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146    Cha pte r  F o u r


              10 4     10 2     10 0         10 4     10 2     10 0
             10 4    Penetration depth (μm)  ohne  10 4  10 4  Penetration depth (μm)  ohne  10 4
                                   50 μm                          50 μm
                                   175 μm                         175 μm
             10 2                  575 μm  10 2  10 2             575 μm  10 2
           Temperature lift (K)  10 –2  10 0  Temperature lift (K)  10 –2  10 0
                                   1 mm
                                                                  1 mm
                                                                  10 mm
                                   10 mm
             10 0
                                            10 0
                                                                       10 –2
                                       10 –2
            10 –4                      10 –4  10 –4                    10 –4
                  Temperature lift with silicon substrate  Temperature lift with glass substrate
              10 –4  10 –2  10 0  10 2  10 4  10 6  10 –4  10 –2  10 0  10 2  10 4  10 6
                       Frequency (Hz)                 Frequency (Hz)
                          (a)                            (b)
                               10 4    10 2     10 0
                                      Penetration depth (μm)  ohne
                                                   50 μm
                             10 2                  175 μm  10 2
                                                   575 μm
                            Temperature lift (K)  10 –2  10 mm  10 0
                                                   1 mm
                             10 0
                                                        10 –2
                             10 –4                      10 –4
                                  Temperature lift with Melinex substrate
                              10 –4  10 –2  10 0  10 2  10 4  10 6
                                        Frequency (Hz)
                                           (c)
          FIGURE 4.17  Calculated temperature lift for different substrates and the multilayer
          model depicted in Fig. 4.14. The substrates are (a) silicon, (b) glass, and (c) PET-foil
          Melinex. The penetration depth of the thermal wave and its assignment to the
          frequency are also indicated (red axis). (See also color insert.)


               sensor element. This, however, is a big advantage for sensors using
               P(VDF-TrFE) because they are not automatically connected to highly
               thermal conductive substrates. Ceramics such as lead zirconate tita-
               nate (PZT), crystals such as triglycine sulfate (TGS), and other pyro-
               electrics are normally fabricated on a silicon substrate, which strongly
               decreases the average temperature lift in the sensor element (com-
               pare to Fig. 4.17a). A comparison of different substrates is thus very
               important. Since one big advantage of the PVDF copolymer is that it
               can be processed successfully on flexible substrates, a comparison of
               the thermal influences of different substrates and their thicknesses
               was made. To compare the results with the work of Setiadi and
                      31
               Regtien,  a calculation with a silicon substrate was done as well. In
               Fig. 4.17 the temperature lift (induced by the absorption of the laser)
               in the sensor element with respect to the ambient temperature is given.
               It is obvious that the silicon substrate has the worst responses in the
               low-frequency range because the substrate acts as a heat sink. The
               different colors in the plot are calculations for different thicknesses of
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