Breakdown voltage

The raw data of the displacement of the VHB sample for the increase of voltage is shown in Figure 4–1. The value of each adjustment voltage is 400 volts by USB voltage supply which is controlled by computer, and confirms data which is stable before adjustment. Because the compression is generated by applied voltage, displacement gradually becomes large with increases voltage. With applied voltage, 0 V, 400 V, 800 V, 1200 V, 1600 V, 2000 V, we can observe alteration of displacement in Figure 4–1.

Meanwhile, by using multimeter and LabVIEW, we can also measure the electrical current. In lower figure in Figure 4–1, we obtain that when increases applied voltage to 2000 V, we observe sudden increasing current. In chapter 2, we discuss about breakdown phenomenon. An important phenomenon at breakdown point is a quietly high current. High current appears in experiment represents appearance of breakdown phenomenon. Due to the statement above, we can speculate that breakdown voltage is equal to 2000 V from the result of experiment.

Then, we discuss that the relationship of displacement and voltage by data of experiment before breakdown point. Compiles data from Figure 4–1, we can see the figure whose x-y coordinate, x-axis is applied voltage and y-axis is displacement in Figure 4–2. It is the first sample in experiment. With the increase of applied voltage from 0 V to 2000 V, displacement gradually becomes large see to Figure 4–2. Similarly, the second, third and forth samples can also be seen in Figure 4–3, Figure 4–4 and Figure 4–5.

Figure 4–1. Displacement vs. Time and Current vs. Time. In upper figure, displacement increases with the increase of applied voltage. The minus sign of displacement indicates that the equivalent direction is compressive. When applied voltage increases to 2000 V, we observe sudden increasing current in lower figure. High current represents appearance of breakdown phenomenon.

400 V

800 V

1200 V

1600 V

2000 V

Breakdown

Time (sec)

Displacement (mm)

Time (sec)

Current (mA)

Voltage off

Voltage off

Figure 4–2. Displacement vs. Voltage. The first sample is in experiment. With the increase of applied voltage from 0 V to 2000 V, displacement gradually becomes large.

As applied voltage achieves 2000 V, breakdown phenomenon appears. The construction of this figure by compiles data from Figure 4–1.

Figure 4–3. Displacement vs. Voltage. The second sample is in experiment. With the increase of applied voltage from 0 V to 2000 V, displacement gradually becomes large.

Voltage (V)

Displacement (mm)

Voltage (V)

Displacement (mm)

Figure 4–4. Displacement vs. Voltage. The third sample is in experiment. With the increase of applied voltage from 0 V to 2000 V, displacement gradually becomes large.

Figure 4–5. Displacement vs. Voltage. The forth sample is in experiment. With the increase of applied voltage from 0 V to 2000 V, displacement gradually becomes large.

Voltage (V)

Displacement (mm)

Voltage (V)

Displacement (mm)

Using experimental data of four samples, we can re-compile the data and express in Figure 4–6. Figure 4–6 shows mean value of measurement and standard deviation.

Then, in order to confirm fit of experimental result and theory in chapter 2, we discuss equation (2. 38). When substituting applied voltage 0 V, 400 V, 800 V, 1200V, 1600V to equation (2.31. a) separately in order to obtain their normalized voltage. Next, substituting normalized voltage to equation (2. 38) and calculates normalized thickness by Matlab, then, actual thickness at applied voltage can be obtained from equation (2.2.

c). Actual thickness at applied voltage is obtained, so does displacement. Depending on applied voltage and displacement by calculating, we can see the figure whose x-y coordinate, x-axis is applied voltage and y-axis is displacement. In Figure 4–7, the red curve represents displacement-applied voltage curve of theory and shows mean value of measurement and standard deviation.

From Figure 4–7, we can observe that it could have larger displacement in the theory. Some possibilities may result in this case. One possibility is friction between VHB sample and sample stage. Friction may loss a little energy which is generated by applied voltage. Because of energy loss, displacement cannot reach the expected result.

Another possibility is effect of fringing electric field as in Figure 4–8. Fringing electric field could generate fringing capacitance. Hence, the result of capacitance measurement is bigger than actual value. Because of this, dielectric constant is also larger than actual value from equation (2. 33). Loss energy which is affected by friction between VHB sample and sample stage is very difficult to predict and calculate. Because of this, try to substitute different value of dielectric constant, 4.7, 4.0, 3.5, 3.0 to equation (2. 31) and separately calculate normalized thickness. Similarly, see the figure in Figure 4–9 whose x-y coordinate, x-axis is applied voltage and y-axis is normalized thickness depending on the result of trying to different value of dielectric constant.

Figure 4–6. Displacement vs. Voltage, shows mean value of measurement and standard deviation.

Figure 4–7. Displacement vs. Voltage, shows mean value of measurement and standard deviation. Red curve is the value of substituting experimental data to theory.

Voltage (V)

Displacement (mm)

Voltage (V)

Displacement (mm)

Figure 4–8. Schematic figure of fringing electric field.

Figure 4–9. Normalized thickness vs. Voltage. With the increase of applied voltage from 0 V to 2000 V, displacement gradually becomes large. Figure illustrates that the result of experiment is close to theoretical value with decreases value of dielectric constant.

When dielectric constant is 3.0, the result of experiment most fits theoretical value.

Fringing electric field

r

3.0 3.5 4.0 4.7

Voltage (V)

Normalized thickness

Figure 4–9 illustrates that the result of experiment is close to theoretical value with

Similarly, the conclusion of chapter 2.5.2 must be revised.

In Ⅰ- region of Figure 2–15.

Meanwhile, normalized electric field at pull-in point can also be

0.7451

In Figure 4–1, we can obtain that when applied voltage increases to 2000 V, we observe sudden increasing current. High current appears in experiment represents appearance of breakdown phenomenon. Because of this, breakdown voltage is 2000 V. As applied voltage is 2000 V, normalized thickness is 0.9928. Substituting normalized thickness to equation (2. 41), we can obtain the breakdown electric field whose value is 4.029

(V/mm). Then, we also can obtain the electric field at pull-in point depending on equation (2. 37) and (4. 1) and the value is 26.89 (V/mm).

Because the breakdown electric field is smaller than the electric field at pull-in point, the result confirms equation (4. 3) and the situation is in Ⅰ- region according to Figure 2–15. We can see in Figure 4–10.This result also expresses that breakdown phenomenon occurs before pull-in effect.

VHB sample is compressed with the increase of applied voltage. This part is expectable. It reaches the critical point with the increase of voltage, and the pull-in effect should be observed. However, it has the real material between compliant electrodes in our theoretical model. Because of this, if pull-in effect occurs in our model, the material between compliant electrodes is going to disappear completely. It is unreasonable depending on incompressible volume and mass conservation. If breakdown phenomenon occurs before pull-in effect, the unreasonable situation does not occur. According to the result of experiment, breakdown phenomenon occurs before pull-in effect. .

Figure 4–10. Normalized thickness vs. Normalized voltage, shows that red line expresses as breakdown phenomenon and pull-in effect occur at the same time. Green line is in Ⅰ- region, shows that breakdown phenomenon occurs before pull-in effect due to experimental result.

Experiment Pull-in=breakdown After pull-in Before pull-in

Normalized voltage

Normalized thickness

Breakdown

Pull-in

Ⅰ

Ⅱ