144 will produce a zero resultant stress at the central of the active piezoelectric layer and
therefore produce zero electrical output power. In reality, however, because of fabrication tolerances, the centroid of the active PZT layer is not exactly coincident with
the neutral axis and therefore a relatively small electrical output is generated when the structure is operating in a bending mode. Sample A1, which has a greater
d
distance from the neutral axis, generates the greatest output power among these samples. These
results verify that the output power can be increased by adjusting the thickness of the non-active component of the unimorph structure according to equations 3-22 and
3-35.
A thinner cantilever theoretically has a lower resonant frequency. However, sample A1 with the thinnest structure has a resonant frequency greater than the thicker sample D5.
This discrepancy can be explained by considering the relative shape of the structure; sample A1 is not a flat structure but rather a U-curve shaped cantilever as shown in
Figure 4-19, which increases the effective thickness of the structure and it therefore resonates at a higher frequency.
Figure 6-17 shows the relationship of optimum resistive load with different samples. Maximum output powers were generated when driving resistive loads
of 30 kΩ, 39 kΩ and 50 kΩ for samples A1, D5 and C3 respectively. This shows that, the thicker the
unimorph cantilever structure, the higher the matching electrical resistive load.
Figure 6-17: Output power as a function of resistive load for samples A1, D5 and C3.
A1 D5
C3
145
6.5.4 Interdigitated Cantilever
An interdigitated electrode IDE pattern printed on a 9 mm long piezoceramic cantilever, with gap between the fingers,
w
gap
of 1.95 mm as shown in Figure 6-18 was tested and compared with plated samples. Theoretically, to obtain optimum performance
the sample has to be polarised at approximately 5 kV to establish a similar electrical field strength of 2.5 MVm as used for the plated electrode samples [104]. However,
electrical sparking was observed at a polarisation voltage of just 350 V and burnt the area near to the base of the substrate, resulting in a short-circuit between the IDE and
the bottom AgPd support layer.
Figure 6-18: Photograph of an IDE sample.
In another experiment, a similar sample, IDa1, was polarised at a lower dc voltage of 300 V, which gives an electric field strength of 154 kVm for an in-plane polarisation
mode. Figure 6-20 shows the experiment output power for the sample at an acceleration level of 0.05 g and 0.5 g. At resonant frequency of 960 Hz, an output power of 5 pW
was measured when driving a resistive l oad of 30 kΩ at an acceleration of 0.05 g. The
output power increased by about a factor of 150 to 745 pW when the IDE cantilever was excited to its resonant frequency with an acceleration of 0.5 g, as shown in Figure 6-19.
A relatively small output power was measured at 8.3 pW from the IDE sample IDa1 compared to plated samples with similar length D3 and C2 as shown in Figure 6-20,
which is attributed to the much lower polarisation voltage used field strength of 154 kVm compared to 2.5 MVm producing correspondingly lower values for the
piezoelectric coefficients.
w
gap
146 Figure 6-21 shows a comparison of the maximum output power and resonant frequency
for sample D3, C2 and IDa1. Sample D3, with thinner non-active PZT protective layer compared to the other samples, was expected to have the lowest resonant frequency at
875 Hz. Although samples C2 and IDa1 were printed with similar numbers of layers of films, their resonant frequencies are slightly different, at 1155 Hz and 960 Hz
respectively. The difference maybe because the effective thickness of an IDE sample is less than the plated sample and therefore resonance occurs at a lower frequency.
Figure 6-19: Output power of sample IDa1 as a function of resistive load at an acceleration of 0.05 g and 0.5 g.
