Capacitive Transducer Strengthening via Ald-enabled Partial-gap Filling

The electromechanical coupling factors (ηe’s) of capacitively-transduced micromechanical resonators have been increased by a factor of 8.1× via a process technology that utilizes atomic layer deposition (ALD) to partially fill the electrode-toresonator gaps of released resonators with high-k dielectric material and thereby achieve effective electrode-to-resonator gap spacings as small as 32 nm. The electromechanical coupling increase afforded by gaps this small not only lowers termination impedances for capacitively-transduced micromechanical filters from the kΩ range to the sub-100Ω range, thereby making them compatible with board-level RF circuits; but does so in a way that reduces micromechanical filter termination resistance RQ much faster than the electrode-to-resonator overlap capacitance Co, thereby also substantially increasing the 1/(RQCo) figure of merit (FOM). INTRODUCTION To date, capacitively transduced micromechanical resonators have posted the highest Q’s of room temperature on-chip resonator technologies, with Q values exceeding 200,000 in the VHF range and exceeding 14,600 in the GHz range [1]. This makes them strong candidates for use as RF channel-selectors in next generation software-defined cognitive radios [2], or as ultra-low noise oscillators in high performance radar applications. Unfortunately, the exceptional Q’s of these resonators are not easy to access, because the impedances they present are often much larger than that of the system that uses them. For example, many of today’s board-level systems are designed around 50Ω impedance, which is much smaller than the 2.8 kΩ termination resistors required by the 163-MHz differential disk array filter of [3]. Thus, even though the filter of [3] attains an impressively low insertion loss of 2.43 dB for a 0.06% bandwidth, it requires an Lnetwork to match to 50Ω. While it is true that as micromechanical filters are integrated together with transistors on single siliconchips impedance requirements will grow to the kΩ range for best performance [4], off-chip board-level applications will still need lower impedance. Pursuant to attaining lower capacitive micromechanical resonator impedances, this work employs atomic layer deposition (ALD) [5] to partially fill the electrode-to-resonator gaps of released disk resonators with high-k dielectric material and thereby achieve substantially smaller gap spacing, as small as 32 nm. This reduction in gap spacing increases the electromechanical coupling factors (ηe’s) of capacitive-transducers by a factor of 8.1×, which not only lowers termination impedances for capacitively transduced micromechanical filters from the kΩ range to the sub-100Ωrange, thereby making them compatible with board-level RF circuits; but does so in a way that reduces micromechanical filter termination resistance RQ much faster than the electrode-toresonator overlap capacitance Co, thereby also substantially increasing the 1/(RQCo) figure of merit (FOM). The increase in the FOM is also n× faster (hence, better) than that of fully-filled solid-dielectric gap methods for Rx reduction [6]. This partial dielectric-filling based approach further prevents shorting of the resonator to its electrode, hence, greatly improves the resilience of micromechanical resonators against ESD or other events that might pull a resonator into its electrode. APPROACHES TO IMPROVING FOM The utility of a 1/(RQCo) figure of merit is perhaps best conveyed by considering a typical micromechanical filter [3][8], such as shown in Fig. 1, and examining how its termination resistance RQ and its input capacitance Co affect its performance. As shown in Fig. 1, the RQ and Co essentially combine to generate a pole at ωb = 1/(RQCo) that sets the 3dB bandwidth of a low-pass filter. If ωb is lower than the center frequency ωo of the filter, then it will add undesired passband loss. This problem is actually fixable by using an (on-chip) inductor to resonate out the Co, but it would be preferable if an inductor were not needed. The needed value for termination resistance RQ is given by