金氧半導體微機電(CMOS-MEMS)震盪器電路為組成感測器系統單晶片的重要元件之一，然而此電路於相位雜訊與溫度穩定性兩方面卻略顯低落。本論文針對全整合式CMOS-MEMS震盪器電路提出改進之設計方法，以其能改善現存CMOS-MEMS震盪器的不足之處。
本文首先提出一整合微型加熱器之雙鉗音叉式共振器，其頻率約為1.2 MHz並內嵌於標準CMOS後段製程。由於借助半導體製程中二氧化矽高熱阻絕率的特性，此溫控共振器的加熱效率高達 266 °C/mW。此外，此共振器之溫度係數亦經過特殊設計，經由材料之被動補償後，其本質溫度係數約僅 +5.1 ppm/°C。因此，結合上述兩項特點並輔以定電阻控溫之概念，此溫控共振器於溫差125°C的範圍內操作時總頻飄約小於120ppm並消耗低於0.5mW的加熱功率，其等效溫度係數低於1 ppm/°C。我們亦設計了低雜訊CMOS震盪器電路，搭配此共振器後其相位雜訊於距震盪頻率1kHz之偏移處為-112 dBc/Hz，於距震盪頻率1kHz之偏移處為-120 dBc/Hz，其消耗功率低於1.3mW。此震盪器之性能與其他state-of-the-art相當。
除了溫控震盪器以外，我們也針對CMOS-MEMS震盪器之相位雜訊做深入的探討，可發現震盪器之近端相位雜訊與共振器的非線性程度高度相關。當我們將震盪器系統操作於極度非線性之區域時，近端相位雜訊能獲得相當程度的改善。此論文中1.2 MHz的CMOS-MEMS雙鉗樑式震盪器最佳的近端相位雜訊為：於距震盪頻率10Hz之偏移處為-77 dBc/Hz，於距震盪頻率100Hz之偏移處為-97 dBc/Hz，其性能指標(FOM)為-176.9dB。而遠端相位雜訊則於共振器之熱雜訊以及電路雜訊相關，無法利用非線性效應改善。
為了徹底改善振盪器性能，本文亦提出了一組新型的CMOS-MEMS後製程。利用CMOS製程中之氮化鈦層，我們可以同時實現較強的機電耦合並能改善震盪器的頻率穩定度。此製程不但解決了傳統CMOS-MEMS共振器中因介電質誘捕多餘電荷所造成頻率隨時間飄移的問題，並可實現高度複雜的共振器結構設計，例如超低溫度係數(sub-ppm/°C TCf)之共振器元件。雖然我們使用0.35 um製程驗證此平台，其概念仍可以向下相容至其他以鋁為後段製程主體的CMOS高階製程節點，例如0.18 um或0.25 um。

This work presents the design and characterization of the monolithic CMOS-MEMS oscillators for temperature compensated clocks. An innovative ovenized double-ended tuning fork (DETF) resonator with an embedded heater trace is implemented for high heating efficiency. The heating efficiency of the resonator is greater than 266 °C/mW, which consumes less than 0.5 mW for 125°C temperature span (-40°C to 85°C). In addition, the resonator is designed to achieve a low temperature coefficient of frequency (TCf) of +5.1 ppm/°C. Combined with micro-oven operations, frequency variation less than 120 ppm across 125°C temperature span is demonstrated under a constant-resistance control. As a result, the compensated TCf less than 1 ppm/°C in this work outperforms other single-chip, BEOL-embedded CMOS-MEMS resonators to date. The monolithic CMOS-MEMS oscillator based on the 1.2-MHz DETF ovenized resonator is also realized in this work. The oscillator phase noise of -112 dBc/Hz at 1-kHz offset and -120 dBc/Hz at 1-MHz offset is demonstrated, which is on par with the state-of-the-art flexural-mode MEMS oscillators but with better circuit integration scheme.

In addition to the ovenized oscillator, the phase noise spectrum of the monolithic CMOS-MEMS resonator is studied in this work. It is recognized that the close-to-carrier phase noise for the MEMS oscillator is mainly dominated by the nonlinear amplitude-to-phase noise conversion effect. By operating the nonlinear oscillator under proper conditions, the nonlinear noise conversion can be suppressed, resulting an improved phase noise. With the 1.2 MHz CMOS-MEMS DETF resonator, the best-case phase noise of -77 dBc/Hz at 10-Hz offset and -97 dBc/Hz at 100-Hz offset is demonstrated, featuring a figure of merit of -176.9 dB.

To further improve the performance for CMOS-MEMS oscillator systems in the future implementations, a titanium nitride composite (TiN-C) MEMS platform is proposed not only for enhanced electrostatic transduction but also for improved frequency stability. The dielectric charging issue for traditional CMOS-MEMS resonators is solved in this platform by means of TiN-based electrodes. Moreover, the sub-ppm/°C TCf is also demonstrated in this work with only passive temperature compensation scheme. Importantly, the proposed platform can be scaled to advanced technology nodes for more functionality and improved performance.

LIST OF FIGURES vi
LIST OF TABLES xiv
CHAPTER 1 Introduction 1
1.1 Micromechanical Resonators 3
1.1.1 Capacitive MEMS Resonators 3
1.1.2 Piezoelectric MEMS Resonators 5
1.2 Micromechanical Oscillators 6
1.3 CMOS-MEMS Technologies 9
1.4 Thesis Organization 13
CHAPTER 2 Mechanical And Electrical Modeling of MEMS Resonators 15
2.1 Modeling of MEMS Resonators 16
2.1.1 Mechanical Resonator Transfer Function 17
2.1.2 Input and Output Transducers 19
2.1.3 Mechanical Resonator Modeling with Electro-Softening Effect 21
2.1.4 Equivalent Series-RLC Circuit Model 23
2.1.5 Modeling the One-Port and Two-Port Resonator 24
2.1.6 Design of Low Impedance Resonators 27
2.2 Temperature Dependency of the MEMS Resonators 28
2.3 Nonlinearity of the MEMS Resonators 31
2.4 Feedthrough Capacitance 33
2.5 Summary 35
CHAPTER 3 Fundamental of MEMS Oscillators 36
3.1 MEMS Oscillator Overview 37
3.2 Topology Selection for the Front-end TIA 38
3.3 Post-TIA Amplifiers 40
3.4 Phase Noise of the CMOS-MEMS Oscillators 42
3.5 Phase Noise of the Nonlinear MEMS Oscillators 45
3.6 Summary 46
CHAPTER 4 Design of Double-Ended Tuning Fork (DETF) CMOS-MEMS Resonator 47
4.1 Resonator Description and CMOS-MEMS Fabrication Process 48
4.2 Resonator Design for Ultra-Low-Power Ovenization 49
4.2.1 Equivalent Circuit Modeling 49
4.2.2 Temperature Coefficient of Frequency (TCf) 52
4.2.3 Design of Ultra-Low-Power Micro-Oven 55
4.3 Q-factor of the CMOS-MEMS Resonator 60
4.3.1 Anchor (Acoustic) Loss 60
4.3.2 Thermoelastic Damping (TED) 61
4.3.3 Material and Interface Loss 62
4.4 CMOS-MEMS Fabrication Results 64
4.5 Measurement Results 65
4.5.1 Measurement Setup 65
4.5.2 Resonator Characterizations 66
4.5.3 Ultra-Low-Power Micro-Oven 68
4.5.4 Ovenized Resonator Characterization 73
4.5.4 Q-Factor of the CMOS-MEMS DETF Resonator 75
4.6 Discussions 77
4.6.1 Discussions on Current Design 77
4.6.2 Suggestions for Future Improvement 78
4.7 Summary 79
4.8 Acknowledgements 79
CHAPTER 5 CMOS-MEMS Oscillator Circuit Design 80
5.1 Symbolic Analysis for the Oscillation Sustaining TIA 80
5.1.1 Shunt-Shunt Feedback Front-End TIA 80
5.1.2 Post-TIA Amplifier 84
5.2 Oscillator Circuit Design 85
5.2.1 Transistor-level Circuit Design 85
5.2.2 Phase Noise of the Oscillator 88
5.3 Experimental Results 89
5.3.1 DETF CMOS-MEMS Oscillator in Vacuum 89
5.3.2 Oscillator Performance with Various Biasing and Environmental Conditions 92
5.4 Discussions 95
5.4.1 Comparison on Oscillator Performance 95
5.4.2 Suggestions for Future Improvement 96
5.5 Summary 97
5.6 Acknowledgements 97
CHAPTER 6 Phase Noise in Nonlinear CMOS-MEMS Oscillators 98
6.1 Background 99
6.1.1 CMOS-MEMS Resonator and Oscillator 100
6.1.2 General Phase Noise Spectrum of CMOS-MEMS Oscillators 101
6.2 Analysis of CMOS-MEMS Oscillators 104
6.2.1 Effect of Gain Compression from the Sustaining Amplifier 104
6.2.2 Effect of Resonator Nonlinearity 105
6.3 CMOS Circuit Design for the Prototype 108
6.3.1 Circuit Topology 108
6.3.2 Noise Analysis 109
6.4 Measurement Results and Discussions 110
6.4.1 Amplitude Controlled CMOS-MEMS Oscillator (OSC-I) 111
6.4.2 Nonlinear CMOS-MEMS Oscillator (OSC-II) 114
6.4.3 Discussions 119
6.5 Summary 121
6.6 Acknowledgements 122
CHAPTER 7 Titanium Nitride (TiN) Based CMOS-MEMS Resonator Platform 123
7.1 TiN in Standard Al-based BEOL 124
7.2 Fabrication Process 126
7.3 Prototyping Resonator Designs 126
7.4 Preliminary Measurement Results 129
7.4.1 Fabrication Results 130
7.4.2 Resonator Frequency and Impedance Characterizations 132
7.4.3 Charging Effects 134
7.4.4Temperature Stability 135
7.5 Summary 136
CHAPTER 8 Conclusions and Future Work 138
8.1 Achievements 138
8.2 Future Research Directions 140
8.2.1 CMOS-MEMS Oscillator with PLL-based Jitter Cleaner 140
8.2.2 Low-Power CMOS-MEMS Oscillator 141
8.2.3 Resistance-Locked-Loop (RLL) for Temperature Compensation 143
8.3 Concluding Remarks 144
APPENDICES 145
BIBLIOGRAPHY 153
PUBLICATION LIST 168
A. Journal Papers (1st author: 5) 168
B. Conference Proceedings (1st author: 9) 169

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