5.6 Measurement of Frequency Dependence

To the day of this writing no tools have been available which allow a direct extraction of the ferroelectric hysteresis for frequencies higher than 1000 Hz. The standard technique for high-frequency measurements is the Sawyer-Tower circuit [MNS+90] which is schematically outlined in Fig. 5.11.

Figure 5.11: Sawyer-Tower circuit

Figure 5.12: Equivalent circuit diagram

In order to produce the high-frequency input signal $V_i(t)$, a function generator is used. The circuit itself consists of the ferroelectric capacitor $C_F$ and a series capacitor $C_S$. The voltage between these two is evaluated with a digitizer.

Figure 5.13: Initial oscillations of the Sawyer-Tower circuit for different ratios of the resistors

Figure 5.14: Distorted output signal

For an exact equivalent circuit the series resistance of $R_F$ and the input impedance $R_i$ of the digitizer have to be considered. $R_F$ is preferably quite high, reasonable values are in the range of $1000\mathrm{M}\Omega$. The typical value for the input impedance $R_i$ is $1\mathrm{M}\Omega$.

MINIMOS-NT allows the simulation of small circuits consisting of discretized and concentrated devices, including the Sawyer-Tower circuit. As the simulation is performed in the time domain, also the initial oscillation of the circuit is obtained. Depending on the initial state of the ferroelectric capacitor and the ratio of the resistances, these oscillations can lead to a significant offset of the output voltage $V_\mathrm{Out}$, and as outlined in Fig. 5.13 several cycles might be necessary until the hysteresis loop gets symmetrical.

Unfortunately, the Sawyer-Tower circuit does not reproduce the exact properties. Prior measurements show that if the series resistance applied is too high, the output will be heavily distorted.

Fig. 5.14 gives the results obtained by simulations which show a good correspondence to the reported measured data [MNS+90]. Also initial oscillations which occur until a stable curve is reached are included in the figure.