A Note on the Vibrations of Scanning Near-Field Optical Microscopy Probe

掃瞄近場顯微鏡微探針之振動分析

張豐宜(Feng-I Chang) ； 盧燈茂(Deng-Maw Lu)

《明新學報》 34卷1期 (2008/02) Pp. 1-9

https://doi.org/10.29688/MHJ.200802.0001

摘要

本文應用拉普拉斯轉換及變數變換法來探討掃瞄近場顯微鏡微探針系統的自然頻率分析。其中利用改變不同的側向彈簧常數及軸向彈簧常數來推導系統的自然頻率表示式。最後，提出一數值實例來計算和說明，其結果歸納如下：(1)當無因次側向彈簧常數遞增時，則有不同的自然頻率在側向彈簧的中間位置亦隨之遞增，(2)當無因次側向彈簧常數變大，則第一個自然頻率亦變大，(3)探針的長度遞減時，則第一個自然頻率將遞增，(4)當無因次軸向彈簧常數大於0.09時，則第一至第五模式的軸向自然頻率將變大。本文所獲得的掃瞄近場顯微鏡微探針之振動分析結果可應用於未來研製新型的微探針系統。

關鍵字

自然頻繁 ； 掃瞄近場顯微鏡 ； 彈簧常數

並列摘要

In this paper, the natural frequencies of a scanning near-field optical microscopy with a optical fiber probe were determined by using Laplace transform with respect to the spatial and time variable. Appling the variety of different parameters of the lateral and axial spring constants, the expressions of the natural frequencies of the system will be derived. A numerical example is presented and many results are obtained, and summarized as follows: (1) when the non-dimensional lateral spring constant increases, then the different natural frequencies at mid-location of the lateral spring become increasing, (2) the first natural frequency gets larger as the non-dimensional lateral spring constant becomes larger, (3) the first natural frequency increases when the probe length decreases, (4) the axial natural frequencies of the first to fifth mode become larger when the non-dimensional axial spring constant is more than the value about 0.09. The results of vibration analysis of the scanning near-field optical microscopy with a optical fiber probe is very important, and it can be applied to design a new type of cantilever probe system in the feature.

並列關鍵字

natural frequencies ； scanning near-field optical microscopy ； spring constant

參考文獻

Betzig, E. Finn, P. L.,Weiner, J. S.(1992).Combined shear force and near-field scanning optical Microscopy.Applied Physics Letters.60,2484-2486.

Binning, Quate, C. F.,Gerber, C.(1986).Atomic force microscope.Physics Review Letters.56,930-933.

Chang, F. I.(2006).Sensitivity analysis of MEMS force sensor beam on the test chip.Journal of Chung Cheng Institute of Technology.34,261-270.

Majumdar, A.,Lai, J.,Chandrachood, M.,Nakabeppu, O.,Wu, Y.,Shi, Z.(1995).Thermal imaging by atomic force microscopy using thermocouple cantilever probes.Review Science Instrumentation.66,3584-3592.

Meirovitch, L.(1967).Analytical methods in vibrations.New York:Macmillan.