**3. Experimental results**

All the measurements have been performed and recorded in a Clean-Room environment, at the temperature T=(231) °C, with a relative humidity RH=(351) %. A nitrogen flux has been used for providing a dry environment for the devices under test. RF measurements have been used as a validation for the state (ON or OFF) of the switches and for their electrical performances before, during and after the voltage application. In particular, after each cycle used for such a measurement, no changes in the electrical performances of the exploited devices has been recorded. A schematic diagram of the measurement bench is shown in Fig. 3. The reliability of the manufactured devices with respect to the charging effects, and specifically the influence of the pulse shape and of the sign of the voltage (positive or negative) on the actuation mechanism, have been studied by using pulse trains where the rise and fall time, as well as the pulse duration and the separation between pulses

Characterization and Modeling of Charging Effects in Dielectrics

response), and the device is in the OFF state (device CL).

switches.

Actually, this occurs during the voltage ramp.

for the Actuation of RF MEMS Ohmic Series and Capacitive Shunt Switches 237

Fig. 2. Coplanar shunt capacitive switch. When the switch is actuated, the bottom side of the

suspended bridge is collapsed, touching the dielectric layer placed along the central conductor of the CPW, providing a shunt to ground in a limited frequency range (resonant

Fig. 3. Schematic diagram of the measurement system used for testing the RF MEMS

have been slowly changed. Moreover, a bi-polar scheme has been applied, with positive voltages followed by negative ones. For the uni-polar experiment as well as for the bi-polar one, the actuation voltage has been recorded when the sudden change in the measured Scattering Parameters due to the bridge collapse was clearly visible on the Vector Analyzer, i.e. by means of an abrupt change in the value of both transmission and return loss.

Fig. 1. Diagram (a) and photo detail (b) of the implemented ohmic series switch configuration. Lateral wings have been included for improving the electrical contact. A number of switches with different geometrical and physical characteristics have been produced on the base of changes with respect to this one. Actually, the number of dimples as well as the thickness of the bridge and other details of the geometry contribute to the electrical performances. When the switch is actuated, the bridge, isolated with respect to the ground, closes the central conductor of the CPW with a metal-to-metal contact and the device is in the ON state (device S1).

Fig. 1. Diagram (a) and photo detail (b) of the implemented ohmic series switch configuration. Lateral wings have been included for improving the electrical contact. A number of switches with different geometrical and physical characteristics have been produced on the base of changes with respect to this one. Actually, the number of dimples as well as the thickness of the bridge and other details of the geometry contribute to the electrical performances. When the switch is actuated, the bridge, isolated with respect to the ground, closes the central conductor of the CPW with a metal-to-metal contact and the

device is in the ON state (device S1).

Fig. 2. Coplanar shunt capacitive switch. When the switch is actuated, the bottom side of the suspended bridge is collapsed, touching the dielectric layer placed along the central conductor of the CPW, providing a shunt to ground in a limited frequency range (resonant response), and the device is in the OFF state (device CL).

Fig. 3. Schematic diagram of the measurement system used for testing the RF MEMS switches.

have been slowly changed. Moreover, a bi-polar scheme has been applied, with positive voltages followed by negative ones. For the uni-polar experiment as well as for the bi-polar one, the actuation voltage has been recorded when the sudden change in the measured Scattering Parameters due to the bridge collapse was clearly visible on the Vector Analyzer, i.e. by means of an abrupt change in the value of both transmission and return loss. Actually, this occurs during the voltage ramp.

Characterization and Modeling of Charging Effects in Dielectrics

30

both trailing and leading edge of the pulse.

Actuation and De-actuation Voltage [V]

Ramp=1 V/sec for both trailing and leading edge of the pulse.

30 V ca.

35

40

45

50

Actuation and De-actuation Voltage [V]

55

60

15 V ca.

65

70

are always positive.

for the Actuation of RF MEMS Ohmic Series and Capacitive Shunt Switches 239

In the following text and figures, results and comments on the performed measurements are presented. First of all, S1 and CL have been actuated by using a uni-polar, positive voltage scheme. For both of them, the actuation as well as the de-actuation voltages have been measured until a *plateau* voltage has been obtained. The results are shown in Fig. 5 and in Fig. 6 with the values of the voltage and time parameters used for the actuation, and obtained for the corresponding de-actuation. In this case, the applied and measured voltages

S1 actuated by positive voltage only

0 2 4 6 8 10 12 14

CL actuated by positive voltage only

 Vact Vdeact

Actuation #

0 2 4 6 8 10 12

 Actuation Voltage Deactuation Voltage

Actuation #

Fig. 6. CL actuated by using positive voltage only. T1=1 min, T2=10 sec, Ramp=1 V/sec, for

Fig. 5. Response of S1 actuated by using positive voltages only. T1=1 min, T2=10 sec,

In particular, we paid attention to:


The first measurements have been performed by using only positive pulses (uni-polar scheme) with a ramp of 1 V/sec and T1=T2=1 min. After that, positive and negative pulses have been used, with the following parameters:


Both devices given in Fig. 2 and in Fig. 3 have been characterized by using the proposed uni-polar and bi-polar schemes as it is explained in detail in the following text. In the unipolar scheme, after the actuation, the switch is maintained at the same voltage during the time T1. Then, the voltage has been decreased down to zero, and in the meantime the deactuation voltage has been measured. The successive ramp was imposed by increasing again the voltage until a new actuation occurs, and also in this case the voltage is maintained constant during the time T1. Every time, the voltage required for the successive actuation was higher than the previous one. The procedure was repeated for recording actuation and de-actuation voltages until a *plateu* value has been obtained. In the bi-polar scheme, the applied DC voltage is composed by positive and negative pulses having a maximum value of ±50 V for the device in Fig. 1 (S1) and ±60 V for the device in Fig. 2 (CL), and in this case the actuation and de-actuation voltages have been measured as absolute values of the imposed pulses. In Fig. 4 the shape of the pulse trains used in the experiments is shown.

Fig. 4. Shape of the pulse trains used for the experiments on the charging effects. (a) is the uni-polar scheme, while (b) is the bi-polar one.

The first measurements have been performed by using only positive pulses (uni-polar scheme) with a ramp of 1 V/sec and T1=T2=1 min. After that, positive and negative pulses

Both devices given in Fig. 2 and in Fig. 3 have been characterized by using the proposed uni-polar and bi-polar schemes as it is explained in detail in the following text. In the unipolar scheme, after the actuation, the switch is maintained at the same voltage during the time T1. Then, the voltage has been decreased down to zero, and in the meantime the deactuation voltage has been measured. The successive ramp was imposed by increasing again the voltage until a new actuation occurs, and also in this case the voltage is maintained constant during the time T1. Every time, the voltage required for the successive actuation was higher than the previous one. The procedure was repeated for recording actuation and de-actuation voltages until a *plateu* value has been obtained. In the bi-polar scheme, the applied DC voltage is composed by positive and negative pulses having a maximum value of ±50 V for the device in Fig. 1 (S1) and ±60 V for the device in Fig. 2 (CL), and in this case the actuation and de-actuation voltages have been measured as absolute values of the imposed pulses. In Fig. 4 the shape of the pulse trains used in the experiments is shown.

Fig. 4. Shape of the pulse trains used for the experiments on the charging effects. (a) is the

uni-polar scheme, while (b) is the bi-polar one.

In particular, we paid attention to:

 Ramp=1 V/sec and 2 V/sec T1= 1 min and 30 sec

 The rise-time and the fall-time of the pulses (ramps) The delay between the positive and the negative pulse

have been used, with the following parameters:

The pulse-width

The applied voltage

T2=10 sec.

In the following text and figures, results and comments on the performed measurements are presented. First of all, S1 and CL have been actuated by using a uni-polar, positive voltage scheme. For both of them, the actuation as well as the de-actuation voltages have been measured until a *plateau* voltage has been obtained. The results are shown in Fig. 5 and in Fig. 6 with the values of the voltage and time parameters used for the actuation, and obtained for the corresponding de-actuation. In this case, the applied and measured voltages are always positive.

Fig. 5. Response of S1 actuated by using positive voltages only. T1=1 min, T2=10 sec, Ramp=1 V/sec for both trailing and leading edge of the pulse.

Fig. 6. CL actuated by using positive voltage only. T1=1 min, T2=10 sec, Ramp=1 V/sec, for both trailing and leading edge of the pulse.

Characterization and Modeling of Charging Effects in Dielectrics

finding is discussed after the presentation of the experimental data.

for the Actuation of RF MEMS Ohmic Series and Capacitive Shunt Switches 241

actuations. It is worth noting that the measured data have been normalized to positive values, and the reader can have the erroneous feeling that the de-actuation voltage is always higher than the actuation one. This is only a false perspective, and the reason for such a

It is worth noting the difference obtained between the results in Fig. 7, Fig. 8 and Fig. 9. Actually, no dependence on the applied ramps has been obtained, but there is a clear evidence that the process is quite slow, because after times in the order of several minutes, i.e. during the experimental procedure, the charging is still present. From the analysis of the figures where both positive and negative voltages have been applied (Fig. 7, 8 and 9), one could conclude that the actuation voltage is lower than the de-actuation one. In fact, this is due to the kind of plot, because only the absolute value of the applied voltage is given, in order to have a continuous curve, with data not jumping from negative to positive values.

The physical reason for that is explained in the discussion at the end of this section.

14 V ca.

In the following Fig. 10 and Fig. 11 the same qualitative results are shown for the device CL, where in 30 minutes ca. the charging effect has been almost completely recovered. It turns out from this finding that the same values for the actuation voltages have been recorded, and the same difference between V(actuation) and V(de-actuation) has been obtained.

0 2 4 6 8 10

 Actuation Voltage Deactuation Voltage

Actuation #

Fig. 9. S1 actuated by using positive and negative voltages. The same parameters used in the previous Fig. 8 have been imposed, i.e.: T1=30 sec, T2=10 sec, |+V|=|-V|=50 volt and Ramp=2 V/sec. The measurement has been performed the day after. The result is quite similar to that shown in Fig. 3, with T1 decreased from 1 min to 30 sec and Ramp passed from 1 V/sec to 2 V/sec. As a consequence, none of the above parameters seems to affect the measures. Moreover, the first actuation is still between 39 and 41 V, but by using positive and negative values it is maintained at a constant value as well as the de-actuation voltage,

Some of the main findings of the performed measurements are in full agreement with those in [34], and in particular with the conclusion that the devices do not fail if they are subjected to a square wave voltage for the actuation when a C/V curve is taken with a slowly varying

and it is lower than in the positive case only.

Actuation and De-actuation Voltage [V]

Therefore, a bi-polar scheme has been applied by measuring the same devices the day after, when the effect of charging was completely removed, leaving them at rest without voltage nor RF signals applied to the device under test. The results are given in Fig. 7 and in Fig. 8, where the absolute value of the applied voltage is plotted as a function of the performed

Fig. 7. S1 actuated by using positive and negative voltages. Only the absolute value of the recorded actuation voltage is plotted, but changed from +V to –V after each pulse, with T1=1 min, T2=10 sec, |+V|=|-V|=50 volt and Ramp=1 V/sec.

Fig. 8. S1 actuated by using positive and negative voltages. Only the absolute value of the voltage is plotted, but changed from +V to –V after each pulse, with T1=30sec, T2=10 sec, |+V|=|-V|=50 volt and Ramp=1 V/sec. The measurement has been performed 5 min after the one shown in Figure 7. The difference between actuation and de-actuation voltages is a bit decreased, which is an indication of a charging partially re-covered.

Therefore, a bi-polar scheme has been applied by measuring the same devices the day after, when the effect of charging was completely removed, leaving them at rest without voltage nor RF signals applied to the device under test. The results are given in Fig. 7 and in Fig. 8, where the absolute value of the applied voltage is plotted as a function of the performed

0 2 4 6 8 10

0 2 4 6 8 10

Actuation #

Fig. 8. S1 actuated by using positive and negative voltages. Only the absolute value of the voltage is plotted, but changed from +V to –V after each pulse, with T1=30sec, T2=10 sec, |+V|=|-V|=50 volt and Ramp=1 V/sec. The measurement has been performed 5 min after the one shown in Figure 7. The difference between actuation and de-actuation voltages is a

Fig. 7. S1 actuated by using positive and negative voltages. Only the absolute value of the recorded actuation voltage is plotted, but changed from +V to –V after each pulse, with

Actuation #

15 V ca.

 Actuation Voltage Deactuation Voltage

 Actuation Voltage Deactuation Voltage

20

26

28

30

32

Actuation and De-actuation Voltage [V]

34

36

38

40

T1=1 min, T2=10 sec, |+V|=|-V|=50 volt and Ramp=1 V/sec.

10 V ca.

bit decreased, which is an indication of a charging partially re-covered.

25

30

35

Actuation and De-actuation Voltage [V]

40

45

actuations. It is worth noting that the measured data have been normalized to positive values, and the reader can have the erroneous feeling that the de-actuation voltage is always higher than the actuation one. This is only a false perspective, and the reason for such a finding is discussed after the presentation of the experimental data.

It is worth noting the difference obtained between the results in Fig. 7, Fig. 8 and Fig. 9. Actually, no dependence on the applied ramps has been obtained, but there is a clear evidence that the process is quite slow, because after times in the order of several minutes, i.e. during the experimental procedure, the charging is still present. From the analysis of the figures where both positive and negative voltages have been applied (Fig. 7, 8 and 9), one could conclude that the actuation voltage is lower than the de-actuation one. In fact, this is due to the kind of plot, because only the absolute value of the applied voltage is given, in order to have a continuous curve, with data not jumping from negative to positive values. The physical reason for that is explained in the discussion at the end of this section.

In the following Fig. 10 and Fig. 11 the same qualitative results are shown for the device CL, where in 30 minutes ca. the charging effect has been almost completely recovered. It turns out from this finding that the same values for the actuation voltages have been recorded, and the same difference between V(actuation) and V(de-actuation) has been obtained.

Fig. 9. S1 actuated by using positive and negative voltages. The same parameters used in the previous Fig. 8 have been imposed, i.e.: T1=30 sec, T2=10 sec, |+V|=|-V|=50 volt and Ramp=2 V/sec. The measurement has been performed the day after. The result is quite similar to that shown in Fig. 3, with T1 decreased from 1 min to 30 sec and Ramp passed from 1 V/sec to 2 V/sec. As a consequence, none of the above parameters seems to affect the measures. Moreover, the first actuation is still between 39 and 41 V, but by using positive and negative values it is maintained at a constant value as well as the de-actuation voltage, and it is lower than in the positive case only.

Some of the main findings of the performed measurements are in full agreement with those in [34], and in particular with the conclusion that the devices do not fail if they are subjected to a square wave voltage for the actuation when a C/V curve is taken with a slowly varying

Characterization and Modeling of Charging Effects in Dielectrics

charge which can be accumulated in the device

exception done for the first actuation

only.

for the Actuation of RF MEMS Ohmic Series and Capacitive Shunt Switches 243

 The absolute value of the actuation voltage Va and of the de-actuation voltage Vd (and the difference between them) is constant when the sign of the pulse is reversed,

 The measured difference in the bi-polar scheme is equal to the difference between the two plateau (i.e. Va,plateau-Vd,plateau) experienced during the charging process when a positive voltage pulse train is applied. This could be used as a measure of the maximum

The absolute value of the actuation voltage for the series switch S1 is almost half of the

 The absolute value of the actuation voltage for the shunt switch CL subjected to positive and negative pulses is around 20 volt Vs the almost 55 volt used for the positive voltage

 The results from the previous two points are "re-normalized" considering that the algebraic sum of the positive actuation voltage (starting from the second actuation), and of the difference between the two plateau values in the case of positive only voltages (Va,plateau-Vd,plateau), gives as a result the first positive actuation voltage. This means that the voltage difference necessary for the actuation is the same. So, when positive and negative voltages are applied to the device S1, for which we have |Va|40 V, then, after the first de-actuation (occurring in this case again at V=40 V after imposing V=50 V) we always get |Va|25 V with a difference of 15 V coming from the extra voltage

 The same result is obtained for the CL configuration, where |Va|50 V, and the first deactuation occurs at |Vd|50 V after imposing a positive voltage V=60 V. After that, the switch is actuated always by applying 20 V. Actually, a difference of 30 V is always observed (in this case this happens independently of the time passed from the previous measurement), in such a way that the sum 20+30=50 V is again the value of the first

As a consequence of the above discussion, both schemes for actuation (uni-polar and bi-polar) are affected by charging mechanisms, because the dielectric is always present. On the other hand, the bi-polar scheme offers the advantage, with respect to the uni-polar one, in terms of the absolute value of the voltage necessary for actuating the device [37]. This is especially good when a high number of actuations are needed for a frequent re-configuration of architectures based on several RF MEMS, and there is no time for a full de-charging of each individual device. In our devices, we believe that the charging exhibits a saturation value due to the maximum number of charges which can be activated on the surface as well as in the bulk of the dielectric, which slowly goes back to the original situation. In this framework, looking at our experimental results, the utilization of positive and negative pulses allows a faster recombination process, and the possibility to drive the device always by means of the same absolute value of the voltage, changing the sign of the applied voltage from one actuation to the successive one. A possible interpretation could be that the de-charging process, usually slow, is accelerated when the device is subjected to a gradient of the electric field, passing from positive to negative values and vice-versa. In the following Fig. 12 the bi-polar scheme

MIM capacitors having the same structure to be used for the actuation pads of the RF MEMS switches have been realized, to study the charging mechanisms related to the materials used

first positive value when a train of positive and negative pulses is used

generated by the charging effect due to the previous actuation.

actuation voltage experienced when positive only pulses are used.

imposed for S1 and the effect on the actuation voltage is shown.

**4. Measurements on test MIM capacitors and discussion** 

Fig. 10. CL actuated by using positive and negative voltages. T1=1 min, T2=10 sec, |+V|=|- V|=60 V and Ramp=1 V/sec.

Fig. 11. CL response by using the same parameters as in the case of Fig. 10, but with Ramp=2 V/sec and measurement performed after 30 min. The difference between the two levels has the same value as before.

voltage. Actually, for slow ramps we never experienced a stuck device for both S1 and CL. On the other hand, the reliability tests previously performed on the same devices were never accompanied by a sticking of the series configuration, in spite of the fact that a faster switching was used in that case [47].

It is clear, in the present experimental results, that charging effects are present in both configurations, affecting in a predictable way the performances of the measured devices. In particular:

30 V ca.

0 2 4 6 8 10

0 2 4 6 8 10

Actuation #

voltage. Actually, for slow ramps we never experienced a stuck device for both S1 and CL. On the other hand, the reliability tests previously performed on the same devices were never accompanied by a sticking of the series configuration, in spite of the fact that a faster

It is clear, in the present experimental results, that charging effects are present in both configurations, affecting in a predictable way the performances of the measured devices.

30 V ca.

Fig. 11. CL response by using the same parameters as in the case of Fig. 10, but with Ramp=2 V/sec and measurement performed after 30 min. The difference between the two

 Actuation Voltage Deactuation Voltage

 Actuation Voltage Deactuation Voltage

Actuation #

Fig. 10. CL actuated by using positive and negative voltages. T1=1 min, T2=10 sec, |+V|=|-

20 24 28

Actuation and De-actuation Voltage [V]

levels has the same value as before.

switching was used in that case [47].

In particular:

Actuation and De-actuation Voltage [V]

V|=60 V and Ramp=1 V/sec.


As a consequence of the above discussion, both schemes for actuation (uni-polar and bi-polar) are affected by charging mechanisms, because the dielectric is always present. On the other hand, the bi-polar scheme offers the advantage, with respect to the uni-polar one, in terms of the absolute value of the voltage necessary for actuating the device [37]. This is especially good when a high number of actuations are needed for a frequent re-configuration of architectures based on several RF MEMS, and there is no time for a full de-charging of each individual device. In our devices, we believe that the charging exhibits a saturation value due to the maximum number of charges which can be activated on the surface as well as in the bulk of the dielectric, which slowly goes back to the original situation. In this framework, looking at our experimental results, the utilization of positive and negative pulses allows a faster recombination process, and the possibility to drive the device always by means of the same absolute value of the voltage, changing the sign of the applied voltage from one actuation to the successive one. A possible interpretation could be that the de-charging process, usually slow, is accelerated when the device is subjected to a gradient of the electric field, passing from positive to negative values and vice-versa. In the following Fig. 12 the bi-polar scheme imposed for S1 and the effect on the actuation voltage is shown.
