Creep and Fatigue Failure in Single- and Double Hot Arm MEMS Thermal Actuators
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Determination of the failure mechanisms of mechanical devices is the key to the design of reliable products. This paper reports an investigation on creep and fatigue failure of microelectromechanical (MEMS) thermal actuators. Finite element modeling is used to predict thermomechanical behavior of actuators under low to moderate voltage differences. The modeling results are compared with experimental results to evaluate the models. Two probable failure modes associated with thermal actuators, that is, fatigue and creep, are investigated, and it is found that creep is the dominant failure mechanism. The creep behaviors of several U-shape and double hot arm thermal MEMS actuators are examined, and their deformation-time curves are obtained numerically and experimentally. The curves follow a typical three-stage creep curve usually observed in metals. The creep life cycles of the devices are compared on the basis of their stress and temperature distributions. This study shows that actuators with the maximum temperature occurring at the location where the high stress is induced have shorter life spans than those experiencing the high stress away from the maximum temperature location. It is concluded that the double hot arm actuators with equal length have longer creep life than the U-shape (single hot arm) actuators.
KeywordsCreep Creep failure Failure mechanism Fatigue failure
Microelectromechanical system (MEMS) actuators enable MEMS devices to interact with their environment and are categorized based on their actuation sources into four main groups: electrostatic, electromagnetic, piezoelectric, and electrothermal actuators. The idea of using thermal expansion in MEMS actuators was first proposed by Guckel et al.  in 1992 and was later implemented by Comtois and Bright  and developed as a practical MEMS device by Burns and Bright . Among thermal actuators, flexural actuators are being widely used in MEMS applications because of their fabrication characteristics. They can be fabricated using most of the surface micromachining processes and can be operated in integrated circuit (IC) device voltage and power ranges. Long-term performance is the major concern with ongoing applications of thermal actuators . Developing a reliable MEMS actuator makes it cost effective and saves repair, reproduction, or even redesign time. An accurate failure model can lead to a safe and reliable design.
The operational conditions of thermal actuators keep them under high temperatures and stresses and make creep a viable mode of failure for these actuators. Stress and temperature distributions are important factors in the creep life cycle. On the other hand, as thermal actuators work mostly as on/off switches, fatigue becomes another possible failure mechanism of thermal actuators. The maximum stress level determination is important in fatigue study. Flexural thermal actuators have different design and operational conditions. The structure and the applied voltage levels have significant influence on the operational stress and temperature distributions in flexural thermal actuators.
The MEMS thermal actuators are primarily fabricated from polysilicon, which is a brittle material that becomes ductile after the transient temperature (813, 933 K , or between 923 and 1023 K ). Teh and Lin  were the first to address “the time-dependent deformation phenomenon of thin films under compressive stress” or “creeplike behavior” of polysilicon. Until now, high-temperature permanent deformation [6, 8, 9] and creep failure [4, 5, 7, 10, 11] of polysilicon microdevices have been reported by several research groups. Tuck et al.  reported that high temperature has a larger effect on creep behavior than high stress and that temperature is a very important variable in causing strain.
There have also been a number of fatigue studies on micropolysilicon samples and devices under electrostatic loading (Brown et al.  and Muhlstein et al. ) and electromechanical loading (Conant and Muller , Comtois et al. , Kapels et al. , Que et al.  Chen et al. [17, 18], Hocheng et al. , and Kung and Chen ). Some of these research works were related to the flexural thermal actuators [2, 4, 14, 15, 20]. Kung and Chen  reported fatigue failure of thermal actuators and fitted the empirical fatigue equations to the experimental data. Conant and Muller  rejected the fatigue failure and indicated that the failure is a time- and temperature-dependent failure. Ritchie et al. , Muhlstein et al. , Alsem et al. , and Kahn et al.  did extensive studies on the cause of fatigue failure and factors influencing its occurrence in polysilicon.
In this study, a comprehensive finite element modeling (FEM) process of the device is introduced. The model is validated based on experiments performed on several U-shape thermal actuators (single hot arm). Different experiments are performed on single and double hot arm thermal actuators. The stress and temperature distributions in the actuators and the effect of their distributions on the creep and fatigue life of the devices are discussed in detail. It is shown that fatigue is not a feasible failure mechanism in the thermal actuators studied in this work and that creep is both a viable and dominant failure mechanism.
Thermal Actuators Finite Element Modeling
As the current consumption in the cold arm is not necessary, the power efficiency of the actuators can be improved by adding a second hot arm . A double hot arm actuator can have hot arms with the equal or unequal length. Figure 1 shows the current path in the double hot arm actuator and the U-shape actuator (single hot arm actuator).
Temperature dependent properties of polysilicon
The convection coefficient is also a temperature-dependent parameter. However, the effect is negligible because of the large outer side of the air part.
The anchor effects were implemented by applying constant temperature at the end of the arms in the electrothermal model and fully constrained boundary condition for the thermomechanical model.
Two sets of experiments were conducted on U-shape and double hot arm actuators to find the failure mechanism of the thermal actuators. First, U-shape thermal actuators underwent a fatigue test. In the second set, a number of U-shape and double hot arm actuators were examined for creep failure.
The FE results showed a maximum stress of about 150 MPa in the U-shaped actuator under 4.5 V. Considering the ultimate strength for polysilicon at the microlevel (which has been reported to be around 4 GPa and endurance of about 2 GPa ), the stress level is very low and hence should not cause fatigue failure . To confirm this, a fatigue test was conducted on a U-shaped thermal actuator. The thermal actuator was under voltage loading with proper frequency. The chip of the actuator was bound to a DIP package, and the voltage was applied on the pads of the actuator. A 4.5 V input was applied to the actuator anchor with 50 HZ frequency with proper probes, and the test was performed under a microscope during the experiment. The real-time simulation of Simulink/Matlab linked to Wincon3.0.2a was used. MultiQ-3 data acquisition card  provided the connection to the real time. At regular intervals, the deflection of the actuator under a constant 4.5 V load was measured. After millions of loading cycles, no change in the deflection was observed. According to the measured deflection and resistance of the actuator, the actuator had infinite life under fatigue loading with no sign of degradation. Fatigue tests at higher voltages were not carried out since the levels of stress in all cases (which are discussed in the section on creep tests) are well below the endurance limit.
The experiments were conducted under a microscope to monitor and measure the changes in the tip deflection of the actuator. The FEM model was used to find the voltage level, based on the desired temperature level of each experiment. Creep experiments at different levels of voltages, temperatures, and stresses were conducted on both U-shape and double hot arm actuators.
A U-shape actuator was loaded under 4.5 V with hot spot temperature of 580 °C. The first 3 h of the creep experiment were done under the microscope, and every 10 min a picture was captured. During this time, no measurable tip deflection was observed. The experiment was continued for 3 days, and no significant change was observed.
As shown in Fig. 13, the highest temperature in the actuator is 965 °C, and it is located at the outer hot arm. The maximum principal stress on the hot spot is 63 MPa. However, the stress at the inner hot arm, where temperature is 910 °C, is 136 MPa. Since the highest temperature and stress positions were not the same, a slower creep trend was expected for this type of double hot arm actuator compared with the unequal-length double hot arm actuators.
Finite element modeling gives an insight into the stress and temperature distributions in MEMS devices. In this study, a modeling approach was used and validated by experimental results. In addition, the actuators were examined by fatigue and creep tests.
A U-shape actuator was tested under fatigue loading and did not show any effect of degradation or failure due to the cyclic load. The observed results were consistent with the studies in the literature stating that fatigue is not a feasible failure mechanism in polysilicon MEMS thermal actuators under operational load. However, in creep tests, eventually all the actuators permanently deflected, and failed, showing that creep is a viable failure mechanism in these thermal actuators.
Several types of the actuators were studied in the creep experiments of U-shape and double hot arm thermal actuators. Two types of double hot arm thermal actuators were tested, equal-length and unequal-length hot arms, which have different stress and temperature distribution profiles. Based on the temperature and stress distribution obtained from the finite element modeling, the highest temperature and stress for equal-length double hot arm thermal actuators were not at the same location (hot spot was at outer hot arm, but maximum principal stress was at the inner hot arm). On the other hand, the hot spot and the highest stress in unequal-length thermal actuators were at the same position (at inner hot arm), causing faster creep deformation. The difference in the creep life is also observed in the double hot arm actuators. It was observed that the permanent deformation in unequal-length thermal actuator started after 1020 min, while under same conditions the same permanent deformation was observed after 215 min in equal-length actuator under the same input voltage (9.3–9.5 V).
The permanent deformation on the equal-length double hot arm actuator occurred near the tip of the actuator. During the experiment the thickness of the outer hot arm decreased, leading to a sudden increase of temperature. The permanent plastic deformation happened at the exact same point. This may be the result of the degradation of yielding stress of the material caused by the high temperature. The strength level fell below this level, and the structure deformed plastically. The observation after relaxation time showed that no recovery occurred at this point.
All actuators had deflected in both in-plane and out-of-plane directions. The tendency of the actuators to deflect out of the plane may be caused by the microstructure defects induced by the fabrication process. This mode of deflection was not expected in the actuators because they were fabricated based on a symmetric structure design. However, the experiment showed that the condition was not symmetric across the beam thickness and the tendency to deflect out-of-plane was high.
From the results, the three common stages of creep behavior were observed in thermal actuators. The strain versus time curve shown in Fig. 16 consists of three regions. The primary creep stage “a” with slight decreasing creep rate, the secondary (and much longer) creep stage “b” with constant creep rate, and the tertiary creep stage “c” with acceleration of creep rate that ultimately leads to failure.
The experimental data and analyses presented in this paper show that the MEMS thermal actuator did not failed because of fatigue. A series of the creep experiments were conducted on MEMS thermal actuators (U-shape and double hot arm thermal actuators). Captured images and the deformation trend on the actuators were presented. The deflection–time curves based on the accurate tip-deflection measurements of the actuators are presented, which show a typical three-stage shape.
All the tested thermal actuators showed time-dependent deformation under stresses and high-temperature conditions. They also experience some level of plasticity caused by material degradation effects at high temperatures. In addition, the creep lifetime of the actuator in which high temperature and high stress are in the same location is less than in the other actuators under the same level of applied voltage. These results demonstrate that creep is both a viable and dominant failure mechanism for the MEMS device considered.
The authors would like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC).
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