Capacitive MEMS Accelerometer Based on Silicon-on-Insulator Technology: Design, Simulation and Radiation Affect

Transcription

1 Capacitive MEMS Accelerometer Based on Silicon-on-Insulator Technology: Design, Simulation and Radiation Affect Abdelhameed E. Sharaf Radiation Engineering Dept., National Center for Radiation Research and Technology, Egyptian Atomic Energy Authority, Cairo, Egypt Received: 30/12/2012 Accepted: 13/3/2013 ABSTRACT This work introduces the design, simulation and the radiation effects for an out of plane micromachined z-axis accelerometer based on the silicon-on-insulator technology. In this design, the response to acceleration is sensed capacitevely via four comb-finger capacitors. This scheme helps the implementation of the sensor by the bulk micromachining process. The simulation results shows a good z-axis sensitivity of 24.14(pm/g) and a total equivalent noise acceleration as small as 3.41(µg/(Hz) 1/2 ) and a minimum off-axis sensitivities of 0.15% and 0.3% in x- and y- directions respectively. The radiation sensitivity depends on the sensing or actuation principle, device design, and radiation-induced trapped charge in dielectrics. Keywords: Capacitive Sensor/ MEMS/ Silicon-On-Insulator/ Finite Element Analysis/ Radiation Effects on MEMS devices. INTRODUCTION MEMS based accelerometer replaces the bulkier one for many applications that require small size, low power, minimum cost etc. Micromachined accelerometers have been got more of attention during the past two decades (1, 2, 3, 4, 5). Micromachined accelerometers find its way for many applications (6, 7, 8, 9). They can be used in different applications areas; such as automotive (6), biomedical (7), industry (8) and military applications (9).There has been a broad interest and research diversity in micromachined accelerometers. This is basically due to their low cost, high reliability, and the ease of their integration with their drive and sense electronics. Various design and fabrication approaches are well covered, especially for rate grade surface micromachined, which are still apart from the desirable inertial grade. The focus on surface micromachined accelerometer is due to the fact that they can be monolithically integrated with their sense circuitry. This is their main advantage over their bulk micromachined counterparts. However, the performance of bulk micromachined accelerometers significantly outperforms the surface micromachined ones. Most of the accelerometer designs in literature focus on silicon based accelerometer due to their compatibility with the IC fabrication technology. Employing other materials in accelerometers, especially metals, can further improve their performance due to their high density, which in turn increases their proof masses and quality factor. This work presents novel idea and approach which are generically applicable to silicon or metal based accelerometers. SENSOR STRUCTURE AND DESIGN The accelerometer is a device used for measuring the acceleration. The output signal of the accelerometer can be integrated to find the distance traveled. The accelerometers operate by measuring the inertial force generated when a mass is accelerated. The inertia force might deflect the suspension of the proof mass. Thus if the deflection is measured the acceleration can be determined. The accelerometer consists mainly of a mass-spring-damper system and a pickoff. The mass-spring- 231

2 damper system is used to interact with the inertia forces and the pickoff is used to put out a signal related to the inertia forces. Figure (1-a) shows a 2D layout of the proposed accelerometer. Whereas a 3D layout shown in figure (1-b). Fig. (1-a): Two dimensional layout of the proposed accelerometer. Fig. (1-b): Three dimensional layout of the proposed accelerometer. The main key feature behind the new accelerometer design is to implement the sensor using bulk micromachined technology. The ideas behind such approaches are developed systematically from the inspection of the key design parameters in the basic analytical equations of typical second order mass-spring-damper systems. The following equations are the fundamental equations relating the key design parameters for the second order mass-spring-damper systems (10) : r k / m (1) Q km / b (2) 2 X static a / r (3) TNEA 4 KT r mq (4) where ω r is the mechanical resonance frequency, k is the spring stiffness constant, m is the vibrating proof mass, Q is the mechanical quality factor, b is the damping factor, X static is the maximum static amplitude at resonance, a is the input acceleration, TNEA is the total noise equivalent acceleration which represents the noise floor for an accelerometer, T is the absolute temperature in Kelvin, and K is the Boltzmann constant. Equations (3) and (4) represent the main accelerometer performance. The key parameters are the proof mass, spring constant and damping. The resonance frequency parameter is affected mainly by the proof mass at a constant stiffness. Thus, the accelerometer performance can be enhanced effectively by increasing the proof mass which consequently leads to reducing the resonance frequency. The idea is that increasing the proof mass thickness results in increasing the accelerometer mass m, further reducing ω r, which results in enhancing static gain and reducing TNEA. Let the thickness of the proof mass be h µm (typical values are between 1-2 µm). If the thickness is increased by a factor n, then the new thickness will increase to n*h µm. We can keep the stiffness constant by increasing the length of the spring to cancel the stiffness increase with the thickness. Consequently, 232

3 the mass m increases by n, ω r decreases by n 0.5, the static displacement increases by n, and the TNEA decreases by n. Thus, the signal to noise ration S/N is enhanced by n 2. This illustrates the advantages of using the bulk micromachining process to fabricate the sensor. The silicon-on-insulator wafers introduce valuable opportunities for implementing bulk micromachined devices with high thickness. ANALYTICAL ANALYSIS Analytical analysis was performed to extract the sense capacitance, capacitance change, resonant frequency and total noise equivalent acceleration. The sensor is designed using a silicon-oninsulator wafer with a thickness of 25 µm. As shown in figure 1 the accelerometer consists of a large central mass with 3000 by 3000 µm 2 in area. The simple type suspension beam is used; with 50 µm in width and 2500 µm in length. The total value of the proof mass is 917 µg and total stiffness constant of 38 N/m 2 this yield to a fundamental frequency of 1024 Hz in the out of plane direction. The comb fingers are 250 µm in length and 200 µm in overlap. The comb finger width is 10 µm and a gap spacing of 5 µm separates between the fixed and moving comb fingers. This results in a large sense capacitance of 7.1 pf. The total static displacement is 2.4 pm for 10 µg input acceleration. The total noise equivalent acceleration is small as 3.41 µg/ Mechanical Modeling: Hz FINITE ELEMENT SIMULATIONS. The sensor sensitivity is 24.14(nm/g) A mechanical modeling was performed to extract the natural frequency as well as the mode shape using the COMSOL finite element pakage. Figure 2 shows the fundamental mode shape and its resonant frequency. It is a translational mode shape along the z-axis or in the out of plane of the wafer. The fundamental mode shows resonance frequency as 1108 Hz. The second and third mode shapes are approximately equal in resonance frequency of 1869 Hz. They have the same mode shape with reverse directions. Figures 3 and 4 show the second and third mode shapes. Fig. (2): The fundamental mode shape along z-axis (out of plane), at a resonance frequency of 1108 Hz. 233

4 Fig. (3): The second mode shape at resonance frequency of 1869 Hz. There is no motion in the x- or y-axes. This is due to the suspension position. The four simple beams used around the proof mass are divided into two sets. The first set consists of two opposite springs and is used to restrict a motion in one direction and the second is used to restrict the motion in the other direction. This will result in very small off-axis sensitivity as well discussed later. Fig. (4): The third mode shape with a resonance frequency of 1869 Hz. Static Analysis: Static analysis was performed to determine the maximum response of the accelerometer due to applied acceleration. The input acceleration to static analysis is simulated as a load vector in three directions with amplitude of 1 g (i.e. 9.8 m/s 2 ). This will result in a maximum output displacement of µm in the out of plane direction (z-axis) as presented in figure 5, and a minimum output displacement in the other two directions, as shown in figures 6 and 7. This is well agreeing with the design aspects in the modal analysis. A plot the von mises stress acting on the sensor is shown in 234

5 figure 8. The high stress values are located at the sensor corners at the contact points with suspension. The maximum stress value is MN/m 2, which is very small than the yield stress of Silicon single crystalline (SSC) which is 7 GN/m 2 (11). Fig. (5): Displacement field, Z component; static analysis of the accelerometer at 1g input acceleration. Fig. (6): Displacement field, X component; static analysis of the accelerometer at 1g input acceleration. 235

6 Fig. (7): Displacement field, Y component; static analysis of the accelerometer at 1g input acceleration Fig. (8): Von Mises stress; static analysis of the accelerometer at 1g input acceleration. Electrostatic modeling: The electrostatic model of the accelerometer was built to find the sense capacitance value. Due to the high number of degree-of-freedom only one fixed comb finger sandwiched by two moving fingers is simulated using the COMSOL finite element software. There are one hundred comb fingers per capacitor and four capacitors per sensor. The total capacitance is equivalent to the simulated capacitance multiplied by four-hundred as the sensor operates at the fundamental resonance frequency and the four capacitors are equally changed with the input acceleration. The simulated capacitance is pf (per finger), which results in a total sense capacitance of 11.07pF. Figure 9 shows the 236

7 simulated model for single electrode using COMSOL, whereas a plot for the electric potential distribution is shown in figure 10. Fig. (9): Simulated capacitance of the comb finger assembly. Fig. (10): the electric potential distribution of the comb finger assembly Frequency Response: The frequency response aims to determine the dynamic behavior of the sensor due to the input accelerations. Different values for acceleration in the three directions are applied. This helps to numerically determine the sensor sensitivity as well as the off-axis sensitivity. Using COMSOL finite element modeling, the input acceleration is modeled as a body force loaded along the three directions. The acceleration is equal to the force divided by the inertial mass. Thus the body force, acting on the proof mass, is equal to the silicon density multiplied by the acceleration. In figures 11 through 13, each figure presents the plot of the displacement field in one direction versus the input acceleration along this direction. 237

8 Fig. (11): the accelerometer response in the z-direction vs. input z-direction acceleration. Fig. (12): X-direction response vs. input acceleration, x-direction. 238

9 Fig. (13): Y-direction response for input acceleration in y-direction. By investigating figures 11, 12 and 13, it is clear that the main response of the accelerometer is in the z-axis (out of plane). The cross axis sensitivities in the x- and y-directions are 0.15% and 0.3% respectively. The cross axis sensitivity is measured by dividing the acceleration response in a given direction by the response in the main designed direction. The cross axis sensitivity gives an indication about how much the sensor immune the acceleration in the undesired directions. Minimum cross axis sensitivity indicated a good sensor design. The analytical and numerical analyses show a good agreement. The results state that a good sensitivity at low input acceleration is present at the same time the total noise equivalent acceleration is very small. Table 1 compares the analytical and numerical analysis achieved of the proposed design with a recently published paper (12). Table (1): comparison between proposed design and a reference design. Parameter Proposed Design results Analytical Numerical Reference design (12) Area (mm2) Structure thickness(µm) Resonance frequency (Hz) Quality factor Sense capacitance (pf) Total mass (mg) Static displacement (µm) Sensitivity (pf/g) Sensitivity (nm/g) TNEA ( µg/ Hz ) % Off-axis sensitivity (S xz) % Off-axis sensitivity (S yz)

10 REVIEW OF RADIATION AFFECTS Combining light weight, low power consumption, small physical size and possible integration with control and sense electronics, MEMS seem ideal for space applications. MEMS have been used as lighter, small or cheaper replacement of bulk parts or as entire new systems. The fields of MEMS applications in space include but not limited to inertial navigation such as accelerometers and gyroscopes, bolometers, RF switches and variable capacitors, optical switching and communications, propulsion and microfluidics. Consisting primarily of trapped electrons, trapped protons and cosmic rays the space radiation environment is strongly time and position dependent. As MEMS devices play an important role in many space applications, the radiation effects on such devices must be studied. Here, a review of different ionized irradiation effects on SOI-MEMS accelerometer will be presented. Gamma irradiation effects: For electrostatic actuators irradiated with CO 60 gamma rays, the capacitance/voltage relationship showed little change. This is likely due to the fact that a significant portion of the energy from the gamma rays is deposited within the silicon substrate, away from the thin film actuators (13). Electron beam irradiation effects: It was estimated that the change of properties of polycrystalline silicon was attributed to three different effects caused by incident electrons of electron beam in polycrystalline silicon (14). First, point defects in polycrystalline silicon were generated by incident electrons of the electron beam, according to the relatively low energy of the electrons (below 5 MeV). Such displacement damage produces displaced atoms and causes the damage of lattice in silicon (14). Second, secondary electrons generated by incident electrons cause the production of electronhole pairs, which is so called ionization. Carriers generated by electron beam irradiation influence the conductivity of polycrystalline silicon in their lifetime. Meanwhile, these carriers excited by electron beam enhance the defect reordering, which is referred as injection annealing too (15, 16). This effect also makes defects reorder to form more stable configurations in polycrystalline silicon. Similar to gamma irradiation, the electron beam irradiation introduced displacement damage also enhances the reordering of the damage (14). Third, for the incident electrons with relatively high energy, the penetration of these electrons in the polycrystalline silicon causes energy transfer to silicon atoms, lattice distortion occurs in the grain neutral region and defects annealing in the grain boundary. Such an effect is so called thermal spike (17). The directions of incident electrons are in the same direction, according to the equidirectional of electrons from the accelerator. The penetration of thermal spike in the grain boundary is relatively vertical (14, 15). CONCLUSION This paper introduces a new scheme to build the out of plane z-axis accelerometer with the SOI wafers. This inherits the advantages of both bulk micromachining as well as the SOI wafer technology to the proposed accelerometer. The proposed accelerometer shows a good performance comparable 240

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