Page 313 - System on Package_ Miniaturization of the Entire System
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Radio Fr equency System-on-Package (RF SOP) 287
Differentiating with respect to temperature and rearranging:
ε ε
TCC = ν c TCC + v c TCC
C m ε m f ε f
m f
In this situation, the first term has more effect because e /e is much larger than e /e . f
m
c
c
Thus, the polymer or filler can significantly affect the composite TCC depending on the
filler morphology and arrangement in the composite.
For most particulate ceramic-polymer composites, the behavior is in the middle of
these two extreme cases. The modified Lichtenecker’s law, commonly used to predict
the effective dielectric constant of polymer-ceramic nanocomposites with different
volume fractions, is expressed as
logε = ν logε + kv logε
c m m f f
where k is a fitting constant subject to the composite material and can be related to the
distribution of filler in the composite material. Differentiating with temperature, the
TCC can be written as
TCC = ν m TCC + kv f TCC f
m
C
The TCC of the composite in this case is linearly dependent on the volume fraction of
the filler and the composite. The filler contribution to the net composite TCC is
dependent both on k and the volume fraction. For well-dispersed suspensions, there is
a strong coupling between the filler particles leading to a higher k. Therefore, the filler
has a strong effect on the permittivity and TCC. For aggregated suspensions, the
permittivity of the matrix has a stronger influence on the composite permittivity and
TCC. In other words, the aggregate composites with widely separate fillers behave
similarly to the case where the fillers are perpendicular to the field because of the weak
dielectric coupling between one aggregate and the other. The TCC does not scale linearly
with the filler content in this case.
The disadvantages of LTCC can be overcome with liquid crystalline polymer based
RF circuits. Current organic-compatible embedded capacitor technologies such as
epoxy-based composites with ceramic fillers are not suitable for high-performance
(higher Q and lower TCC) RF capacitor requirements because they may not achieve a
dielectric loss less than 0.02 and a TCC within 300 ppm/°C, even with the best ceramic
fillers [54]. Low-loss polymers such as bisbenzocyclobutene (BCB) and polytetra-
fluoroethylene (PTFE) are easily amenable to thick-film formation and can be filled
with ceramic fillers.
Composite-type integrated capacitors for applications demanding precise
capacitance control can be based on a simple mixture of polymer and paraelectric
ceramic particles. Paraelectric ceramics such as Ta O , SiO , and Al O appear to be
2
5
2
3
2
suitable in these applications. They have a much lower dielectric constant compared to
ferroelectric ceramic particles, but their capacitance value is much more stable with
regard to most of the processing conditions. Among them, Ta O is promising because
5
2
it has a dielectric constant of 24, relatively higher compared to any other paraelectrics,
and exhibits a moderate positive temperature coefficient of capacitance, ranging from
+200 to +400 ppm/°C [55]. It is thought that this positive TCC of Ta O can compensate
2 5
the negative TCC of a high-Q polymer itself, giving rise to the nearly zero TCC