Vibrational spectra of nanowires measured using laser Doppler vibrometry and STM studies of epitaxial graphene

A few of the many applications for nanowires are high-aspect ratio conductive atomic force microscope (AFM) cantilever tips, force and mass sensors, and high-frequency resonators. Reliable estimates for the elastic modulus of nanowires and the quality factor of their oscillations are of interest to help enable these applications. Furthermore, a real-time, non-destructive technique to measure the vibrational spectra of nanowires will help enable sensor applications based on nanowires and the use of nanowires as AFM cantilevers (rather than as tips for AFM cantilevers). Laser Doppler vibrometry is used to measure the vibration spectra of individual cantilevered nanowires, specifically multiwalled carbon nanotubes (MWNTs) and silver gallium nanoneedles. Since the entire vibration spectrum is measured with high frequency resolution (100 Hz for a 10 MHz frequency scan), the resonant frequencies and quality factors of the nanowires are accurately determined. Using Euler-Bernoulli beam theory, the elastic modulus and spring constant can be calculated from the resonance frequencies of the oscillation spectrum and the dimensions of the nanowires, which are obtained from parallel SEM studies. Because the diameters of the nanowires studied are smaller than the wavelength of the vibrometer\u27s laser, Mie scattering is used to estimate the lower diameter limit for nanowires whose vibration can be measured in this way. The techniques developed in this thesis can be used to measure the vibrational spectra of any suspended nanowire with high frequency resolution. Two different nanowires were measured–MWNTs and Ag2Ga nanoneedles. Measurements of the thermal vibration spectra of MWNTs under ambient conditions showed that the elastic modulus, E, of plasma-enhanced chemical vapor deposition (PECVD) MWNTs is 37±26 GPa, well within the range of E previously reported for CVD-grown MWNTs. Since the Ag2Ga nanoneedles have a greater optical scattering efficiency than MWNTs, their vibration spectra was more extensively studied. The thermal vibration spectra of Ag2Ga nanoneedles was measured under both ambient and low-vacuum conditions. The operational deflection shapes of the vibrating Ag2Ga nanoneedles was also measured, allowing confirmation of the eigenmodes of vibration. The modulus of the crystalline nanoneedles was 84.3±1.0 GPa. Gas damping is the dominate mechanism of energy loss for nanowires oscillating under ambient conditions. The measured quality factors, Q, of oscillation are in line with theoretical predictions of air damping in the free molecular gas damping regime. In the free molecular regime, Qgas is linearly proportional to the density and diameter of the nanowire and inversely proportional to the air pressure. Since the density of the Ag2Ga nanoneedles is three times that of the MWNTs, the Ag2Ga nanoneedles have greater Q at atmospheric pressures. Our initial measurements of Q for Ag2Ga nanoneedles in low-vacuum (10 Torr) suggest that the intrinsic Q of these nanoneedles may be on the order of 1000. The epitaxial carbon that grows after heating (0001¯) silicon carbide (SiC) to high temperatures (1450–1600°) in vacuum was also studied. At these high temperatures, the surface Si atoms sublime and the remaining C atoms reconstruct to form graphene. X-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM) were used to characterize the quality of the few-layer graphene (FLG) surface. The XPS studies were useful in confirming the graphitic composition and measuring the thickness of the FLG samples. STM studies revealed a wide variety of nanometer-scale features that include sharp carbon-rich ridges, moiré superlattices, one-dimensional line defects, and grain boundaries. By imaging these features with atomic scale resolution, considerable insight into the growth mechanisms of FLG on the carbon-face of SiC is obtained