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BULLETIN OF THE POLISH ACADEMY OF SCIENCES
TECHNICAL SCIENCES, Vol. 61, No. 2, 2013
DOI: 10.2478/bpasts-2013-0050
Comparison of experimental and modelling results
of thermal properties in Cu-AlN composite materials
M. CHMIELEWSKI1∗and W. WEGLEWSKI2
1Institute of Electronic Materials Technology, 133 Wolczynska St., 01-919 Warsaw, Poland
2Institute of Fundamental Technological Research, 5B Pawińskiego St., 02-106 Warsaw, Poland
Abstract. Copper-based composites could be widely used in automotive, electronic or electrical industry due to their very promising thermal
properties. In the present paper, Cu-AlN metal matrix composites with ceramic volume fractions between 0.1 and 0.4 were fabricated by hot
pressing method in vacuum. Dependence of the coefficient of thermal expansion (CTE) and the thermal conductivity (TC) on the chemical
composition of composites has been investigated. The measured values of the thermal expansion coefficient have been compared with the
analytical models’ predictions. A numerical model based on FEAP 7.5 in 3D space has been used to evaluate the influence of the porosity
on the thermal properties (thermal conductivity) of the composite. A fairly good correlation between the FEM results and the experimental
measurements has been obtained.
Key words: thermal properties, porosity, copper-based composites.
1. Introduction
Microelectronic circuits require contact with a high thermal
conductivity as well as controlled low coefficients of thermal
expansion of heat-sink materials to remove the heat generat-
ed during their working period [1]. The fulfillment of these
requirements by conventional materials is practically impossi-
ble. MMCs are most widely used in electronic packaging due
to their unique properties combining a high thermal conduc-
tivity (due to the metal matrix) and a low coefficient of ther-
mal expansion (due to the ceramic reinforcement). Such com-
bination allows designing new materials with a wide range
of thermal properties. Many studies were devoted in the past
to the design and fabrication of advanced materials charac-
terized by a very good thermal conductivity, such as Cu-Mo,
Cu-Be, Cu-Cf, SiC-Cu, SiC-Al, AlN-Al [2–3] and, more re-
cently, AlN-Cu composite materials [4–8]. The latter mate-
rial is a particularly attractive candidate for application as
a heat dissipation material. Aluminium nitride has advanta-
geous mechanical and electrical properties and a low thermal
expansion coefficient (4.0×10−61/K) close to that of sili-
con (2.7×10−61/K), which prevents high residual thermal
stresses induction [7]. This property is crucial since the fail-
ure of electronic devices takes place most frequently due to
high residual stresses induced as a result of the mismatch be-
tween the thermal expansion coefficients of a substrate and a
semiconductor component. The thermal conductivity of poly-
crystalline aluminium nitride is slightly below 200 W/mK.
Copper with a thermal conductivity of about 400 W/mK is
used whenever both high thermal and electric conductivities
are required, but the application range of this material is lim-
ited because of its unsatisfactory mechanical properties, es-
pecially at elevated temperatures. Moreover, the high thermal
expansion coefficient of copper (16.5×10−61/K) may re-
sult in considerable residual stresses induction and in thermal
dilatation occurring when copper components are subject to
substantial temperature variations.
With regard to the fabrication of Cu-AlN composites there
are not too many works reported in the literature [8, 9]. The
authors of [8] employed a hot pressing method to obtain Cu-
AlN composite materials at 1050◦C. They used presintered
AlN-Y2O3grains (75–150 µm) after the pulverization process.
Using higher temperatures is limited by the melting point of
copper (1083◦C) and lack of wettabillity of aluminium ni-
tride by liquid copper [9]. This disadvantage can be changed
by modifying of ceramic substrate by different techniques like:
ion implantation or ion beam treatment [10–13]. In [14] the
spark plasma sintering (SPS) process was applied to obtain
functionally graded materials containing Cu-AlN composite
layers.
Some properties of composite materials can be deter-
mined using numerical modelling, replacing often cumber-
some and costly experimental tests [15]. Modelling was use-
ful for the prediction of the most significant properties in the
early stages of the material technology design process. On the
other hand, by means of experimental testing one is able to
verify the assumptions of proposed theoretical models. There-
fore, theoretical modelling and experimental measurements
are complementary and help to understand the correlations
between the theory and practical aspects of real materials
analysis.
The objective of this paper is: (i) to manufacture Cu-AlN
metal matrix composite materials using a hot pressing method
in vacuum, (ii) to characterise its microstructure and measure
thermo-mechanical properties (CTE, TC) depending on the
volume fraction of the components, and (iii) to develop and
∗e-mail: marcin.chmielewski@itme.edu.pl
507
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M. Chmielewski and W. Weglewski
verify numerical models capable of predicting the thermal
conductivity for the manufactured Cu-AlN composites.
2. Experimental procedure
Copper powder (average grain size 40 µm) with a commercial
purity of more than 99.99% was used as the metal matrix.
Aluminium nitride particles of a mean size of about 2 µm
strengthened the copper matrix. Figure 1 shows the powders
used in the experiments.
a)
b)
Fig. 1. SEM images of starting materials aluminium nitride (a) and
copper powder (b)
The Cu-AlN composite materials with volume fractions
of AlN varying from 0.1 to 0.4 were prepared by a powder
metallurgy process. The powder mixtures were obtained in a
mechanical mixing process using a planetary ball mill (Pul-
verisette 6, Fritsch) with tungsten carbide balls (∅10 mm).
The mixing process was conducted in a N2atmosphere with
the rotational speed of 200 rpm and the time of mixing was
4 h. Ball–to–powder ratio (BPR) was approximately 5:1. Pre-
sented mixing conditions were selected after the preliminary
tests described in papers [16, 17]. The morphology of the
obtained powder mixtures is presented in Fig. 2.
a)
b)
c)
Fig. 2. SEM images of 80Cu-20AlN powder mixtures
Microstructural examinations showed large variations in
the size and shape of the obtained powder mixtures. In the
case of a higher volume fraction of copper (90–80 vol%) the
average grain size of mixtures is about 10 µm after 4-hours
of the mixing process. Larger grains can be distinguished
(max. 30–40 µm) in the structure of the powder mixtures.
508 Bull. Pol. Ac.: Tech. 61(2) 2013
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Comparison of experimental and modelling results of thermal properties...
Their shape is rather irregular, but some of them tend to
have a spherical form. As a result of the grains breakage as
the milling process is continued, sharp edges appear and the
grains take flake-like shapes. Aluminium nitride particles are
placed on the surface of larger copper grains. Some of them
form agglomerates. For higher content of aluminium nitride
(30–40 vol%) the grain size is decreased to about 5 µm. In
this case, the shape of grains is more uniform and spheri-
cal particles are dominant. The amount of observed ceramic
agglomerates is raising.
The composite powders were consolidated using a hot-
pressing method in vacuum (10−3Tr) at 600◦C and the pres-
sure of 415 MPa for 30 min.
The microstructure and thermal properties of the fabri-
cated Cu-AlN composites were evaluated. The densities of
composites were measured by the Archimedes method. The
obtained results were compared with theoretical densities es-
timated from the rule of mixtures. The microstructure of Cu-
AlN composites was examined using scanning electron mi-
croscopy (SEM).
The thermal expansion coefficient was measured using a
vertical direct dilatometer. The samples were heated up to the
temperature of 600◦C in a protective argon atmosphere at a
rate of 5◦C/min, maintained at this temperature for 5 min
and, then, cooled down in an oven at an average rate of 2
to 3◦C/min. The values of the thermal expansion coefficient
were determined based on the measurements of the elonga-
tion of the samples as a function of the temperature, using
the equation:
α=∆l
l0·∆T,(1)
where ∆l/∆T– the rate of change of the linear dimension per
unit change in temperature, l0– initial length of the sample.
The thermal diffusivity Dwas measured at room tem-
perature by a laser flash method (LFA 457, Netzsch). The
front face of the measured sample was homogeneously heat-
ed by an unfocused laser pulse. On the rear face of the sample
the temperature increase was measured as a function of time.
The mathematical analysis of this temperature/time function
allows the determination of the thermal diffusivity D. For adi-
abatic conditions, the diffusivity can be calculated from the
following equation [18]:
D= 0.1388 ·l2
t0.5
,(2)
where D– diffusivity in mm2/s, l– sample thickness in mm,
t0.5– time at 50% of the temperature increase, measured at
the rear side of the sample in s.
The specific heat was evaluated for each composition
based on the rule of mixture.
The experimental results of the thermal diffusivity and
calculated values of the specific heat were used to estimate
the thermal conductivity K. It can be determined from the
relation:
K=ρ·cp·D, (3)
where K– thermal conductivity in W/mK, ρ– density in
g/cm3,cp– specific heat in J/gK, D– diffusivity in mm2/s.
3. Results and discussion
3.1. Measurements of thermal properties. Theoretical den-
sity of the composites was defined for the assumed vol-
ume contents, using the density of aluminium nitride ρAlN =
3.20 g/cm3and the density of copper ρCu = 8.96 g/cm3. Ta-
ble 1 shows the densities of the produced hot-pressed Cu-AlN
composite materials.
Table 1
Densities of hot-pressed Cu-AlN composites
Chemical
composition
(vol.%)
Theoretical
density
(g/cm3)
Measured
density
(g/cm3)
Relative
density
(%)
90Cu-10AlN 8.38 8.27 98.6
80Cu-20AlN 7.81 7.69 98.4
70Cu-30AlN 7.23 7.08 97.9
60Cu-40AlN 6.66 6.45 96.9
The hot-pressed Cu-AlN composites demonstrate a good
densification as confirmed by the data of density measure-
ments. Relative densities exceed 96% in all examined cases.
It can be stated that the greater volume fraction of aluminium
nitride, the lower density of composite materials. Due to a
higher sintering temperature of AlN (over 1600◦C [19]), the
degree of densification between ceramic particles is not high
and, therefore, porosity appears. The hot pressing process is
conducted at a much lower temperature than in the case of
the AlN sintering process, but a particularly high pressure
used ensures continuation of the densification process. At the
temperature of 600◦C copper exhibits good plasticity. That is
why, we can presume that hard ceramic particles are pressed
into the plastic copper matrix.
The behaviour of composite elements at the grain bound-
aries was investigated using scanning electron microscopy.
The examples of Cu-AlN composite materials are presented
in Fig. 3.
The SEM observations did not show the presence of
porosity at the interface of the copper/aluminium nitride grain
boundary. However, in few cases some cracks and disconti-
nuity of the structure were found (Fig. 3b). The porosity of
composite materials is, in most cases, located between ceram-
ic grains (Fig. 3a). Their amount is raising with the increase
of the ceramic phase content. It appears that the main densi-
fication mechanism is that of the diffusion of copper towards
ceramic grains and plastic deformations of copper particles
during the sintering process.
The major drawback of pure copper is a particularly high
value of the thermal expansion coefficient (16.8×10−61/K).
The mismatch between copper and semiconductor materials
can be tailored by changing the aluminum nitride volume frac-
tion. Figure 4 shows the results of thermal expansion coeffi-
cient measurements for different Cu-AlN composite compo-
sition at room temperature.
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M. Chmielewski and W. Weglewski
a)
b)
Fig. 3. SEM images of example composites obtained by hot pressing
method: a) 80Cu-20AlN, b) 70Cu-10AlN
Fig. 4. Thermal expansion coefficient (at room temperature) for hot
pressed Cu-AlN composite materials
The values of the thermal expansion coefficient were de-
termined in the form of the average coefficients αT0−T1,
which are most often used. These coefficients describe the
average thermal expansion of the material within the temper-
ature range from the initial temperature T0(usually 0◦C or
20◦C) to the upper temperature limit T1. For each sample,
the initial temperature was T0= 20◦C, whereas the temper-
ature limit was 50, 75, 100, 125, . . . , 600◦C. The calculated
values of these coefficients (determined according to the pro-
cedure described below) are presented as diagrams in Fig. 5
and discussed with reference to the results.
a)
b)
c)
d)
Fig. 5. Comparison of the calculated and measured coefficients of
thermal expansion for different ceramic phase content: a) 10% AlN,
b) 20% AlN c) 30% of AlN d) 40% of AlN (solid lines – analytical
models, dashed lines – measured CTE)
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Comparison of experimental and modelling results of thermal properties...
It can be seen that the addition of ceramic phase caused
the decrease of the thermal expansion coefficient of Cu-AlN
composites, when compared to pure copper. This effect was
better visible once the ceramic phase content was increased.
The results of the measurements do not significantly differ
from the analytical estimates furnished by the rule of mix-
ture. The mismatch appears due to the presence of a third
phase (pores) in the composite material.
The results of the measured thermal diffusivity and, thus,
the thermal conductivity of the obtained composite materials
are presented in Table 2.
Table 2
Results of thermal diffusivity and thermal conductivity of Cu-AlN
composite materials at 50◦C
Chemical
composition
(vol.%)
Thermal
diffusivity D
(mm2/s)
Thermal
conductivity K
(W/mK)
90Cu-10AlN 91.75 304.45
80Cu-20AlN 74.85 238.75
70Cu-30AlN 71.62 223.36
60Cu-40AlN 54.94 164.40
For all the examined samples, the thermal conductivity
turned out to be lower than expected from the properties of
the constituent materials (rule of mixtures). The composite
with the highest copper content (90%) had the highest ther-
mal conductivity (slightly above 300 W/mK). As could be
expected, the thermal conductivity of composites decreased
with the increasing ceramic content. However, this drop was
greater than that resulting from the calculations. This adverse
effect can be explained by the increased porosity of the com-
posite, which has an essential effect on the thermal conduc-
tivity since the pores present between non-sintered ceramic
grains constitute a barrier to heat transfer.
3.2. Modelling of Cu-AlN thermal properties. The mod-
elling of the thermal properties of composites is of great in-
terest in many heat transfer applications. Two types of models
of the thermal properties of a material, namely analytical and
numerical [20], are present in the literature. Usually, the Voigt
and Reuss bounds [21] and the Hashin-Shtrikman bounds [22–
24] are used for-preliminary and fast verification of the pro-
duced composites. A number of other theoretical models such
as Turner model [25], Kernel model [26], Maxwell-Eucken
model or the Effective Medium Theory [27] are reported in
the professional literature. When the reinforcement of a par-
ticular composite material takes the form of spherical parti-
cles or fibers the numerical modeling is commonly applied
[28, 29].
In this paper we decided to use the classical Voigt-Reuss
and Hashin-Shtrikman bounds for a fast evaluation of the qual-
ity of the composite, and to subsequently build up a more pre-
cise numerical model enabling the investigation of the influ-
ence of the residual porosity on the material’s properties. The
experimental data of the effective coefficient of thermal expan-
sion and the thermal conductivity will be compared with the
coefficient obtained from the analytical and numerical models.
The following two FE material models were implemented: (i)
an ideal material with no residual porosity, and (ii) a porous
material where the finite element mesh was modified to allow
for a third component (pores).
The roughest estimates of the effective material proper-
ties but, at the same time, the most widely used ones, are the
Voigt and Reuss bounds. The Voigt upper bound is derived
under the assumption of uniform stress distribution, whereas
the Reuss lower bound under the assumption of uniform strain
distribution. This leads to the solution of elasticity equations,
where the stiffness tensor is equal to the average values of the
matrix and inclusions stiffness tensors, while the compliance
tensor is equal to the average values of the matrix and inclu-
sions compliance tensors. The Voigt and Reuss bounds can
be expressed as [30]:
αV=f1E1α1+f2E2α2
f1E1+f2E2
,
αR=f1α2+f1α2,
(4)
where f– the volume fraction, α– the coefficient of ther-
mal expansion, E– the Young’s modulus, indices 1and 2
denote copper and aluminium nitride phase, respectively. The
Voigt and Reuss bounds of the thermal conductivity take the
following form [29]:
kV=f1k1+f2k2,
kR=k1k2
f1k2+f2k1
.(5)
The bounds derived by Hashin and Shtrikman [22, 23]
provide a very good prediction of the experimental data. Orig-
inally, they suggested analytical equations for the calculation
of the bulk and shear modulus. For computing the effective
thermal properties of a composite the effective elastic con-
stants calculated from the Hashin-Shtrikman model are used
to solve the elasticity equations. This leads to the following
equation for the upper and lower value of the effective coef-
ficient of thermal expansion:
αu=α1−(α1−α2)K2(3K1+ 4G1)f2
K1(3K2+ 4G1) + 4(K2−K1)G1f2
,
αl=α2−(α2−α1)K1(3K2+ 4G1)f1
K2(3K1+ 4G2) + 4(K1−K2)G2f1
,
(6)
where Kand G– bulk and shear modulus respectively, and
the effective thermal conductivity (Eq. (7)) [23]:
ku=f1k1+f2k2−f1f2(k1−k2)2
3k1−f1(k1−k2),
kl=f1k1+f2k2−f1f2(k1−k2)2
3k2+f2(k1−k2).
(7)
The coefficients of thermal expansion calculated from those
analytical models were used for the first verification of the
experimental data. In the present study, it is assumed that
elastic moduli of Cu and AlN are constant, irrespective of the
temperature. The values of Young’s, bulk and shear moduli
as well as Poisson’s ratio are given in Table 3. On the other
hand, the coefficients of thermal expansion of Cu and AlN are
regarded as temperature dependent parameters (cf. Table 4).
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Table 3
Elastic modulus of Cu and AlN
Material Young modulus (GPa) Bulk modulus (GPa) Shear modulus (GPa) Poisson ratio
AlN 310 172 129 0.21
Cu 130 72.5 54.3 0.35
Table 4
Coefficient of thermal expansion for Cu and AlN
T (◦C) 25 125 225 325 425 525 625 725 825
AlN (×10−61/K) 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6
Cu (×10−61/K) 16.79 17.39 18.05 18.78 19.58 20.45 21.39 22.4 23.49
A comparison of the analytical estimates and the measured
coefficient of thermal expansion values for different contents
of AlN is depicted in Fig. 5.
The measured coefficients of thermal expansion for all the
considered contents of AlN fall between the analytical bounds.
For lower temperature, the experimental data are below the
Voigt lower bound due to the measurement device inaccuracy
at a lower temperature range. The existing porosity has only a
small effect on the value of coefficients of thermal expansion
because of the real composition of the composite, which dif-
fers from the theoretical one. The large CTE of the air (about
3.5e-3 1/K) which fills the pores cannot lead to the increase
of the composite’s CTE because the air thermal expansion is
blocked by the pores’ walls.
The values of the thermal conductivity used for the calcu-
lation were as follows: 398 W/mK and 120 W/mK for copper
and aluminium nitride, respectively. It was assumed that the
pores are filled with air (assumed thermal conductivity of air
was 0.0257 W/mK). Here, the influence of residual porosity is
much more pronounced than for the thermal expansion - the
measured data fell below analytical predictions for the whole
range of AlN contents.
A FEM model using a academic program FEAP ver. 7.5
was developed. Two FE meshes were implemented: (i) without
porosity to provide control calculations of the thermal con-
ductivity and to make comparison with the analytical models,
and (ii) with different porosities for different composites (cf.
Table 1). In both cases a finite element mesh was generated as
voxels of AlN randomly immersed in the copper matrix [30].
The numerical representation of the specimen (unit cell) is
presented in Fig. 6.
Fig. 6. The example of FE unit cell used in the modelling (gray
elements represent copper, white – aluminium nitride, and black –
pores)
Hexagonal, 8-nodes thermal elements which solve the lin-
ear Fourier heat conduction equation in a three-dimensional
domain were used (Eq. (8)):
q=−keff ∆T , (8)
where q– thermal flux, kef f – effective thermal conductivity
and ∆T=Thot −Tcold.
The temperature on the two opposite faces of the speci-
men was constant but one face was set as hot (Thot = 100),
the opposite face was kept cold (Tcold = 0), whereas the re-
maining ones were assumed to be adiabatic. Following Floury
at al. [31] the effective thermal conductivity was described by
Eq. (9):
keff =−Q1
A
L
(T1
hot −T1
cold),(9)
where L– the length of the unit cell side, A– the cross-
section area of the unit cell (A=L2),T1
hot −T1
cold – the
temperature difference across the unit cell, Q1– the over-
all heat flux into the unit cell obtained by integrating fluxes
across the inlet face of unit cells (Eq. (10)):
Q1=Z
A
−k∂T
∂z dxdy. (10)
The above equation was used for all unit cells in order to
calculate the thermal flux and the effective thermal conductiv-
ity. The results obtained from the FE model with and without
porosity are presented in Fig. 7.
The mesh without porosity was applied to verify if the
implementation of the thermal conductivity model was suc-
cessful. The results derived from it should lie between the
Hashin-Shtrikman bounds. As one can see, the results from
the numerical modelling for the no-porosity case lie exactly
between the bounds (triangles in Fig. 7). The next step was
the implementation of the FE mesh with the residual porosity.
Using the data from Table 1, the porosity equals 1.4%, 1.6%,
2.1% and 3.1% for the AlN content of 10%, 20%, 30% and
40%, respectively. Material porosity results in a substantial
decrease of the thermal conductivity, which is much larger
than for an ideal material (diamond symbols in Fig. 7). The
numerical results are close to the experimental data for all
AlN contents.
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Comparison of experimental and modelling results of thermal properties...
Fig. 7. Comparison of the calculated (analytically and numerical-
ly) and measured thermal conductivity for different ceramic phase
contents
This simple numerical model can also be employed to pro-
vide reliable approximations of thermal properties of compos-
ites with different compositions. It can help materials design
engineers to assess the influence of the porosity in a particular
composite material prior to its processing.
4. Conclusions
The paper presents results of experimental and modeling stud-
ies concerning thermal properties of the Cu-AlN composite
materials, which are of crucial importance when they are to
be used in heat-dissipating systems. The technological con-
ditions allowing to obtain almost fully dense composite ma-
terials were elaborated using hot pressing method. The in-
crease of porosity with the raise of ceramic volume content
in the composite was observed. The increasing porosity of
these composites was the principal reason why their thermal
conductivity is lower than expected. Some cracks observed in
the composite structure have also negative influence on their
thermal properties. Comparing the previous results of other
authors [32] obtained results are very promising in the elec-
tronic applications.
From the presented analytical and numerical models it can
be concluded that the residual porosity has a minor influence
on the coefficients of thermal expansion values but leads to
a large decrease of the thermal conductivity of a composite,
especially when compared to an ideal material (without poros-
ity). A good prediction of the thermal conductivity was ob-
tained from the FE model of a material with residual porosity.
The difference between the results obtained from the model
and the experimental data does not exceed 5%. The proposed
numerical model can be easily extended to predict the thermal
properties of other composites, and can, thus, be helpful in
the composite materials design.
Acknowledgements. This work was supported by the Polish
Ministry of Science and Higher Education (the project No
N508 3086 33).
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