Bongsang Kim

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.

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.

Impact of geometry on thermoelastic dissipation in micromechanical resonant beams

Thermoelastic dissipation (TED) is analyzed for complex geometries of micromechanical resonators, demonstrating the impact of resonator design (i.e., slots machined into flexural beams) on TED-limited quality factor. Zener first described TED for simple beams in 1937. This work extends beyond simple beams into arbitrary geometries, verifying simulations that completely capture the coupled physics that occur. Novel geometries of slots engineered at specific locations within the flexural resonator beams are utilized. These slots drastically affect the thermal-mechanical coupling and have an impact on the quality factor, providing resonators with quality factors higher than those predicted by simple Zener theory. The ideal location for maximum impact of slots is determined to be in regions of high strain. We have demonstrated the ability to predict and control the quality factor of micromechanical resonators limited by thermoelastic dissipation. This enables tuning of the quality factor by structure design without the need to scale its size, thus allowing for enhanced design optimization

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.

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.

Effects of stress on the temperature coefficient of frequency in double clamped resonators

This paper presents a theoretical framework for evaluating the temperature coefficient of frequency (TCf) of double clamped resonators due to stresses induced by the die and through die packaging. It is desirable to have a zero TCf such that the resonator frequency is stable over a broad temperature range. The TCf depends on how the resonators material properties, dimensions, and stresses change with temperature. A passive method of using thin film induced stresses in an encapsulated resonator to compensate for material softening is explored. By using a combination of finite element and analytical models it is possible to predict the TCf and improve thermal frequency stability of micromachined resonators.

A study of electrostatic force nonlinearities in resonant microstructures

This letter investigates the nature of amplitude frequency (A-f) dependence caused by nonlinearities in the parallel plate electrostatic transduced in resonant microstructures. We present analytical and experimental evidences that the A-f nonlinearities are practically always dominated by third order nonlinear terms. For an electrostatically unbalanced system, we show that the bias voltage at which second and third order nonlinearities have equal impact on A-f dependence corresponds to ∼90% of the dc pull-in voltage.

Hydrogen diffusion and pressure control of encapsulated MEMS resonators

We have investigated the diffusion of hydrogen through the oxide and silicon of our single-wafer vacuum package. We have encapsulated micromechanical silicon resonators in vacuum beneath a 20 /spl mu/m polysilicon layer. While we have not been able to measure any change in pressure of parts at room temperature over a period of nine months, we have been able to accelerate the diffusion of hydrogen through the encapsulation using elevated temperatures. While placing encapsulated resonators in elevated temperature, we select the furnace gas condition to diffuse hydrogen gas in or out. This is an enabling step toward forecasting long-term hermiticity of the encapsulation, and it provides the ability to set the pressure inside the encapsulation with a simple set of furnace processes. Also, the ability of the encapsulation to withstand more than twenty of these temperature cycles between room temperature and 300/spl deg/C-400/spl deg/C is evidence of the robustness of the package.