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研究生： 李偲豪
Lee, Shih-Hao
論文名稱： 奈米尺度下脈衝雷射與物質作用之熱效應模擬研究
Simulation study of thermodynamical interaction between pulsed-laser and condensed matter in nano-scales
指導教授： 陳寬任
Chen, Kuan-Ren
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2003
畢業學年度： 91
語文別： 英文
論文頁數： 57
外文關鍵詞： laser ablation, enthalpy, thermal conductivity
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    • A numerical thermodynamic model is developed to study the interaction between laser and condensed matter in nano-scales. The model employs a finite difference method to solve the heat flow equation with enthalpy, temperature, thermal conductivity, and a state diagram.

    When a laser shoots on the material, it will cause the variation of the material's enthalpy, that produces a temperature gradient inside the material. Heat conduction due to the gradient is determined by a heat flow equation. Many phenomena including phase changes can occur.

    For numerical studies, it is important to used discrete methods to describe the continuous real word. We divide material into several finite small cells, and each cell has its physical values of temperature, enthalpy, thermal conductivity and phase state. The enthalpy of each cell at next time step is calculated fromthe physical values of adjacent cells by the heat flow equation. Then, the other physical values are obtained from the enthalpy. Therefore, by repeating the numerical calculation process, the dynamic process of the laser annealing and ablation is known.

    The understanding of this dynamical process is important for pulsed laser deposition. We can reveal the state of the dynamical source of the sprayed particles. The laser ablation has many applications, including the thin film growth in industry and academia, laser eye operation in the ophthalmology department, CD burner maker and semiconductor chip maker. Furthermore, this numerical model may also be applied to study the thermodynamical issues in nano-sciences (e.g., nano-optics.)

    1 Introduction 1 2 Thermodynamic model 4 2.1 Laser-condensed-matter interaction . . . . 5 2.1.1 The dimension of this system . . . 5 2.1.2 The type of laser and laser pulse . 5 2.1.3 The reflectivity of material surface. 6 2.1.4 The absorption of the laser energy by the material . 7 2.1.5 Heat conduction . . . . . . . . . . .9 2.2 State diagrams . . . . . . . . . . . . . 10 2.2.1 Enthalpy state . . . . . . . . . . .10 2.2.2 Phase state . . . . . . . . . . . . 11 2.2.3 Temperature . . . . . . . . . . . . 12 2.3 Thermal conductivity . . . . . . . . . . .13 2.3.1 Thermal conductivity of solid silicon 14 2.3.2 Thermal conductivity of liquid silicon14 2.3.3 Thermal conductivity of vapor silicon 14 2.3.4 Thermal conductivity of mush silicon .15 2.4 Phenomenon of the phase front . . . . . . . 15 3 Numerical method 16 3.1 System dimension . . . . . . . . . . . . . .16 3.1.1 Set up the system nodes . . . . . . . 16 3.1.2 Dynamic extend nodes . . . . . . . . .17 3.2 Absorption of laser energy in each cell . . 18 3.3 Finite difference equation of thermal conduction . . .18 3.3.1 The equation form in general nodes . .18 3.3.2 The equation form in bounded nodes . .19 3.3.3 The equation form in extended nodes . 20 3.4 Phase front location and velocity . . . . . 21 3.4.1 The position of phase front . . . . . 21 3.4.2 The velocity of phase front . . . . . 22 4 Numerical results 23 4.1 A typical case . . . . . . . . . . . . . . .23 4.2 The phenomenon under different laser energy density . . .45 4.2.1 The maximum vaporization depth . . . .45 4.2.2 The maximum recession speeds . . . . .46 4.2.3 The maximum surface temperature . . . 49 4.3 The phenomenon under different vapor pressure50 4.3.1 The time of silicon beginning to melt or to boil . . .50 4.3.2 The maximum recession speed . . . . . 52 4.3.3 The laser energy threshold . . . . . .54 5 Summary and discussion 55

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