An Analytical Formulation of the Radio-Frequency Response of Piezoelectric Contour-Mode MEMS Resonators Verified by Measurements

Stegner, J.; Gropp, S.; Podoskin, D.; Stehr, U.; Hoffmann, Martin; Hein, Matthias

doi:10.1109/fcs.2018.8597517

Cited by 1 publication

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“…These formulae can be simplified for a contour-mode resonator, exemplarily illustrated as a cuboid of piezoelectric material in Figure 1 [ 9 , 11 ].…”

Section: Methodsmentioning

confidence: 99%

“…In a contour-mode resonator, the electrical field is oriented in vertical direction only, and the mechanical stress only in lateral direction, i.e.,

[ 9 , 11 , 12 ]. The given simplifications lead to:

…”

Section: Methodsmentioning

confidence: 99%

“…The mechanical behaviour of the contour-mode resonator can be described using a laterally vibrating bar, as depicted in Figure 2 [ 9 , 17 ]. As shown in Figure 1 , the bar is a cuboid having a cross-sectional area A and a total width w and is excited by an external force F in x -direction.…”

Section: Methodsmentioning

confidence: 99%

“…The deformation in turn leads to a mechanical strain

and eventually a mechanical stress difference between the left and right-hand sides of the slice, leading to:

. According to Newton’s second law, the sum of forces acting on a piece of material leads to an accelerating force

, resulting in [ 9 , 13 , 17 , 18 ]:

…”

Section: Methodsmentioning

confidence: 99%

“…In this paper, an analytical design model for contour-mode MEMS resonators based on the derivations of the equivalent-circuit parameters as functions of the resonator geometry in [ 9 ] is presented, which requires only a few characteristic RF parameters, such as the resonant frequency

and the quality factor Q . Furthermore, the temperature dependent RF behaviour is modelled analytically using closed-form expressions.…”

Section: Introductionmentioning

confidence: 99%

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An Analytical Temperature-Dependent Design Model for Contour-Mode MEMS Resonators and Oscillators Verified by Measurements

Stegner

Gropp

Podoskin

et al. 2018

Sensors

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The importance of micro-electromechanical systems (MEMS) for radio-frequency (RF) applications is rapidly growing. In RF mobile-communication systems, MEMS-based circuits enable a compact implementation, low power consumption and high RF performance, e.g., bulk-acoustic wave filters with low insertion loss and low noise or fast and reliable MEMS switches. However, the cross-hierarchical modelling of micro-electronic and micro-electromechanical constituents together in one multi-physical design process is still not as established as the design of integrated micro-electronic circuits, such as operational amplifiers. To close the gap between micro-electronics and micro-electromechanics, this paper presents an analytical approach towards the linear top-down design of MEMS resonators, based on their electrical specification, by the solution of the mechanical wave equation. In view of the central importance of thermal effects for the performance and stability of MEMS-based RF circuits, the temperature dependence was included in the model; the aim was to study the variations of the RF parameters of the resonators and to enable a temperature dependent MEMS oscillator simulation. The variations of the resonator parameters with respect to the ambient temperature were then verified by RF measurements in a vacuum chamber at temperatures between −35 ∘C and 85 ∘C. The systematic body of data revealed temperature coefficients of the resonant frequency between −26 ppm/K and −20 ppm/K, which are in good agreement with other data from the literature. Based on the MEMS resonator model derived, a MEMS oscillator was designed, simulated, and measured in a vacuum chamber yielding a measured temperature coefficient of the oscillation frequency of −26.3 ppm/K. The difference of the temperature coefficients of frequency of oscillator and resonator turned out to be mainly influenced by the limited Q-factor of the MEMS device. In both studies, the analytical model and the measurement showed very good agreement in terms of temperature dependence and the prediction of fabrication results of the resonators designed. This analytical modelling approach serves therefore as an important step towards the design and simulation of micro-electronics and micro-electromechanics in one uniform design process. Furthermore, temperature dependences of MEMS oscillators can now be studied by simulations instead of time-consuming and complex measurements.

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“…These formulae can be simplified for a contour-mode resonator, exemplarily illustrated as a cuboid of piezoelectric material in Figure 1 [ 9 , 11 ].…”

Section: Methodsmentioning

confidence: 99%

“…In a contour-mode resonator, the electrical field is oriented in vertical direction only, and the mechanical stress only in lateral direction, i.e.,

[ 9 , 11 , 12 ]. The given simplifications lead to:

…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…The deformation in turn leads to a mechanical strain

and eventually a mechanical stress difference between the left and right-hand sides of the slice, leading to:

. According to Newton’s second law, the sum of forces acting on a piece of material leads to an accelerating force

, resulting in [ 9 , 13 , 17 , 18 ]:

…”

Section: Methodsmentioning

confidence: 99%

and the quality factor Q . Furthermore, the temperature dependent RF behaviour is modelled analytically using closed-form expressions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Analytical Temperature-Dependent Design Model for Contour-Mode MEMS Resonators and Oscillators Verified by Measurements

Stegner

Gropp

Podoskin

et al. 2018

Sensors

Self Cite

View full text Add to dashboard Cite

show abstract

An Analytical Formulation of the Radio-Frequency Response of Piezoelectric Contour-Mode MEMS Resonators Verified by Measurements

Cited by 1 publication

References 4 publications

An Analytical Temperature-Dependent Design Model for Contour-Mode MEMS Resonators and Oscillators Verified by Measurements

An Analytical Temperature-Dependent Design Model for Contour-Mode MEMS Resonators and Oscillators Verified by Measurements

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