Mehmet Akgul

Oscillator far-from-carrier phase noise reduction via nano-scale gap tuning of micromechanical resonators

Substantial improvements in the far-from-carrier phase noise of oscillators referenced to stand-alone (as opposed to arrayed) capacitively transduced microme-chanical disk resonators have been attained via the use of atomic layer deposition (ALD) to tune the electrode-to-resonator capacitive gaps. Specifically, ALD of about 30nm of hafnia (HfO2) onto the surface of a released 60-MHz micromechanical disk resonator to reduce its effective resonator-to electrode gap size from 92nm to 32nm provides an increase in power handling leading to more than 15–20dB reduction in the far-from-carrier phase noise of an oscillator referenced to this resonator. This ALD-enabled nano-scale gap tuning provides a simple and effective method to satisfy increasing demands for higher short-term stability in frequency references for electronic applications.

Hot filament CVD conductive microcrystalline diamond for high Q, high acoustic velocity micromechanical resonators

A capacitively transduced micromechanical resonator constructed in hot filament CVD boron-doped microcrystalline diamond (MCD) structural material has posted a measured Q of 146,580 at 232.441 kHz, which is 3× higher than the previous high for conductive polydiamond. Moreover, radial-contour mode disk resonators fabricated in the same MCD film and using material mismatched stems, cf., Figure 1, exhibit a Q of 71,400 at 299.86 MHz, which is the highest series-resonant Q yet measured for any on-chip resonator at this frequency. The material used here further exhibits an acoustic velocity of 18,516 m/s, which is now the highest to date among available surface micromachinable materials. For many potential applications, the hot filament CVD method demonstrated in this work is quite enabling, since it provides a much less expensive method than microwave CVD based alternatives for depositing doped CVD diamond over large wafers (e.g., 8”) for batch fabrication.

2.97-GHz CVD diamond ring resonator with Q >40,000

A capacitive-gap transduced micromechanical ring resonator based on a radial contour vibration mode and constructed from hot filament CVD boron-doped microcrystalline diamond has achieved a Q of 42,900 at 2.9685GHz that represents the highest series-resonant Q yet measured at this frequency for any on-chip room temperature resonator, as well as the highest f·Q of 1.27×1014 for acoustic resonators, besting even macroscopic bulk-mode devices. Values like these in a device occupying only 870μm2 may soon make possible on-chip realizations of RF channelizers and ultra-low phase-noise GHz oscillators for secure communications.

Micromechanical Resonant Displacement Gain Stages

Micromechanical resonant displacement gain stages have been demonstrated that employ directionally engineered stiffnesses in resonant structures to effect displacement amplification from a driven input axis to an output axis. Specifically, the introduction of slots along the output axis of a 53-MHz wine-glass mode disk resonator structure realizes a single gain stage with a measured input-to-output displacement amplification of 3.08x. Multiple such mechanical displacement gain stages can then be cascaded in series via half-wavelength beam couplers to achieve multiplicative gain factors; e.g., two cascaded gain stages achieve a total measured gain of 7.94x. The devices have also been operated as resonant switches, where displacement gain allows impact switching via actuation voltages of only 400mV, which is 6x smaller than for previous resoswitches without displacement gain. The availability of such high frequency displacement gain strategies for resonant switches may soon allow purely mechanical periodic switching applications (such as power amplifiers and power converters) with much higher efficiencies than current transistor-based versions.

Voltage-controlled tuning to optimize MEMS resonator array-composite output power

A voltage controlled electrical stiffness tuning method has been demonstrated to correct phase and amplitude mismatches between the constituent resonators in a half-wavelength (λ/2) mechanically coupled array-composite towards maximizing its output power. Via tuning, a nine-disk array-composite using 3 output resonators achieves an output current 2.91× larger than that of a single one of its constituent resonators, and only a bit short of the 3× theoretical maximum. Without tuning, the array-composite achieves only 2.78× the current of a single device, and the deviation from ideal is expected to increase with the number of resonators in the array. The amount of tuning available can be tailored in numerous ways, from sizing of electrode-to-disk gap spacing, to specifying the number of devices in the array involved with tuning, to simple variation of voltages across selected electrode-to-resonator gaps. By raising the power output of a high-Q micromechanical disk-array composite resonator, the method and design of this work stand to greatly lower the phase noise of oscillators referenced to such devices.

Acceleration sensitivity of small-gap capacitive micromechanical resonator oscillators

The vector components of acceleration sensitivity Γ for a closed-loop oscillator referenced to a wine-glass disk array-composite resonator employing tiny (∼92nm) electrode-to-resonator capacitive transducer gaps were measured along axes perpendicular and parallel to the substrate to be Γvertical∼13.6ppb/g and Γlateral∼4.92ppb/g, respectively, which are on par with commercial quartz-based oscillator products. Interestingly, the measured acceleration sensitivity greatly exceeds the prediction of theory. In particular, models for frequency shifts due to variations in electrical stiffness and mechanical stress predict acceleration sensitivities orders of magnitude lower than measured here. Consideration of other microphonic contributors reveals that the measurements of this work were probably limited by the bond wires and package stresses of the board-level realization of the oscillator, so are very likely not representative of the performance actually achievable by a fully-integrated micromechanical resonator oscillator, where MEMS and transistors share a single chip. Still, the measured microphonic performance on par with mid-grade quartz oscillators at least provides some reassurance that the tiny electrode-to-resonator gaps used in high frequency capacitively transduced micromechanical resonators will not compromise the stabilities of oscillators referenced to them in conventional applications that currently accept mid-grade quartz resonators.

A passband-corrected high rejection channel-select micromechanical disk filter

The introduction of a 39nm-gap capacitive transducer, voltage-controlled frequency tuning, and a stress relieving coupled array design has enabled a 0.09% bandwidth 223.4-MHz channel-select filter with only 2.7dB of in-band insertion loss and 50dB of out-of-channel interferer rejection. This amount of rejection is more than 23dB better than a previous capacitive-gap transduced filter design that did not benefit from sub-50nm gaps. It also comes in tandem with a 20dB shape factor of 2.7 realized by a hierarchical mechanical circuit design utilizing 206 resonant micromechanical circuit elements, all contained in an area footprint (sans bond pads) of only 600μm×420μm. The key to such low insertion loss for this tiny percent bandwidth is Qs >8,800 supplied by polysilicon disk resonators employing for the first time capacitive transducer gaps small enough to generate coupling strengths on the order of (Cx /Co) ~0.1%, which is a 6.1× improvement over previous efforts. Defensive strategies built into the array-composite design hierarchy counter process variations via electrical stiffness tuning, and alleviate stress by allocating displacement-buffer devices to increase filter performance and yield. This filter is the first demonstrated that truly offers low insertion loss and high rejection channel-selection for ultra-low power communication front-ends targeted for autonomous sensor networks.

A negative-capacitance equivalent circuit model for parallel-plate capacitive-gap-transduced micromechanical resonators

A small-signal equivalent circuit for parallelplate capacitive-gap-transduced micromechanical resonators is introduced that employs negative capacitance to model the dependence of resonance frequency on electrical stiffness in a way that facilitates circuit analysis, that better elucidates the mechanisms behind certain potentially puzzling measured phenomena, and that inspires circuit topologies that maximize performance in specific applications. For this work, a micromechanical disk resonator serves as the vehicle with which to derive the equivalent circuits for both radial-contour and wine-glass modes, which are then used in circuit simulations (via simulation) to match measurements on actual fabricated devices. The new circuit model not only correctly predicts the dependence of electrical stiffness on the impedances loading the input and output electrodes of parallel-plate capacitive- gap-transduced micromechanical device, but does so in a visually intuitive way that identifies current drive as most appropriate for applications that must be stable against environmental perturbations, such as acceleration or power supply variations. Measurements on fabricated devices confirm predictions by the new model of up to 4× improvement in frequency stability against dc-bias voltage variations for contour- mode disk resonators as the resistance loading their ports increases. By enhancing circuit visualization, this circuit model makes more obvious the circuit design procedures and topologies most beneficial for certain mechanical circuits, e.g., filters and oscillators.

Hollow stems for higher micromechanical disk resonator quality factor

The use of hollow support stems to reduce energy loss to the substrate while supporting all-polysilicon UHF micromechanical disk resonators has enabled quality factors as high as 56,061 at 329 MHz and 93,231 at 178 MHz - values now in the same range as previous disk resonators employing multiple materials with more complex fabrication processes. With a substantially smaller cross-sectional area compared with the full stems used by predecessors, the hollow stem of this work effectively squeezes the energy conduit between the disk structure and the substrate, thereby suppressing energy loss and maximizing Q for devices operating in radial-contour and whispering gallery modes. Measurements confirm Q enhancements of 2.6× for contour modes at 154 MHz and 2.9× for wine glass modes around 112 MHz over values previously achieved by full stem all-polysilicon disk resonators with identical dimensions. The measured results not only demonstrate an effective Q-enhancement method with minimal increase in fabrication complexity, but also provide insights into anchor loss mechanisms that have been largely responsible for limiting the Qs attainable by all-polysilicon capacitively-transduced MEMS resonators.

Micromechanical disk array for enhanced frequency stability against bias voltage fluctuations

A 215-MHz polysilicon capacitive-gap transduced micromechanical resonator array employing 50 mechanically coupled radial-contour mode disks - the largest such array yet fabricated and measured - has achieved 3.5× better frequency stability than single stand-alone disks against fluctuations in the dc bias voltage (VP) normally applied across electrode-to-resonator gaps during device operation. The key to enhanced frequency stability is the electrode-to-resonator capacitance (Co) generated by the parallel combination of input/output electrodes overlapping each resonator in the array that in turn reduces the efficacy of the bias voltage-controlled electrical stiffness. Here, a new equivalent circuit based on negative capacitance provides improved visualization that helps to identify methods to suppress electrical stiffness induced frequency variation. The circuit model indicates that the more resonators in an array, the smaller the frequency shift imposed by a given bias voltage change. Both modeling and measurement suggest that the most stable MEMS-based oscillators (e.g., against supply noise and acceleration) are ones that utilize mechanically-coupled arrays of resonators.