5.3 Comparison to Measurement

Figure 5.1: Comparison simulation to measurement, Supplier 1

The extraction of time- and material-parameters is a very sensitive task for successful transient simulation. In the context of this work, these parameters have been extracted for two different specimen of PZT, which were produced by two different industrial suppliers.

For both materials similar values for the material parameters were found, and a good fit between the simulated and the measured Q/V characteristics was obtained. These Q/V characteristics are plotted in Fig. 5.1 and Fig. 5.2.

Figure 5.2: Comparison simulation to measurement, Supplier 2

Figure 5.3: Comparison simulation to measurement, coercive field

In both figures full cycles of the measured hysteresis curve are plotted in dashed lines. A close analysis of the data shows that the up loop and the down loop do not show a perfect symmetry. This is related to non ideal material properties which can be introduced into the simulator by application of two different sets of hysteresis parameters for the respective direction. As this is of minor relevance for the analysis of frequency dependence, the investigations were focused on one out of these two branches.

The measured data available for the second specimen covered the complete frequency range up to 100kHz, without any gap. This allows the extraction and analysis of the frequency dependence of decisive material properties like coercive field and remanent polarization. The coercive field is of highest importance for the device performance, as it specifies the strength of the field necessary to change the information inside the device and thus the supply voltage. Fig. 5.3 compares the prediction of the simulation with the measured values. The measured data are plotted point by point, the simulation results in a straight line. At higher frequencies the coercive fields in the up and down direction show a significant discrepancy, therefore both values are plotted.