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«by Vikram Atul Thakar A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical ...»

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Vikram Atul Thakar

A dissertation submitted in partial fulfillment

of the requirements for the degree of

Doctor of Philosophy

(Mechanical Engineering)

in The University of Michigan


Doctoral Committee:

Assistant Professor Mina Rais-Zadeh, Chair

Professor Yogesh Gianchandani

Professor Karl Grosh Professor Khalil Najafi © Vikram Thakar All rights reserved 2014


To Friends and Family ii Acknowledgements First and foremost I would like to thank my advisor, Professor Mina Rais- Zadeh, for providing me the opportunity to pursue this research and supporting me through the years. I also thank my thesis committee members, Professor Karl Grosh, Professor Khalil Najafi, and Professor Yogesh Gianchandani for their help and support. Through interactions with them during research meetings, academic conferences and course work, I have grown both as a researcher and as an individual.

I would like to take this opportunity to thank my group members in the resonant MEMS group. Yonghyun, Zhengzheng and Vikrant have provided a good source of intellectual stimulation through discussions and played the role of family away from home. Azadeh, Adam and more recently Muzhi, Cesar and Feng have continued that tradition. I will be forever grateful for their help and support and for providing a friendly and conducive research environment in the lab.

WIMS, the umbrella organization for research in Microsystems at the University of Michigan has played a strong role in my development as a MEMS researcher. This work has benefited profusely due to the ancillary support provided through WIMS to student members.

This work would not have been complete without the support, guidance and the patience of the Lurie Nanofabrication Facility staff. I would like to thank them for bearing with me through the years and supporting my research efforts in the iii cleanroom. I would also like to thank my colleagues working in the cleanroom for providing ample company, moral support and process training. The long nights spent in the cleanroom were enjoyable to a large part due to their support and friendship. In particular, I would like to thank Dr. Jae Yoong Cho, Dr. Razi-ul Haque, Dr. Erkan Aktakka, Dr. Ali Besharatian, Dr. Tao Ling, Dr. Zongliang Cao, Katherine Knisely, Dr. Anurag Tripathi, Dr. Seokjun Park, Dr. Animesh Banerjee, Dr. Ayan Das, Professor Gaurav Bahl, Dr. Anne Itsuno, Dr. Alex Kaplan, Kyunghoon Lee, Yi Yuan, Stacey Tang, Jun Tang for their advice and support.

My friends at Michigan, Girish Kulkarni, Siddharth Gaba, Saniya Deshpande, Deepti Joshi, Kishore Aravamudhan, Jallal El-Hazzat, Dr. Victor Lee, Ning Gulari, Dr. Seow Yuen Yee, Dr. Naveen Gupta, Sarang Supekar and Prasad Shingne have given me plenty of reasons to smile and am truly grateful for their support.

My friends from India have kept in touch and have constantly motivated me to work harder to accomplish my goals. I came to Michigan in 2008 with their encouragement and support and I am extremely happy that their support continues to this day.

I would like to thank my cousins who helped me settle down in the US through moral, emotional and financial support. My nephew, Advay and niece Avani have been a treat to interact with and my life has been truly enriched by their presence.

Finally, I want to express my deepest appreciation to my parents and sister who have always encouraged me to pursue my dreams. This thesis would not have been possible without their unconditional love and support.

–  –  –



List of Figures

List of Tables


Chapter 1 Introduction to Resonators and Frequency References

1.1 Background and Motivation

1.2 Classification of Micromachined Resonators

1.2.1 Electrostatic Actuation

1.2.2 Piezoelectric Actuation

1.2.3 Other Actuation Mechanisms

1.3 Loss Mechanisms in Mechanical Resonators

1.4 Temperature Compensation of Micromachined Resonators

1.5 Temperature stable precision timing references

1.6 Research Objectives

1.7 Organization of Thesis

–  –  –


2.1 Flexural Mode Resonators

2.1.1 Position dependence of passive compensation

2.1.2 Experimental Verification

2.1.3 Fabrication process

2.1.4 Resonator Design

2.1.5 Measured Results

2.1.6 Active Temperature Compensation

2.1.7 Estimation of Resonator Stability

2.1.8 Flexural-Mode Resonator: Summary of Results

2.2 Coupled-Ring Resonators

2.2.1 Device Structure

2.2.2 Device Geometry

2.2.3 Temperature Compensation

2.2.4 Resonator Fabrication

2.2.5 Measured Results

Chapter 3 Description of the Multi-Resonator Clock and its Implementation. 51

3.1 Description of the Multi-Resonator Clock

3.2 Sensitivity to Resonator Drift

–  –  –

3.3.1 Non-uniform temperature distribution in measurement chamber.. 56 3.3.2 Temperature sensor calibration error

3.4 Other sources of non-idealities

3.5 Oscillator Implementation

3.5.1 Oscillator Circuit

3.5.2 Oscillator Measurements

3.6 System Implementation

3.6.1 Oscillator Temperature Dependence

3.6.2 Estimation of system multipliers

3.6.3 Clock Measurement Results

3.7 Discussion

Chapter 4 Experimental Investigation of Loss Mechanisms in Lamé-Mode Resonators

4.1 Electrostatically Actuated Lamé-Mode Resonators

4.1.1 Device structure

4.1.2 Estimation of anchor loss

4.1.3 Optimization of tether geometry for Lamé-mode resonators......... 77 4.1.4 Origin of anchor loss in Lamé-mode resonators

4.1.5 Experimental Verification

–  –  –

4.2.1 Fabrication process of temperature-compensated capacitive Lamémode resonators

4.2.2 Measured Results

4.3 Piezoelectrically Actuated Temperature-Compensated Lamé Resonators 91 4.3.1 Resonator Design

4.3.2 Fabrication process of temperature-compensated piezoelectrically actuated Lamé resonators

4.3.3 Measured Results

4.4 Conclusions

Chapter 5 Acoustically Coupled AlN-on-Silicon Filters

5.1 Introduction and Motivation

5.2 Thickness-Extension Acoustically Coupled Filters

5.2.1 Working Principle

5.2.2 Equivalent Electrical Model of Acoustically Coupled Filters...... 110 5.2.3 Fabrication Process

5.2.4 Measurement Results

5.2.5 Finite Element Modeling of Acoustically Coupled filters........... 119 5.2.6 Design guidelines for acoustically coupled filters

5.3 In-plane acoustically coupled filters

–  –  –

5.3.2 Finite element modeling of the filter response

5.3.3 Measured Results

5.3.4 In-plane filters: Merits and Challenges

5.4 Conclusions

Chapter 6 Future Work

6.1 Summary

6.2 Future Research Directions

6.2.1 Clock Implementation

6.2.2 AlN-on-Silicon Lamé-Mode Resonators

6.2.3 In-Plane Acoustically Coupled Filters

Appendix A-1 Dispersion Curves


–  –  –

Figure 1-1: Block diagram of a MEMS oscillator.

Figure 1-2: Classification of micro-mechanical resonators based on their transduction mechanism.

Figure 1-3: (Left) SEM image of an electrostatically-actuated Lamé-mode resonator [12].

(Right) A schematic of the resonator highlighting the important parameters.

Figure 1-4 : (Left) A SEM image of a piezoelectrically actuated AlN-on-silicon flexuralmode resonator. (Right) A schematic of the resonator highlighting the top electrode layout designed to excite the in-plane flexural mode piezoelectrically.

Figure 1-5: Classification of the important loss mechanisms in resonators.

Figure 1-6: Block diagram of the proposed multi-resonator temperature stable frequency reference.

Figure 2-1: A schematic view of the AlN-on-silicon resonator, showing the flexural mode of operation. The tuning electrodes are not shown in this schematic.

Figure 2-2: (a) Simulated mode shape and (b) simulated strain energy density along section A-A'. (c) A close-up view of the strain energy density variation across the resonator flange cross-section. The overlaid parabolic curve (in black) represents the variation of the strain across the width of the resonator flange. The color spectrum in (a) plots the total displacement and in (b) and (c) plots the strain energy density................. 25 Figure 2-3: Location of oxide-refilled trenches within the resonator (not to scale).

Trenches with similar hatch/fill patterns form a trench pair. The section A-A' corresponds to that seen in Figure 2-2.

Figure 2-4: Plot showing the variation in strain energy density (normalized) across the width of the resonator. Only one half of the flange width is shown here. The TCF of the composite resonator is plotted as a function of the trench location. A clear correlation between the strain energy across the trench and the resonator TCF can be observed. In all cases, the width of the oxide trenches is 5.5 µm and the total volume of oxide is the same.

Figure 2-5: Different trench configurations used in the experimental verification of passive temperature compensation. All trenches have the same dimensions and are shown

–  –  –

Figure 2-6: Fabrication process flow of the AlN-on-silicon flexural-mode resonators.... 30 Figure 2-7: (a) An SEM image of a fabricated resonator. There are a total of eight tuning electrodes, which can be used for tuning the center frequency. (b) A close-up view showing the metal routing on the central rod. The black line (dash-dot) marks the outline of the resonating body.

Figure 2-8: Cross-section SEM images showing the oxide-refilled trenches for a two trench sample. The close-up view on the right reveals small air pockets formed during the refill process, which is caused as an effect of scalloping seen during the trench DRIE... 32 Figure 2-9: Measured response of the resonators with (a) no TCF compensation (b) single oxide-refilled trench (c) two oxide-refilled trenches and (d) three oxide-refilled trenches.

All measurements are taken in vacuum and at room temperature.

Figure 2-10: Measured resonance frequency as a function of temperature for different trench configurations. In case of no trench and single trench resonators, the TCF value is averaged across the temperature range. For the case of two and three trench devices, the TCF value is estimated at 25 °C.

Figure 2-11: Measured peak frequency shift in parts per million (ppm) as a function of temperature for different trench configurations. Inset: measured results in a smaller ppm range.

Figure 2-12: Measured and calculated frequency tuning as a function of applied DC voltage for a trenchless device. (a) The change in peak frequency and (b) the total frequency tuning in ppm.

Figure 2-13: (a) Measured frequency change with temperature for a three trench device.

The tuned frequency with applied DC voltage is also plotted to demonstrate the viability of this approach in achieving temperature stable resonators. (b) Tuned peak frequency as a function of temperature and voltage. The graph details the tuning error for multiple measurements (total 20 readings at each temperature) at each voltage setting and the average value. The tuning error is within 1 ppm and is set by power supply fluctuations, resonator drift and the stability of the temperature controller.

Figure 2-14: Cross-section schematic of the AlN-on-silicon flexura-mode resonator, detailing the stack layers and the measurement conditions for piezoelectric tuning........ 40 Figure 2-15: Measured bidirectional frequency tuning using the piezoelectric effect. The total tuning range is measured to be 5 Hz for a three-trench device. The tuning range can be significantly improved by improving the thickness ratio of AlN to silicon in the device.

xi Figure 2-16: Measured drift of the resonator center frequency (a) without and (b) with feedback control loop. (c) Histogram plot of the resonator center frequency with feedback control showing the calculated statistical parameters assuming a Gaussian distribution.

The resonator intrinsic drift is seen to be better than 110 ppb (3σ number).

Figure 2-17: Schematic of a temperature-compensated coupled-ring breathing-mode resonator. The oxide-refilled regions are clearly marked for clarity. Note that the schematic does not show the piezoelectric stack.

Figure 2-18: Simulated mode shape of the coupled-ring resonator

Figure 2-19: Simulated turnover temperature for the compensated ring resonators as a function of 'edge' spacing. This dimension is marked for clarity in Figure 2-17. Note that all devices have the same 23.5 μm width of silicon dioxide

Figure 2-20: Process flow used in the fabrication of the ring resonators.

Figure 2-21: Cross-section SEM view of the oxide-refilled trenches within the silicon volume

Figure 2-22: SEM view showing a fully released temperature compensated ring resonator.

Note that the oxide rings are not visible due to the presence of the piezoelectric stack... 48 Figure 2-23: Measured frequency response for three temperature-compensated resonators.

The measured result for an uncompensated ring resonator is also included for comparison.

All measurements are carried out at room temperature and pressure with input power of dBm.

Figure 2-24: Measured relative frequency shift in ppm as a function of temperature for the three temperature-compensated resonators shown in Figure 2-23

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