Thermal Deformation Suppression Chip Based on Material Symmetry Design for Single Center Supported MEMS Devices

Structural thermal deformation is an important factor that affects the performance of MEMS devices. The mismatch of thermal expansion coefficient (CTE) between different materials is a major source. For single center supported MEMS devices, expansion difference between device and the substrate leads to the out of plane thermal deformation of the structure, resulting in the performance deterioration. This paper presents a thermal deformation suppression chip (TDSC) for single center supporting MEMS devices. It is fabricated by the MEMS process and consists of an upper plate and a lower plate. The materials of the upper and lower plates are the same as those of the device substrate and structure respectively. The principle of TDSC to suppress thermal deformation is material symmetry design. Single center anchor is adapted to connect the upper and lower plates. Besides, the center anchor can also isolate the packaging stress generated between TDSC and package shell. In this paper, center supported quadruple mass gyroscope (CSQMG) is used to verify the effect of TDSC. Finite element simulation shows that the thermal deformation suppression effect is determined by radius of TDSC anchor, and the deformation can be suppressed to 0. The conclusion is confirmed by White light interference experiment. In addition, the experiment results also show that the TDSC effectively reduce the thermal out-of-plane deformation after packaging, which is even better than that of the gyroscope without any packaging. It is further proved that TDSC can also significantly improve the temperature performance of the CSQMG. Moreover, the TDSC has simple process steps, small chip area, low cost, and is suitable for various MEMS devices with single center anchor.


I. INTRODUCTION
MEMS (microelectromechanical system) is an interdisciplinary technology field, involving microelectronics, machinery, optics, biology, materials, physics, chemistry, signal processing, and other disciplines. Microsensors based on MEMS technology have the advantages of small size, low power consumption, and low cost. MEMS devices have a significant impact on consumption, industry, and other important fields. With the developments in technology, The associate editor coordinating the review of this manuscript and approving it for publication was Sanket Goel . the requirement for the accuracy and environmental adaptability of MEMS devices has significantly increased [1], [2].
Mechanical deformation is an important factor affecting the performance of sensors. Some MEMS devices such as gyroscope [3], [4], pressure sensor [5], [6], and accelerometer [7] work on the principle of force conversion. In such cases, these sensors convert the external signals (acceleration, angular velocity, pressure) to electrical signals, and detect the electrical signals to achieve high-precision measurement. However, thermal deformation directly leads to output error [8]. In general, stress and thermal deformation occur together. Structural stress will cause stiffness asymmetry, coupling modal motion, and frequency drift [9]. Some reports demonstrate that thermal stress can cause deformation or even fatigue fracture in the movable structure, which have the most direct impact on output, and the relationship between thermal deformation and temperature is normally nonlinear. Thus, the performance of the device will be worse under the condition of variable temperature [10]- [12]. Consequently, stress and thermal deformation minimization has become an important issue.
Generally, a main source of thermal deformation is the coefficient of thermal expansion (CTE) mismatch [13]- [15] For most solid materials, when the temperature of an object with a length L changes, the free thermal expanding is defined by where α T is the coefficient of thermal expansion (CTE) of the object and T 0 is the reference temperature. For some MEMS devices, the material of device is different from that of the substrate, which is determined by process method, such as hemispherical resonator gyro, device based on the silicon on glass (SOG). Besides, MEMS packaging is used to protect device structures and provide electrical interconnection. MEMS devices and matching circuit chips are encapsulated in a shell to form a micro-sensor, which can be used independently. It is really difficult to select the same material as the device to complete packaging. During the packaging process, the chip experiences heating and cooling. Different expansion of MEMS structure, substrate and packaging leads to stress and structural deformation. [13]- [16]. There are three commonly used methods to reduce the stress. (1) Material selection: Materials whose CTE is similar to silicon are selected to complete the MEMS device packaging [18]- [20]. (2) Packaging method: The effect of die-bonding process on MEMS device performance was studied. Experimentally model used a distributed system-level nodal modeling in [21]. The research works in [22]- [24] focused on the attachment process such as the attachment area, attachment position, and four-dot die-attach process.
(3) Stress isolation structures: Low stress packaging of micro machine accelerometer is reported in [9]. Stress relief structures formed around the periphery of the MEMS die was proposed in [9], [25]- [27]. A packaging-stress isolation structure designed on the handle layer of SOI is presented in [28], [29]. Besides, a two orthogonal stress-immunity structure [30] were designed to improve the temperature robustness of double-clamped MEMS sensors. However, the above method mentioned play a role of stress buffer to reduce the packaging stress, but the problem of CTE mismatch between the device structure and the substrate is not solved.
To suppress the thermal deformation caused by CTE mismatch, in addition to isolate packaging stress. A thermal deformation suppression chip (TDSC) for single center supported MEMS devices is presented. The chip is manufactured by the MEMS process and consists of an upper plate and a lower plate. The material of the upper plates is the same as that of the device substrate. So structure-substrate-TDSC is a sandwich like design. The position symmetry design of the materials can achieve the suppression of thermal deformation. A complete finite element model is established to verify the effect of TDSC. White-light interferometer is used to measure thermal deformation. The experiments show that the out-ofplane deformation can be eliminated by changing the anchor radius of TDSC. Temperature experiment is also performed to verify that the device deformation is insensitive to temperature variations due to the TDSC.
The paper is organized as follows: in section II, single center supported MEMS gyroscope is taken as an example to analyze the effect of CTE mismatch and the principle of TDSC. Section III describes the construction of the model to explore the relationship between anchor size of TDSC and thermal deformation. Section IV presents the experimental verification of the TDSC. Finally, the conclusion is presented in Section V.

A. ANALYSIS FOR THERMAL DEFORMATION OF SINGLE CENTER SUPPORTED MEMS GYROSCOPE
The MEMS resonant gyroscope has become one of the most important MEMS inertial sensors for detecting the angular velocity. Most MEMS resonant gyros work on the Coriolis principle. First, the electrostatic force is used to induce proof mass vibration. Then, under external angular velocity, the Coriolis force which is perpendicular to the driving direction and the direction of angular velocity is applied to the mass. The external angular velocity can be obtained by measuring the Coriolis force [3], [4]. As shown in Fig. 1(a), it is common to find clampedclamped structures in the design of MEMS gyroscope [29]. However, due to the mismatch of the CTEs between the substrate and the device layer, expansion difference between structure and anchor will generate considerable stress. Aiming at the above problems, the single anchor design shown in Fig. 1(b) can effectively avoid internal stress. However, although the problem of internal stress is avoided by design, unexpected deformation shown in Fig.2 still exists, When VOLUME 8, 2020  Structure of Center Support Quadruple Mass Gyroscope, with four proof masses connected through the N-shape-beams and the Y-shape-beams, supported by a single center support anchor. 0 < l low < l up or l low < l up < 0, umbrella-shaped deformation shown in Fig. 2(a) occurs and it gets reversed when 0 < l up < l low or l low < l up < 0, as shown in Fig. 2(b). It should be noted that out-of-plane deformation occurs even for the gyroscope without any packaging, and deformation increases after packaging [17]. The thermal outof-plane deformation leads to coupling signals and zero-bias changing, which is usually nonlinear with temperature and unpredictable. Thus, as for single center supported MEMS device, it is very important to reduce the deformation.

B. PRINCIPLE OF THERMAL DEFORMATION SUPPRESSION CHIP
As shown in Fig.3, the center supported quadruple mass gyroscope (CSQMG) is a typical MEMS device as described above [31], [32]. The CSQMG consists of four symmetrical proof masses, folding beams, and support frames. The movable structure is attached to the substrate by the center support anchor. To minimize the stress generated at the design level, clamped-clamped structure is avoided.
In this work, the CSQMG is fabricated based on the SOG process. Fig. 4(a) shows the process steps. A Pyrex substrate wafer and a silicon device wafer (100) were prepared for the gyro process. First, a 200nm thick Ti/Pt/Au layer was patterned using the liftoff process in the Pyrex wafer. Then, on one side of the silicon wafer, an anchor area with the height of 20µm was etched by DRIE. Afterwards, the device wafer and the substrate wafer were anodically bonded together at a temperature of 350 • C with a DC voltage of approximately 500 V. Finally, the other side of the silicon wafer was thinned to 100 µm and released using the second DRIE step. As we know, the material of gyroscope structure is silicon but the substrate is Pyrex 7740 glass. Problem of CTE mismatch exists, so umbrella-shaped thermal deformation is the most important problem. Next, we will introduce TDSC to solve this problem.
For TDSC, we also adopt the single center anchor support design. It can be fabricated by the conventional MEMS process. The chip is obtained through two steps: 1) 50/200 nm Ti/Au was patterned as the mask. Then the Pyrex glass was put into the BOE solution(20:1), and the corrosion process lasted for 6.7 hours, forming a 20.5um anchor step. 2)Removing the metal mask, and the glass wafer is bonded to a silicon wafer ( Fig. 4(b)). After wafer dicing, the chips are adhered use ABLEBOND JM7000 on ceramic shell to formed gyroscope with TDSC. Control the adhesive curing temperature within the range of 150 • C to 350 • C and curing under 300 • C for 15 minutes and cool to the room temperature. As shown in Fig. 5. The TDSC is located between the MEMS gyroscope substrate and the package shell. It is composed of upper and lower plates. The upper plate is attached to the substrate of gyro and is made of the same material as the MEMS device substrate. The upper and lower plates are bonded together by small central anchor.
The TDSC has two main functions. First, it works in isolating the packaging stress. Because of material matching, no packaging stress generates on the substrate of MEMS gyroscope. However, stress still occurs in areas where the CTEs are mismatched, such as (1) between the lower plate and ceramic shell and (2) between the upper plate and the lower plate. It is evident that all stress is transferred to the CSQMG structure only through the central anchor of TDSC. Accordingly, the single central anchor design isolates part of the packaging stress.  The second function of the TDSC is suppressing the outof-plane deformation of the CSQMG through symmetrical material setup. And the function is the purpose of TDSC. To explain the principle of symmetrical material setup further, we simplify the analysis using the follow assumptions: 1 Different component are considered as unions. The shape variables are the same at the contact surface.
2) The gyroscope deformation is determined by the thermal expansion of point A and B shown in Fig. 6. When l B > l A , umbrella-shaped deformation as Fig2.(a) occurs, and when l A > l B , anti-umbrella-shaped deformation occurs., and when l A = l B , no deformation is caused, which is the ideal state.
We defined two types of gyroscope: type I gyroscope was the packaged CSQMG without TDSC and type II gyroscope was without TDSC.
For the type I gyroscope, l A is regarded as the free expansion of silicon anchor with radius l A . The material setup is Si-Glass-AlN from the top to the bottom. According to the CTE data provided in [10], the CTE of Si and glass is shown in the Fig. 7. Pyrex7740 Glass CTE α glass is larger than that of Si CTE α Si before 109.5 • , resulting in more thermal expansion on substrate glass. The thermal expansion difference between the substrate and the gyro structure forms the internal stress along the radial distribution on the material mismatch interface, which is proportional to the radius, resulting in the deformation of the gyro structure. Because the ceramic shell (AlN) CTE α c is 3.3 ppm/ • , so the deformation will be more obvious after being adhered to ceramic shell.
For the type II gyroscope, When TDSC is introduced, the material setup of type I gyroscope is ''Si-Glass-Si-AlN'', and the CTE order is ''small-large-small-larger'', which is like a sandwich structure. For the substrate, we hope that the CTE mismatch of the upper and lower surfaces can be adjusted to the same and opposite, resulting in no thermal deformation occurring on the surface of gyro. The thermal expansion of point A and B in the Fig. 6 can be expressed by equation (3): We call the f a contribution function, which is TDSC's contribution to l B .The contribution can be either negative or positive. In other word, the inequality, |f | > 0, is not always true. Changing the l B to equal l A is the purpose of contribution function, resulting in no thermal deformation on gyro structure. Obviously all that is connected to the glass is only the center support anchor of TDSC, and the CTE of silicon and shell is constant, so the dimension of the anchor is the key factor that determines the deformation state of gyroscope, so the function is related to the anchor parameter of TDSC when the overall size is determined. However, it is difficult to obtain the accurate value of the distribution force on the material mismatch interface and the deformation caused using mathematical method. In the next chapter, the finite element simulation is carried out simulation for studying.

A. FE MODELING
To study the modified function mentioned above and verify the effect on stress isolation, the finite element (FE) analysis model for the two types of gyroscope were built in COMSOL Multiphysics for comparison and verification. In the simulation, the upper plate material was made as silicon and the lower plate was Pyrex7740 glass. In the packaging process, the gyroscope chip was attached to the ceramic shell using an Ag adhesive at a temperature of 200 • C; therefore, the structure was assumed to have no thermal expansion at 200 • C. Additionally, the ceramic base bottom was constrained as the datum plane for calculating, which was required in the emulator. To reduce computation complexity, the models were simplified by replacing the irrelevant comb part with flat plate. Stationary simulation was carried out at 293.15K. The model dimension details are shown in Table 1.

B. CONTRIBUTION FUNCTION OF TDSC
According to Chapter II, both the packaging stress and out-ofplane deformation are caused by CTE mismatching. TDSC is a way to solve the problem through material symmetry setup. TDSC makes the equivalent CTE of the substrate the same as the structure, so as to achieve the purpose of restraining thermal deformation. All the parameters shown in Table 1 may determine the deformation state of gyroscope. However, considering the process steps, experimental verification cost and practicability, we choose the dimension of the TDSC anchor as the key factor. We expect to obtain the optimal dimensions for no deformation. Meanwhile, the packaging stability and process simplicity should be considered, which means that the anchor height should be small, and the area should be as large as possible. A cutting line a-b-c-d-e through the proof mass, frame, and center support anchor was created to describe the umbrella-shaped deformation of CSQMG (Fig. 8). The height difference between the center (point c)  The result of the diameter simulation is shown in Fig. 9(a). the z axis is the maximum warpage (the height difference between point a and point c in Fig.8). With the change in the size of the anchor, the out-of-plane deformation surface passes through the zero-deformation plane. We consider two curves with an anchor height of 20 and 100µm, respectively, and draw them in Fig. 9(b). The result shows that the outof-plane deformation is independent of anchor height and is mainly affected by the radius of anchor.  As the radius increased, the gyroscope gradually changed from reverse deformation to positive deformation, so zerodeformation can be achieved by changing the radius of anchor. To clearly demonstrate the zero-deformation of CSQMG, we chose a height and radius of 20 and 2120 µm, respectively, to simulate the out-of-plane deformation of two types of gyroscope. As shown in Fig. 10, the abscissa represents the position of the cutting line, where the coordinate of point C is 0. For the type I gyroscope, the maximum warpage is 0.1895µm. Owing to the TDSC, the out-of-plane deformation of type II gyroscope is almost completely suppressed, the maximum warpage is only 0.0049 um.

C. SIMULATION OF PACKAGING STRESS ISOLATION
As mentioned above, thermal deformation suppression and packaging stress isolation is two function of the TDSC. The transfer channel of the packaging stress follows the path: lower plate-central anchor-upper plate-gyroscope. It is evident that the central anchor is the only way to transfer the packaging stress. Stationary simulation was carried out to obtain the effect of TDSC on stress distribution at 25 • .  In simulation, the mismatch between the thermal expansion coefficients was the only source of stress. Ignoring the external stress effects, we set the ceramic thickness so large that no fixed stress will transfer to the gyroscope. Besides, the stress type is equivalent von Mises stress, which is an equivalent stress based on shear strain energy. It is defined: where a 1 , a 2 , a 3 is the first, second and third principal stresses. As shown in Fig.11, packaging stress occur in where the CTEs mismatch. The thermal stress of type I gyroscope is generated in the follow two places: 1) The bottom of gyro substrate and the ceramic shell; 2) The gyro anchor and substrate. On the substrate, it is obvious that the former account for a large stress. For type II gyroscope shown in Fig.11 (b), the stress is mainly concentrated between the ceramic shell and the lower plate, even though stress in the lower plate is larger than that in the substrate of type I gyroscope. Almost VOLUME 8, 2020 all the packaging stress is concentrated in the area under the anchor of TDSC.
To accurately show the stress isolation effect, average stress of surface of substrate and surface of gyro is calculated for comparison. The result is shown in Table 2. The stresses in the surface of substrate of type I gyroscope and type II gyroscope are 29.4 and 0.76 MPa, respectively, and those in the surface of gyro are 11.873 and 0.642 MPa, respectively, so the TDSC also plays a role in packaging stress isolation.

IV. EXPERIMENTAL VERIFICATION A. EXPERIMENT SETUP
In this work, the CSQMG and TDSC were fabricated and packaged into type I and II gyroscope. In the experiment, the while light interferometer, Bruker Contour GT-IM shown in Fig.12, was used to measure the out-of-plane deformation. The test temperature was controlled by a small heater. We chose the edge of the movable structure area as the observation window. The window includes the movable structure and the static comb, the static comb is bonded to the substrate. Thus, we take the height difference between the movable structure and the static comb as the out-of-plane deformation of the gyro. To ensure the accuracy of test results, all four mass were measured for each gyro. Each mass contained two test points. The average measurement value of eight points ( Fig.12) was taken as the deformation value of the gyro.

B. OUT-OF-PLANE DEFORMATION
Firstly, the relationship between the anchor radius (r) of TDSC and the out-of-plane deformation ( z) was measured. As shown in Fig.9, the point of zero deformation is between 1500 and 2500µm. The fitted curve is approximately linear. Therefore, the radius of the experiment is set between 1000-2500µm. the simulation and experimental results are fitted linearly for simplify. TDSC with four different sizes was processed, as shown in Fig. 12. Then, these chips were packaged with CSQMG and tested under the same conditions. The results of experiment ( z 1 ) and simulation ( z 2 ) are shown in Fig. 14. The relationships are fitted as following.
The experimental results are in accordance with the simulation results. With the change of anchor radius, the deformation state turns from anti-umbrella shape to umbrella shape, and goes through no deformation state. For the radius of zero-deformation, experiment and simulation are 2307.3 and 2140.3µm, respectively, with a 7.8% relative error. Because simplified gyroscope model is used in the simulation and the influence of adhesives is neglected. The mismatch between the values of thermal expansion is the only source of out-ofplane deformation, and we ignore the residual stress in chip processing, which is difficult to estimate.
Then, we choose the TDSC with 2500um to verify the effect of TDSC on suppressing the out-of-plane deformation. Firstly, 10 gyroscopes without packaging were measured by the while light interferometer As shown in Table 3, the initial thermal out-of-plane deformation is distributed between 0.0047µm and 0.1138µm. The initial deformation is caused by residual stress in the wafer process, like anodic bonding. Then, the 10 gyroscopes are packaged into 5 type I and 5 type II gyroscopes, and measured again. Figs.13(a) and (b) show the measured result of type I and type II gyroscopes before and after packaging, respectively, which is just one of all measurement points. The average measurement value of eight points data is listed in Table 3.
To clearly describe the suppression effect of TDSC on thermal deformation, the thermal deformation variation after packaging of the two types of gyros are shown in figure 15. The blue bar is the type I gyroscope, and the thermal outof-plane deformation after packaging is obviously increased. For the type II gyroscope (red bar), which is packaged with TDSC, the thermal deformation variation is smaller than that of type I gyroscope, or even smaller than 0, which means that thermal deformation of type II gyroscope is smaller than gyro without any packaging. Actually, the packaging stress is never smaller than that without packaging, the TDSC suppresses the deformation directly by material symmetry setting.

C. TEMPERATURE EXPERIMENT
Temperature is the most significant factor that affects the output of a MEMS gyroscope. Temperature also causes stress variation. To verify the improvements in the temperature performance of gyroscope with TDSC, white light interference experiment under variable temperature conditions was conducted. In the experiment, two types of gyroscopes were heated from 20 • C to 140 • C and measured. We set every 20 • C as a measuring point and keep each point for 2 hours. As shown in Fig. 16, the deformation decreases with the increase in temperature because the operating temperature of packaging is usually higher (T < T 0 in equation (1)). VOLUME 8, 2020  For type I gyroscope, the deformation changes from 0.2423 to 0.085µm. The deformation change in the whole temperature experiment is 0.1573µm, and that of type II gyroscope is 0.0257µm, which is only 0.15 times of that of type I gyroscope. It is obvious that type II gyroscope is more insensitive to temperature change, which means that TDSC can not only reduce the umbrella-shaped deformation but also enhance the robustness of the gyroscope in variable temperature environment.

V. CONCLUSION AND DISCUSSION
From the above experimental results, TDSC can restrain the out-of-plane deformation of single anchor device structure, which is helpful to improve the performance and thermal environment adaptability of MEMS devices. In addition, the following further improvements can be applied to TDSC: 1) The TDSC is suitable for MEMS devices with various substrates. The material of the upper and lower plate should be the same as that of the MEMS device and substrate. The TDSC can be manufactured simultaneously with MEMS devices. First, the substrate of the device wafer must be etched to create the anchor. Then, the device wafer after anchor etching is bonded to the lower plate wafer. Finally, the MEMS devices with TDSC can be obtained by scribing. However, this method adds the processing steps of MEMS devices and the substrate layer may have the problem of secondary bonding. In comparison to the TDSC processed separately, the effect of stress isolation will be weakened due to the decrease in the thickness of the upper plate.
2) The lower plate of TDSC can also be etched to form the stress isolation pattern, which can further help to obtain a better stress isolation effect. The effect of the overall size of TDSC on the stress isolation effect can be neglected. The upper plate area is large enough to ensure the operability of subsequent packaging. Therefore, once a TDSC is processed, it can be applied to other MEMS devices with the same substrate. In summary, to solve the problem of thermal deformation caused by CTEs mismatch, a thermal deformation suppression chip (TDSC) based on MEMS process is proposed. The principle of TDSC is building a sandwich like material symmetrical structure, to achieve the CTEs' mismatch symmetrical between the two surface of device substrate. Besides, Single anchor support design is adopted, and the CTE mismatch can be adjusted by the size of single anchor. This study focuses on center supported quadruple mass gyroscope to establish the mathematical and finite element models of TDSC, providing the influence of TDSC on packaging stress distribution and out-of-plane deformation of MEMS gyroscope. In addition, the white light interferometer experiment was carried out. Simulation and experiment show that the optimal effect of thermal deformation suppression can be achieved by changing the anchor radius, and out-of-plane deformation was significantly reduced in the gyroscopes with TDSC, which is better than that of the gyroscope without packaging. Simultaneously, we also demonstrate the ability of TDSC to improve the thermal environment adaptability of the MEMS gyroscope. Furthermore, chip-level format makes TDSC suitable for other MEMS devices with single center anchor.