|dc.description.abstract||Brittle materials are widely used as structural materials in microelectromechanical systems (MEMS). Their mechanical properties make them suitable for high-temperature environments where MEMS are exposed to different types of failure modes such as fractures and fast aging. A fracture happens when the material splits into two or more pieces due to exceeding the material’s maximum strength. High temperature accelerates fracture in materials leading to premature failure due to crack growth. Thus, it is crucial to understand the relationship between temperature and fracture strength in MEMS materials. Researchers have measured fracture strength for brittle materials using different structures and methodologies, but there is still not a standard accepted methodology to measure it in microstructures.
In this research, a new methodology using MEMS devices to determine fracture strength at high temperatures is developed. The methodology is designed to address three significant aspects that are currently a drawback in MEMS fracture strength testing. The first aspect is the simplicity of the test setup. The methodology reduces sources of error and variables involved in the measurement of the fracture strength using stress due to thermal mismatch. The tested structures are designed using a silicon substrate and a silicon nitride thin film directly deposited onto the substrate. The thin film is patterned into a suspended dog-bone shaped bridge and it has a stress concentration section right in the middle of the bridge. The coefficient of thermal expansion (CTE) mismatch between the materials provides the stress to break the thin film as the materials expand due to the temperature change. By applying stress directly to the device, a test setup composed of a reduced amount of elements is implemented, which makes the experiment accessible and straightforward for its replication. The second aspect is the speed of the test methodology. The stress concentration section makes it possible for the thin film to fracture in minutes as the temperature is increased. Increasing or decreasing the ramping of the temperature controls the speed of the test and opens the possibility for this methodology to be accelerated. The third aspect is the number of samples that are tested at the same time. The structures providing their stress allow for the testing of several devices arrays at a time, where each device will break as the temperature is increased.
The material tested in this study a silicon nitride thin film deposited using low-pressure chemical vapor deposition (CVD), which is patterned into three different shapes with different lengths to test the effect of geometry variation in the fracture strength. During testing, the temperature of the devices was increased from room temperature to 1000 °C using a furnace with a ramp of 98 °C/minute for 10 minutes. The breaking temperature of each device was recorded during the experiment with its respective length and shape. The fracture strength is determined using finite element analysis (FEA) in COMSOL multi-physics for the devices of each shape. The FEA study models the behavior of the structures as the temperature increases and simulates the stress up to the breaking temperature of the device, which is recorded at the concentration section of the thin film. The fracture changed from 0.24 GPa to 2.84 GPa for devices of shape #1, from 0.26 GPa to 2.98 GPa for devices of shape #2 and from 0.22 GPa to 2.1 GPa for devices of shape #3. These values are used to plot the fracture strength of the thin film as a function of temperature. A Weibull statistical approach used to determine the probability of failure of the material predicted ~80% at stresses ranging from 0.37 GPa to 0.44 GPa. From the results, it is concluded that although there is an effect from the geometry, it is secondary to the impact the temperature has on the fracture strength. As for the increasing fracture strength as temperature rises, this is attributed to the deformation of the silicon substrate attenuating the effect of the CTE mismatch, which is not accounted for in the current simulation setup.
The analytical model used to determine the fracture strength of each device was constructed from the displacement on the thin film due to the stress and the influence of temperature and geometry change in the material properties of the material. The experimental data is used as input and the plotted results show a similar trend as the one observed for the simulation results. The data follows exponential growth for every shape at 400 °C when a decrease in the fracture strength is expected. The fracture changed from 0.704 GPa to 6.48 GPa for devices of shape #1, from 0.838 GPa to 9.54 GPa for devices of shape #2 and from 0.764 GPa to 7.5 GPa for devices of shape #3. Although the trend matched in both analytical and FEA simulation with the exponential growth of the fracture strength, the magnitudes showed a discrepancy. The reasons for the differences are mainly due to the significance given to the geometry change of the film in the analytical model, which is shown by how the only shape that is not symmetrical has a remarkably increased value of fracture strength compared to the other two shapes. It is also essential to have in mind that the analytical model is constructed based on a uniaxial model, while the FEA simulation does consider the stress the device is submitted to from every direction.
Lastly, this work presents an improved methodology, which incorporates additional structures to characterize material properties for the thin film material that are involved in the fracture strength determination. All the structures are fabricated together using the same process to produce a high-temperature MEMS testing chip. The varying parameters of the first tested structures is reduced by decreasing the geometrical variation of the different shapes. From the previous results, the need to monitor strain throughout the experiment is determined. The new devices implement the deposition of metallic markers near a stress concentration section for optical measurements, which are used to monitor the strain of the thin films. Measuring the strain allows for the incorporation of the creep effect in the involved materials and understand its interaction with the fracture. The strain is also useful as an indicator of thermal buckling or deformation in the substrate. Hence, the presented work paves the way for future research that will improve the testing of fracture strength on brittle thin films for MEMS devices. Based on the knowledge acquired, the new proposed devices will be of great help to understand the relationship between temperature and the mechanics of materials as well as to perform rapid testing materials at high temperatures.||en