Manu Agarwal

Long-Term and Accelerated Life Testing of a Novel Single-Wafer Vacuum Encapsulation for MEMS Resonators

We have developed a single-wafer vacuum encapsulation for microelectromechanical systems (MEMS), using a thick (20-mum) polysilicon encapsulation to package micromechanical resonators in a pressure <1 Pa. The encapsulation is robust enough to withstand standard back-end processing steps, such as wafer dicing, die handling, and injection molding of plastic. We have continuously monitored the pressure of encapsulated resonators at ambient temperature for more than 10 000 h and have seen no measurable change of pressure inside the encapsulation. We have subjected packaged resonators to >600 cycles of -50 to 80degC, and no measurable change in cavity pressure was seen. We have also performed accelerated leakage tests by driving hydrogen gas in and out of the encapsulation at elevated temperature. Two results have come from these hydrogen diffusion tests. First, hydrogen diffusion rates through the encapsulation at temperatures 300-400degC have been determined. Second, the package was shown to withstand multiple temperature cycles between room and 300-400degC without showing any adverse affects. The high robustness and stability of the encapsulation can be attributed to the clean, high-temperature environment during the sealing process

Temperature-compensated high-stability silicon resonators

Composite micromechanical resonators were encapsulated in a hermetic environment using a wafer-scale encapsulation process compatible with complementary metal-oxide semiconductor processing. The resonator structure is comprised of single crystal silicon with a silicon dioxide coating and shows a frequency-temperature sensitivity that is comparable to uncompensated quartz crystal resonators. A frequency variation of less than 200ppm is achieved over a −40–125°C temperature range. The resonator exhibits a quadratic temperature behavior with a turnover temperature at which the frequency becomes insensitive to small temperature changes. The turnover temperature can be controlled for use in high precision frequency references.

Limits of quality factor in bulk-mode micromechanical resonators

In this paper we present the dominant energy loss mechanisms and quality factor (Q) limits in bulk mode micromechanical resonators. We demonstrate that in resonators with an appropriately designed stem connection to anchor the maximum achievable Q limit is set by either Thermoelastic dissipation (TED) or the Akhieser effect (AKE). Furthermore, we suggest a choice of materials for achieving maximum Qs in micromechanical resonators. It is established here that silicon resonators can theoretically achieve higher Qs than quartz and we predict that by using alternative materials, such as silicon carbide, it is possible to surpass the Q of quartz by more than an order of magnitude.

Frequency stability of wafer-scale encapsulated MEMS resonators

This paper presents an investigation of the long-term frequency stability of wafer-scale encapsulated silicon MEMS resonators. Two aspects of stability were examined: long-term stability over time and temperature-related hysteresis. Encapsulated resonators were tested over a period of 8,000 hours in constant environmental temperature of 25/spl deg/C /spl plusmn/ 0.1/spl deg/C. No measurable drift, burn-in time, or other changes in resonant frequencies were detected. Another experiment was performed to investigate the stability of the resonators with temperature cycling. The resonant frequency was measured between each cycle for more than 450 temperature cycles from -50/spl deg/C to +80/spl deg/C. Additional data is presented for short-term hysteresis measurements -10/spl deg/C to +80/spl deg/C temperature cycle. No detectable hysteresis was observed in either of the temperature cycle experiments. These series of experiments demonstrate resonant frequency stability of wafer-scale silicon based MEMS resonators.

Thermal Isolation of Encapsulated MEMS Resonators

This paper presents an in-chip thermal-isolation technique for a micro-ovenized microelectromechanical-system resonator. Resonators with a microoven can be used for high-precision feedback control of temperature to compensate for the temperature dependence of resonator frequency over a wide temperature range. However, ovenization requires power consumption for heating, and the thermal time constant must be minimized for effective temperature control. This paper demonstrates an efficient local-thermal-isolation mechanism, which can reduce the power requirement to a few milliwatts and the thermal time constant to a few milliseconds. In this method, the mechanical suspension of the resonator is modified to provide thermal isolation and include an integrated resistive heater. This combination provides mechanical suspension, electrical heating, and thermal isolation in a compact structure that requires low heating power and has a small thermal time constant. A power consumption of approximately 12 mW for a 125degC temperature rise and a thermal time constant ranging from 7 to 10 ms is reported in this paper, which is orders of magnitude lower than that of commercially available ovenized quartz resonators. A CMOS-compatible wafer-scale encapsulation process is used to fabricate this device, and the thermal-isolation design is achieved without any modification to the existing resonator fabrication process.

Using the temperature dependence of resonator quality factor as a thermometer

Silicon micromechanical resonators have been designed to have a quality factor (Q) that is a strong function of temperature. This is an ideal sensor for the temperature of the resonator—it is instantaneous, consumes no power, and indicates the temperature of the resonator structure with high sensitivity. The authors present a practical implementation of an oscillator system using these resonators with a temperature resolution of better than 0.002°C. The Q(T) signal is uniquely suited for implementing feedback control of the resonator temperature, thereby stabilizing the frequency silicon micromechanical resonators and enabling their use in high-stability frequency reference applications.

Multimode thermoelastic dissipation

In this paper, we investigate thermoelastic dissipation (TED) in systems whose thermal response is characterized by multiple time constants. Zener [Phys. Rev. 52, 230 (1937)] analyzed TED in a cantilever with the assumption that heat transfer is one dimensional. He showed that a single thermal mode was dominant and arrived at a formula for quantifying the quality factor of a resonating cantilever. In this paper, we present a formulation of thermoelastic damping based on entropy generation that accounts for heat transfer in three dimensions and still enables analytical closed form solutions for energy loss estimation in a variety of resonating structures. We apply this solution technique for estimation of quality factor in bulk mode, torsional, and flexural resonators. We show that the thermoelastic damping limited quality factor in bulk mode resonators with resonator frequency much larger than the eigenfrequencies of the dominant thermal modes is inversely proportional to the frequency of the resonator un...

Optimal drive condition for nonlinearity reduction in electrostatic microresonators

A model for the amplitude-frequency (A-f) effect in electrostatic microresonators is presented. This effect is an undesired nonlinear phenomenon that sets the maximum usable oscillation current and thereby degrades the resonator’s signal-to-noise ratio and performance. The model developed in this letter provides analytical expressions for the A-f effect and derives an optimal bias condition that maximizes the usable current. In addition, the authors present experimental data for a double-ended-tuning-fork resonator. Using the derived bias condition, an improvement of more than two times in the sustainable oscillation current has been achieved.

Composite flexural-mode resonator with controllable turnover temperature

This paper presents the design and characterization of a flexural mode composite resonator whose inherent frequency sensitivity to temperature changes is reduced. The resonator is an encapsulated single anchor, double ended tuning fork (DETF) composed of single crystal silicon with a silicon dioxide coating. The frequency variation with temperature of the composite resonator exhibits a turnover temperature at which the frequency does not change with temperature. The turnover temperature can be controlled by varying the thickness of the silicon dioxide. This useful characteristic could be combined with active temperature compensation for more precise timing applications. The fabricated devices show a temperature sensitivity that is comparable to a quartz crystal tuning fork resonator.

Cmos-Compatible Dual-Resonator MEMS Temperature Sensor with Milli-Degree Accuracy

This paper presents a dual-resonator design which, not only enables temperature sensing of the resonators but also acts as a general-purpose temperature sensor. The frequency stability of the temperature compensated resonator depends on the accuracy with which the temperature of the resonator is measured. The dual-resonator design, described here, produces temperature-dependent beat frequency which is inherent to the resonator and thus eliminates any spatial and temporal thermal lag associated with the use of an external temperature sensor. Furthermore, this design can also be used as a CMOS-compatible digital temperature sensor. In this work, we achieved the sensor resolution of approximately 0.008degC which is comparable to that of the best CMOS temperature sensors available today.