Mapping nanoscale dynamic properties of suspended and supported multi-layer graphene membranes via contact resonance and ultrasonic scanning probe microscopies

Graphene's (GR) remarkable mechanical and electrical properties - such as its Young's modulus, lowmass per unit area, natural atomic flatness and electrical conductance - would make it an ideal material for micro and nanoelectromechanical systems (MEMS and NEMS). However, the difficulty of attaching GR to supports coupled with naturally occurring internal defects in a few layer GR can significantly adversely affect the performance of such devices. Here, we have used a combined contact resonance atomic force microscopy (CR-AFM) and ultrasonic force microscopy (UFM) approach to characterise and map with nanoscale spatial resolution GR membrane properties inaccessible to most conventional scanning probe characterisation techniques. Using a multi-layer GR plate (membrane) suspended over a round hole we show that this combined approach allows access to the mechanical properties, internal structure and attachment geometry of the membrane providing information about both the supported and suspended regions of the system. We show that UFM allows the precise geometrical position of the supported membrane-substrate contact to be located and provides indication of the local variation of its quality in the contact areas. At the same time, we show that by mapping the position sensitive frequency and phase response of CR-AFM response, one can reliably quantify the membrane stiffness, and image the defects in the suspended area of the membrane. The phase and amplitude of experimental CR-AFM measurements show excellent agreement with an analytical model accounting for the resonance of the combined CR-AFM probe-membrane system. The combination of UFM and CR-AFM provide an beneficial combination for investigation of few-layer NEMS systems based on two dimensional materials

Comparison of Local Dynamic Response of MEMS Nanostructures Using Ultrasonic Force Microscopy and Laser Doppler Vibrometry

Development of novel high frequency Si, Si3N4, and graphene based micro-and nano-electromechanical systems (MEMS and NEMS) requires suitable characterization methods with nanoscale spatial resolution, high frequency (HF) response and high sensitivity. As spatial resolution of existing methods such as Laser Doppler Vibrometry (LDV) is limited by the light wavelength to the micrometre scale [1], it is tempting to use atomic force microscope (AFM) techniques offering nanoscale resolution. Here we use AFM to analyse the vibrations of nanoscale thin membranes over the frequency range from kHz to several MHz using both linear and nonlinear mechanisms for their excitation and detection. Our model system is a Si3N4 membrane (200 nm thickness, 500x500 um2, Agar Scientific) on a Si substrate. The AFM (Multimode, Nanoscope 8, Bruker) was modified with a piezoceramic transducer driven by the function generator to excite sample vibrations from kHz to about 10 MHz, with the resulting cantilever deflection detected by a standard lock-in-amplifier. The reference optical vibrometry (OFV-2670 and UHF-120, Polytec) found the membrane fundamental vibrational mode at ~250 KHz suggesting it to be under high tensile stress. The core idea of our study was to explore the possibility of detection HF membrane vibrations via AFM and effect of the probing tip contact on the resonance frequency. We used three AFM modes: 1) Force Modulation Microscopy (FMM) with tip vibrations detected at the excitation frequency, 2) nonlinear off-resonance regime where HF sample vibration is modulated at low frequency, and cantilever response measured at the modulation frequency (Ultrasonic Force Microscopy, UFM [2]), 3) UFM resonance regime, where the modulation frequency was around the membrane resonance (M-UFM). While the edge of a membrane was not detectable via topography, it was clearly visible in all ultrasonic modes. FMM mapping at swept excitation frequency showed that the cantilever-tip loading of the membrane increasingly shifted the resonance frequency down as the tip moved towards the centre, with the maximum response reached at a certain distance from the edge, suggesting an optimum position for the detection of vibrations. In M-UFM mode we found that the membrane resonance was also detectable, even though there was no resonance frequency component in the driving oscillation spectrum. We attributed this to the nonlinear nature of the tip-membrane interaction that produced the localised force at the resonance modulation frequency. This study shows that ultrasonic AFM modes will allow the exploration of the vibration of MEMS/NEMS structures of sub-um dimensions including 2D materials based NEMS. [1] Gates RS, Pratt JR, Nanotechnology, 2012, 23(37). [2] Bosse JL et al., Journal of Applied Physics, 2014, 115(14):144304