Simulation research on structure-related thermal drifts of sensing capacitances of MEMS inertial sensors

HU Qi-fang, XING Chao-yang, LIU Guo-wen

(Beijing Institute of Aerospace Control Devices, Beijing 100094, China)

Simulation research on structure-related thermal drifts of sensing capacitances of MEMS inertial sensors

HU Qi-fang, XING Chao-yang, LIU Guo-wen

(Beijing Institute of Aerospace Control Devices, Beijing 100094, China)

The precision of the inertial navigation is highly related with the thermal stability of MEMS inertial sensor devices. The structure-related thermal drift is mainly caused by the mismatch stresses of MEMS material, the fabrication-induced stress, and the packaging stress. This paper focuses on the FEM simulation researches of standard bulk silicon MEMS inertial devices. Based on ANSYS FEM simulation, the FEM models of common beam-mass structures in MEMS inertial devices are built,including cantilever beam, double-clamped beams, L-shaped beams, and diagonal-suspension beams.Based on thermal-mechanical coupling simulation, the distributions of thermal mismatch stresses in these structures and the resulting structural deformation are studied. Based on the coupling simulation of multi-physics fields in full temperature range from -40℃ to 60℃, the packaging-induced stress and the stress-temperature relationship of various chip-bonding methods are evaluated, including single-point chip bonding, multi-points chip bonding, and whole area bonding. In addition, the isolation effects of different substrate thicknesses on the packaging-induced stress are shown by analysis and research.

MEMS; inertial sensor; thermal drift; packaging stress

The MEMS (micro-electromechanical system) inertial measurement units (IMU) integrating with GPS are widely used in the navigation system of unmanned aerial vehicle, guided missile, and pilotless automobile. However, if the GPS signal is lost, the navigation accuracy are determined by the standalone pure MEMS inertial measurement units[1]. The bias drift is the most important issue of high performance MEMS inertial sensors,including MEMS gyroscopes and MEMS accelerometers.The bias drift of MEMS inertial sensors is related withvarious factors, including temperature, long term stress release, and vibration shocks, and etc[2-3]. The temperature bias drift (TBD) of MEMS inertial sensor’s outputs mainly comes from interface circuits, MEMS structures and packaging[4-7]. The structure-related MEMS TBDs are generally caused by the material thermal miss match of silicon, boron silicate glass, metal or ceramic substrates,adhesive glue. On the other hand, the beam-mass structure design of inertial sensors also has strong influence on the TBD reduction. This paper focuses on the analysis and the compensation for the TBD of four typical beam-mass structures of Z-axis MEMS inertial sensors,including single cantilever suspension, double-cantilever suspension, L-shaped beam rotational symmetry suspension, and diagonal suspension. The MEMS’s moveable structures are defined as highly doped N-type(100) single crystal silicon, and the substrate of the modes are Pyrex? 7740 boron silicate glass. The sensor elements of the modes are out-of-plane MEMS capacitive between proof mass and glass substrate. The FEM 3D structures are designed, modeled, and simulated using commercial finite element software ANSYS?.

1 Structure and design

The basic structures of the four typical inertial MEMS structures are given by Fig.1. The moveable MEMS structures are the proof mass and the suspension beams, in which the proof mass converts the external acceleration into the inertial force. The beam-mass structures are fixed on the substrate by anchors. The lower surface of the proof mass and the upper surface of the substrate form the MEMS capacitor, whose capacitance varies when the proof mass goes up and down. The suspension beams are set to much more thinner than the proof masses to increase the Z-axis inertial sensitivity.The fabrication of the Z-axis sensitive inertial sensor beam-mass structures is generally consisted of six steps.First, the silicon wafer is etched using inductively coupled plasma etching (ICP) of silicon to form the MEMS capacitance shallow groove. Then followed the second ICP etching step to fabricate the beam structure.After that, a third ICP etching process is proceeded on the same side of the silicon wafer to from half of the proof mass, and move the beams to the center (along Z-axis) of the proof mass simultaneously. After the etching processes, the silicon wafer is anodically bonded to the fabricated glass electrode wafer. After that, the structure layer is thinned in the KOH anisotropic wet etching solution. Finally, the proof mass is etched using ICP, and the beam-mass structure is released.

Fig.1 Schematic of the Z-axis sensitive inertial MEMS

The designs and the feature dimensions of the four elaborated beam-mass structures are shown in Fig.2(a) to Fig.2(d). In the case of Type-I, as shown in Fig.2(a), the cantilever beam is fixed to the proof mass from the left side, and the anchor is placed on the left side of the cantilever beam. The area of the proof mass is 2000×2000μm2, and the thickness is 100 μm. The topological dimensions of the cantilever beam is 450 μm(L)×520 μm(W), and the beam’s thickness is 20 μm. The beam-mass structure of Type-I is frequently used in the mediumprecision MEMS sandwich capacitance accelerometer[8].The beam-mass structure of Type-II uses double cantilever beams to suspend the proof mass on the same side,as shown in Fig.2(b). The beam length of the two cantilever beams is also 450 μm, and the beam width of the suspension beam is half of the beam’s of Type-I. The separate distance of the double beams is 1000 μm, and the proof-mass size is also the same as that of Type-I.Therefore, the beam mass structure of Type-I and Type II get the same vertical stiffness, and the torsional stiffness of Type-II will be larger than that of Type-I. The beammass structure of Type-II is fit for the high-precision inertial MEMS sensors with large proof mass and sensing capacitance[9-10]. Type-III and Type-IV models are both four beam suspension structures, as shown in Fig.2(c) and Fig.2(d). In Type-III model, the four suspension beams are all L-shaped, which are connected to the proof mass corners symmetrically. The proof mass of Type-III is also 2000μm×2000μm with the thickness of 100μm. The L-shaped beam’s width is 100μm, and the thickness is 10μm. The total length of the L-shaped beam with two conjunctions is 750μm, as shown in Fig.2(c).The MEMS accelerometers with beam-mass structure of Type-III have advantages of small chip sizes, large proof mass, and therefore high sensitivity[11-15]. The fourth type of beam-mass structure has four double-clamped beams connecting to the proof mass along the diagonal direction.The beam width is 100μm, the same as Type-III, and the beam length is 450μm. The Type-IV beam mass structureis normally adopted in capacitive triaxial accelerometer[16].

The MEMS inertial sensor structures have been modeled using ANSYS to assess the basic mechanical performances and thermal-structure properties. The FEM models consist of two materials including N-type(100)single crystal silicon, on which the movable MEMS structure are fabricated, and the boron silicate glass,which act as the substrates. The MEMS structure models are constructed and meshed in ANSYS using 3D element Solid185 with eight nodes, as shown in Fig.2. The material properties used in the model as well as in FEM simulations are shown in Tab.1.

Tab.2 gives the ANSYS simulation results of first three modes of the four beam-mass structures. The first vibration modes of Type-I model to Type-IV model are all vibration mode along Z-axis. The resonant frequencies are 1965 Hz, 1968 Hz, 2000 Hz, and 2006 Hz respectively,which are nearly around 2000 Hz. This shows that the four types of beam-mass structure models get the same vertical stiffness. The weight of the silicon proof mass and the damping factors of the four models are also the same, therefore the four beam-mass structures get identical second-order inertial system model. The second vibration mode shape is torsion motion along Y-axis. The second mode frequency of double-cantilever suspension beam-mass structure (Type-II) is 10 times higher than that of the first mode frequency, and the third mode frequency is 22 times higher than that of the first mode frequency. For high performance uniaxial MEMS accelerometer, the Type-II model exhibits the best modes separation of the four models and the Type-I model is the suboptimal option. The second- and the third-order vibration modes of Type-III and Type-IV are only 1～2 times of the first vibration mode. Therefore the last two types of the beam-mass structures are fit for the multi-axis MEMS accelerometers or the MEMS accelerometers not sensitive to the cross-axis acceleration’s influence.

Fig.2 Dimensions of the four beam-mass structures and the correlated FEM models

Tab.1 Parameters of the MEMS materials

2 Structural thermal analysis

The structure-related thermal drifts of the MEMS inertial sensors are verified though the temperaturedependent variation of MEMS capacitance. Fig.3 gives the FEM model of the MEMS beam-mass structure(Type-I). The 3D structural is sweep meshed using SOLID element to get uniform and symmetric FEM model. The top electrode of the MEMS capacitive is the down surface of the proof mass, and the bottom electrode of the MEMS capacitive is part of the glass substrate,which faces the proof mass. The MEMS capacitance electrodes meshing start from the outline equal intervaldivision. Each side of the MEMS capacitance electrodes is divided into 58 Equal segments. Therefore, the two electrodes are meshed into 3364 FEM surface units. The MEMS capacitive real-time values during the simulation are evaluated using formula (1), which gives as

where, C is the real-time MEMS capacitive value, ΔSiis the area of the surface element, Ztop_iis the top electrode node’s real-time Z-coordinate value, and Zbottom_iis the bottom electrode node’s real-time Z-coordinate value.

Tab.2 First three modes of the four types of MEMS inertial sensors beam-mass structures

Fig.3 FEM model of the MEMS beam-mass structure (Type-I)

Fig.4 Chip bonding method on the substrate bottom surface

Fig.5 shows the MEMS capacitance thermal drift of the four beam-mass structures. The glass substrate thickness is set as 500μm, that commonly used to fabricated silicon on glass MEMS sensors. The chip die adhesive method in the simulation is center point method.The FEM simulation is proceed in the temperature range from -40℃～+60℃, and the Simulation temperature interval is 10℃. As shown, All four types of the beam-mass structures shows positive temperature coefficient, which means the gap between the MEMS capacitors are reduced due to the structural deformation under the temperature rising. the L-shaped beam rotational symmetry suspension beam-mass structure(Type-III) shows the lowest structural thermal drift,because the silicon-glass thermal miss match stress of Type-III can be released though the beam-mass structure in plane torsion deflection. The single cantilever beam-mass structure(Type-I) and the double cantilevers beam-mass structure (Type-II) have very close capacitance thermal drift curves. The MEMS capacitance thermal drift of double cantilevers beam-mass structure is slightly higher than the single cantilever ones. It is suggested that the double cantilevers beam-mass structure (Type-II) is easier to transfer the stress to the cantilever beams due to the large span of the two beam anchors. The last type of beam-mass structure with four diagonal suspension beam (Type-IV) shows the most obvious MEMS capacitance thermal drift effect, because the thermal-structure cannot release effectively though the structure deformation.

Fig.5 Comparison on the MEMS capacitance thermal drifts(Center adhesive)

The influence of the glass substrate thickness factor on the thermal-structure drift is present in Fig.6. The glass substrate thickness variation range from 300μm to 1000μm, and the thickness interval is 100μm. The chip packaging still chose the center adhesion from. In general, the substrate thickness has slightly influence on the MEMS capacitance thermal drift. For Type-I, Type-II,Type-IV structures, the capacitive thermal drift ratio slightly increased (for type III, it’s decrease) when the substrate thickness increase from 300μm to 500μm.while the substrate thickness increase from 500μm to 1000μm, the show thermal drift ratio of the four structures show no significant changes. This has also prove the correctness of using the 500μm thick glass wafer as the conventional SOG-MEMS substrate.

Fig.6 Glass substrate thickness factor related MEMS capacitance thermal drift simulation

The simulations of the packaging and structure related thermal drift are carried out on the dummy models using center point, three points, and whole area chip adhesive methods. The beam-mass structures with single or double suspension cantilever exhibit similar simulation results, as shown in Fig.7(a)(b). For Type-I and Type-II models, the thermal drift of has positive temperature coefficient when using center point chip adhesive method.However, if Type-I and Type-II models using three points chip adhesive method, the temperature coefficient turn negative. In case of adopting the whole area chip adhesive,the thermal drift curve still have negative temperature coefficient, and the slop of the curve is higher than using the three-point adhesive method. The borosilicate glass has larger coefficient of thermal expansion than the silicon.Therefore, the glass substrate generates more expansion volume, when the ambient temperature increases. Fig.8(a)gives the thermal expansion simulation results of the Type-II model (with 500 μm glass substrate, and center point chip adhesion) under 60℃ ambient temperature.The maximum deflection appeared on the root of the cantilever beams, and the two beams are bended down to the substrate. Therefore, the proof mass that attach to the cantilever beams deflect downward leading to a decrease in the capacitance gap and increase of the capacitance value (positive thermal expansion coefficient). Fig.8(b) is the thermal-structure simulation result of the Type-II model using three points adhesive method. The free expansion of glass substrate is constrained leading to the bending of the glass substrate, which cause the capacitance air gap increase and the capacitance value decrease.In the macroscopic aspect, it shows the negative temperature coefficient.

Compared with Type-I and Type-II models, the chip adhesion methods of Type-III and the Type-IV models have different effect on the thermal-structure performance of these structures. As shown in Fig.7(c)(d), the chips with adhesion center points get positive thermal expansion coefficients. If the packaging method is changed into three-point adhesion method, the curve slope is increased, which indicates that the structure deformation gets serious, as shown in Fig.8(a) and Fig.8(b). When the whole-area adhesive method is adopted, the thermal expansion coefficient will be negative. The thermalmechanical deflection simulation results of Type-IV give some explanation of this phenomenon.

Fig.7 Comparison on MEMS capacitance thermal drifts of the structures using different chip adhesive methods

Fig.8 Thermal-mechanical deflection of Type-II structure using the two adhesive methods

Fig.9(a) gives the thermal expansion simulation results of the Type-IV model (with 500 μm glass substrate and center-point chip adhesion) under 60℃ ambient temperature. The beams are bended downward, which lead to the proof mass deflect to counter electrode and finally cause the positive thermal coefficient of the MEMS capacitive. Fig.9(b) gives the thermal-structure simulation results of the Type-IV model using three-point adhesive method. The free expansion of glass substrate is constrained, leading to the bending of the glass substrate. The silicon proof mass is pulled down to the MEMS’s counter electrode, for the four corners of the proof mass are connected to the substrate. Therefore, the temperature coefficient of Type-IV structure using three-point adhesive method keeps positive thermal coefficient.

Fig.9 Thermal-mechanical deflection of Type-IV structure

3 Conclusion

In summary, four types of typical MEMS inertial sensor beam-mass structures are modeled using finite element software ANSYS. Beam-mass structures with cantilever beams have best separation performance for vibration modes and have relatively low thermal- structure temperature coefficient. The double cantilever beammass structure is fit for the high performance Z-axis sandwich accelerometers. The beam-mass structure with four L-shaped beams rotational symmetry suspension has the lowest thermal-structure temperature coefficient. However,the second and the third modes of this structure are close to the first vibration mode, which will lead to the crossaxis sensitivity. The diagonal suspension beam-mass structure shows the worst temperature stability, and the sensing modal isolation is not prominent. Therefore, this kind of beam structure is only fit for the multi-axis MEMS initial sensors at consumer electronics level.

The glass substrate thickness variation does not bring significant impact on the models’ thermal drifts. The MEMS inertial senor chip level bonding method has notable impact on the bonding stress and MEMS inertial sensor temperature stability. The center point adhesive method induces least thermal drift to the device. However,the chip bonding strength is also an important indicator of MEMS inertial sensor bonding. Three-point MEMS chip adhesive method is a compromise choice between the sensor temperature stability and the chip bonding strength.

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MEMS慣性器件敏感電容結構相關溫度漂移特性仿真

胡啟方，邢朝洋，劉國文
（北京航天控制儀器研究所，北京 100094）

基于MEMS器件的微型慣導系統的精度和MEMS慣性器件的全溫穩定性具有很高的相關性。MEMS結構相關的溫度漂移主要來自材料之間的熱失配應力，工藝引入的應力，以及封裝應力等。而相關應力在MEMS結構中的分布以及所造成的應變又和MEMS結構具有一定相關性。通過ANSYS有限元分析軟件建立了多種MEMS慣性器件常用梁-質量塊結構的FEM模型，具體包括懸臂梁結構、雙端固支梁結構、L形梁結構、對角支撐梁結構。通過熱-力耦合仿真，研究了熱失配應力在上述結構中的分布以及所產生的結構變形。對比分析了不同芯片粘膠形式，包括中心粘膠、三點粘膠、整片粘膠對上述MEMS結構引入的封裝應力以及其全溫（-40℃～60℃）溫度漂移特性。此外，還分析研究了不同襯底厚度對MEMS結構封裝應力的隔離效果。

MEMS；慣性器件；溫度漂移；封裝應力

U666.1

：A

1005-6734(2017)03-0370-08

2017-02-16；

：2017-05-26

北京市自然科學基金（4142058）

胡啟方（1981—），男，工程師，從MEMS器件設計和制造。E-mail: pkumems@163.com

聯 系 人：邢朝洋（1979—），男，研究員。E-mail: mems13@163.com

10.13695/j.cnki.12-1222/o3.2017.03.017