Ville Kaajakari

Square-extensional mode single-crystal silicon micromechanical resonator for low-phase-noise oscillator applications

A micromechanical 13.1-MHz bulk acoustic mode silicon resonator having a high quality factor (Q=130 000) and high maximum drive level (P= 0.12 mW at the hysteresis limit) is demonstrated. The prototype resonator is fabricated of single-crystal silicon by reactive ion etching of a silicon-on-insulator wafer. A demonstration oscillator based on the new resonator shows single-sideband phase noise of -138 dBc/Hz at 1 kHz offset from the carrier.

Square-extensional mode single-crystal silicon micromechanical RF-resonator

A micromechanical 13.1 MHz bulk acoustic mode (BAW) silicon resonator is demonstrated. The vibration mode can be characterized as a 2-D plate expansion that preserves the original square shape. The prototype resonator is fabricated of single-crystal silicon by reactive ion etching a silicon-on-insulator (SOI) wafer. The measured high quality factor (Q=130000) and current output (i/sub MAX/ /spl ap/ 160 /spl mu/A) make the resonator suitable for reference oscillator applications. An electrical equivalent circuit based on physical device parameters is derived and experimentally verified.

Phase noise in capacitively coupled micromechanical oscillators

Phase noise in capacitively coupled micro-resonator-based oscillators is investigated. A detailed analysis of noise mixing mechanisms in the resonator is presented, and the capacitive transduction is shown to be the dominant mechanism for low-frequency 1/f-noise mixing into the carrier sidebands. Thus, the capacitively coupled micromechanical resonators are expected to be more prone to the 1/f-noise aliasing than piezoelectrically coupled resonators. The analytical work is complemented with simulations, and a highly efficient and accurate simulation method for a quantitative noise analysis in closed-loop oscillator applications is presented. Measured phase noise for a microresonator-based oscillator is found to agree with the developed analytical and simulated noise models.

Electrostatic transducers for micromechanical resonators: free space and solid dielectric

Three electrostatic transduction methods are analyzed for a micromechanical, longitudinal mode, beam resonator. The conventional parallel plate transducer placed at the location of maximum displacement is compared to two solid, dielectric transducers internal to the resonator. Although the solid dielectric offers higher permittivity than the free-space-filled transducers, the unfavorable locations of the internal transducers reduce or even remove the performance advantage of the higher permittivity

Temperature measurement and compensation based on two vibrating modes of a bulk acoustic mode microresonator

A method to detect the temperature of a micromechanical resonator by measuring the frequency- shifts of two different eigenmodes is presented. The resonator is a square-extensional bulk-acoustic-resonator with two fundamental modes of vibration. The modes feature different temperature coefficients of the frequency and therefore by measuring the frequency change of both modes of vibration the temperature information can be deduced. The measured temperature is used to mathematically compensate for the temperature induced drift of the second eigenmode. The advantage of the demonstrated in-situ temperature measurement is that as no external temperature sensor is needed, the resonator temperature is accurately measured and hysteresis arising from different temperature time constants for heating and cooling of the sensor and resonator is eliminated.

Stability of wafer level vacuum encapsulated single-crystal silicon resonators

The stability of wafer level vacuum encapsulated micromechanical resonators is characterized. The resonators are etched of silicon-on-insulator (SOI) wafers using deep reactive ion etching (DRIE) and encapsulated with anodic bonding. Bulk acoustic wave (BAW) resonators show drift better than 0.1 ppm/month demonstrating that the stability requirements for a reference oscillator can be met with MEMS. The drift of flexural resonators range from 4 ppm/month to over 500 ppm/month depending on resonator anchoring. The large drift exhibited by some flexural resonator types is attributed to packaging related stresses.

Intermodulation in capacitively coupled microelectromechanical filters

A compact model for third-order intermodulation in capacitively coupled microelectromechanical filters is derived. A simple expression for the input third-order intercept point is given. This is valuable in designing micromechanical filters, for example, for communication applications. The validity of the analytic model is verified with numerical harmonic-balance simulations and experimental measurements.

Low noise, low power micromechanical oscillator

A 180-nm gap micromechanical resonator biased at 20 V and full custom integrated electronics are used to implement a 13-MHz oscillator that has noise floor of -147 dBc/Hz and power consumption of 240 /spl mu/W including both the loop amplifier and the buffer to a 10-pF load. The design of Pierce type MEMS oscillator is discussed in terms of noise, power, and oscillator stability.

Nonlinearities in single-crystal silicon micromechanical resonators

The fundamental performance limit of single-crystal silicon resonators set by device nonlinearities in characterized. Using Leesons model for near carrier phase noise, the nonlinearity is shown to set the scaling limit in miniaturizing oscillators. A circuit model based on discretization of distributed mass and nonlinear elasticity is introduced to accurately simulate the large amplitude vibrations. Based on published data for the third-order silicon stiffness tensor, the fundamental material nonlinearity limit is estimated. This theoretical limit is compared to measured nonlinearities in bulk acoustic wave (BAW) micromechanical resonators. The material set and measured nonlinearities are of same order-of-magnitude showing that the maximum vibration amplitude of studied BAW microresonators is near the fundamental limit. The maximum strain for single-crystal silicon resonators set by hysteresis limit is estimated to be 2/spl middot/10/sup -3/ (fracture limit 10/sup -2/), which corresponds to the maximum energy density of E/sub m//V=3/spl middot/10/sup 5/ J/m/sup 3/. This value is at least two orders-of-magnitude higher than for shear-mode quartz resonators, which partially compensates for the small size of MEMS components.

Third-order intermodulation in microelectromechanical filters coupled with capacitive transducers

Third-order intermodulation in capacitively coupled microelectromechanical filters is analyzed. Parallel-plate transducers are assumed and, in addition to the capacitive nonlinearities, also the usually much weaker second- and third-order mechanical resonator nonlinearities are taken into account. Closed-form expressions for the output signal-to-interference ratio (SIR) and input intercept point are derived. The analytical results are verified in experiments and in numerical harmonic-balance simulations. It is shown that intermodulation as a function of frequency is asymmetric with respect to the passband. The results are valuable in designing micromechanical filters, for example, for communication applications.