A New Charge Sensing Scheme Using the Anti-Symmetric Vibration of Coupled Mechanical Resonators


Hajime Okamoto, Koji Onomitsu, and Hiroshi Yamaguchi
Physical Science Laboratory

 High-sensitive charge detection using a micromechanical resonator has recently attracted great attention [1]. There is however a drawback in such mechanical sensing in that the vibration of the resonator itself causes backaction on the object to be measured. In this study, we propose a new mechanical sensing protocol that suppresses the vibrational backaction based on the unexcited anti-symmetric vibration mode in two GaAs based coupled micromechanical resonators [Figs. 1(a) and 1(b)]. When the two resonators are perfectly coupled and simultaneously driven, the anti-symmetric vibration mode is not excited because the out-of-phase vibration is cancelled by the in-phase actuation [Fig. 1(c)]. However, once the frequency of one of the resonators is detuned by added charges via the piezoelectric effect in GaAs, the perfect coupling is broken and the anti-symmetric mode is excited [Fig. 1(c)]. Therefore, by monitoring the change in the amplitude of the anti-symmetric mode one can detect charges that are added to the resonator.
 The two elastically coupled doubly-clamped beams consist of i -GaAs, n -GaAs, and GaAs/AlGaAs superlattice layers and Au gates [Figs. 1(a) and 1(b)]. The frequency of beam B is matched to that of beam A by using the photothermal frequency shift induced by HeNe laser irradiation [2]. The two beams are simultaneously actuated by a piezo-actuator set beneath the resonators in a vacuum at room temperature, while the mechanical motion of beam B is detected with the reflected laser via optical interferometry. Highly-sensitive charge detection is demonstrated by applying a low-frequency (313 Hz) gate voltage to beam A. This gate modulation induces an electric field between the top gate and the n -GaAs layer, resulting in piezoelectric stress in the longitudinal ([110]) direction. This causes the frequency detuning and therefore breaking the symmetry of the anti-symmetric vibration mode. The change in the vibrational amplitude is detected with a spectrum analyzer via lock-in detection of the output signal from the interferometer. The charge sensitivity is derived from the corresponding noise spectrum and the highest sensitivity of 147 e/Hz0.5 is obtained at room temperature [Fig. 1(d)] [3]. Because this sensing scheme is based on the unexcited initial state, the vibration backaction can be minimized. This sensing scheme can also be extended for mass sensing.

[1] A. N. Cleland and M. L. Roukes, Nature 392 (1998) 160.
[2] H. Okamoto et al., Appl. Phys. Express 2 (2009) 062202.
[3] H. Okamoto et al., Appl. Phys. Lett. 98 (2011) 014103.

Fig. 1. (a) A schematic drawing of the coupled resonators. (b) Optical micrograph of the sample. (c) Change in
the anti-symmetric mode by DC detuning. (d) Charge noise spectrum for the actuation frequency of 753.5

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