AK
A. Keşkekler
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1
Nonlinear Force Field Resonator Tuning
Leveraging Nonlinear Force Spring Softening to Enhance MEMS Membrane Resonator Responsivity
Microelectromechanical resonator sensors are crucial in the cutting-edge technologies used in our everyday communication, timekeeping and computing systems. Their extreme sensing capabilities make them ideal candidates for the innovation of future technologies. However, with our ever-growing desire for faster communication, more sensitive systems, and more advanced technologies comes the need for a new generation of resonator sensors. This next generation will have to be faster, more accurate, and just as cheap as their predecessors if they are to enable the rapid growth of our technological needs. In this thesis, we investigate recently fabricated state-of-the-art extreme aspect ratio membrane resonators. The characteristics of extreme aspect ratio membrane resonator sensors are researched, and
the effects of nonlinear forces on their operation are explored. Some of these nonlinear attractive forces, such as the Casimir effect, are common to the extreme dimensions of these resonators. Another common nonlinear attractive force in MEMS, the electrostatic force, and its effects on resonator operation and output are investigated as well. Analytical models are fashioned and a FEM model is produced and validated using experimental results, showing it reflects reality. FEM simulations show that for these extreme aspect ratio resonators, the nonlinear softening effect is solely responsible for the change in the eigenfrequency which proves to be able to boost the responsivity of these resonators by factors of hundreds to thousands. Models are investigated for both conductors and dielectric resonators with different geometries and different material parameters, which all show these results. Responsivities of 133.2 kHz/kPa and 1.6 kHz/nm are found, which exceed the state-of-the-art. The negative effects of nonlinear forces such as pull-in are considered, investigated, and models are produced which predict them to prevent device failure. Furthermore, the role of crucial resonator parameters is investigated to aid future research in leveraging this potential new technique of enhancing sensor capabilities. ...
the effects of nonlinear forces on their operation are explored. Some of these nonlinear attractive forces, such as the Casimir effect, are common to the extreme dimensions of these resonators. Another common nonlinear attractive force in MEMS, the electrostatic force, and its effects on resonator operation and output are investigated as well. Analytical models are fashioned and a FEM model is produced and validated using experimental results, showing it reflects reality. FEM simulations show that for these extreme aspect ratio resonators, the nonlinear softening effect is solely responsible for the change in the eigenfrequency which proves to be able to boost the responsivity of these resonators by factors of hundreds to thousands. Models are investigated for both conductors and dielectric resonators with different geometries and different material parameters, which all show these results. Responsivities of 133.2 kHz/kPa and 1.6 kHz/nm are found, which exceed the state-of-the-art. The negative effects of nonlinear forces such as pull-in are considered, investigated, and models are produced which predict them to prevent device failure. Furthermore, the role of crucial resonator parameters is investigated to aid future research in leveraging this potential new technique of enhancing sensor capabilities. ...
Microelectromechanical resonator sensors are crucial in the cutting-edge technologies used in our everyday communication, timekeeping and computing systems. Their extreme sensing capabilities make them ideal candidates for the innovation of future technologies. However, with our ever-growing desire for faster communication, more sensitive systems, and more advanced technologies comes the need for a new generation of resonator sensors. This next generation will have to be faster, more accurate, and just as cheap as their predecessors if they are to enable the rapid growth of our technological needs. In this thesis, we investigate recently fabricated state-of-the-art extreme aspect ratio membrane resonators. The characteristics of extreme aspect ratio membrane resonator sensors are researched, and
the effects of nonlinear forces on their operation are explored. Some of these nonlinear attractive forces, such as the Casimir effect, are common to the extreme dimensions of these resonators. Another common nonlinear attractive force in MEMS, the electrostatic force, and its effects on resonator operation and output are investigated as well. Analytical models are fashioned and a FEM model is produced and validated using experimental results, showing it reflects reality. FEM simulations show that for these extreme aspect ratio resonators, the nonlinear softening effect is solely responsible for the change in the eigenfrequency which proves to be able to boost the responsivity of these resonators by factors of hundreds to thousands. Models are investigated for both conductors and dielectric resonators with different geometries and different material parameters, which all show these results. Responsivities of 133.2 kHz/kPa and 1.6 kHz/nm are found, which exceed the state-of-the-art. The negative effects of nonlinear forces such as pull-in are considered, investigated, and models are produced which predict them to prevent device failure. Furthermore, the role of crucial resonator parameters is investigated to aid future research in leveraging this potential new technique of enhancing sensor capabilities.
the effects of nonlinear forces on their operation are explored. Some of these nonlinear attractive forces, such as the Casimir effect, are common to the extreme dimensions of these resonators. Another common nonlinear attractive force in MEMS, the electrostatic force, and its effects on resonator operation and output are investigated as well. Analytical models are fashioned and a FEM model is produced and validated using experimental results, showing it reflects reality. FEM simulations show that for these extreme aspect ratio resonators, the nonlinear softening effect is solely responsible for the change in the eigenfrequency which proves to be able to boost the responsivity of these resonators by factors of hundreds to thousands. Models are investigated for both conductors and dielectric resonators with different geometries and different material parameters, which all show these results. Responsivities of 133.2 kHz/kPa and 1.6 kHz/nm are found, which exceed the state-of-the-art. The negative effects of nonlinear forces such as pull-in are considered, investigated, and models are produced which predict them to prevent device failure. Furthermore, the role of crucial resonator parameters is investigated to aid future research in leveraging this potential new technique of enhancing sensor capabilities.
Micro- and nanoelectromechanical (MEM/NEM) resonators are used in numerous fields of engineering and are crucial for time keeping, synchronization, and sensing applications. These systems are subjected to energy dissipation, which is a limiting factor in the performance. Extensive understanding is essential when nonlinearities show up in both stiffness and dissipation, to design appropriately. Focusing on dissipative mechanisms, this paper explores the vibrational behavior of a suspended clamped-clamped beam fabricated from silicon-nitride in the nonlinear regime. This study reveals a notorious decay in ringdown, when the resonator is decoupled from its vibrational power. A sustained amplitude is observed for up to 8 seconds. Though the exact source of this anomaly remains elusive, it is suggested that it might include modal coupling and/or optomechanical effects
...
Micro- and nanoelectromechanical (MEM/NEM) resonators are used in numerous fields of engineering and are crucial for time keeping, synchronization, and sensing applications. These systems are subjected to energy dissipation, which is a limiting factor in the performance. Extensive understanding is essential when nonlinearities show up in both stiffness and dissipation, to design appropriately. Focusing on dissipative mechanisms, this paper explores the vibrational behavior of a suspended clamped-clamped beam fabricated from silicon-nitride in the nonlinear regime. This study reveals a notorious decay in ringdown, when the resonator is decoupled from its vibrational power. A sustained amplitude is observed for up to 8 seconds. Though the exact source of this anomaly remains elusive, it is suggested that it might include modal coupling and/or optomechanical effects
Mode coupling in nanomechanical string resonators
Towards Fermi-Pasta-Ulam-Tsingou mechanics
In the early years of numerical simulation methods, Fermi, Pasta, Ulam and Tsingou (FPUT) discovered that an undamped, weakly nonlinear equation describing the motion of a chain of masses and springs could show complex dynamics. Integration of these equations froma n initial displacement in the formof the fundamental mode resulted in significant mode coupling: energy was transferred from the fundamental mode to several other modes, before the energy would return to the initial condition. To date, very little observations of such behavior in mechanical vibrations have been reported. Recent developments in fabrication of high stress Silicon-Nitride (Si3N4) string resonators have shown that it is possible to generate resonators with extremely high Q-factors, proving a potential testbed for these mechanics. This research shows, through modal conversionof the FPUT potential, that one may observe significant FPUT behavior in systems with non-integer frequency ratios and certain coupling coefficients. In addition, it is shown that for the default FPUT beta-model, the effect of damping is negligible for fundamental mode Q-factors higher than 10,000. Simulations of the experimental
frequency response of a high-Q Si3N4 string resonator show that the nonlinear dynamics of these resonators may be approximated by an analytical model that does not possess the required frequency ratios and coupling coefficients for FPUT behavior. Another string model, for which no mechanical equivalent
has (yet) been found, may potentially show FPUT behavior. Several string-like resonator designs are tested using a numerical tool which can extract the modal coefficients. These resonators are modelled using simplified
deformation models, which account only for axial deformation of the structure. The results for various string-like designs show that the eigenfrequencies and nonlinearity may be engineered easily, but these do
not generate the required coupling coefficient for FPUT behavior. ...
frequency response of a high-Q Si3N4 string resonator show that the nonlinear dynamics of these resonators may be approximated by an analytical model that does not possess the required frequency ratios and coupling coefficients for FPUT behavior. Another string model, for which no mechanical equivalent
has (yet) been found, may potentially show FPUT behavior. Several string-like resonator designs are tested using a numerical tool which can extract the modal coefficients. These resonators are modelled using simplified
deformation models, which account only for axial deformation of the structure. The results for various string-like designs show that the eigenfrequencies and nonlinearity may be engineered easily, but these do
not generate the required coupling coefficient for FPUT behavior. ...
In the early years of numerical simulation methods, Fermi, Pasta, Ulam and Tsingou (FPUT) discovered that an undamped, weakly nonlinear equation describing the motion of a chain of masses and springs could show complex dynamics. Integration of these equations froma n initial displacement in the formof the fundamental mode resulted in significant mode coupling: energy was transferred from the fundamental mode to several other modes, before the energy would return to the initial condition. To date, very little observations of such behavior in mechanical vibrations have been reported. Recent developments in fabrication of high stress Silicon-Nitride (Si3N4) string resonators have shown that it is possible to generate resonators with extremely high Q-factors, proving a potential testbed for these mechanics. This research shows, through modal conversionof the FPUT potential, that one may observe significant FPUT behavior in systems with non-integer frequency ratios and certain coupling coefficients. In addition, it is shown that for the default FPUT beta-model, the effect of damping is negligible for fundamental mode Q-factors higher than 10,000. Simulations of the experimental
frequency response of a high-Q Si3N4 string resonator show that the nonlinear dynamics of these resonators may be approximated by an analytical model that does not possess the required frequency ratios and coupling coefficients for FPUT behavior. Another string model, for which no mechanical equivalent
has (yet) been found, may potentially show FPUT behavior. Several string-like resonator designs are tested using a numerical tool which can extract the modal coefficients. These resonators are modelled using simplified
deformation models, which account only for axial deformation of the structure. The results for various string-like designs show that the eigenfrequencies and nonlinearity may be engineered easily, but these do
not generate the required coupling coefficient for FPUT behavior.
frequency response of a high-Q Si3N4 string resonator show that the nonlinear dynamics of these resonators may be approximated by an analytical model that does not possess the required frequency ratios and coupling coefficients for FPUT behavior. Another string model, for which no mechanical equivalent
has (yet) been found, may potentially show FPUT behavior. Several string-like resonator designs are tested using a numerical tool which can extract the modal coefficients. These resonators are modelled using simplified
deformation models, which account only for axial deformation of the structure. The results for various string-like designs show that the eigenfrequencies and nonlinearity may be engineered easily, but these do
not generate the required coupling coefficient for FPUT behavior.
In pursuit of extremely sensitive sensors, the dimensions of these sensors get smaller and smaller. Small scale resonators are commonly used as sensors by relating changes in the dynamic behaviour to a sensed quantity. Conventionally, the dynamics used for sensing are in the linear regime. But at smaller scales the dynamic range of the linear regime decreases. Therefore, it is of interest to investigate the dynamic behaviour in the nonlinear regime, as with the decreasing scale of the resonators this becomes inevitable. Especially, little is known about the frequency stability in this region. The frequency stability is an indication for the potential sensitivity that the resonator can have as sensor. By using phase locked loop (PLL) the frequency stability around the resonance frequency of nonlinear resonators can be obtained. This research contains attempts to control multilayer graphene drums around its fundamental resonance frequency with PLL. In addition, the frequency stability at these points are presented by measure of the Allan deviation. There are roughly two different distributions of the frequency stability over the frequency response obtained. One resonator shows behaviour attributed to internal resonance. This internal resonance is linked to an increase of nonlinear damping. Combining that with a simple simulation model, a relation was found between increased nonlinear damping and an improvement of frequency stability.
...
In pursuit of extremely sensitive sensors, the dimensions of these sensors get smaller and smaller. Small scale resonators are commonly used as sensors by relating changes in the dynamic behaviour to a sensed quantity. Conventionally, the dynamics used for sensing are in the linear regime. But at smaller scales the dynamic range of the linear regime decreases. Therefore, it is of interest to investigate the dynamic behaviour in the nonlinear regime, as with the decreasing scale of the resonators this becomes inevitable. Especially, little is known about the frequency stability in this region. The frequency stability is an indication for the potential sensitivity that the resonator can have as sensor. By using phase locked loop (PLL) the frequency stability around the resonance frequency of nonlinear resonators can be obtained. This research contains attempts to control multilayer graphene drums around its fundamental resonance frequency with PLL. In addition, the frequency stability at these points are presented by measure of the Allan deviation. There are roughly two different distributions of the frequency stability over the frequency response obtained. One resonator shows behaviour attributed to internal resonance. This internal resonance is linked to an increase of nonlinear damping. Combining that with a simple simulation model, a relation was found between increased nonlinear damping and an improvement of frequency stability.