**5. Dielectric polarization and Poole-Frenkel effect in RF MEMS and MIM**

On the time scale of interest to the RF-MEMS capacitive switches response (i.e. greater than 1 μsec) an electric field can interact with the dielectric film in two primary ways. These are: (i) the re-orientation of defects having an electric dipole moment, such as complex defects, and (ii) the translational motion of charge carriers, which usually involve simple defects such as vacancies, ionic interstitials and defect electronic species. These processes give rise to the dipolar (PD) and the intrinsic space charge (PSC-i) polarization mechanisms, respectively. Moreover, when the dielectric is in contact with conducting electrodes charges are injected through the trap assisted tunneling and/or the Poole-Frenkel effect [69] giving rise to extrinsic space charge polarization (PSC-e) whose polarity is opposite with respect to the other two cases. In RF-MEMS capacitive switches during the actuation all the polarization mechanisms occur simultaneously and the macroscopic polarization is given by

$$P\_{\text{tot}} = P\_D + P\_{\text{SC}-i} - P\_{\text{SC}-e} \tag{4}$$

Now, from elementary physics it is known that the electric displacement *D*, defined as the total charge density on the electrodes, will be given by *D EP* <sup>0</sup> , where *E* is the applied field and *P* the dielectric material polarization. The resulting polarization *P* may be further divided into two parts according to the time constant response [70]:

a) An almost instantaneous polarization due to the displacement of the electrons with respect to the nuclei. The time constant of the process is about 10-16 sec and defines the high frequency dielectric constant that is related to the refractive index.

b) A delayed time dependent polarization *P*(*t*), which determines the dielectric charging in MEMS, starting from zero at *t*=0, due to the orientation of dipoles and the distribution of free charges in the dielectric, the dipolar and space charge polarization respectively. Moreover the growth of these polarization components may be described in the form of *Pt P jj j* <sup>0</sup> <sup>1</sup> *<sup>f</sup> <sup>t</sup>* . The index *j* refers to each polarization mechanisms, and *fj*(*t*) are

exponential decay functions of the form exp *t* . Here *τ* is the process time and *β* the

stretch factor. If *β*=1 the charging/discharging process is governed by the Debye law. In disordered systems like the amorphous oxides, which possess a degree of disorder, *β*<1 and the charging/discharging process is described by the stretched exponential law.

In the case of a MEMS switch that operates under the waveforms in Fig. 4, the dielectric is subjected to charging when the bridge is in the DOWN position and discharging in the UP position, independently of the ON or OFF functionality of the device. More specifically, when a uni-polar pulse train is applied (Fig. 4 (a)) then the device is subjected to contact-less

Characterization and Modeling of Charging Effects in Dielectrics

(Deact) of both S1 and CL devices.

a longitudinal polarization across substrate.

temperature oxide), as it is shown in Fig. 19 (a).

investigation.

*V*

for the Actuation of RF MEMS Ohmic Series and Capacitive Shunt Switches 259

0 0

 V0 ΔV β Ν\* Fig. 5 Act 13.5 54.4 0.69 1.67

Fig. 6 Act 27.0 54.5 1 1.67

Table 2. Fitted values for the exponential trend of the actuation (Act) and de-actuation

top ones. Moreover, these charges have a small influence on the dielectric polarization.

Another possible situation could be the charging between the actuation pads and the ground plane of CPW across the substrate dielectric [73]. This charging process gives rise to a longitudinal polarization across the substrate oxide that behaves like the dipolar polarization. The values of *N\** for actuation and de-actuation agree with the presence of both mechanisms, which is a slower build-up of space charge polarization and competition from

Applying a bipolar bias scheme we observe that both actuation and de-actuation voltages do not vary significantly with time, as it is also the case for other recently considered RF MEMS switch configurations, like the miniature one [74]. This can be easily attributed to the field induced charging/discharging processes. A significant difference that arises from the bipolar actuation is the reversal of magnitude of actuation and de-actuation voltages. This behavior has been occasionally observed but not investigated in depth. If we take into account that in MEMS switches the charging is asymmetric, a reason that leads to stiction even under bipolar actuation, we may assume that this effect is probably responsible for the observed reversal. In such a case the value of *Ppo* will change polarity and magnitude after each change of the actuation voltage polarity. In any case the observed behavior is under

Concerning the charging effects in a MIM capacitor, let' analyse as an example experimental results based on silicon dioxide deposited by means of a low temperature process (LTO=low

The fitting results reveal that the dominant mechanism is the space charge polarization (*Pj*<0). Moreover, it is worth noting that the actuation voltage increases faster than the de-actuation one. Such a behavior can result from a faster increase of space charge polarization or decrease of dipolar polarization when the bridge is non-actuated. Taking into account that the dipolar polarization in SiO2 is characterized by long time constants (fig. 4 of [72]), we are led to the conclusion that the differences in the increase of actuation and de-actuation voltages arise from the mechanisms involved in charge injection and collection, respectively. This can be easily understood if we bear in mind that the charge injection occurs under high electric field and that the trap assisted tunneling charging process gives rise to a spatial distribution of charges in the vicinity of the injecting contacts. During the OFF state, where no bias is applied, the trapped charges (located at the dielectric free surface) are emitted and finally collected by the bottom electrode. The charge collection, which takes place through diffusion and drift in the presence of local electric fields, is complex owing to multi trapping processes. Regarding the charges that are injected from the bottom electrode, they are collected much sooner than the

<sup>1</sup> 1, ,

 

Deact 29.5 33.2 0.96 1.96

Deact 36.8 22.4 0.83 2.5

(8)

*<sup>j</sup> <sup>D</sup> <sup>j</sup> SC <sup>j</sup> z P zP P*

charging below pull-in and pull-out. Above pull-in and pull-out the device is subjected to contact charging.

If we assume that at room temperature the density of free charges in the LTO, i.e. SiO2 deposited at low temperature, is very low we can re-write Eq. (4) as:

$$P = P\_D - P\_{\text{SC}} \tag{5}$$

where *PSC* is the space charge polarization of extrinsic origin. When we apply a pulse train the following will occur:


Due to the dielectric film polarization the pull-in and pull-out voltages will be determined by:

$$V\_{pi} = \sqrt{\frac{8kz^3}{27\varepsilon\_0 A}} - \frac{z\_1 P\_{pi}}{\varepsilon\_0} \; ; \; V\_{po} = \sqrt{\frac{2kz\_1^2 \left(z - z\_1\right)}{\varepsilon\_0 A}} - \frac{z\_1 P\_{po}}{\varepsilon\_0} \tag{6}$$

In the Si3N4 dielectric it has been shown that, at room temperature, the space charge polarization induced by the charge injection is the dominant mechanism [71][72]. If we assume that the same effect holds for SiO2 we are led to the conclusion that the pull-out voltage will increase with time when a uni-polar pulse train is applied.

The dependence of the actuation and de-actuation voltages on the number of cycles was fitted for the exploited RF MEMS devices S1 and CL studied in the previous sections, by assuming that the charging process follows the stretched exponential law.

The fitting of data has been performed as a function of the number of cycles (*N*), since each cycle maintains a constant shape and represents a certain effective ON and OFF time. This is particularly useful in actual devices, when the reliability can be determined by the number of total actuations as well as the total time during which the RF MEMS switch remains actuated. The differences in the effective ON and OFF times will reflect in the number of cycles (*N\**) that corresponds to the process time *τ*. According to Eq. (6), and in agreement with the above discussed growth for the polarization, we can apply the following equation to describe the evolution of the pull-in and pull-out voltages as a function of time/number of cycles.

$$V\_j(N) = V\_{0,j} - \frac{z\_1 P\_j}{\varepsilon\_0} \cdot \left\{ 1 - \exp\left[ -\left(\frac{N}{N\_j^\*}\right)^\beta \right] \right\} \tag{7}$$

where *z1* is the dielectric thickness, *j* an index that stands for actuation (pull-in) and deactuation (pull-out) while *V0,j* represents the pull-in and pull-out voltages that are determined by the electro-mechanical model.

The fitting results show excellent agreement with the experimental data, and the fitting parameters are listed in Table 2, with reference to Fig. 5 and Fig 6 of the current contribution.

Here it must be pointed out that:

charging below pull-in and pull-out. Above pull-in and pull-out the device is subjected to

If we assume that at room temperature the density of free charges in the LTO, i.e. SiO2

where *PSC* is the space charge polarization of extrinsic origin. When we apply a pulse train

during the contact-less charging the electric field increases the dipolar polarization and

 during the contact charging the high electric field causes a further increase of the dipolar polarization, and through the charge injection contributes to the build-up of

Due to the dielectric film polarization the pull-in and pull-out voltages will be determined by:

*po*

In the Si3N4 dielectric it has been shown that, at room temperature, the space charge polarization induced by the charge injection is the dominant mechanism [71][72]. If we assume that the same effect holds for SiO2 we are led to the conclusion that the pull-out

The dependence of the actuation and de-actuation voltages on the number of cycles was fitted for the exploited RF MEMS devices S1 and CL studied in the previous sections, by

The fitting of data has been performed as a function of the number of cycles (*N*), since each cycle maintains a constant shape and represents a certain effective ON and OFF time. This is particularly useful in actual devices, when the reliability can be determined by the number of total actuations as well as the total time during which the RF MEMS switch remains actuated. The differences in the effective ON and OFF times will reflect in the number of cycles (*N\**) that corresponds to the process time *τ*. According to Eq. (6), and in agreement with the above discussed growth for the polarization, we can apply the following equation to describe the evolution of the pull-in and pull-out voltages as a function of time/number

> 0, \* <sup>0</sup> 1 exp *<sup>j</sup>*

where *z1* is the dielectric thickness, *j* an index that stands for actuation (pull-in) and deactuation (pull-out) while *V0,j* represents the pull-in and pull-out voltages that are

The fitting results show excellent agreement with the experimental data, and the fitting parameters are listed in Table 2, with reference to Fig. 5 and Fig 6 of the current

*z P <sup>N</sup> VN V*

*j*

(7)

*N*

; <sup>2</sup>

*V*

*PP P D SC* (5)

1 1 1 0 0 2 *po*

(6)

*kz z z z P*

*A*

deposited at low temperature, is very low we can re-write Eq. (4) as:

assists to re-distribution and dissipation of injected charges

3

*kz z P*

voltage will increase with time when a uni-polar pulse train is applied.

assuming that the charging process follows the stretched exponential law.

<sup>1</sup>

*j j*

determined by the electro-mechanical model.

Here it must be pointed out that:

8 27

*A*

*pi*

*V*

1 0 0

*pi*

contact charging.

the following will occur:

of cycles.

contribution.

space charge polarization


<sup>1</sup> 1, , *<sup>j</sup> <sup>D</sup> <sup>j</sup> SC <sup>j</sup> z P zP P V* (8)

Table 2. Fitted values for the exponential trend of the actuation (Act) and de-actuation (Deact) of both S1 and CL devices.

The fitting results reveal that the dominant mechanism is the space charge polarization (*Pj*<0). Moreover, it is worth noting that the actuation voltage increases faster than the de-actuation one. Such a behavior can result from a faster increase of space charge polarization or decrease of dipolar polarization when the bridge is non-actuated. Taking into account that the dipolar polarization in SiO2 is characterized by long time constants (fig. 4 of [72]), we are led to the conclusion that the differences in the increase of actuation and de-actuation voltages arise from the mechanisms involved in charge injection and collection, respectively. This can be easily understood if we bear in mind that the charge injection occurs under high electric field and that the trap assisted tunneling charging process gives rise to a spatial distribution of charges in the vicinity of the injecting contacts. During the OFF state, where no bias is applied, the trapped charges (located at the dielectric free surface) are emitted and finally collected by the bottom electrode. The charge collection, which takes place through diffusion and drift in the presence of local electric fields, is complex owing to multi trapping processes. Regarding the charges that are injected from the bottom electrode, they are collected much sooner than the top ones. Moreover, these charges have a small influence on the dielectric polarization.

Another possible situation could be the charging between the actuation pads and the ground plane of CPW across the substrate dielectric [73]. This charging process gives rise to a longitudinal polarization across the substrate oxide that behaves like the dipolar polarization. The values of *N\** for actuation and de-actuation agree with the presence of both mechanisms, which is a slower build-up of space charge polarization and competition from a longitudinal polarization across substrate.

Applying a bipolar bias scheme we observe that both actuation and de-actuation voltages do not vary significantly with time, as it is also the case for other recently considered RF MEMS switch configurations, like the miniature one [74]. This can be easily attributed to the field induced charging/discharging processes. A significant difference that arises from the bipolar actuation is the reversal of magnitude of actuation and de-actuation voltages. This behavior has been occasionally observed but not investigated in depth. If we take into account that in MEMS switches the charging is asymmetric, a reason that leads to stiction even under bipolar actuation, we may assume that this effect is probably responsible for the observed reversal. In such a case the value of *Ppo* will change polarity and magnitude after each change of the actuation voltage polarity. In any case the observed behavior is under investigation.

Concerning the charging effects in a MIM capacitor, let' analyse as an example experimental results based on silicon dioxide deposited by means of a low temperature process (LTO=low temperature oxide), as it is shown in Fig. 19 (a).

Characterization and Modeling of Charging Effects in Dielectrics

improving the quality of the dielectric material.

for preventing the charging itself.

for the Actuation of RF MEMS Ohmic Series and Capacitive Shunt Switches 261

To better investigate this aspect, an additional characterization was performed on a sample with the same structure for the bottom and for the top electrodes and with Si3N4 as dielectric. Two samples have been measured: (i) the first one in the usual way, by means of a slow voltage ramp, and (ii) another one by imposing a typical stress used for the switches, subjecting it to a high number of DC pulses and measuring the characteristic current vs voltage after that. Actually, 104 pulses with a pulse-width τ = 250 ms and with a period T = 500 ms (duty cycle = τ/T = 50%), with a voltage V=50 volt, have been used. As a result, the low voltage response has been "rectified" as it is shown in Fig. 28, where the initial behavior is almost constant, as expected by a dielectric material without free charges incorporated. We believe that such a trend can be justified by the neutralization of surface free charges at the interface between the dielectric layer and the top metal, where, due to the roughness, charges are trapped but free to contribute when a DC field is imposed. The energy released by the DC input pulses, provided quickly with respect to the time constants for the material de-charging, was high enough to favor the re-combination of the charges, thus locally

Fig. 28. Measured trend of the current as a function of the applied voltage for a MIM made by Si3N4 before (curve a) and after (curve b) cycling the sample with pulses as high as 50 volt. Generally, a linear response is always obtained as a function of the applied voltage, while a constant value is expected for an almost ideal dielectric material. By cycling the sample such a response is flattened, maybe due to the re-combination of residual charges belonging to defects of the material surface coming out from the technological process. Actually, a comparison has been done between the charging response of MIM capacitors and RF MEMS switches, and the differences coming from such an analysis have been discussed with emphasis on the different times needed for re-storing the initial conditions or

The MIM was made by a poly-silicon layer as the bottom electrode, with metal on the top side (top electrode) and LTO as a dielectric layer. The structure emulates the situation of a fully collapsed bridge by means of a lateral actuation, where poly-silicon is used as the material for the feeding lines and for the pad under bridge, while LTO is deposited on the top of it to provide an electrical isolation; the metal on the top is equivalent to the bridge touching the actuation electrode when the voltage is applied. Such an arrangement, i.e. a multilayer polysilicon/dielectric/metal, is also a source of further injection of charges, because polysilicon is not just a bad conductor and it can also contribute at the interface polysilicon/dielectric. The sample was measured by repeating a slow voltage ramp three times and measuring the corresponding current. In particular, a ramp rate dV/dt=0.05 V/sec and a maximum voltage of 80 volt were imposed. As expected, the charging process is enhanced, and this is evidenced by the current drop after each ramp, but the effect is less important the third time, thus demonstrating the saturation of the charge injected in the sample, as also experienced in the real MEMS switches already discussed in this paper.

As already outlined, the measured trend of the current is not ideal for the exploited sample and for similar ones based on silicon nitride, and a linear response is always obtained as a function of the applied voltage, while a constant value is expected for an almost ideal dielectric material at low voltage values, i.e. in a range up to, at least, 20-25 volt for typical dielectric materials used in microelectronics. The same data of Fig. 19 (a) have been plotted in Fig. 27, by using I/V vs V1/2, to check the Poole-Frenkel effect. Actually, the current dependence on bias seems to be determined by the Poole-Frenkel effect when the applied bias exceeds the value of 50 volt:

$$I(V) = I\_0 E \exp\left(b\_{\rm PF}^\* \sqrt{E} - \frac{\Phi\_n}{kT}\right) \text{ where } b\_{\rm PF}^\* = \frac{1}{kT} \sqrt{\frac{q^3}{\pi \varepsilon \varepsilon\_0}}\tag{9}$$

The change of bPF in SiN has been investigated by S.P. Lau et al. and attributed to large concentration of defects in SiN and the formation of defect band. Taking into account the increase of bPF with the applied electrical stress we are led to the conclusion that the latter decreases the density of traps in the SiN film [75].

Fig. 27. I/V curve as a function of the V1/2 by using data from Fig. 19 (a).

The MIM was made by a poly-silicon layer as the bottom electrode, with metal on the top side (top electrode) and LTO as a dielectric layer. The structure emulates the situation of a fully collapsed bridge by means of a lateral actuation, where poly-silicon is used as the material for the feeding lines and for the pad under bridge, while LTO is deposited on the top of it to provide an electrical isolation; the metal on the top is equivalent to the bridge touching the actuation electrode when the voltage is applied. Such an arrangement, i.e. a multilayer polysilicon/dielectric/metal, is also a source of further injection of charges, because polysilicon is not just a bad conductor and it can also contribute at the interface polysilicon/dielectric. The sample was measured by repeating a slow voltage ramp three times and measuring the corresponding current. In particular, a ramp rate dV/dt=0.05 V/sec and a maximum voltage of 80 volt were imposed. As expected, the charging process is enhanced, and this is evidenced by the current drop after each ramp, but the effect is less important the third time, thus demonstrating the saturation of the charge injected in the sample, as also experienced in the real MEMS switches already discussed in this paper. As already outlined, the measured trend of the current is not ideal for the exploited sample and for similar ones based on silicon nitride, and a linear response is always obtained as a function of the applied voltage, while a constant value is expected for an almost ideal dielectric material at low voltage values, i.e. in a range up to, at least, 20-25 volt for typical dielectric materials used in microelectronics. The same data of Fig. 19 (a) have been plotted in Fig. 27, by using I/V vs V1/2, to check the Poole-Frenkel effect. Actually, the current dependence on bias seems to be determined by the Poole-Frenkel effect when the applied

*kT*

The change of bPF in SiN has been investigated by S.P. Lau et al. and attributed to large concentration of defects in SiN and the formation of defect band. Taking into account the increase of bPF with the applied electrical stress we are led to the conclusion that the latter

where

<sup>3</sup> \*

1

*PF <sup>q</sup> <sup>b</sup> kT*

0

(9)

bias exceeds the value of 50 volt:

 \* <sup>0</sup> exp *<sup>n</sup> PF IV IE b E*

decreases the density of traps in the SiN film [75].

Fig. 27. I/V curve as a function of the V1/2 by using data from Fig. 19 (a).

To better investigate this aspect, an additional characterization was performed on a sample with the same structure for the bottom and for the top electrodes and with Si3N4 as dielectric. Two samples have been measured: (i) the first one in the usual way, by means of a slow voltage ramp, and (ii) another one by imposing a typical stress used for the switches, subjecting it to a high number of DC pulses and measuring the characteristic current vs voltage after that. Actually, 104 pulses with a pulse-width τ = 250 ms and with a period T = 500 ms (duty cycle = τ/T = 50%), with a voltage V=50 volt, have been used. As a result, the low voltage response has been "rectified" as it is shown in Fig. 28, where the initial behavior is almost constant, as expected by a dielectric material without free charges incorporated. We believe that such a trend can be justified by the neutralization of surface free charges at the interface between the dielectric layer and the top metal, where, due to the roughness, charges are trapped but free to contribute when a DC field is imposed. The energy released by the DC input pulses, provided quickly with respect to the time constants for the material de-charging, was high enough to favor the re-combination of the charges, thus locally improving the quality of the dielectric material.

Fig. 28. Measured trend of the current as a function of the applied voltage for a MIM made by Si3N4 before (curve a) and after (curve b) cycling the sample with pulses as high as 50 volt. Generally, a linear response is always obtained as a function of the applied voltage, while a constant value is expected for an almost ideal dielectric material. By cycling the sample such a response is flattened, maybe due to the re-combination of residual charges belonging to defects of the material surface coming out from the technological process. Actually, a comparison has been done between the charging response of MIM capacitors and RF MEMS switches, and the differences coming from such an analysis have been discussed with emphasis on the different times needed for re-storing the initial conditions or for preventing the charging itself.

Characterization and Modeling of Charging Effects in Dielectrics

MIM structures (see Fig. 16).

**7. Acknowledgment** 

**8. References** 

"High Reliability MEMS Redundancy Switch".

Noordwijk, Netherlands, 2006,

Artech House, Boston, 1999.

Hoboken, New Jersey, USA, 2003.

Boston, 2002.

communications. *Proc. IEEE* 1998, 86, 1756-1768.

[6] Senturia, S. *Microsystem Design*, Springer, New York, 2001.

subjected to such an electrical stress.

for the Actuation of RF MEMS Ohmic Series and Capacitive Shunt Switches 263

not a complete spontaneous restoring of the initial conditions, against the previous finding for RF MEMS switches. *This could be an evidence that the charging effects occurring in the actual MEMS device cannot be completely emulated by a MIM structure, as the times for restoring the initial conditions are quite different between them. Anyway, in spite of a possible indication for different processes, due to the actuation itself, the charging properties of the material used for the actuation pads will be always present.* In the case of the measured switches, TEOS was used for the actuation pads, which exhibits quite pronounced charging effects as evidenced also in

Moreover, better performances in the I Vs V response can be obtained when the MIM is subjected to several pulses, analogously to those used in operating conditions for RF MEMS, maybe due to recombination of charges (left free from the technological process) when

Concerning the materials and the deposition techniques, from the results shown in Table 1 and from the plots is difficult to draw a final conclusion, but one can see that generally Si3N4 exhibits an almost linear response for the current as a function of the applied voltage in a voltage range wider with respect to SiO2 (LTO, TEOS). Moreover, the PECVD HF Nitride deposited at 300 °C looks like better also in terms of current reversal with respect to TEOS, and it is attributed to a higher densification temperature (Fig. 21). Actually, charge injection is present in both materials owing to the non-ideal response of the I Vs V curve, which should be flat at low voltages, but a strong non-linear behaviour due to the Poole-Frenkel

Work partially funded by the European Space Agency (ESA) Contract 20847/07/NL/GLC

Adriano Cola from CNR-IMM Lecce and Luigi Mariucci from CNR-IMM Roma are kindly

[1] Hopkinson, J.; Wilson, E. On the capacity and residual charge of dielectrics as affected by temperature and time. *Phil. Trans. Roy. Soc. London. A* 1897, 189, 109-135. [2] Binet, G.; Freire, M.; Van Eesbeek, M.; Daly, E.; Drolshagen, G.; Henriksen, T.; Thirkettle,

[4] Nguyen, C.T.-C.; Katehi, L.P.B.; Rebeiz, G.M. Micromachined devices for wireless

[5] De Los Santos, H.J. *Introduction to Microelectromechanical (MEM) Microwave Systems*,

[7] De Los Santos, H.J. *RF MEMS Circuit Design for Wireless Communications*, Artech House,

[8] Rebeiz, G. M. *RF MEMS Theory, Design, and Technology,* 1st Ed.; John Wiley & Sons:

 https://iti.esa.int/iti/resource/Space\_Specifications\_Checklist.doc. [3] Asokan, T. Ceramic dielectrics for space applications. *Curr. Sci.* 2000, 79, 348-351.

A.; Poinas, P.; Eiden, M.; Guglielmi, M. *Space specifications check list*; ESA-ESTEC:

effect is obtained only for *V* > 50-60 V for Si3N4 and for *V* > 20-30 V for SiO2.

acknowledged for helpful discussions on charge effects in MIM structures.
