Finite element simulation and experiment of residual stress evolution in MEMS structures

The MEMS device structure is usually formed by the combination of thick film and thin film deposition of many different materials, and the residual stress generated in the process of integration/superposition of different materials has a significant impact on the performance and reliability of the device.In this study, a test structure of a multilayer thin film was designed and processed. Based on this, finite element modeling analysis and reliability experiment, analyze the evolution of residual stress and construct the corresponding theoretical analysis model. The finite element modeling analysis can characterize the evolution and distribution laws of residual stress. The reliability experiment is mainly by carrying out the temperature shock experiment, and measuring the resistance value, resonance frequency and the surface morphology of the device, so as to better reflect the change of residual stress. Through this study, the resonant frequency and surface morphology of the device can reflect the residual stress of the device, which provides help for the test and analysis of the residual stress. To a certain extent, it can help reduce the harm caused by the residual stress in the design and manufacturing process, and improve the performance and reliability of MEMS devices.


Introduction
By taking advantage of the advantages of mass manufacturing, microelectronics machinery Systems (MEMS) technology has revolutionized various sensors and actuators in scale, performance, and cost, and is widely used in various fields, including communications, automotive, biomedical, industrial control, etc [1] .Usually, MEMS devices range in size from a CSMNT-2023 Journal of Physics: Conference Series 2740 (2024) 012038 IOP Publishing doi:10.1088/1742-6596/2740/1/012038 2 few hundred nanometers to millimeters, facing more factors to consider while reducing the size, cost and power consumption of sensors.
Factors such as surface tension, viscosity, extrusion membrane damping and residual stress have become important factors affecting the performance and reliability of MEMS devices [2,3] .Among them, the residual stress has a serious impact on the packaging [4] , bonding [5,6,7] and thin film layer [8,9,10,11] of MEMS devices.Residual stress mainly comes from the following four aspects: thermal stress, lattice mismatch, internal stress, and plastic stress [12] .It is of great significance to study the evolution and distribution of residual stress on MEMS devices, which is of great significance to improve the reliability of MEMS devices.J. Auersperg et al. studied the effect of residual stress on cracking and peeling risk of pressure sensors in avionics micro-electro-mechanical systems through experimental and nonlinear finite element simulations [13] .The results show that the residual stress has a great influence on the local stress of the sensor (detection sheet-SiO2/Si interface).G. Massimino et al. used COMSOL to study residual stress during the manufacturing of a piezoelectric micromechanical ultrasonic transducer (PMUT) [14] .It is found that the residual stress has an important effect on the stiffness of the film, significantly changing the first natural frequency of PMUT.BIE Xiaorui et al. systematically studied the frequency drift law of MSRA in the temperature range of 0 ~50°C through finite element simulation [15] .In addition, the influence of changes in package structural parameters and material properties on MSRA frequency drift is analyzed.Provides design principles for MSRA package design to help reduce the effects of thermal stress caused by temperature changes on the package.
Thermal stress caused by the mismatch of the coefficients of thermal expansion(CTE) in the multilayer structure is often the main cause of the failure of the thin film devices [16,17] .Peng et al. used the finite element method to model and simulate a simulated test structure and observe the mechanical response of the beam by calculating the residual stress of the film, a technique that can be used to monitor the magnitude of stress in the film, saving operation time and cost [18] .Amruta Ranjan Behera et al. proposed a technique for estimating the residual stress and Young's modulus of compressive stressed films using micromachined beams, making it more reliable to estimate the residual stress of post-manufacturing test and measurement [19] .
At present, there is no complete test and evaluation standard for the residual stress of MEMS devices in the industry.The residual stress is one of the most important influencing factors in the integration of thin films on different substrates and the development of MEMS devices.Therefore, it is particularly important to study the evolution and distribution of residual stress in the multilayer structure thin film structure, which will bring significant improvement to the performance and reliability of MEMS devices.
In this paper, the test structure of multilayer film is modeled and simulated based on COMSOL, the relevant parameter scanning of residual stress is set, the evolution and distribution law of residual stress on the test structure of multilayer film are observed, and the relevant theoretical model is constructed.Secondly, the temperature shock experiment is carried out on the test structure of the multilayer film, and the resistance value, resonant frequency [20] and surface topography/height difference are measured after each experimental cycle, and the experiment is carried out until the device fails or achieves the expected effect.Relevant data is recorded and collated to characterize changes in residual stress.

Samples
This test sample is a thermistor with a four-cantilever support of a multilayer film with two resistances on each sample.The specific structure is shown in Figure 1.

Finite Element Analysis
In order to study the thermal stress condition of MEMS multilayer film structure thermistor, the device was modeled and analyzed by multiphysics field simulation of thermal expansion based on solid mechanics and solid heat transfer.The simplified finite element model is shown in Fig. 2.

Experiment
The test link is mainly through the temperature impact test of the sample, which establishes the residual stress caused by different film materials due to the inconsistent coefficients of thermal expansion.Then, the evolution of the residual stress can be observed and analyzed.

A experimental procedure
The overall experimental procedures are performed as follows： (1) Measure the initial values of the resistance, resonant frequency,and height difference of the sample at room temperature.
(2) Place the sample in a temperature shock test chamber and set the temperature shock conditions:The temperature of the high temperature chamber is 125 ℃ ,and the low temperature chamber is set to -55℃.It is left at each temperature for 15 minutes and removed after every 100 temperature shocks.
(3) Take out the sample and place it at room temperature to measure its resistance value,resonance frequency,and surface morphology (height difference).analysis system.This test used the Polytec MSA-600-VD scanning laser vibration measurement modal analysis system to perform modal measurements on the thin film portion of the thermistor sensitive structure.

Surface morphology (height difference) test
Under the action of residual stress, MEMS sensitive structures will undergo certain changes.In order to understand the evolution process of residual stress, it is necessary to observe the surface morphology of MEMS sensitive structures.This experiment uses Keyence VK-X260K 3D optical profilometer.

Result and Discussion
During the simulation of the device with finite elements, it is obvious from the results in Figure 4 that the material deforms repeatedly under the effect of temperature shocks.In the part with silicon substrate, the surface of the device buckles at the edge part of the silicon substrate, and there is a tendency of relative collapse in the sensitive structure part.This tendency is also verified experimentally.As shown in Figure 8: In this experiment, we are more concerned about the morphology change of the sensitive structure part, because it is greatly related to the failure of the device.Through the optical profilometer magnified fifty times for comparison, to observe the effect of residual stress on the middle truncated part of the sensitive structure of the device under different times of temperature cycling, it can be found that with the increase of the number of temperature shock experiments, the sensitive part of the structure of the device has a tendency to sink relatively.Figure 9 shows the morphology change of the sensitive structure part of the #2 sample, and it can be clearly seen that the sensitive part of the device structure has a relative sinking trend.The resonance frequency of the samples was measured, and the resonance frequency of the samples was in the range of 53Hz~56Hz, and the resonance frequency of the samples showed an overall decreasing trend with the increase of the number of temperature shock experiments.

Conclusions
Through finite element modeling and analysis of the device, the stresses are mainly concentrated on the LP-SiN layer, Pt layer, and PE-SiN layer during the temperature cycling experiments, and the main stress tensor directions are in the XX direction and YY direction.The temperature shock environment of alternating hot and cold can provide mechanisms such as internal structural changes and movement of dislocations and defects in the material to reduce or eliminate the residual stresses.Combined with the experimental results, it can be seen that the overhanging multilayer thin-film structure partially produces subsidence, from which it can be inferred that the change of the surface morphology of the multilayer thin-film structure can characterize the change of the residual stresses to a certain extent.

7.Acknowledgments:
The authors gratefully acknowledge the financial supports by the National Key R&D Program of China(Grant number 2020YFB2008900).

Figure 1 .
Figure 1.Four-cantilever support film structure thermistor sample.(a)Side view of the sample; (b) Overall top view of the sample;(c)Physical picture under the optical microscope; (d)The physical picture under the contometer.Table 1.Sample symbols and definitions.Heating resistor Design resistance value(ohm) Corresponding interface Rh1 230 Pad1,Pad2 Rh2 230 Pad3,Pad4

Figure 2 .Figure 3 .
Figure 2. Finite element modeling of MEMS multilayer film structure thermistor.In the heat flux of the solid heat transfer term, the external temperature function pw1(t) is set to simulate the temperature change of the temperature shock test condition cycle, and the ambient temperature is set to simulate the pre-experiment ambient temperature.The stress distributions in the three states are obtained as shown in Fig. 3:

Figure 4 .
Figure 4. Displacement magnitude at the surface of the LP-TEOS layer.Figure 4 shows the topography of the LP-TEOS layer on the device surface on a straight line through the middle of the sensitive structure.The figure characterizes the surface topography by displacements at various points on the line.

Figure 4
Figure 4. Displacement magnitude at the surface of the LP-TEOS layer.Figure 4 shows the topography of the LP-TEOS layer on the device surface on a straight line through the middle of the sensitive structure.The figure characterizes the surface topography by displacements at various points on the line.

Figure 5 .
Figure 5. Stresses in films in layers below a point on a cantilever beam.(a)Von Mises stresses； (b)Stress tensor in XX direction； (c)Stress tensor in YY direction； (d)Stress tensor in ZZ direction.Measurements of stresses in different layers of the same X and Y coordinates give the effect of Fig. 5(a).The stresses shown are the Von Mises stresses, and only the magnitude of the force is shown in this figure.5(b)(c)(d)shows the stress tensor in the XX, YY, and ZZ directions, respectively.

( 4 )Figure 6 .
Figure 6.Polytec MSA-600-VD scanning laser vibration measurement and modalanalysis system.This test used the Polytec MSA-600-VD scanning laser vibration measurement modal analysis system to perform modal measurements on the thin film portion of the thermistor sensitive structure.

Figure 9 .Figure 10 .
Figure 9. Trends in deformation of sensitive structures during temperature shock experiments.