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
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                                                                  5
                                                                       2
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                                                                              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
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                    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
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