Performance of compliant mechanisms applied to a modified shape accelerometer of single and double layer

M. Tecpoyotl-Torres, R. Cabello-Ruiz, P. Vargas-Chable, J. G. Vera-Dimas, A. Ocampo-Diaz Research Institute of Basic and Applied Sciences-Research Center of Engineering and Applied Sciences (IICBA-CIICAp), of Autonomous University of the State of Morelos (UAEM), Morelos, México Technologic University Emiliano Zapata (UTEZ), Emiliano Zapata, Morelos, Mexico Chemical Sciences and Engineering Faculty, of Autonomous University of the State of Morelos (UAEM), México


INTRODUCTION
Accelerometers measure the acceleration of an object by utilizing the classical Newtonian Law of Forces, where forces of the same magnitude will be generated in the opposite direction of the applied force. This force is normally detected by a movable part in the accelerometer and is translated into electrical signal using various electrical principles for further processing and data extraction [1]. These measurements are performed in one, two or three orthogonal axes. The acceleration measurements are typically used to calculate in-plane velocity and position, inclination, tilt or orientation in two or three dimensions with respect to the acceleration of gravity (g, equivalent to 9.81 m/s 2 ), as well as to measure vibration and impact [1][2][3]. The first batch-fabricatable accelerometer was reported in 1979 [4]. It was capable of measuring accelerations from 0.001 to 50g over a 100 Hz bandwidth. Since 1990, accelerometers are commercialized and widely used in the automobile industries for triggering air-bag system in convertibles [1]. They have seen significant success in a large spectrum of applications, ranging from the automotive control and safety systems, consumer electronics for mobile, gaming, wearable and healthcare devices, and also in industrial,  [2,[5][6][7][8][9]. Capacitance accelerometers may be more suitable for some applications like automotive crash detection and air-bag deployment (high g force, such as 50g) [2]. Combination of desirable features like small size, low power dissipation, high sensitivity and low cost are nearly always needed for many of their applications [2]. Part of their research is focused on the optimization of the devices sensitivity, looking for a better efficiency. There are diverse types of accelerometers in the market, in [1] they are classified as: Capacitive, Piezoelectric, Piezoresistive, Hall Effect, Magneto resistive, Heat Transfer, Optical, and Tunnelling. Several materials have been studied to provide some advantages in the fabrication or in the response of accelerometers, as in [10]. A study of a controllable aluminium doped zinc oxide (AZO) patterning by wet etching for MEMS applications is given in [11].
Other structures have been developed to increase the displacement obtained in several accelerometers, such as mechanical amplifier, which can transform the displacement applied to the input in an amplified version of it, obtained at the output of the system. Mechanical amplifiers can have very simple geometries, as lever devices [12][13][14]. More complex devices are also implemented, such as the Displacementamplifying Compliant Mechanism (DaCM) shown in [15]. DaCMs are compliant equivalent of displacementamplifying levers, but they do not transfer the entire energy available to them at the input to the output because some of it is stored as the elastic strain energy within the mechanism [16]. A DaCM is used in [17] to enhance both the sensitivity and bandwidth of in-plane capacitive micromachined accelerometer. The input of the DaCM is attached to the proof-mass, allowing to obtain amplification or gain of mechanical signals, due to the assembling of simple parts such as rigid beams connected by assembly bolts [18].
This paper is focused on capacitive accelerometers, which uses the change in capacitance as a mean for measuring the acceleration of an object. They consist of a moveable central proof mass which provides the necessary inertia for providing the acceleration force for measurement, a fixed capacitive electrode to form a capacitor with the moveable proof mass, an anchor for providing support and springs to provide the flexure of the proof mass. Structural supports of mass are called suspension beams.
The objectives of this work are, by means of simulation and using the in-plane mode: a. Make variations in the thickness of the moveable central proof mass, made with a Silicon layer, from 25 to 30 µm to observe the changes produced in Sx, and in the operation frequency for a single capacitive accelerometer with extended beams (CAEB) and for the arrangement CAEB-DaCM. b. Analyse the change on the Sx and operation frequency when a second layer made of Aluminium, Silicon Nitride or Copper (materials commonly used in MEMS fabrication) is deposited over a Silicon layer of thickness t1=25 µm and to perform variations in the thicknesses of t2, from 1 up to 5 µm. c. Demonstrate that the implementation of double-layer DaCMs improves Sx and operation frequency in the double-layer accelerometers, with the proposed materials. d. Perform a sweep of gravity values to know the operating limit of double-layer CAEB and CAEB-DaCM.
Extreme operating conditions were obtained using the analysis of stress.

RESEARCH METHOD
For the case of capacitive accelerometer, Sx, can be calculated from (1) where m is the mass of the system, a is the acceleration, and k is the stiffness or spring constant, given by: where E is the Young´s modulus of material, t, wb and lb are the thickness, width and length of the suspension beams, respectively. The accelerometer will have an adequate Sx corresponding to each acceleration value, as long as no resonance frequencies are present. It is well known, that before any resonance frequency is generated, the device will operate in accordance with the design requirements. For this reason, it is recommended to design devices for high operating frequencies in order to avoid low resonance frequencies.
where N is the number of suspension beams. About the implemented devices, CAEB is depicted in Figure 1, its elements and dimensions, are given in Table 1. Table 2  Silicon CAEB of constant thickness, considering the in-plane mode and one g applied were published in [19]; they are used in this paper only for comparison purposes.

RESULTS AND ANALYSIS
In all simulated cases of subsections 3.1-3.3, one g is applied at Y axis direction.

Displacement sensitivity and operating frequency of Silicon CAEB of different thickness
In Table 3, calculated (with eq. (1-3)) and simulated values of parameters under analysis are shown. There are very small variations in both parameters, which can be considered as negligible. However, it is important to mention that there are very small percentages of variation between the theoretical and simulated results, of 0.46% and 0.15%, for the displacement sensitivity and the operation, respectively. It can be said that the proposed equations and the boundary conditions (fixed anchors) established in the simulation of the devices are adequate, since they provide variations of less than 1%, in both cases.

Displacement sensitivity and operating frequency of double layer CAEB
In Table 4, parameter values for the CAEB are shown, when Silicon layer of 25 μm thickness was used and another layer was added. In Figure 2, a representative case of Sx and operating frequency of a double-layer CAEB is shown (the rest of cases are similar). Figures of Silicon CAEB were reported in [19]. From (1-3), Sx and operation frequency have a direct and inversely proportional relationships to the mass of the system, respectively. This fact is also observed in the results shown in Table 4. For example, the structure made with additional Copper layer has higher Sx (45.18 μm/g). However; it is the one with the lowest operation frequency (74.22 Hz). The opposite case is shown by the structure with additional layer of Aluminium Nitride, which presents higher frequency (187.6 Hz), but lower Sx value (7.06 μm/g).

Displacement sensitivity and operating frequency of double layer CAEB-DaCM.
For the CAEB structure made only with Silicon, the implementation of a DaCM improves both parameters simultaneously [19]. In this subsection, the effect of displacement amplifier on the CAEB of Silicon, with different thicknesses as shown in Table 5, and with double-layer also with different thickness as shown in Table 6. The shape of the displacement amplifier is similar to the given in [19]. For each case of double-layer CAEBs, the corresponding displacement amplifiers, have also an additional layer. In Figure 3, a representative case of the behaviour of the displacement sensitivity and the operating frequency of double layer CAEB-DaCM, are shown. Silicon case was previously reported [19]. Width of CAEB was reduced at one half of the original size, shown in Figure 1, in order to obtain lower mass to improve the operation frequency, since the implementation of the DaCM will improve Sx. The total length of displacement amplifier is 11 mm and its width is 3.5 mm.
Differences in the parameter values for the case of variation parameters for Silicon CAEB-DaCM, as shown in Table 5, are negligible for the case of Sx and slight for operation frequency, when additional layer has different thickness as shown in Table 6. From Table 6, although the increment occurs in both parameter values, it is much higher in the case of the operation frequency, compared to the case of single CAEB structure response. Table 7 shows the percentages of improvement in operation frequency, from 61.6% (for Aluminium Nitride over Silicon) up to 70% (for Aluminium over Silicon). While, Sx shows improvements from 13.56 up to 30.87 µm/g. In both cases, a second layer thickness of 1 µm was considered.

Range of g for single and double layer CAEB.
The range of gravities for operation will be determined, verifying that the elastic limit in the normal effort is not exceeded in each case. Limit values of gravity are given in Tables 8 and 9 for CAEB made with Silicon and double layer, respectively. In all cases, the changes on the normal stress values are small for the considered thickness values. Gravity values are smaller in the case of double layer CAEB. In Figure 4, the zone with maximum Normal Stress for the case of CAEB of double layer made with Aluminium over Silicon is shown, as representative case. The zone of the higher normal stress for all these cases is located at the same extreme of the corresponding suspension beam.

Range of g for CAEB with DaCM
The limit values of gravity are shown in Tables 10 and 11, for CAEB-DaCM Silicon and double layer structures. It is remarkable for the cases with additional layers, under a not linear variations. Again, gravity values for double layer CAEB-DaCM are considerably reduced, comparing with the implementation only with Silicon, except for the case of Copper over Silicon, with t2=1 um. Figure 5 shows the maximum normal stress zone, for a representative system made with Aluminium over Silicon (all cases have similar zone location).   For two layer CAEB: Sx and operation frequency, have a direct and inversely proportional relationships to the proof mass, respectively, as for case of the previous case, in accordance to Equations (1-3). The lower values of Sx (9.12 μm/g) correspond to an additional layer of Aluminium Nitride (with t2 of 5 μm) and the bigger one (15.20 μm/g) corresponds to Cooper (with t2=5 μm). The lower values of operation frequency (127.87 Hz) correspond for Copper (with t2 of 5 μm) and the bigger value (165.06 Hz) to Aluminium Nitride (with t2=5 μm), for operation frequency. This value of Sx exceeds the corresponding value of the Silicon CAEB by 40.87%, while the bigger value of (Aluminium Nitride over Silicon) exceeds the same reference by 8.73%.
For Silicon CAEB-DaCM: A light increment in Sx, and a stronger one in operation frequency were obtained (13.15 μm/g and 245.62 Hz, equivalent to 21.87% and 61.78%, respectively), compared to the Silicon CAEB parameter values without displacement amplifier.
CAEB-DaCM with additional Copper layer: It has higher Sx (19.31 μm/g). However, it is the one with the lowest operation frequency (203.23 Hz). The opposite case is presented by the structure with additional layer of Aluminium Nitride, which presents higher frequency (262.28 Hz), but lower Sx (11.58 μm/g).
Gravities´ swept applied to single and double-layer CAEB accelerometers: the effect of their thickness was not relevant, in each case. But, the range is considerably reduced for the double layer cases, in comparison with the single layer CAEB, especially for Copper over Silicon (75%). For Aluminium Nitride (t2=1µm) over Silicon, the reduction is of (66.66%).
Gravities´ swept applied to CAEB-DaCMs systems: g values are considerable reduced when a second layer is implemented. It was observed that different values of gravities produce maximum normal stress values, depending of its thickness value, under a nonlinear tendence.
Values of tensile yield strength are near for Silicon and Copper, but differences on the limit operation range of g values for single and double layer (made with Copper) CAEB-DaCM are considerable, varying from 100g (for 25 μm) up to 105g (for 29 μm), for the Silicon case, and from 102g (for 25μm/1μm) down to 56g (for 25μm/5μm), for the double layer case, improving the double layer CAEB response. The lower value of g corresponds to the case of additional layer of Aluminium Nitride over Silicon with a thickness ratio of 25μm/2μm, of only 16g. CAEB-DaCM of the analysed cases could be used for different applications, in accordance to the requirements of displacement sensitivity, operation frequency or acceleration range.