*1.2.1 Passive compensation for TCEM*

The current passive compensation technology for temperature coefficient of elastic modulus (TCEM) includes electrostatic stiffness modification, composite structure, and high doping. Melamud et al. [36] proposed a Si-SiO2 composite resonator, as shown in **Figure 2a**. SiO2 covers the surface of the silicon beam to form a composite resonator beam. Because TCEMs of silicon and SiO2 are negative and positive, respectively, the Si-SiO2 composite resonator can realize the passive compensation for the thermal drift of frequency. Liu et al. [37] also proposed an Al/ SiO2 composite MEMS resonator with the passive compensation ability for the thermal drift of frequency.

TCEM of single crystal silicon can also be compensated by high doping. A suggested mechanism is that heavy doping strains the crystal lattice and shifts the electronic energy bands, resulting in a flow of charge carriers to minimize the free energy, thereby changing the elastic properties [38]. Hajjam [39] reported a high phosphorus-doped silicon MEMS resonator with thermal drift of frequency down to 1.5 ppm/°C. Samarao [40] reported that MEMS resonator with high concentration

of boron doping and aluminum has thermal drifts of 1.5 and 2.7 ppm/°C,

drift of frequency over 90°C full scale is obtained.

*Reliability of Microelectromechanical Systems Devices DOI: http://dx.doi.org/10.5772/intechopen.86754*

thermal drift, as shown in **Figure 2c**.

*1.2.2 Passive compensation for thermal stress/deformation*

structure is proposed to improve the thermal stability.

**2. Reliability analysis and experiments**

**2.1 Reliability regarding viscoelasticity**

*2.1.1 Polymer viscoelasticity*

**93**

The result of passive compensation depends on the precise structure design and is susceptible to fabrication error. As such, passive compensation generally cannot suppress the thermal drift fully. In several reports, active compensation and passive compensation are incorporated to suppress the thermal drift. For instance, Lee et al. [41] incorporate the electrostatic stiffness and Si-SiO2 composite structure to compensate the thermal drift of the frequency of MEMS resonator. As such, 2.5 ppm

The improvement on structure design or package to suppress the thermal stress/ deformation is an effective passive compensation technology for thermal stress/

The soft adhesive attaching, such as using rubber adhesive with an elastic modulus lower than 10M, is commonly employed to suppress thermal stress/deformation induced by the package [42]. Furthermore, the soft attaching area is also reduced to obtain lower thermal stress/deformation. Besides the passive compensation technology in packaging, improvement on structure design is also successfully employed to suppress thermal stress/deformation. Wang et al. [43] proposed a pressure sensor structure that can isolate stress, as shown in **Figure 2b**. They used cantilever beam to suspend the detection component of the pressure sensor, thereby isolating the influence of encapsulation effect on the sensor. Based on a floating ring, Hsieh et al. [44] suggested a three-axis piezo-resistive accelerometer with low

*1.2.3 Making the TCEM and thermal stress/deformation compensate each other*

It is very promising to make the TCEM and thermal stress/deformation balance each other out. Hsu et al. [45] used thermal deformation to adjust the capacitance gap, so as to achieve the automatic adjustment of electrostatic stiffness and compensation for the variation of mechanical stiffness induced by temperature. Myers et al. [46] employed the thermal stress caused by the mismatch of CTE to compensate the frequency drift induced by TCEM. In this chapter, the thermal analysis is carried out in order to investigate the impacts of a structured layout of a sensing element on the drift over temperature of micro-accelerometers, and an optimized

Viscoelasticity is a distinguishing characteristic of materials such as polymer. It exhibits both elastic and viscous behavior. The elasticity responding to stress is instantaneous, while the viscous response is time-dependent and varies with temperature. The viscoelastic behavior can be expressed with Hookean springs and Newtonian dashpot, which correspond to elastic and viscous properties, respectively. To measure the viscoelastic characteristics, stress relaxation or creep tests are

often implemented. Stress relaxation of viscoelastic materials is commonly

respectively.

deformation.

#### **Figure 2.**

*MEMS devices with passive compensation, the ability of isolating the thermal stress. (a) Composite resonator [36], (b) pressure sensor isolating the thermal stress [43], and (c) three-axis piezo-resistive accelerometer pressure sensor isolating the thermal stress [44].*

*Reliability of Microelectromechanical Systems Devices DOI: http://dx.doi.org/10.5772/intechopen.86754*

**1.2 Passive compensation**

thermal drift of frequency.

*1.2.1 Passive compensation for TCEM*

*Reliability and Maintenance - An Overview of Cases*

tion.

**Figure 2.**

**92**

*pressure sensor isolating the thermal stress [44].*

Active compensation is simpler and uncomplicated; however, it typically involves the additional circuitry and power consumption. On the contrary, the passive compensation does not need the additional circuitry and power consump-

The current passive compensation technology for temperature coefficient of elastic modulus (TCEM) includes electrostatic stiffness modification, composite structure, and high doping. Melamud et al. [36] proposed a Si-SiO2 composite resonator, as shown in **Figure 2a**. SiO2 covers the surface of the silicon beam to form a composite resonator beam. Because TCEMs of silicon and SiO2 are negative and positive, respectively, the Si-SiO2 composite resonator can realize the passive compensation for the thermal drift of frequency. Liu et al. [37] also proposed an Al/ SiO2 composite MEMS resonator with the passive compensation ability for the

TCEM of single crystal silicon can also be compensated by high doping. A suggested mechanism is that heavy doping strains the crystal lattice and shifts the electronic energy bands, resulting in a flow of charge carriers to minimize the free energy, thereby changing the elastic properties [38]. Hajjam [39] reported a high phosphorus-doped silicon MEMS resonator with thermal drift of frequency down to 1.5 ppm/°C. Samarao [40] reported that MEMS resonator with high concentration

*MEMS devices with passive compensation, the ability of isolating the thermal stress. (a) Composite resonator [36], (b) pressure sensor isolating the thermal stress [43], and (c) three-axis piezo-resistive accelerometer*

of boron doping and aluminum has thermal drifts of 1.5 and 2.7 ppm/°C, respectively.

The result of passive compensation depends on the precise structure design and is susceptible to fabrication error. As such, passive compensation generally cannot suppress the thermal drift fully. In several reports, active compensation and passive compensation are incorporated to suppress the thermal drift. For instance, Lee et al. [41] incorporate the electrostatic stiffness and Si-SiO2 composite structure to compensate the thermal drift of the frequency of MEMS resonator. As such, 2.5 ppm drift of frequency over 90°C full scale is obtained.
