetry.
A portion of each sample was examined using x-ray diffraction analysis. The experimental
set up consisted of an x-ray diffractometer operating in a standard θ-2θ geometry. The radiation,
produced from a Cu anode, was filtered with a Ni foil. The resulting x-rays were primarily CuKα radiation. All Bragg peaks associated with the crystalline metals and alloys of this study are
indexed for Cu-Kα radiation with an average wavelength of 0.15418 nm .
As the sample was cut up to perform x-ray diffraction analysis, it was also prepared for
heating in a differential scanning calorimeter. Trimmed portions of the diffusion couple were
stacked into an Al pan. Typical sample masses were between 1.2 and 3.5 mg (six or more DSC
samples were available from an as-prepared thin film). Once massed, each sample was
hermetically sealed in the Al pan in an Ar atmosphere of 10 kPa. Samples were then heated in a
commercially available differential scanning calorimeter at either 10 or 20 K/min. The upper
temperature, where an anneal was performed (10-20 minutes), was between 600 and 650 K. A
scan of this type was performed three times consecutively on each sample. To obtain the signal
associated with solid state reactions taking place in the diffusion couple, the third run was
subtracted from the first.
III. Results and Discussion
A. X-ray diffraction analysis
We first present results of the structural analysis of Cu/a-Si multilayered composites after
high temperature anneals. The formation of Cu silicides is confirmed by means of x-ray diffraction
of the samples after cooling, and considered in the context of previous investigations that
generally report the initial growth of Cu3Si at the Cu/Si interfaces. The results provide an
indication of the phase formation sequence that is elucidated when the calorimetry results are also
considered.
X-ray diffraction profiles for different Cu/a-Si composites after annealing at high
temperature (600 – 650 K) are shown in Fig. 2. The x-ray diffraction profile for an Si rich sample,
Cu55Si45, is displayed in Fig. 2(a), while the average stoichiometries of the samples in Fig. 2(b)
through 2(d) are Cu74Si26, Cu76Si24, and Cu83Si17, respectively. Each different composite was
heated to 600 K or above, and annealed for between ten and twenty minutes. After cooling to
room temperature, x-ray diffraction analysis was performed. The results of Fig. 2 are typical of
those observed for a number of different samples after heating to high temperatures.
4
Analysis of the x-ray
diffraction profiles of Fig. 2(a-d)
indicate that the phases formed in a
Cu/a-Si composite upon solid state
reaction to high temperature are
consistent with the equilibrium
phases corresponding to the average
stoichiometry of the composite.
Considering each of these phases in
turn, we examine the most Si rich
equilibrium phase, Cu3Si, first.
There
have
been
numerous
crystallographic reports on the
structure of Cu3Si29-32. The most
recent report29 summarizes the
existing work and provides a basis
for identifying the Cu3Si phase
despite the existence of an
orthorhombic
superstructure31:
a=7.676 nm, b=0.700 nm, c= 2.194
nm. Myers and Follstaedt29 point
out that the majority of the lines
observed in a diffraction profile (xray or electron) for Cu3Si can be
indexed to a smaller hexagonal
Figure 2- X-ray diffraction data for Cu/a-Si multilayers after heating in
lattice (a= 0.404 nm and c = 0.244
a differential scanning calorimeter (DSC) to high temperature (600-650
nm)
contained
within
the
K). These profiles are for samples of different average stoichiometries,
superlattice. Table 2 summarizes the
where the Cu content increases from top to bottom: (a) Cu55Si45, (b)
Cu74Si26, (c) Cu76Si24, and (d) Cu83Si17. Where appropriate, peaks are
d spacings that were observed for
indexed to equilibrium Cu silicide phases.
Cu3Si grown in our thin film
diffusion couples and compares our results to those found in Ref. 29. Figs. 2(a and b) indicate that
for stoichiometries of 75at% Cu and less, Cu3Si is the phase formed, as expected from the Cu-Si
phase diagram (c.f. Fig. 1). The third x-ray diffraction profile of Fig. 2(c) is typical of that for a
sample of intermediate composition between the equilibrium phases Cu3Si and Cu15Si4. Using a
calculated pattern based on an experimental study33,34, peaks in this scan are indexed to the cubic
structure of Cu15Si4. Bragg peaks identified with the Cu3Si are also observed in the scan of Fig.
2(c), as would be expected for the average composite stoichiometry. The x-ray diffraction profile
of Fig. 2(d), for a composite of average stoichiometry Cu5Si and λ = 136 nm, can be readily
indexed. The intensity and angles of the observed Bragg peaks are consistent with the equilibrium
Cu5Si phase.
5
Chromik, Neils and Cotts
Hexagonal Sublattice,
Cu3Si
Myers and Follstaedt
3.54
3.50 (10 1 0)
3.50 vw
3.19
2.68
2.45
2.34
2.13
2.09
2.07
2.03
3.24 vw
2.44 (0001)
2.02 (11 2 0)
2.54
2.45 w
2.31 w
2.12 m
2.02 st
2.00 (10 1 1)
1.95
1.83 w
1.79 w
1.76
1.75 (20 2 0)
1.59
1.56 (11 2 1)
1.43
1.42 (20 2 1)
1.43 m
1.23
1.17
1.22 (0002)
1.22 w
1.17 m
1.17 (30 3 0)
1.01
Table II- A collection of the d-spacings observed for the Cu3Si phase (η′′) by this group and a report by Myers and
Follstaedt. All entries are in units of 10-10 m.
The x-ray diffraction data of Fig. 3 reflect structural changes in Cu/a-Si composites upon
initial heating from room temperature. The data in Fig. 3 are for a Cu5Si composite in the asprepared condition, Fig. 3(a), and for similar samples after heating at 20 K/min to a temperature
of 465 K, Fig. 3(b), and to a temperature of
545 K, Fig. 3(c). New Bragg peaks observed in
these x-ray diffraction profiles after the samples
were heated can be identified with the Cu3Si
phase. Present in all three profiles are also five
Bragg reflections from crystalline Cu. For the
sample heated to 545 K, there is a peak at
44.58 degrees, which is indexed to the most
intense reflection for Cu3Si from the hexagonal
sublattice (11 2 0) 29. For the profile of the
sample heated to 465 K, this same reflection for
Cu3Si is also evident as a shoulder next to the
(111) reflection for Cu. The results of the x-ray
diffraction studies are consistent with the
Figure 3- X-ray diffraction data for a Cu/a-Si multilayer
observation that Cu3Si grows first in these
(Cu83Si17 average stoichiometry): (a) as prepared, (b) heated to
composites.
465 K, (c) heated to 545 K. Peaks are indexed to crystalline
Cu (appearing in all of the profiles here) and the silicide phase
Cu3Si.
6
B. Calorimetry
A calorimetric examination of the
course of solid state reactions in Cu/a-Si
multilayers in conjunction with x-ray
diffraction studies provides a clear indication
of the phase formation sequence of different
Cu-silicides. Analysis of the calorimetric data
provides a quantitative characterization of the
growth kinetics of Cu3Si in our composites.
We find that the general nature of the reaction
depends upon the individual layer thickness.
For Cu/a-Si multilayers with larger
Figure 4- A collection of plots of heat flow per unit
values of λ, the general course of solid state interfacial area versus temperature (measured using
reactions in Cu/a-Si is illustrated in Fig. 4. differential scanning calorimetry) for Cu/a-Si multilayers of
Distinctly different behaviors are seen in different stoichiometries that were heated from room
temperature. The average stoichiometry of the samples
calorimetric investigations of composites for λ becomes more Cu rich from top to bottom: (a) Cu55Si45 and λ=
values significantly less than 30 nm (as seen 142 nm, (b) Cu75Si25 and λ = 66 nm, (c) Cu76Si24 and λ= 96
below). The plots of heat flow (normalized nm, and (d) Cu83Si17 and λ = 136 nm. Various peaks in the
by the interfacial area of a particular heat flow are labeled and have been attributed to either Cu
silicide formation or the recovery of disordered Cu3Si. A
composite) versus temperature in Fig. 4 are vertical line marks the beginning of an isotherm at 600 K.
for four samples of different average
stoichiometries and values of λ (Fig. 4(a) –
Cu55Si45 and λ= 142 nm, Fig. 4(b) - Cu75Si25 and λ = 66 nm, Fig. 4(c) - Cu76Si24 and λ= 96 nm,
and Fig. 4(d) - Cu83Si17 and λ = 136 nm). The composites were heated at a constant rate of 10
K/min from a temperature of 300 K to 600 K, where they were annealed for 300 s. These data
reveal common features of solid state reactions in Cu/a-Si diffusion couples.
The initial growth of Cu3Si at the Cu/a-Si interfaces dominates the low temperature
calorimetry data for composites with larger values of λ. Upon heating such a Cu/a-Si composite
(30 nm < λ < 200 nm), a heat flow signal is first observed at a temperature of about 350 K (Fig.
4). The reaction rate tends to increase with increasing temperature, reaching a maximum at a
temperature close to 510 K (e. g. peak A in Fig. 4, the peak temperature depends upon the values
of heating rate and λ). The x-ray diffraction analysis that we presented in Figs. 2 and 3 indicates
that this main calorimetry peak (peak A) corresponds to the formation of Cu3Si, consistent with
previous studies of this system. We find that the other peaks (B, C and D in Fig. 4) correspond to
different physical transformations.
Calorimetry peaks observed at higher temperatures (peaks B and C in Fig. 4) are identified
with the formation of the more Cu rich equilibrium Cu-Si compounds. A clear example is
provided in Fig. 4(d), a plot of heat flow versus temperature for a composite of average
stoichiometry Cu5Si. The main calorimetry peak (labeled A) has been correlated with the
formation of Cu3Si. X-ray diffraction data for this sample of average stoichiometry Cu5Si after
cooling to room temperature revealed evidence of the equilibrium Cu5Si phase; thus we identify
the higher temperature calorimetry peak (peak B) with the formation of Cu5Si. The second peak
(labeled C) in the calorimetry scan of Fig. 4(c) generally appears only for compositions between
Cu3Si and Cu5Si, i.e. close to that of the equilibrium composition, Cu15Si4. X-ray diffraction
7
analysis (c.f. Fig. 2(c)) of samples exhibiting
peak C provided identification of the phase
Cu15Si4 . Thus, we attribute this calorimetry
signal (peak C) to the growth of Cu15Si4 .
The high temperature calorimetry
peaks which we have identified with the
formation of Cu rich, equilibrium Cu-Si
compounds are sometimes observed at
significantly smaller amplitude in plots of heat
flow versus temperature for Cu3Si
composites, depending on values of heating
rate and modulation (λ). Higher heating rates
or larger values of λ tend to result in larger
amplitudes of the heat flow peaks observed at
higher temperature peaks for Cu3Si
composites (Fig. 5). We interpret the
occurrence of these higher temperature peaks
in Cu3Si composites (which we have linked to
the formation of Cu rich compounds) as
resulting from the lack of a complete reaction
of the Cu and a-Si layers to form Cu3Si before
the nucleation temperature of the remaining
phases occurs. These additional peaks may
also be due in part to small errors in layer
thicknesses.
A small, additional heat flow peak
Figure 5- Two sets of plots of the heat flow versus
temperature for samples of average stoichiometry Cu3Si and
λ= 160 nm. Two portions of each sample were heated at 10
K/min (dotted line) and 20 K/min (solid line). A vertical
line marks the beginning of an isotherm at 600 K.
[labeled peak D, clearest in Fig. 4(a) and (c)] is
generally observed at a temperature of about
430 K, although with varying amplitudes as can
be seen in Fig. 4. This peak corresponds to a
relatively small enthalpy release, between 0 and
-0.5 kJ/mol, as opposed to the magnitude of the
large peak (peak A), which is approximately 10 kJ/mol. No new Bragg peaks are found in xray diffraction profiles of samples heated to a
temperature just above this calorimetry peak
(peak D) and cooled to room temperature (c.f.
Fig. 3(b)). In the following discussion, an
examination of reactions in composites of
different values of λ is used to connect this
small calorimetric signal with the recovery of
disordered, 7 nm thick layers of Cu3Si existing
at the Cu/a-Si interfaces before reaction in the
calorimeter.
Figure 6- Three plots of heat flow versus temperature
measured by differential scanning calorimetry for samples with
average stoichiometry Cu3Si and (a) λ= 5.2 nm, (b) λ= 10 nm,
and (c) λ= 32 nm.
8
The nature of solid state reactions observed in Cu/a-Si composites prepared with smaller
values of λ was found to be different than those of larger modulation. Upon heating a Cu/a-Si
composite (λ 30 nm), calorimetry data revealed traces similar to those observed for the
recovery of a disordered phase35-37 rather than a composite reacting by nucleation and growth of a
new phase. To illustrate these points, the heat flow versus temperature is plotted in Fig. 6 (a) (c) for composites of Cu3Si stoichiometry and values of λ equal to 5.2, 10 and 32 nm,
respectively, that were heated at 10 K/min. The peaks are relatively small compared to those in
Fig. 4, and the first peak is now at 450 K or below. Distinct peaks are observed at higher
temperatures, as observed for the recrystallization of alloys with a high density of defects.
C. Structural Characterization of Cu/a-Si Multilayers
Because of the energetic nature of sputter deposition, one expects that there may be
interdiffusion at the Cu/a-Si interfaces in a multilayered sample during deposition. Growth of an
interlayer (sometimes amorphous) in as prepared sputtered thin films has been observed before for
other metal-silicide systems38-40. This interlayer, whatever its composition, changes the initial state
of the sample from the ideal situation of two pure elements. The existence of such an interlayer is
consistent with the calorimetry observations for λ 30 nm.
To confirm our interpretation of the calorimetry data for the small modulation samples we
conducted a transmission electron microscopy investigation of such samples. For instance, a Cu/aSi composite of smaller modulation length (λ = 10 nm) and total film thickness 70 nm was floated
off of the NaCl substrate, rinsed with deionized water, placed on a Cu grid, and examined by
means of transmission electron microscopy. Electron diffraction and bright field transmission
electron microscopy were performed on this sample in plane view. The sample was
polycrystalline with grain size on the order of 10 nm. Electron diffraction results revealed rings
that were indexed to the Cu3Si phase.
The indication is that a layer of Cu3Si forms at the Cu/a-Si interfaces during sample
fabrication. The x-ray diffraction results indicate that this phase is highly disordered. If a high
density of defects were found in the alloy,
the recovery process in this phase upon
heating could account for a small,
exothermic reaction. Given these facts
and the calorimetry results for small λ
value samples, we conclude that the peak
at approximately 430 K in calorimetry
scans for thicker layered composites
(peak D in Fig. 4) corresponds to the
recovery of disordered Cu3Si found at the
Cu/Si interfaces. This conclusion is
further substantiated with an investigation
of the dependence upon λ of the
integrated enthalpy release (section D).
Figure 7- Low angle x-ray diffraction results for two Cu/a-Si
Despite the apparent existence of multilayers of Cu3Si stoichiometry and (a) λ= 100 nm, and (b) λ= 23
an interlayer in the Cu/a-Si diffusion nm.
couples, low angle x-ray diffraction
9
shows that samples are typically well layered structures. Figure 7 displays the data obtained for
low angle x-ray diffraction experiments performed on Cu/a-Si multilayers with Cu3Si
stoichiometry and two different modulations: λ= 100 nm [Fig 7(a)] and λ= 23 nm [Fig 7 (b)].
The existence of many distinct peaks at low angle indicates a layered structure for our thin films.
Simulations of the low angle spectra for the two samples of Fig. 7 were carried out using
commercially available software. The simulations, which included a 4 nm thick interlayer of
Cu3Si, are in qualitative agreement with the data obtained for both samples of Fig. 7. The
indication from the simulations is that the interfacial roughness in our samples is at most 1.0 nm.
The consistency of the layered structure and interface quality is also reflected in
differential scanning calorimetry data. If we assume relatively smooth interfaces in our
multilayers, then our corresponding calorimetry data should scale directly with interfacial area.
However, we note that processes such as recovery and recrystallization (labeled D in Fig. 4) that
are not occurring at an interface should not scale directly with the interfacial area of the diffusion
couple. In Fig. 8, we plot the heat flow per interfacial area, measured by differential scanning
calorimetry, versus temperature for samples with three different modulations: 160 nm (solid line),
86 nm (long dash) and 66 nm (short dash). For three separate samples with three distinctly
different values of layer modulation, λ, the signal associated with the growth of Cu3Si scales with
the interfacial area.
At the lowest
temperatures (less than 410 K) in Fig. 8,
we see good agreement between heat flow
data for the three different samples.
However, the low temperature peak
centered at approximately 420 K that was
associated with a recovery process does
not scale well with interfacial area. At
higher temperatures (440-470 K) the traces
of Fig. 8 once again scale well with
interfacial area, in a temperature range
where we observed solid state reactions to
form Cu3Si. The indication from low angle
x-ray diffraction and this examination of
Figure 8- A set of differential scanning calorimetry data (heat
the calorimetry data is that our samples are
flow per unit interfacial area versus temperature) for samples
with average stoichiometry Cu3Si and three different
layered structures with well defined
modulations: λ= 160 nm (solid line), λ= 96 nm (long dash), and
interfacial area. This conclusion allows us
λ= 86 nm (short dash). A vertical line marks the beginning of an
to examine the kinetics of formation of
isotherm at 600 K.
Cu3Si (section E).
10
D. Enthalpy of Formation for Cu3Si
Measurements of the heat of formation as a function of modulation length also indicate
significant premixing at the Cu/a-Si interfaces. For a determination of the enthalpy of formation of
Cu3Si from Cu and a-Si, multilayer samples were prepared with the average stoichiometry of this
phase. A variety of modulations were used, ranging from 5.2 to 160 nm. Figure 8 is a plot of
heat flow, measured by differential scanning calorimetry, versus temperature for samples with
three different bilayer thicknesses: 160 nm (solid line), 86 nm (long dash) and 66 nm (short dash).
If an interlayer forms in as-prepared sputtered thin films, the amount of enthalpy obtained
upon reacting a multilayer should vary with the modulation, λ. When sample preparation
conditions (pressure, sputtering power and rates, etc.) are kept the same, the interlayer will be
approximately the same thickness in every sample, independent of λ For values of λ greater than
2λο (twice the thickness of the interlayer), the relation of a measured heat of formation to the
modulation may be written as38,41:
2 λ $ ∆ H gd
∆ H = ∆ H$ −
(1)
λ
where ∆Ho is the heat of formation with an absence of an interlayer, ∆H gd is the heat of
formation of the interlayer.
Fig. 9 is a plot of the absolute value of the measured heat of formation, ∆H , versus
inverse bilayer thickness, λ-1, for the formation of Cu3Si from thin film Cu/a-Si diffusion couples.
As expected, the heat of formation that was determined using differential scanning calorimetry is
not a constant with respect to λ. In this plot, there is a range of values of λ-1 (0.005 to 0.05 nm-1)
which was well studied. In this range, ∆H was found to vary linearly with λ-1, consistent with Eq.
1. However, for shorter modulations than
defined by this range, ∆H was observed to
be a constant. From linear fits to the data
in the two regions (c.f. Fig. 9), a bulk heat
of formation, ∆Ho, was determined and an
estimate of the thickness of the interlayer,
λo, in as prepared diffusion couples. The
interlayer thickness, λo (~ 7 nm), is taken
from the intercept of the two linear fits
shown in Fig. 8. The bulk heat of
formation of Cu3Si from Cu and a-Si, from
the y-intercept of the fit to the data of
greater values of λ, was found to be -13.6
± 0.3 kJ/mol.
Figure 9- A plot of the measured enthalpy of formation of Cu3Si
from Cu and a-Si versus the inverse modulation, λ-1. At larger
An estimate of the heat of
lambda, the enthalpy varied linearly with inverse modulation. At
formation for the reaction 3Cu + x-Si
smaller modulations (below 15 nm), the enthalpy was found to be
Cu3Si, where x-Si denotes crystalline
a constant. From the y-intercept (λÆ∞) of the large lambda fit,
the enthalpy of formation of Cu3Si from Cu and a-Si was found to
silicon, is performed based upon the results
be -13.6±0.3 kJ/mol. The intercept of the two fits provides an
and previous measurements of the
estimate of the thickness of the intermixed layer (≈ 7 nm) at the
crystallization enthalpy of a-Si. Many
Cu/a-Si interfaces in our thin film multilayers.
Æ
11
measurements of the heat of crystallization,
∆Hx , of a-Si are available42-44. Using a
value of ∆Hx = -11.6±0.4 kJ/mol which is
based on a set of measurements from this
group, we estimate the heat of formation
of Cu3Si from Cu and x-Si to be –10.7
±0.3 kJ/mol. While ours is apparently the
first measurement of the heat of formation
of Cu3Si, we can compare our result with a
previous theoretical estimate of this
quantity, ∆H = -2.7 kJ/mol45. Similar
disparities between estimates and actual Figure 10- A plot of the enthalpy of formation of of Cu silicides
measurements have been observed in many versus atomic percent Si. Enthalpies of formation from Cu and xSi for two equilibrium phases (Cu3Si and Cu5Si) are shown on this
metal-Si systems in the past.
plot and a determination for the Cu rich stoichiometry Cu89Si11.
Measurements of the enthalpies of The lines for equilibrium phase mixtures between Cu and x-Si
formation for other Cu silicides were also (solid line) and Cu and a-Si (dashed line) are also plotted here.
made. Two stoichiometries other than
Cu83Si17 and
Cu75Si25 were chosen:
Cu89Si11. The first of these corresponds to the stoichiometry for the equilibrium silicide phase
Cu5Si. The second lies in a region where a complete reaction to equilibrium would result in a
phase mixture of Cu5Si and excess Cu. A high temperature phase does exist that is more Cu rich
than Cu5Si (c.f. Fig. 1), but the lower phase boundary for this phase is higher in temperature than
the range of our experiments. Measurements of the enthalpy of formation at these two
stoichiometries were done using only one value for the sample modulation for each stoichiometry:
136 nm for Cu83Si17 and 196 nm for Cu89Si11. Thus, the correction for the defective Cu3Si at the
interfaces of the diffusion couples was determined using the results of the Cu3Si investigation.
With this correction achieved, the enthalpy of formation for bulk Cu5Si forming from Cu and a-Si
was found to be –10.5±0.6 kJ/mol. In the two-phase region (Cu89Si11) the enthalpy of formation
was found to be –7.5±1.2 kJ/mol. These two points along with the determination for Cu3Si are
plotted in Fig. 10 as the enthalpy of formation versus atomic percent Si. The solid, horizontal line
in Fig. 10 represents a phase mixture between crystalline Cu and crystalline Si, while the dashed
line represents a phase mixture between crystalline Cu and amorphous Si. The points in Fig. 10
are values for the enthalpy of formation of these alloys and phase mixtures from Cu and x-Si, i.e.
–6.2±1.0 kJ/mol for Cu89Si11 and -8.6±0.5 kJ/mol for Cu5Si.
E. Growth Kinetics for Cu3Si
The reaction kinetics for the formation of Cu3Si from Cu/a-Si diffusion couples were
investigated using differential scanning calorimetry. This technique utilizes our measurement of
heat flow and the planar geometry of our diffusion couples to provide a direct calculation of
reaction constants for any temperature during a DSC heating curve. These calculations are
accomplished using the relation of the heat flow to the reaction rate for planar, one-dimensional
growth46:
A ρ ∆H dx
dH
=
(2)
dt
M dt
12
where A is the interfacial area, ∆H is the heat of reaction, and ρ and M are the density and molar
mass of the growing silicide. For the case where the growth of the silicide is diffusion controlled
the thickness of the silicide, x follows a parabolic growth law:
dx k 2
(3)
=
dt 2 x
where t is the time and k2 is the temperature dependent reaction constant. Thus, with diffusion
limited growth assumed or independently verified, a reaction constant may be determined by
integrating Eq. 2 with respect to time and combining the result with Eqs. 2 and 3 to yield:
2
 M 
dH
 H
k = 2 
(4)
dt
 A ρ ∆H 
Reaction constants for the growth of Cu3Si in the temperature range of 450-500 K were
determined from heat flow data using Eq. 4. In general, one expects that the temperature
dependence of the reaction constant is Arrhenius, indicating thermally activated growth:
2

k 2 = k $ exp − Ea
(5)
k b T 

where k b is Boltzmann’s constant, E a is the activation energy and ko is the pre-factor.
Fig. 11 is a plot of the logarithm of the reaction constants measured as described above
versus inverse temperature. Four sets of data are provided in this graph for three of which are for
samples of Cu3Si stoichiometry of different modulations: 86 nm (q), 96 nm (c) and 160 nm (°).
The last set contained in Fig. 11 are reaction constants calculated from linear fits to portions to
isothermal DSC data (plotted as &). These
measurements of the reaction constant, k2,
from isothermal data are in good
agreement with those determined from
constant heating rate data. They also
provided a verification of diffusion limited
growth that was assumed for the
determinations of k2 from constant heating
rate data. From numerous fits to data of
reaction constants from samples with
modulation of λ > 66 nm, the best
determination of the pre-factor and
activation energy is kο= 1.5x10-3 cm2/s and
E a = 0.98 eV.
2
Figure 11- A plot of the logarithm of the reaction constant, k ,
Some of the previous work
versus inverse temperature times one thousand for three different
suggests that at temperatures below 750 K
samples of average stoichiometry Cu3Si and modulation: 86 nm (q),
grain boundary diffusion is generally the
96 nm (c) and 160 nm (°) and one of Cu5Si stoichiometry and λ=
136 nm (&). The data plotted as hollow symbols is the average of
dominant growth mechanism of Cu3Si in
reaction constants determined from five or more separate DSC
Cu/Si diffusion couples15. Fig. 12 is an
experiments (constant heating rate data) on a given sample. The
Arrhenius plot of the reaction constants
solid symbol data is from linear fits to plots of H2 versus t for
isothermal portions of DSC scans. For clarity, error bars are shown
measured here and those determined by
for the 160 nm modulation (°) only.
other investigators10-12,16. Becht et. al.
13
observed a distinct change in the activation
energy of the reaction process from 1.1
eV/atom to 1.8 eV/atom at a temperature of
743 K. Based upon this observation and
changes in sample morphology they
concluded that bulk diffusion was the
dominant growth process at the highest
temperatures, with grain boundary diffusion
dominant below 743 K. In diffusion couples
of Si and phosphorus-doped Cu (one atomic
percent P), results at high temperature were
similar, but the apparent grain boundary
diffusion
mechanism
dominated
at
temperatures up to 803 K, with a larger
reaction constant observed, and a slightly
different activation energy (0.94 eV/atom).
The values of k2 reported by other
investigators generally are in the range of the
values
(or
their
low
temperature
extrapolation) reported by Becht et. al.
Becht considered most of the data of the
previous investigators plotted in Fig. 12, and
concluded that these reflected a grain
boundary diffusion mechanism.
The magnitude of the reaction
Figure 12- An Arrhenius plot (logarithm of the reaction
constant versus inverse temperature) of the results of many
constants for the formation of Cu3Si in our
investigations of the growth of Cu3Si: this work (q), Hong,
thin film Cu/a-Si diffusion couples were
et. al. (c), Veer, et. al. (°), Ward and Carroll (♦), Onishi
found to be about three orders of magnitude
and Miura (), and Becht, et. al. (y) [see Refs. 15-19]. The
lines on this plot were taken from the three forms of the
smaller than previously observed in
reaction constant for different diffusion mechanisms found
neighboring or overlapping temperature
by Becht, et. al.: bulk, grain boundary (with and without
ranges. The activation energy we observed,
phosphorous impurities).
E a = 0.98 eV, was similar to those observed
by other investigators (c.f. Table 1). It should be noted that the order of magnitude of the reaction
constants we observed is close to those of an extrapolation of the curve which Becht, et. al.
identified with bulk diffusion. Apparently, the microstructure of the Cu3Si grown from a-Si and
sputtered Cu does not afford the high rates of grain boundary diffusion observed in samples of
Cu3Si grown from crystalline Si and single crystal Cu. These results are consistent with previous
results in the sense that grain boundary diffusion is often sensitive to sample morphology. It is
surprising that a small grained sample such as those typically prepared by sputtering would have
lower grain boundary diffusion rates than larger grained, bulk samples. Our lower values of
reaction constant may be due to the disordered nature of the Cu3Si layer that grows over these
length scales. Also, no preferred orientation of crystallites was found in our Cu3Si layers, so that if
certain grain boundaries provide short circuits for diffusion these are not available in any
continuous paths.
14
IV. Conclusions
We determined the heat of formation of Cu3Si from a-Si and Cu to be -13.6 kJ/mol and
calculated the heat of formation of Cu3Si forming from x-Si and Cu to be -10.7 kJ/mol. We
observed the reaction sequence in Cu/a-Si composites upon heating from room temperature. We
found that Cu3Si forms first at room temperature, but the other equilibrium silicides, Cu15Si4 and
Cu5Si would form at higher temperatures when the supply of Si was depleted. Reaction constants
for the formation of Cu3Si were reported and compared to previous measurements. We found that
by the variation of the microstructure afforded by sputter deposition that distinctly slower (3
orders of magnitude) growth for Cu3Si was afforded than in the case of bulk diffusion couples.
Acknowledgements
We gratefully acknowledge the support of the National Science Foundation, DMR-9202595
and DUE-9452604, and the Integrated Electronics Engineering Research Center (IEEC) located
in the Watson School at Binghamton University. The IEEC receives funding from the New York
State Science and Technology Foundation, the National Science Foundation and a consortium of
industrial members.
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