研究目的
Investigating the effect of geometric parameters of an atomic force microscopy smart piezoelectric cantilever on the quality of different rough surface topographies by considering capillary force.
研究成果
The Timoshenko beam theory provides more accurate modeling of AFM piezoelectric micro-cantilever vibrations compared to Euler-Bernoulli theory, reducing error in frequency and amplitude predictions. Higher vibration modes offer better accuracy in surface topography, with shorter time delays in tapping mode. Sensitivity analysis shows that length parameters, particularly the first section length and tip length, have the most significant impact on natural frequencies and topography quality, while width parameters have minimal effect. This approach enhances the quality of AFM topography images by improving the understanding of geometric parameter influences.
研究不足
The study assumes a moist environment with specific force constants; effects of temperature variations and liquid environments are not fully explored. The model is based on Timoshenko beam theory, which may have limitations for very high-frequency modes or complex material behaviors. Experimental validation is limited to glass surfaces, and applicability to other materials or conditions may require further investigation.
1：Experimental Design and Method Selection:
The study uses Timoshenko beam theory to model the piezoelectric micro-cantilever (MC) vibration in a moist environment. Hamilton's principle is applied to derive governing equations, and the finite element method (FEM) with Galerkin theory is used for discretization. The Newmark algorithm is employed for time response analysis, and sensitivity analysis is conducted using Sobol and Efast methods.
2：Sample Selection and Data Sources:
Simulations are performed for rectangular and triangular surface roughness forms, and experimental data from glass surface topography is used for validation. The glass surface profile is obtained from AFM measurements.
3：List of Experimental Equipment and Materials:
The MC consists of silicon cantilever, gold electrodes, zinc oxide piezoelectric layer, and silicon tip. Specific geometric and material constants are provided in tables (e.g., lengths, widths, thicknesses, densities, Young's moduli).
4：Experimental Procedures and Operational Workflow:
The MC is modeled as a four-layer beam. Frequency and time responses are calculated far from and close to the sample surface. Surface topography is simulated in tapping and non-contact modes, considering Van der Waals, capillary, and contact forces. Scanning speed is set to 1 μm/s.
5：Data Analysis Methods:
MATLAB software is used for simulations. Frequency response is analyzed using Laplace transform, and time response is computed with the Newmark method. Sensitivity analysis evaluates the effect of geometric parameters on natural frequencies, topography depth, and time delay.
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