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Integrated Pyr oelectric Sensors     149

                             Temperature lift         Current response
                                        10 nm      10 nm
                                        150 nm  10 –7  150 nm
                     10 2               400 nm     400 nm
                                        1 μm       1 μm
                    Temperature lift (K)  10 –2  100 μm  Current (A)  10 –8  100 μm
                                                   10 μm
                                        10 μm
                     10 0
                                              10 –9
                    10 –4
                      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)
                             Temperature lift         Current response
                     10 4
                                        10 nm      10 nm
                                        150 nm  10 –6  150 nm
                     10 2               400 nm     400 nm
                                        1 μm
                    Temperature lift (K)  10 –2  10 μm  Current (A)  10 –7  10 μm
                                                   1 μm
                     10 0
                                                   100 μm
                                        100 μm
                    10 –4                     10 –8
                    10 –6                     10 –9
                      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)
                                             (b)
                             Temperature lift         Current response
                     10 4
                                        10 nm      10 nm
                                        150 nm     150 nm
                     10 2               400 nm     400 nm
                                        1 μm  10 –7  1 μm
                    Temperature lift (K)  10 –2  100 μm  Current (A)  10 –8  100 μm
                                                   10 μm
                                        10 μm
                     10 0
                    10 –4
                                              10 –9
                      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)
                                             (c)
               FIGURE 4.19  Temperature lift and current response with different
               thicknesses of the pyroelectric layer on 200 μm thick substrate of (a) glass,
               (b) silicon, and (c) PET, calculated for the values of R = 100 MΩ and C = 75 pF.
                                                     i            i
               (See also color insert.)
               basically frequency-independent below 1 Hz, and this level increases
               with the resistance (Fig. 4.20).

               Two-Dimensional Model
               The one-dimensional model gives a relatively good picture of the ther-
               mal penetration of the device and is, by the use of an appropriate
               equivalent circuit, able to explain the measured pyroelectric responses
               very well. However, since it is a one-dimensional model, no information
               on the lateral resolution can be obtained from this approach. A two-
               dimensional model of the heat transfer in the sensor element was there-
               fore developed to give further insight in the lateral thermal distribution.
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