Optional FE Device Polarization (Y) FIGURE 49.4 Sawyer Tower circuit. It requires charge to rotate or flip a domain. Thus, there is charge flow associated with the rearrangement of the polarization in the ferroelectric material. If a bipolar, repetitive signal is applied to a ferroelectric material, its hysteresis loop is traced out and the charge in the circuit can be measured using the Sawyer Tower circuit ( Fig. 49.4). In some cases the drive signal to the material is not repetitive and only a single cycle is used. In that case the starting point and the end point do not have the same polarization value and the hysteresis curve will not close on itself The charge flow through the sample is due to the rearrangement of the polarization vectors in the domains (the polarization) and contributions from the static capacity and losses(Co and R, in Fig. 49.3). The charge is integrated by the measuring capacitor which is in series with the sample. The measuring capacitor is sufficiently large to avoid a significant voltage loss. The polarization is plotted on a X-Y scope or plotter against the applied voltage and therefore the applied field. Ferroelectric and piezoelectric materials are lossy. This will distort the shape of the hysteresis loop and can even lead to incorrect identification of materials as ferroelectric when they merely have nonlinear conduction characteristics. A resistive component(from R, in Fig. 49.3)will introduce a phase shift in the polarization signal. Thus the display has an elliptical component, which looks like the beginnings of the opening of a hysteresis loop. However, if the horizontal signal has the same phase shift, the influence of this lossy component is eliminated, because it is in effect subtracted. Obtaining the exact match is the function of the optional phase ifter, and in the original circuits a bridge was constructed which had a second measuring capacitor in the comparison arm(identical to the one in series with the sample). The phase was then matched with adjustable high-voltage components which match Co and This design is inconvenient to implement and modern Sawyer Tower circuits have the capability to shift the reference phase either electronically or digitally to compensate for the loss and static components. a contem porary version, which has compensation and no voltage loss across the integrating capacitor, is shown in Fig. 49.5. The op-amp integrator provides a virtual ground at the input, reducing the voltage loss to negligible values. The output from this circuit is the sum of the polarization and the capacitive and loss components These contributions can be canceled using a purely real (resistive)and a purely imaginary(capacitive, 90 phaseshift) compensation component proportional to the drive across the sample. Both need to be scaled magnitude adjustments)to match them to the device being measured and then have to be subtracted(adding negatively) from the output of the op amp. The remainder is the polarization. The hysteresis for typical ferroelectrics is frequency dependent and traditionally the reported values of the polarization are measured at 50 or 60 Hz. The improved version of the Sawyer Tower( Fig. 49.6)circuit allows us to cancel Co and R, and the losses, thus determining the active component. This is important in the development of materials for ferroelectric memory applications. It is far easier to judge the squareness of the loop when the inactive components are canceled. Also, by calibrating the"magnitude controls"the value of the inactive components can be read off directly. In typical measurements the resonance is far above the frequencies used, so ignoring the inductance in the equivalent circuit is justified c 2000 by CRC Press LLC© 2000 by CRC Press LLC It requires charge to rotate or flip a domain. Thus, there is charge flow associated with the rearrangement of the polarization in the ferroelectric material. If a bipolar,repetitive signal is applied to a ferroelectric material, its hysteresis loop is traced out and the charge in the circuit can be measured using the Sawyer Tower circuit (Fig. 49.4). In some cases the drive signal to the material is not repetitive and only a single cycle is used. In that case the starting point and the end point do not have the same polarization value and the hysteresis curve will not close on itself. The charge flow through the sample is due to the rearrangement of the polarization vectors in the domains (the polarization) and contributions from the static capacity and losses (Co and Rd in Fig. 49.3). The charge is integrated by the measuring capacitor which is in series with the sample. The measuring capacitor is sufficiently large to avoid a significant voltage loss. The polarization is plotted on a X-Y scope or plotter against the applied voltage and therefore the applied field. Ferroelectric and piezoelectric materials are lossy. This will distort the shape of the hysteresis loop and can even lead to incorrect identification of materials as ferroelectric when they merely have nonlinear conduction characteristics. A resistive component (from Rd in Fig. 49.3) will introduce a phase shift in the polarization signal. Thus the display has an elliptical component, which looks like the beginnings of the opening of a hysteresis loop. However, if the horizontal signal has the same phase shift, the influence of this lossy component is eliminated, because it is in effect subtracted. Obtaining the exact match is the function of the optional phase shifter, and in the original circuits a bridge was constructed which had a second measuring capacitor in the comparison arm (identical to the one in series with the sample). The phase was then matched with adjustable high-voltage components which match Co and Rd. This design is inconvenient to implement and modern Sawyer Tower circuits have the capability to shift the reference phase either electronically or digitally to compensate for the loss and static components. A contem￾porary version, which has compensation and no voltage loss across the integrating capacitor, is shown in Fig. 49.5. The op-amp integrator provides a virtual ground at the input, reducing the voltage loss to negligible values. The output from this circuit is the sum of the polarization and the capacitive and loss components. These contributions can be canceled using a purely real (resistive) and a purely imaginary (capacitive, 90° phaseshift) compensation component proportional to the drive across the sample. Both need to be scaled (magnitude adjustments) to match them to the device being measured and then have to be subtracted (adding negatively) from the output of the op amp. The remainder is the polarization. The hysteresis for typical ferroelectrics is frequency dependent and traditionally the reported values of the polarization are measured at 50 or 60 Hz. The improved version of the Sawyer Tower (Fig. 49.6) circuit allows us to cancel Co and Rd and the losses, thus determining the active component. This is important in the development of materials for ferroelectric memory applications. It is far easier to judge the squareness of the loop when the inactive components are canceled. Also, by calibrating the “magnitude controls” the value of the inactive components can be read off directly. In typical measurements the resonance is far above the frequencies used, so ignoring the inductance in the equivalent circuit is justified. FIGURE 49.4 Sawyer Tower circuit