Research On Amplitude And Phase Response Based On Weakly Driven Graphene Nanomechanical Vibration

Since its discovery in 2004,graphene has attracted a lot of attention because of its unusual two-dimensional structure and potential applications.Because of its special mechanical properties and low mass density,graphene is an ideal material for nanomechanical resonators.Because of their small size,ultra-low mass and high elastic modulus,graphene resonators can vibrate at high frequencies(up to hundreds of megahertz)using low drive powers,and their mechanical vibrations are extremely sensitive to fluctuations of electron charge and spin,photon absorption,and adsorbed mass.Such high sensitivity brings hope for the study of new physical phenomena,and has great significance for basic research and various nanomechanical applications.However,the sensitivity of graphene resonators is greatly limited by environmental noise.To solve this problem,here we demonstrate a cross-correlation power spectrum density technique and a signal averaging technique to minimize noise in the measurement system of graphene resonators.Our experimental results show that,compared with the conventional auto-correlation power spectrum technique used in fast Fourier transform analyzers,the cross-correlation power spectrum and signal averaging technology proposed in this paper improve the signal-to-noise ratio(SNR)to 20.4 dB and 39.7 dB,respectively.Finally,the ringdown,phase response and phase modulation of the graphene resonator are measured experimentally based on the signal averaging technique,which demonstrates the versatility of our measurement technique.The main research content of this paper is as follows:(1)Two denoising schemes of cross-correlation power spectrum and signal average are proposed.We used STEMlab122-16 FPGA board by Red Pitaya to build a signal acquisition system,and processed the acquired signals with Matlab.We achieved the detection of weak drive response of graphene resonators and presented a quantitative comparison with conventional auto-correlation power spectrum technique.The advantages of the proposed scheme are:(ⅰ)the SNR of the resonator response signal is greatly improved;(ⅱ)the miniaturization and low cost of signal acquisition system are realized.(2)Based on our signal averaging technique,we measured the ringdown of the resonator under different initial drive powers.This measurement consists in driving the resonator,then stopping the drive and measuring the vibrations as mechanical energy freely decays.From this,we quantified the linear and the nonlinear dissipation of the resonator,and compared with an alternate measurement based on the resonance linewidth.(3)We built a IQ demodulation technique and combined it with our signal averaging technique to measure the amplitude response and phase response of the resonator.By comparing the phase and amplitude response curves measured by IQ demodulation technique and VNA under the same conditions,we found that the resonant peak and phase step position measured by both of them basically coincide,which verified the accuracy of the phase-frequency and amplitude-frequency curves measured by IQ demodulation technique.(4)Finally,we modulated strain within the resonator harmonically to induce a phase modulation of graphene vibrations.We did it by applying a low frequency modulation voltage between the graphene and the gate electrode.Vibrational phase modulations are usually done at kilohertz frequencies(such as in bolometers,for example),we succeeded in measuring phase modulations at frequencies as high as 15 MHz using efficient noise cancelation techniques.