Concepts and Key Technologies of Microelectromechanical Systems Resonators
Abstract
:1. Introduction
2. MEMS Resonator Operation Principle
2.1. Equivalent Model
2.2. Vibration Modes
2.3. Transduction Mechanisms
3. Performance and Optimization
3.1. Quality Factor
3.1.1. Air Damping Loss
3.1.2. Anchor Loss
3.1.3. Thermoelastic Loss
3.1.4. Other Losses
3.2. Motional Resistance
3.3. Frequency Accuracy
3.3.1. Mechanical Trimming
3.3.2. Electrical Tuning
3.4. Temperature Stability
3.4.1. Passive Compensation
3.4.2. Active Compensation
4. Summary and Future Perspective
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Structure and Mode | Resonant Frequency | Parameter |
---|---|---|
Cantilever beam | resonant frequency mode coefficient modulus of elasticity density device thickness device length mode number device width device radius Poisson’s ratio feature size for LE mode for WE mode and for radial extension shear modulus constant parameter frequency parameter. | |
Double-clamped tuning fork | ||
Circular membrane | ||
Extension mode | ||
FBAR | ||
Lamé | ||
Face shear | ||
Wineglass |
Type | Frequency | Q | Pressure (mTorr) | Transmission (dB) | Vibration Modes | Reference | Schematic Illustration |
---|---|---|---|---|---|---|---|
Capacitive | 32.768 kHz | ~15,000 | 50 | −74 | Flexural | [22] | |
Capacitive | 6.35 MHz | 1,700,000 | 0.15 | −17 | Lamé | [26] | |
Capacitive | 51.3 MHz | 128,400 | 0.08 | −90 | Lamé | [27] | |
Capacitive | 107.3 MHz | 11,000 | Standard atmosphere | −80 | Whispering gallery | [28] | |
Capacitive | 150.9 MHz | 18,000 | 0.225 | −72 | Radial-contour | [24] | |
Piezoelectric | 10 MHz | 4682 | Standard atmosphere | −20 | Width expansion | [29] | |
Piezoelectric | 14.02 MHz | 5000 | ~mTorr | −24 | Length extension | [23] | |
Piezoelectric | 48.14 MHz | 10,000 | ~mTorr | −8 | Width expansion | [23] | |
Piezoelectric | 52 MHz | 4743 | Standard atmosphere | −25 | Lateral-extension | [30] | |
Piezoelectric | 882 MHz | 220 | Standard atmosphere | −46 | Contour mode | [31] |
Frequency | Mode | Type | Original Q | Enhanced Q | Methods | Reference | Schematic Illustration |
---|---|---|---|---|---|---|---|
52 MHz | Lateral-extension | Anchor loss | 606 | 4743 | Frame structure with PnC | [30] | |
51.3 MHz | Lamé | Anchor loss | 56,400 | 128,400 | The beam with root slots | [27] | |
10.03 MHz | Lateral mode | Anchor loss | 2618 | 3945 | Reflective structures | [41] | |
10.03 MHz | Lateral mode | Anchor loss | 2618 | 4522 | PnC | [41] | |
10 MHz | Width expansion | Anchor loss | 1570 | 4682 | PnC + Reflector | [29] | |
610 kHz | Flexural mode | TED | 13,000 | 16,000 | Slots | [50] | |
400 kHz | Flexural mode | TED | 15,000 | 40,000 | Slots | [51] | |
20 kHz | Flexural mode | Coating loss | 3000 | 8000 | Coating coverage | [52] |
Frequency (MHz) | Type | Methods | Reference | Stability |
---|---|---|---|---|
0.39 | In-plane flexural | SiO2 | [95] | 1.7 ppm/°C [10 °C to 90 °C] |
1 | DETF | SiO2 | [89] | −0.02 ppm/°C2 [−55 °C to 125 °C] |
1.024 | DETF | SiO2 | [92] | −0.02 ppm/°C2 [−40 °C to 120 °C] |
711 | Lamb Wave | SiO2 | [94] | −0.021 [−55 °C to 125 °C] |
0.47 | DETF | Doping | [104] | 190 ppm [5 °C to 85 °C] |
9 | Lateral extensional | Doping | [101] | ±20 ppm [−40 °C to 85 °C] |
10 | square extensional | Doping | [101] | ±16 ppm [−40 °C to 85 °C] |
23 | Extensional mode | Doping | [90] | 10 ppm [−40 °C to 85 °C] |
25.09 | Lateral extensional | Doping | [88] | 245 ppm [−40 °C to 85 °C] |
24.44 | Width extensional | Doping and SiO2 | [112] | ±21.5 ppm [−40 °C to 85 °C] |
Frequency (MHz) | Type | Methods | Reference | Stability |
---|---|---|---|---|
2.92 | Free-free beam | Electrostatic | [118] | 0.44 ppm/°C 25 °C to 55 |
5.5 | I-shaped bulk | Electrostatic | [11] | 39 ppm 25 °C to 125 °C |
1.126 | DETF | SiO2+ electrostatic | [117] | ±2.5 ppm −10 °C to 80 °C |
0.54 | In-plane flexural | Doping and Single-Temperature Calibration | [123] | ±8 ppm 5 °C to 85 °C |
77.7 | Lamé mode | Oven control | [127] | ±0.3 ppm −25 °C to 85 °C |
1.2 | DETF | Oven control | [124] | ±1 ppm −20 °C to 80 °C |
1.2 | DETF | Calibration and control | [124] | ±0.05 ppm −20 °C to 80 °C |
1.2 | Plate Bending | Doping and control | [133] | ±25 ppb −40 °C to 40 °C |
10 | Length-extensional | Doping and control | [128] | ±0.5 ppm −35 °C to 85 °C |
13 | Lamé | Doping and control | [133] | ±5 ppb −40 °C to 40 °C |
42.7 | Shear mode | Doping and control | [130] | ±0.4 ppm −40 °C to 80 °C |
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Feng, T.; Yuan, Q.; Yu, D.; Wu, B.; Wang, H. Concepts and Key Technologies of Microelectromechanical Systems Resonators. Micromachines 2022, 13, 2195. https://doi.org/10.3390/mi13122195
Feng T, Yuan Q, Yu D, Wu B, Wang H. Concepts and Key Technologies of Microelectromechanical Systems Resonators. Micromachines. 2022; 13(12):2195. https://doi.org/10.3390/mi13122195
Chicago/Turabian StyleFeng, Tianren, Quan Yuan, Duli Yu, Bo Wu, and Hui Wang. 2022. "Concepts and Key Technologies of Microelectromechanical Systems Resonators" Micromachines 13, no. 12: 2195. https://doi.org/10.3390/mi13122195