Quantitative measurement of local elasticity of SiO_x film by atomic force acoustic microscopy

In this paper the elastic properties of SiOx film are investigated quantitatively for local fixed point and qualitatively for overall area by atomic force acoustic microscopy （AFAM） in which the sample is vibrated at the ultrasonic frequency while the sample surface is touched and scanned with the tip contacting the sample respectively for fixed point and continuous measurements. The SiOx films on the silicon wafers are prepared by the plasma enhanced chemical vapour deposition （PECVD）, The local contact stiffness of the tip-SiOx film is calculated from the contact resonance spectrum measured with the atomic force acoustic microscopy. Using the reference approach, indentation modulus of SiOx film for fixed point is obtained. The images of cantilever amplitude are also visualized and analysed when the SiOx surface is excited at a fixed frequency. The results show that the acoustic amplitude images can reflect the elastic properties of the sample.

Evaluating Local Elasticity of the Metal Nano-films Quantitatively Based on Referencing Approach of Atomic Force Acoustic Microscopy

Traditional technique such nanoindenter（NI） can＇t measure the local elastic modulus at nano-scale（lateral）. Atomic force acoustic microscopy （AFAM） is a dynamic method, which can quantitatively determine indentation modulus by measuring the contact resonance spectra for high order modes of the cantilever. But there are few reports on the effect of experimental factors, such length of cantilever, contact stiffness on measured value. For three different samples, including copper（Cu） film with 110 nm thickness, zinc（Zn） film of 90 nm thickness and glass slides, are prepared and tested, using referencing approach in which measurements are performed on the test and reference samples （it＇s elastic modulus is known）, and their contact resonance spectra are measured used the AFAM system experimentally. According to the vibration theory, from the lowest two contact resonance frequencies, the tip-sample contact stiffness is calculated, and then the values for the elastic properties of test sample, such as the indentation modulus, are determined. Using AFAM system, the measured indentation modulus of copper nano-film, zinc nano-film and glass slides are 113.53 GPa, 87.92 GPa and 57.04 GPa, which are agreement with literature values Mcu--105-130 GPa, Mzn = 88.44 GPa and Molass = 50-90 GPa. Furthermore, the sensitivity of contact resonance frequency to contact stiffness is analyzed theoretically. The results show that for the cantilevers with the length 160 pm, 225 μm and 520 μm respectively, when contact stiffness increases from 400 N/m to 600 N/m, the increments of first contact resonance frequency are 126 kHz, 93 kHz and 0.6 kHz, which show that the sensitivity of the contact resonance frequency to the contact stiffness reduces with the length of cantilever increasing. The novel method presented can characterize elastic modulus of near surface for nano-film and bulk material, and local elasticity of near surface can be evaluated by optimizing the experimental parameters using the AFAM system.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

BEHAVIOR AS t→∞ OF THE SOLUTIONS OF THE LINEAR SYSTEM OF ELASTIC THEORY ON NON－STAR－SHAPED EXTERIOR DOMAINS

The behavior as t→∞ of solutions of the linear system of elastic equations defined on anon-star-tshaped exterior domains in Rn (n≥3) is discussed.It has showed that the local energydecays with arate of t-1+H (0≤H≤1),nonuniformly with respect to the geometrical propertiesof the obstacle.and when n is odd the local energy decays exponentially.For the classical elasticwave,when n=3,the behavior of the solution of the nonhomogeneous system with a right sideterm periodical with respect to time t is discussed.