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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
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