運用混合微分轉換法求解薄膜受超短脈衝雷射作用之研究

An Application of the Hybrid Differential Transform Method for Studying a Thin Film Exposed to Ultrashort Pulsed Lasers

白桂霖(Kuei-Lin Pai)

指導教授 ： 駱正穎

國立虎尾科技大學/工程學院/航空與電子科技研究所/碩士(2009年)

https://doi.org/10.6827/NFU.2009.00070

摘要

超短波脈衝雷射廣泛應用在工程領域，尤其在微尺寸的元件或系統製造過程。研究超短波脈衝雷射引起的熱變形是為了避免熱損壞。本文運用微分轉換混合有限差分法求解於薄膜受超短脈衝雷射作用下之熱變形研究，採用之數學模型為二階段雙曲線熱傳模式。首先利用微分轉換法將時域之系統統御方程式轉換成頻域之方程式，而後再對轉換後統御方程式於空間域進行有限差分離散化，最後經由疊代法求解後，再以數值逆微分轉換求取系統變數。微分轉換法的優點是可將線性或非線性微分方程轉換成疊代方程式，並可將邊界條件，經過轉換後簡化為初始值條件。本文提供短脈衝雷射加工之條件下，工件之晶格溫度，電子溫度，熱通量與應變之全場解。研究結果說明晶格溫度和應變之間耦合的效果，以及各材料與加工參數之影響。經由選取適當的差分格點數，並能有效抑制位於熱傳波前的數值震盪現象發生。本文亦展示了微分轉換混合有限差分法可有效地運用於二階段雙曲線熱傳方程式。

關鍵字

超短波脈衝雷射 ； 熱變形 ； 微分轉換法 ； 二階段雙曲線

並列摘要

Ultrashort-pulsed lasers have been extensively applied in engineering problems, especially in the manufacture of micro size parts or systems. Studying the thermal deformation induced by ultrashort-pulsed lasers is important for preventing thermal damage. This article presents an application of the hybrid differential transform and finite difference method for studying thermal deformation in a thin film exposed to ultrashort pulsed lasers. The mathematic model of the problem is based on two-step hyperbolic transfer equations. Firstly, the differential transform technique is used to transform the governing equations as well as boundary conditions from the time domains into the spectrum domain. Secondly, the resulting transformed equations are discretized by the finite difference method. Thirdly, the spectrum functions are determined through a recursive procedure. Finally, all system variables are obtained by using the numerical inversion of differential transform. The merit of the present method lies on the transformation of differential equation into the recursive forms which are much easier to solve systematically. The present study obtains the full field solutions of electronic temperature, lattice temperature, heat flux stresses and strains of a thin film in the manufacturing process. It accounts for the coupling effects between lattice temperature and strain rate, as well as for the hot-electron-blast effect in momentum transfer .The numerical oscillations which often arise in the vicinity of sharp discontinuities can be successfully suppressed with an appropriate grid number used in the model. The thesis demonstrates the feasible application of the hybrid differential transform technique in solving the two-step hyperbolic heat transfer problems.

並列關鍵字

Ultrashort-pulsed lasers ； thermal deformation ； differential transform method ； two-step hyperbolic

參考文獻

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