Failure predictive model of capacitive RF-MEMS

Microelectronics Reliability 45 (2005) 1770–1775 www.elsevier.com/locate/microrel

Failure Predictive Model of Capacitive RF-MEMS S. Mellé (1), D. De Conto(1) , L. Mazenq(1), D. Dubuc(1), B. Poussard (1), C. Bordas (1), K. Grenier(1) , L.Bary (1), O. Vendier(2) ,J.L. Muraro (2) , J.L. Cazaux(2) and R. Plana(1) (1)

(2)

LAAS-CNRS, 7, Av. du Colonel Ro che, 31077 Toulouse Cedex 4, France Alcatel Space Industries, 26, Av. Jean François Champollion 31100 Toulouse, France Phone : +33-5-61-33-64-06, Fax : +33-5-61-33-69-69, E-mail : [email protected]

Abstract — This paper reports on the investigation of the failure mechanism in capacitive RF-MEMS through an efficient analysis methodology. We demonstrate that the physical origin of the dielectric charging is the leakage current through the RF-MEMS dielectric. To monitor the kinetic of this failure phenomenon, we introduce a useful parameter, which corresponds to the shift rate of the actuation voltages (SRAV) and an appropriate reliability-driven electrical stress parameter, which takes the contact quality between the bridge and the dielectric into account. We finally propose a figure of merit, derived from a predictive model, which quantifies the capacitive RF MEMS reliability and open the door to the prediction of lifetime as well as its optimization and/or acceleration for testing. Ó 2005 Elsevier Ltd. All rights reserved.

I. INTRODUCTION The use of microelectromechanical (MEM) switches for the future communication applications is getting more and more attractive. The numerous advantages of MEM devices (low power consumption, low losses, high isolation and high linearity) indeed answer to the continuous rise of system performances requirements and their operating frequencies [1]. But today, the main limiting factor which slows down the integration of RF-MEMS in industrial applications corresponds to their reliability troubles that are still unsolved and under discussion. The main cause of failure of these structures (electrostatically actuated) is related to the dielectric charging [2-4] which modeling is the current hot topic in RF-MEMS researches. The aim is to model the failure mechanism in order to : • Optimize the RF-MEMS reliability and to improve the lifetime of theses devices both in the technological and technical (design and actuation) points of view. • Find some accelerating factor in order to define efficient tes t procedure s of devices set. In this paper, we present our research focused on this topic. The second part details the in-house developed tools and investigation methodologies, which originality consists in the use of high frequency performances (Scattering parameters) measurement and monitoring during the lifetime. The third part deals with the two main failure modes which appear in capacitive RF-MEMS: stiction and screening. These modes will then permits to quantify how the physical mechanisms translate into failure and to evaluate the lifetime parameter. The physical modeling of the failure phenomenon is addressed in the fourth part. This modeling takes all the driving parameters (electrical stress, temperature, …) into account. We finally introduce a Figure Of Merit (FoM) of RF-MEMS reliability and lifetime. This FoM then quantifies the ability of the dielectric not to accumulate charges. The benefits of this figure reside in

providing an appropriate comparison between technologies and devices process in a different manner. II. EXPERIMENTAL TEST BENCH FOR FAILURE ANALYSIS OF CAPACITIVE RF-MEMS The structure under investigation corresponds to gold bridge over a 50Ω characteristic -impedance coplanar line. The fig. 1 describes such a structure in which the dielectric over the center conductor of the line prohibits a DC contact between conductors. The movable bridge is electrostatically actuated by applying a DC voltage on the central conductor of the CPW line and pulls down the bridge in contact with the dielectric, which translates to a high capacitor value prohibiting the signal flow. The dielectric is a PECVD silicon nitride with thicknesses typically between 0.1µm to 0.3µm and, regarding the required DC Voltage to actuate the bridge (tens of volts), is stressed with electric field greater than 1 MV/cm. This high electrical field translates into failure of the dielectric -and then of the MEMS switches-. It is now wellestablished that this mechanism corresponds to the most important one, which limits the lifetime of capacitive RFMEMS.

Fig. 1 : Microphotography of the device under test

0026-2714/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2005.07.092

S. Melle´ et al. / Microelectronics Reliability 45 (2005) 1770–1775 A. Test set description To investigate this new type of components, both in term of RF, electromechanical and reliability performances, we have developed a specific test-set associated to an original methodologies. The fig.2 describes the developed test set, which originality, compared with others from different institutes, is to monitor the behavior of the MEMS regarding their RF-performances thanks to a Vector Network Analyzer.

Vshift =

•

Arbitrary function generator

•

High voltage amplifier

Multimeter

10dB coupler

RF power detector

Digital oscilloscope

Fig. 2 : RF MEMS reliability test set

This test setup is organized in three parts. The first one (in red on fig. 2) deals with the switch actuation thanks to a high voltage amplifier driven by a waveform generator. Various waveform signals can be obtained with voltage values ranging from -100V to +100V, and frequency ranging from 1Hz to 16MHz and with a controllable duty cycle. Different type of waveform can then be experimented in order to improve the reliability of RF-MEMS. The second part (in green on fig. 2) of the test set is dedicated to the microwave performances measurement of the switches up to 40 GHz through a vector network analyzer (VNA). This part permits to monitor the RF performances of the bridge versus the applied voltage at any time. We can then extract all the RF and electromechanical (threshold voltages) performances during lifetime tests (cycling or other types of stresses). Finally, a 10dB coupler, a RF power detector and a digital oscilloscope constitute the third part of the test set (in blue on fig. 3) and allow monitoring the switching times of the bridge. This test set is fully remote thanks to an in -house software, which controls all the instruments through an HPIB bus and can then be used to carry out reliability investigations. B. Failure Investigation methodology Some publications [2,3] already gives qualitative description of the failure mechanism. The high voltage through the dielectric translates into leakage current and then stored charges (called dielectric charging ). The threshold voltages of the bridge are then shift thanks to the following equation [3] :

(1)

Thanks to this failure description, we have developed a specific failure analysis methodology, which consists in:

GP-IB

RF MEMS

ρ × ediel 2 × ε0 × εr

In (1), e die l and εr corresponds to the dielectric thickness and relative permittivity and ρ the charge density stored trough the dielectric, considered here as uniform.

PC In- house Software

Vector network analyzer

1771

Applying a stress to the bridge. As the stress corresponds to the applied voltage, we actuate the bridge periodically with a fixed voltage waveform, amplitude and frequency (we call this test: cycling). Monitoring one or several performances of the bridge in order to detect some degradations or failure.

As the cause of the failure corresponds to the shift of the threshold voltages of the MEMS, we have decided to monitor the threshold voltages of the MEMS. They have been extracted from the measurement of the S21 parameter, which reflects the bridge state for different applied DC voltages as illustrated in fig. 3. Applied voltage (V) -50

-40

-30

-20

-10

0

10

20

30

40

50

0

Vpdinitial

after 6.000 cycles

Vpu-

Vpu+

-5

Vpd+

-10

-15

-20 S21 (dB)

Fig. 3 : Transmission parameter S21 (at 10 GHz) versus applied DC voltage / before and after a cycling test

Thanks to this measurement, we can extract the pull-down voltages , which correspond to the positive and negative voltage above which the bridge goes in contact with the dielectric. The pull-up voltages can also be determined; they constitute the voltages under which the bridge, initially stuck, goes in the up position. These parameters will serve as the state parameters of the dielectric charging and then will be systematically monitored during the stress step of the RF-MEMS.

S. Melle´ et al. / Microelectronics Reliability 45 (2005) 1770–1775

1772

III. FAILURE MODES We have already introduced that the failure phenomenon in capacitive RF-MEMS corresponds to the dielectric charging. This paragraph details how this phenomenon translates into failure. We have to consider two failure modes, which mainly appear in capacitive RF-MEMS [4]: 1)

The stiction of bridge. The MEMS remains stuck on the dielectric without any applied voltage. This situation is described in the fig. 4, which represents the electromechanical behavior of the bridge before (black) and after (grey) an electrical stress (a cycling test). -40

-30

-20

-10

0

10

Vshift = Vapplied − V pd 0

20

30

40

50

0

Stiction of the bridge

(3)

We want to outline that the first failure mode, which would appear will depend on the pull-in and pull-up threshold voltages but also on the maximum applied voltage. For example, stiction will appear first if:

V pu0 < Vapplied − V pi0

Maximum applied voltage = 45v

Applied voltage (V) -50

This failure mode appears when the pull-in voltage goes beyond (because of the threshold voltages shift) the maximum applied voltage (see fig. 5). This situation occurs when the voltage shift corresponds to the difference between the maximum applied voltage and the initial pull-down one:

(4)

This equation demonstrates that, if the applied voltage is sufficiently high, the stiction will be the main noticeable failure mode.

-5

Before stress

IV. FAILURE ANALYSIS

-10

We now need to establish the physical analysis of the failure mechanism through the investigation of the dielectric charging kinetic.

After stress -15

A. Kinetic of the failure phenomenon

-20 S21 (dB)

Fig. 4 :Stiction of the bridge In this situation, the shift of the actuation voltages is sufficient to cancel the negative pull up voltage (Vpu-). As the consequence, for no applied voltage, the MEMS exhibits 5 dB of isolation, which corresponds to a down state of the movable bridge. It is clear that this situation appears when the shift of the threshold voltages reaches the initial pull up voltage value (Vpu0):

Vshift = V pu 0 2)

(2)

The screening of the bridge. The MEMS remains in the up-position even with an applied voltage. -40

-30

-20

-10

0

10

20

0

-5

Before stress

To measure the kinetic of the dielectric charging, we have introduced the shift rate of the actuation voltages parameter (SRAV). This parameter corresponds to the actuation voltages drift value normalized by the time during which the bridge is in contact with the dielectric [5]. For example, fig. 3 shows a shift of the actuation voltages (∆v) of 6V after 6000 cycles, with an applied signal featuring a 100 Hz frequency. Then, we have estimated a SRAV of:

SRAV =

Maximum applied voltage = 35v

Applied voltage (V) -50

To investigate the kinetic of the dielectric charging, we have cycled microswitches applying a square signal to the central conductor of the CPW line and we have monitored the actuation voltages evolution.

30

40

50

=

∆Vth ∆Vth = ∆τ down Nc × Duty

6V 6000 × 0.50

Fc

(5)

= 0 ,2 V s = 12 V min 100

Where Nc, Fc and Duty correspond to the number of cycle, the cycling frequency and the duty cycles of the actuation voltage respectively.

-10

After stress -15

-20 S21 (dB)

Fig. 5 :Screening of the bridge

Different microswitches have been investigated and the results of the actuation voltages behaviour are summarized in fig. 6. The SRAV is plotted versus the stress voltage, which corresponds to the DC applied one.

S. Melle´ et al. / Microelectronics Reliability 45 (2005) 1770–1775 fig. 7). The ideal structure is stressed by the equivalent electrical field, which intensity corresponds to the real electrical field inside the dielectric. This corresponds to an effective field: Eeff. We then demonstrate that the value of the effective field value into the dielectric is:

SRAV (V/min)

1000

100

B

Eeff =

10

A

1 30

40

1773

50

60

70

80

90

Applied Voltage (V)

Fig. 6 : SRAV parameter for different types of switches and different stress voltages. Thanks to ref [6], the lifetime should decrease with the applied stress voltage and then the SRAV parameter should increase with this parameter. Indeed, we ‘globally’ observe a more important SRAV parameter for larger applied voltage (see the round marks in fig. 6). But, we have also detected different behaviours (see diamond marks in fig. 6). Indeed, for the two switches referred by the ‘A’ letter, we observe two different shift rates (3.2V/min and 12V/min) for a same applied voltage (40V). Moreover, we observe that for the switches referred by the ‘B’ letter, the larger SRAV corresponds to the lower applied voltage. This clearly indicates that the SRAV parameter can’t only be considered versus the applied stress voltage and demonstrates that others quantities have to be taken into account to describe the phenomenon.

E Conth

(6)

Con

where Conth and Con corresponds to the expected (theoretical) capacitor in the on state (Conth) and to the measured one (Con), which depends on the switch itself(design and technology). We have then considered and plotted all the measured SRAVs versus the effective applied field in fig. 8. Switches B

1000

100 SRAV (V/min)

10

1 0

20

40

60

80

100

120

Stress field (V/µm)

Fig. 8 : SRAV parameter versus the effective applied field

B. Impacting parameters, which drive the failure mechanisms. This paragraph will introduce a suitable parameter, which takes the real electrical stress through the dielectric into account. It is well known that the roughness of the central line (induced by the fabrication process) is conformed by the dielectric but not by the bridge as the sacrificial layer used to realize the air gap has a sufficient conformal shaping. This roughness translates into a non-ideal contact (illustrated in fig. 7) which severely degrades the microwave performances in term of isolation.

The re sults are now relevant with the fact that the larger the applied voltage is , the earlier the failure occurs [6], the highest the SRAV parameter is . This proves that the dielectric charging depends on the electric field inside the dielectric, which corresponds to the applied voltage divided by the dielectric thickness and normalized by the contact quality (Conth/Con). V. FAILURE MECHANISM MODEL Thanks to the SRAV and effective electrical stress (Eeff) parameters, we now propose a physical model of the dielectric charging kinetic. A- Physic of Failure and proposed model

Eeff Q = Con × Q = Conth × ediel e diel Fig. 7 : Non-ideal Contact and ideal structures E

It is also intuitive that the dielectric roughness has an impact on the electric field inside the dielectric , which is the cause of the dielectric charging. To calculate the real electrical field inside the dielectric, we compare the real structure to an ideal equivalent one, which has the same charge on metallic arm (see

As already introduced, the physical origin of the dielectric charging is the leakage current through the dielectric. We then investigate the conduction mechanisms , which take place into dielectrics thanks to MIM capacitors with the same dielectric layer used in MEMS devices. The measurements have been analysed in order to identify the signature of the type of the conduction mechanisms (Schottky, Ohmic, ionic, Frenkel-Poole, …) [7]. The Frenkel-

S. Melle´ et al. / Microelectronics Reliability 45 (2005) 1770–1775

1774

Poole (F.-P.) behavior has been identified as showed in fig. 9. It presents indeed the measurement of the leakage current of a MIM capacitor versus the applied voltage in the Frenkel-Poole graph (ln(J/E) vs √E) and demonstrates the F.-P. conduction as both measured and theoretical slopes well agree for usable stress voltage through the dielectric. -21

-23

Ln (J/E)

-25

MIM Capacitor -27

Noise floor of the test set -29

Theoretical F.-P.

(

)

 − q φ B − qE / πε 0 ε r  J = σ PF × E × exp   kT  

-31

The good agreement between the model and the measurements validates the proposed theory, especially the definition of the effective electrical stress (Eeff) and the proposed proportionality between the leakage current and the stored charges. This mo del is fundamental both for: • The optimisation of the RF-MEMS reliability as we have now accessed to the different parameters which drive the lifetime of the devices and we then are able to define a strategy to minimize all the contributions. • The definition of time saving reliability test procedure. We can then define accelerating factors (Temperature, electrical stress) and deduce from the model the nominal lifetime with different operating conditions.

-33 0

5000

10000

15000

20000

25000

1/2

√ E (V/m)

Fig. 9 : Current leakage vs applied voltage of a MIM capacitor To quantify the dielectric charging phenomenon, we have considered that the accumulation of charges within the dielectric is proportional to the leakage current density. As the threshold voltages shift is proportional to the stored charges (see equation (1)), we obtain:

∆V J ∝ρ ∝ = SRAV ∆τ down

(7)

We already have identified the current density (see the insert in the fig. 9) through the dielectric and are then able to express the SRAV parameter:

q  (8) q  − qφB  SRAV∝ σFP × exp × Eeff × exp Eeff  kT πε ε  kT  0 r   In the equation (8), the considered electric field corresponds to the effective one and σFP and φB correspond to F.-P. conductivity and height barrier of traps respectively. To validate this proposed model, we have drawn the SRAV theoretical behaviour with the experimental datas in fig. 10. 10000

B- Figure of Merit of RF-MEMS reliability Thanks to this model, we finally propose a Figure of Merit (FoM) (see equation 9) of the RF-MEMS reliability, which normalises the SRAV parameter with the electrical stress to only represent the intrinsic quality of the dielectric regarding the lifetime ability of the RF-MEMS.

      SRAV FoM =     q q  Eeff × exp Eeff      kT πε0εr  

−1

(9)

This FoM is defined as inversely proportional to the SRAV as the higher the SRAV is, the worse the dielectric is, the lower the FoM should be. In order to correlate this FoM with a lifetime figure, we have to express the SRAV parameter in function of the classical figures given to describe the reliability of RF-MEMS : Number of cycle (Nc), cycling frequency (Fc), Duty cycles (Duty) and threshold voltages (Vpu and Vpd). We only consider the stiction failure mode as we have seen that, with appropriate applied voltage, this mode is the first to appear. In this case, we already have shown (see equation 2) that the critical (which translate into failure) shift of the actuation voltage corresponds to the pull-up voltage of the RF-MEMS. Consequently, we obtain:

1000 100 SRAV (V/min) 10 1 0,1 0

20

40

60

80

100

120

Stress field (V/µm)

Fig. 10 : SRAV parameter vs stress field : theory and experiments

(10)  ∆Vth  V ∆Vth  = = pu N × Duty ∆τ down  ∆τ down critical Fc Thanks to this equation, we can then express the FoM regarding the maximum number of cycles, the bridge properties (pull-up voltage, dielectric thickness and permittivity) and the

SRAV=

S. Melle´ et al. / Microelectronics Reliability 45 (2005) 1770–1775 electrical conditions: cycling frequency, duty cycle and applied (stress) voltage:

FoM =

 q Nc× Duty  q Eeff  (11) × Eeff× exp  πε ε Vh × Fc  kT 0 r  

We want to outline that this figure of merit only depends on the intrinsic dielectric properties and the greater the FoM is, the higher the lifetime will be. The great benefit of the proposed FoM is its usefulness to compare the reliability properties of different types of capacitive RF-MEMS. The fig. 11 presents the FoM of published RF-MEMS [6, 8-10] both for unipolar and bipolar actuation waveform.

1E+16

[10]

Bipolar Actuation

1E+15

[9]

FoM 1E+14

[6]

1E+13 1E+12

[8]

LAAS Work

1E+11 0

20

40 60 Applied voltage

A CKNOWLEDGEMENT This works has been done in collaboration with CNES and Alcatel Space and with the Support of the NoE AMICOM. REFERENCES G.M.Rebeiz, “RF MEMS switches and switch circuits”, 2001 [2] R.Reid, “Dielectric charging effects on capacitive MEMS actuators”, workshop 2002 IEEE MTT-S. [3] X. Rottenberg, B.Nauwelaers, W.De Raedt and H.A.C. Tilmans, “Distributed Dielectric Charging and Its Impact on RF MEMS Devices”, EUMC, 2004. [4] S. Mellé, F. Flourens, D. Dubuc, K. Grenier, P. Pons, J.L. Muraro, Y.Segui and R. Plana, “Investigation of dielectric degradation of microwave capacitive microswitches”, IEEE MEMS 2004. [5] W.M.Van Spengen, Robert Puers, Robert Mertens, I.DeWolf, “Experimental characterization of stiction due to charging in RF MEMS”, IEDM, 2002. [6] C.Goldsmith, J.Ehmke, A.Malczewski, B.Pillans, S.Eshelman, Z.Yao, L.Brank, M.Eberly, “Lifetime characterization of capacitve RF MEMS switches”, IEEE International Microwave Symposium, vol.1, May 2001. [7] S.M.Sze, “Physics of semiconductor devices”, 1981 [8] W.M. Van Spengen, R. Puers, R. Mertens, I. DeWolf, “Experimental characterization of stiction due to charging in RF MEMS”, IEDM 2003, pp. 901-904 [9] J. Qing, Y. Shi, W. Li, Z. Lai, Z. Zhu, P. Xin, “Ka -Band Distributed MEMS Phase Shifter on Silicon Using AlSi Suspended Membrane”, Journal of Microelectromechanical Systems, Vol. 13, n°3, June 2004, pp. 542, 549. [10] D. Mercier, K. Van Caekenberghe, G.M. Rebeiz, “Miniature RF MEMS Switched Capacitors”, IMS-MTT 2005, Long Beach USA, June 2005 [1]

LAAS Work

1E+17

low contact quality MEMS. It is then mandatory to take this parameter into account. We finally proposed a figure of Merit of capacitive RF-MEMS lifetime , which reflects the ability of the dielectric to slow down the dielectric charging. Thanks to this FoM, comparison between technologies of capacitive RFMEMS is now relevant and can open the door to the improvement strategies of RF-MEMS reliability. An other possible use of the proposed FoM concerns the definition of accelerated test procedure, which is necessary to generalize the reliability investigation on set of devices.

80

100

Fig. 11: FoM of different capacitive RF-MEMS Different values of FoM have then been estimated. We can also note that 1 decade of the FoM corresponds to one decade of lifetime for the same stress condition and same pull-up voltage. This FoM is drawn versus the applied voltage, which have to be taken into account as it accelerate the failure of the switch as illustrated in fig. 10. The main result of fig. 11 corresponds to the great interest of the bipolar actuation voltage as it increases the FoM and then the lifetime by four orders of magnitude. V. CONCLUSION This paper has presented our reliability investigation of capacitive RF-MEMS reliability. We have developed a specific test set associated with an efficient methodology to monitor and quantify the failure of RF-MEMS. Thanks to these tools, we have carried out investigations on the dielectric charging and demonstrated that the origin of this phenomenon is the Frenkel – Poole current leakage through the dielectric. It has also been shown that the leakage current and then the dielectric charging effect are driven by the electrical applied stress normalized by the contact quality of RF-MEMS. This point is crucial as high reliability behaviour can be demonstrated on poor MEMS RF-performances especially with

1775