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Radio Fr equency System-on-Package (RF SOP) 285
Comparing Materials and TCC Properties
A high dielectric constant (K) invariably comes with either a negative or positive TCC.
Fillers can be selected to compensate for each other or compensate with the polymer TCC,
leading to a lower TCC. It is important to have a flat TCC over a large temperature range.
Hence, paraelectric fillers are preferred to ferroelectric fillers since their capacitance value
is much more stable with regard to most processing parameters such as temperature and
frequency [93]. Figure 5.23 shows the relation between the TCC and K of various materials
and the TCC compensation in the composite system. There is no reliable data on the TCC
characteristics of polymers. This is even more complicated because the TCC of capacitors
in the buildup layers depends on the substrate thermomechanical properties. Literature
data only allude to the properties of bulk materials and thin films but not for powders.
This makes the design of low-loss and low-TCC composites even more complicated.
Photopolymer composites have been proposed. A tight tolerance can be achieved with
thin-film photolithography. Other parameters that control tolerance are thickness control
and uniform dispersion of ceramic fillers to prevent material inhomogeneities.
TCC Compensation in Polymer-Based Composites
The filler contribution to the net composite TCC is dependent on its volume fraction and
the distribution of filler in the composite material as well. The dielectric constant of
composites with fillers perfectly aligned parallel to the electric field strength can be
modeled as
ε = ν ε + v ε
c m m f f
where e , e and e are the dielectric constants of nanocomposite, matrix, and ceramic
c m f
filler, respectively, and u and u are the volume fraction of matrix and ceramic filler,
f
m
respectively. In this case, the TCC of the composite can be obtained by simple differentiation
with respect to temperature and by rearranging the equation:
dε dε dε
c = ν m + v f
dT m dT f dT
Dividing the equation by e and rearranging leads to
c
1 dε
TCC = c
C ε c dT
ε ε
TCC = ν m TCC + v f TCC
C m ε m f ε f
c c
In this case, the TCC of the filler influences the composite TCC to a large extent because
e /e is larger than e /e .
f
c
c
m
If the composites have fillers aligned perpendicularly to the electric field, the
dielectric constant is modeled as
1 = ν m + v f
ε ε ε
c m f