Chandra M. Jha

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.

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.

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.

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.

High resolution microresonator-based digital temperature sensor

A digital temperature sensing technique using a complementary metal oxide semiconductor (CMOS) compatible encapsulated microresonator is presented. This technique leverages our ability to select the temperature dependence of the resonant frequency for micromechanical silicon resonators by adjusting the relative thickness of a SiO2 compensating layer. A dual-resonator design is described that includes a pair of resonators with differential temperature compensations so that the difference between the two resonant frequencies is a sensitive function of temperature. The authors demonstrate a temperature resolution of approximately 0.008°C for 1s averaging time, which is better than that of the best CMOS temperature sensors available today.

Nonlinear Characterization of Electrostatic MEMS Resonators

Encapsulated micromechanical resonator technology is becoming important as a potential replacement for quartz for several applications. In this work we report the nonlinear characterization, particularly the A-f effect, in these resonators. The A-f effect in quartz has been well studied in the 1970s and 1980s (Gagnepain, 1981) and (Gagnepain, 1987), as it dictates the maximum power (current) that can be handled by the resonator. MEMS resonators tend to have a strong A-f effect compared to quartz, and this is the reason for the low power handling in these devices in comparison to quartz crystal resonators. In this work we report the mechanism of nonlinearities in these devices and find design guidelines to improve performance