Evaluation of Creep in RF MEMS Devices

Evaluation of Creep in RF MEMS Devices

Marcel van Gils, Jeroen Bielen, Gavin McDonaldNXP Semiconductors

Gerstweg 2, 6534 AE Nijmegen, The Netherlandsmarcel.van.gilsWnxp.com

AbstractRF MEMS are capacitive switches consisting of a

suspended aluminum beam that can be pulled down byelectrostatic force. At elevated temperatures and highmechanical stresses the aluminum beam can exhibit creepphenomena that result in shifting of device parameters asa function of time. Experimental and numericalmethodologies are presented for measuring and predictingthe effect of creep on the RF MEMS device performance.A constitutive creep model is implemented in a FiniteElement code where the parameters of this constitutivemodel for creep in thin aluminum layers are determinedby wafer curvature experiments. In order to distinguishcreep effect from charging effects, special test structuresare designed. Simulations on the test with differentgeometries indicate the effect of creep and can result indesign rules for the RF MEMS switches. The numericalpredictions and the measured degradation on the RFMEMS switches are compared and conclusions are drawnwith respect to the methodology.

1. IntroductionThe development and production of MEMS

(microelectromechanical systems) devices has shown arapid growth over the last 15 years. Their unique physicalproperties through the combination of electrical andmechanical functions have resulted in applications notpossible with alternative techniques. However, despite theapparent potential of MEMS many ideas never came toproduction due to roadblocks. One of the challengingfields in the commercialization of MEMS is reliability.Due to the nature ofMEMS the reliability is often uniquefor the specific MEMS technology and highlymultiphysical.

One of the promising MEMS devices is the radiofrequency (RF) capacitive switch [1]. The potential use ofthese switches is in adaptive antenna matching for GSMmobile phones. An SEM photograph of the NXP RFMEMS switch is visible in Figure 1. The switch consistsof a 3-5 tm thick aluminum top electrode that issuspended 1-3 tm above a bottom electrode. A siliconnitride layer is deposited on top of the bottom electrodeand acts as a dielectric. By applying a voltage differencebetween the top and bottom electrode an electrostaticforce is generated which pulls the top plate down towardsthe bottom electrode (see Figure 2). At a certain voltagedifference (the pull-in voltage) the electrostatic forceexceeds the spring force of the suspended aluminumstructures and causes the plate to snap down on the siliconnitride layer.

-springs

F

f _1_I

1 r

I- Top electrode

'SiI con Nitride

dielectric

Bottom electrode

Figure 2: Principle ofelectrostatic actuation

For a 1-D approximation of the switch the voltage atwhich this occurs can be derived analytically and yieldsthe expression for the pull-in voltage V,, [ 14]:

8kg3

VPi = 27A(1)

with k the spring stiffness, g the initial gap (g=h+d Ed), Athe surface of the electrode and ,o the dielectric constantof air.

The resulting characteristic of the RF MEMS switch isbest visualized using the resulting capacitance versus

voltage curve. A typical example of such a C-V curve isvisualized in Figure 3 illustrating the hysteresis behaviorand the symmetric actuation at both negative and positivevoltages.

In the application the RF MEMS device is switchedbetween the low capacitance at the open state (OV) andthe high capacitance at a voltage above V 1. Thecapacitance ratio between the open and closed state is an

important characteristic of the switch.

Figure 1: RFMEMS capacitive switch

16

14

12

10

a 8

-40 -20 0

V [V]

20 Vpi 40

Figure 3: Typical C-Vcurve ofthe RFMEMS switch showing asymmetric curve

One of the most important reliability aspects of the RFMEMS switch is the change of the C-V curve that canresult in a non-functional device. The two most importantfailure mechanisms causing a potential change of the C-Vcurve are charging of the SiN layer [2-4] and mechanicalcreep of the aluminium top electrode. Charging occursduring prolonged actuation of the switch at high voltageswhere the resulting electrical field causes trapping ofelectrons in the SiN layer. The resulting charge in the SiNlayer shields the external applied voltage causing achange in the total electrostatic force and thus a shift ofthe C-V curve. When the build-up charge is high enoughit will finally lead to sticking of the device where at 0 Vthe amount of trapped charge is high enough to keep theswitch in the down state. Several groups during the last 7years have investigated this charging effect and theresulting sticking behaviour. Figure 4 shows a typicalresult of the shift of the C-V curve due to prolongedactuation and the final sticking of the switch duringreliability testing at accelerated conditions.

16

12

U_ tot-

t24 -3

0-40 -30 -20 -10 0 10 20 30 40

V [V]

Figure 4: Typical shift ofC-Vcurve due to prolonged actuation oftheRFMEMS switch during accelerated testing

The amount of papers investigating creep failuremechanisms is limited [5-8]. However, for MEMSdevices based on metal alloys such as aluminum, creepcould occur during application of the device wheninsufficient care is taken. From equation (1) it is clear that

a change in the gap due to creep phenomena will have alarge impact in the resulting V , value. Therefore it isimportant to investigate the creep properties of thematerials used and to optimize the design of the RFMEMS devices or the used materials in order to limit theeffect of creep. This paper focuses on experimental andnumerical methodologies to evaluate the occurrence ofcreep in RF MEMS devices. Because during applicationthe charging and creep phenomena occur simultaneously,it is important to be able to distinguish between the twofailure mechanisms.

2. Creep properties of thin film aluminumThe material used as the moving top electrode in the

RF MEMS devices is an aluminum based alloy which isdeposited in commercial PVD equipment. The thicknessof the aluminum layer is approximately 3-5 rtm. It is wellknown that the behavior of materials at these small lengthscales does not necessarily correspond to the behavior ofbulk materials. This is due to the fact that the grain sizesare in the same order of magnitude as compared to thecharacteristic dimensions of the structures, whichinvalidates the use of properties measured on bulkspecimen and may imply that continuum mechanics nolonger apply. Studies related to this size effect arenumerous during the last 10-15 years [9-11]. Due to thissize effect and the small dimension of the devices ofinterest, novel experimental methods and material modelsare required. However, at the present date no validatedand usable constitutive models based on themicrostructure of the material are available in commercialfinite element codes. Therefore we stick to the continuumbased constitutive equations of elasticity, plasticity andcreep.

Creep is usually characterized by measuring the creepstrain evolution at a certain constant stress level. Thereare different stages of creep as can be seen in Figure 5.The first stage is called primary creep and shows adecreasing creep rate. The next stage is secondary orsteady state creep: equilibrium is established between thedeformation and recovery mechanics. For lifetimepredictions this steady state creep is the most importantregion and most constitutive creep models are developedfor this region. The last stage is called tertiary creep andshows an increasing creep finally resulting in failure.

l 1 11 /.~~~~~~~~~~~~11 -

Figure 5: Typical creep strain evolution at a constant stress levelshowingprimary, secondary and tertiary creep regions

The techniques commonly used in literature formeasuring the creep properties of thin (aluminum) layersare wafer curvature, nano-indentation or the use ofdedicated test structures. These techniques all have theirspecific pro and cons:- The wafer curvature technique uses standard (silicon)wafers where on one side a layer of aluminum isdeposited. The curvature of the wafer is measured asfunction of temperature and time. The stress (7m in thealuminum layer can be calculated from this curvatureusing the well-known Stoney's equation:

am = ( I R -R19 (2)6(1-av) tf - I

with Es and vs the Young's modulus and Poisson's ratioof the substrate, respectively; ts the substrate thicknessand tf the film thickness. R2 is the radius of curvature afterprocessing and R1 the initial radius of curvature of thewafer before film deposition.

Advantages of the wafer curvature method are itssimplicity and accuracy. A disadvantage is the fact thatthe thin film is not free standing because it is constrainedby the silicon substrate. This could influence plasticityand creep behavior because the constraint surface canhinder dislocation movements. Another disadvantage isthe fact that the stress and temperature levels can't becontrolled independently.- With nano-indentation a small, sharp diamond tip isindented in the material. From the resulting force-displacement curve the constitutive behavior of thematerial can be extracted. Advantage of this technique isthe ability to control the stress levels. A drawback is thefact that only a very small volume of the material istested, which is not necessarily representative for theoverall behavior. Another drawback is the interpretationof the data, which requires sophisticated finite elementsimulations to extract the constitutive models.- The use of dedicated test structures, which resemble theactual device, is usually preferred. However, it is oftendifficult to accurately control and measure the smallforces and displacements.

In this paper both the wafer curvature technique anddedicated test structures are used for characterizing thecreep behavior of the aluminum material. Modlinski andco-authors have published data for creep relaxation usingthe wafer curvature technique [5-8]. In these papersmeasured data for AlCu is presented together with a fittedconstitutive creep model. Because the investigatedmaterial and thickness are comparable to our material, weused this data as start of our creep investigation. In [7] thecreep relaxation was measured at 72 °C and 101 °C andthe following relation, based on dislocation glide, is fittedto the data:

kT FacG0 ac1CT=- lniexpi- ++t

a L kT kT ]

with

AFa=3

(4)

t[ ]( E ) (,'\AF0 (5)

co the biaxial stress at the beginning of the

relaxation, k the Boltzmann constant, )O a constant and T

the absolute emperature. The fitted values of iF and rfor AlCu are 4 eV and 252 MPa respectively.3. Numerical methodologies

The Finite Element method is used for predicting thebehavior of the RF MEMS switches. This is a challengingtask due to the multiphysical and nonlinear behavior ofthe switch:- The electrostatic force for each lateral position should

be predicted as function of the displacement of thetop electrode.

- The electrostatic force is non-linearly dependent onthe gap. Combined with the linear dependency of thespring force this results in a non-linear response withsnap-back behavior and unstable equilibrium.

- Plasticity and creep in the aluminum during actuationshould be taken into account resulting in non-linearmaterial behavior.

A detailed description of the simulation methodologywith respect to the first two points is presented in theseproceedings [15]. In this paper the creep constitutivemodel for aluminum is added to the presentedmethodology. This creep equation is implemented in thecommercial finite element program ANSYS multiphysics9.0® [12] using a steady-state creep equation of theexponential form:

vn= Clexp 7vm C3 (6)

Equation (3) can be rewritten in the form of equation (6)as shown in [8,13]

With this implementation the creep relaxation wafercurvature measurements are reproduced. The predictedstress relaxation curves are visualized in Figure 6 andindicate the correctness of the FE implementation. Thepredicted strain rate as function of the Von Mises stress isplotted in Figure 7 for the two different temperatures. It isclear that a large stress dependency exists with significantstrain rates starting at 80 MPa.

(3)

95r

90

k85ia)

80

.75

LU

700

- Simulation T = 72 °C--- Simulation T = 101 °C- Experimental data fit T = 72 °C--- Experimental data fit T = 101 °C

0.5 1 1.5 2 2.5 3 3.5 4Time [s] x 104

Figure 6: Isothermal stress relaxation experimental datafits comparedwith the FEpredictions

1. OOE-06

1. OOE-08

en

0.

2 1.OOE-10

- 1.OOE-12

un 1.OOE-14

T 1.00E-16

1 .OOE-18

1. OOE-200 20 40 60 80 100

Von Mises stress [MPa]

Figure 7: Creep strain rate asfunction ofthe Von Mises stress

--.....72 C_~ 101 C

First electodeSe rde1e.de Tidelectrode

Figure 8: Schematic ofthe designed test structure showing a centralelectrode together with two side electrode which can be actuated

separately.

For evaluating creep the idea is to actuate the middleelectrode above the pull-in voltage. After actuation themiddle plate is contacting the SiN surface whereas theside electrodes and the springs will deform but will nottouch the SiN layer. Charging at the side electrodes andthe springs will be minimized because there is no contactwith the SiN layer The ratio in stiffness between thespring and the side electrode will determine the amount ofdeflections in the spring and side electrodes.

After actuation of the middle plate additional voltagescan be placed on the side electrodes in order to create anelectrostatic force, which further deflects the sideelectrodes and springs. In case of creep the springs willshow an increased deflection as function of time. This canbe monitored using electrical and optical measurementtechniques. The principle of the test structure is alsovisualized in Figure 9.

Center Edge SpringIm

I -.O I"

VI

Electrode 1 Electrode 2Electrode 2

4. Experimental procedures

4.1 Test structuresIn order to evaluate the occurrence of creep on the RF

MEMS switches, dedicated test structures are designedand manufactured. The manufacturing process used tofabricate the test structures is identical to the NXP RFMEMS process. This facilitates the transformation of theresults to the actual RF MEMS devices.

An important characteristic of the test structures is theability to distinguish between deformation due tocharging and that due to creep. For the actual RF MEMSswitches this is difficult because both result in similarshifts of the C-V curve. Figure 8 is a FE model showingthe principle of the designed test structure. The topelectrode consists of three portions that can be actuatedseparately by three independent bottom electrodes.

Figure 9: Side view schematic ofthe designed test structure illustratingthe workingprinciple.

Eight different versions with varying spring lengthand electrode size are fabricated of this test structure.

5. Results

5.1 ExperimentsFigure 10 shows photographs of two test structures

with different spring length fabricated in the RF MEMSprocess. The shorter spring length of the left structure willhave higher stress levels during actuation and thus ahigher risk of creep strain evolution at elevatedtemperatures.

-.11

_0.

higher temperatures. This pefmanentcaused by the developed creep strainsdeformation.

3.5snap down

3.0 -=

a. b.

Figure 10: Photographs oftwofabricated test structures (creepO5 andcreepO8) with different spring lengths.

For triggering creep the creepO5 structure is actuatedat different temperatures during a prolonged time.Voltage is applied at the central electrode until the centralelectrode is pulled down on the SiN layer. While keepingthis voltage on the central electrode an additional voltageof 30V is applied on the right electrode causing a furtherdeflection of the side electrode and an increase inmechanical stresses in the spring. The deflection of theelectrodes is measured with a white light interferometer atcertain time intervals. A typical measured shape of thestructure is depicted in Figure 11 showing the deflectionsof the springs and the slope of the right electrode.

E 2.5

*°2=2.0#'az v0

0.

c, 1.0

0.5

deformation isand the plastic

* 25C* 75CA1OOC

AMP tII1

I I

\ after actuationI

I I

F)t- initial deflectionI* I

a I

after relIaxation0.0

0 5 10 15 20 25

Time (h)

Figure 12: Measured creep deflectionfor creepO5 structure at 3different temperatures. Relaxation data obtained after 11 days but

visualized on arbitrary time in the graphfor comparison.

5.2 SimulationsThe experiment at 75 °C on the creepO5 structurespresented in the previous section is also simulated withthe FE methodology described in section 3. The VonMises stresses in the spring of the structure predicted after8.5 hours of actuation at are visualized in Figure 13. Fromthis picture it is clear that stress concentrations exist nearthe corners and that the overall stress levels are relativehigh compared with values in Figure 7.

1 ' ' ; 'A'TIP

lM

Figure 11: Deflection ofthe creepO5 test structure during actuationmeasured with white light interferometry.

When creep strains accumulate, it causes the sideelectrode to further deflect and thus reduce the gap. At acertain critical deflection the side electrode will show apull-in behavior and snaps down on the SiN layer. Afterthis pull-in the test is stopped and the system is allowed torecover. For short springs it is possible that this pull-in ofthe side electrodes causes plastic deformation of thesprings, which also prohibits recovery.

In Figure 12 the deflection at the end of the spring(point A in Figure 8) is plotted as function of time. Fromthis graph it appears that at 25 °C no creep effects arevisible. However, at 75 °C and 100 °C a clear increase indeflection is measured which finally results in a snapdown of the side electrode. After relaxation (> 11 days) apermanent deformation is measured which is larger for

Figure 13: Predicted Von Mises stress levels in the springs ofteststructure creepO5

The predicted equivalent creep strains after 8.5 hoursof actuation are visualized in Figure 14. The comparisonbetween the predicted increase of deflection and themeasured values is visualized in Figure 15.

-Mj

rTN

Figure 14: Predicted equivalent creep strain levels in the springs ofteststructure creepO5 after 8.5 hours actuation at 75 'C

3.5

3.0E

2.5._

0- 2.0

cor- 1.50

C._

.0 1.00

0.5

*-

**

*"

~~~~~~~* * 0 **

- Experiment- Simulation-

0.00 2 4 6

Time (hrs)

8 10

Figure 15: Comparison between measured andpredicted deflection dueto creep at 75 °Cfor the creepO5 structure.

It is clear that although both the experimental resultsand the numerical prediction show a creep effect, thedifference is large. Apparently the creep constitutiveequation from literature for AlCu is not representative forour material.

6. ConclusionsWe presented a combined experimental and numerical

methodology for the evaluation of creep in the aluminumtop electrode of RF MEMS switches. The FE model forthe RF MEMS switches including the creep constitutiveequation is capable of predicting the creep relaxationmeasurements. Measurements on the designed teststructures indicated the occurrence of creep in the springs.However, the predicted creep levels for the test structuresare much lower than the observed values.

Further evaluation of creep degradation using thesetest structures will be performed in the future. Inconjunction to these test we will also perform curvaturerelaxation measurements on the material used in the RF

MEMS switches in order to optimise our constitutivecreep equation.

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