(54.236.58.220) 您好!臺灣時間:2021/02/27 12:41
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:王世維
研究生(外文):Wang, Shyh-Wei
論文名稱:波茲曼傳輸方程式離子植入模擬-物理模式及數值技術
論文名稱(外文):Ion Implantation Simulation Using Stepwise Boltzmann Transport Equation-Physical Models and Numerical Techniques
指導教授:郭雙發
指導教授(外文):Shung-Fa Guo
學位類別:博士
校院名稱:國立交通大學
系所名稱:電子工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1998
畢業學年度:86
語文別:中文
論文頁數:2
中文關鍵詞:波茲曼傳輸方程式離子植入模擬核子散設射截面不等分能量分格動量矩陣平行處理的多元素標靶的離子植入模擬
外文關鍵詞:Boltzmann transport equationion implantation simulationnuclear differential scattering cross-sectionnon-uniform energy grid momentum matrixparallel multi-component target implantation simulation
相關次數:
  • 被引用被引用:0
  • 點閱點閱:129
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
在本研究中﹐我們提出一些新的物理模式及數值技術以改善現有的波
茲曼傳輸方程式離子植入模擬程式。我們發展出有理式近似的核子散設射
截面函數和直接的核子散射截面計算方法。對於在波茲曼傳輸方程式中記
錄離子能量大小及方向角度的動量矩陣﹐則首次採用不等分離子能量分格
的動量矩陣。並且成功地運用於非晶質離子植入及回彈原子分佈的模擬運
算。 在波茲曼傳輸方程式中﹐散射效應均以散射截面來表示。在
本研究中﹐我們首先針對核子散射截面的計算方法做了深入的探討。先前
﹐Linhard等人提出近似的核子散射截面函數﹐但我們發現現存的散射截
面函數運算式均不夠準確或過於繁複﹐因此我們發展出較有效率的有理式
表示式。然而﹐為了較精確地描述核子散射現象﹐我們更進一步發展出一
套直接計算核子散射截面的方法。由Biersack計算散射角度的魔術公式﹐
我們反向計算而建立壹組入射參數對應能量及散射角的關係﹐在模擬過程
中﹐再採用內插法找出入射參數﹐並直接計算出核子散射截面。經與實驗
及蒙地卡羅(Monte Carlo)模擬程式結果比較後﹐我們發現採用直接算法
可以得到比較正確的模擬結果﹐以硼離子植入矽標靶為例﹐與蒙地卡羅結
果比較下﹐投射距離的誤差可降至10%以下。 對於較重的離子入射問
題﹐我們發現採用不等分離子能量分格的動量矩陣將可以得到較正確的結
果﹐這是因為較嚴謹地考量了低能量的部份和精準地計算停止繼續運動離
子的個數的關係。以100 keV鉍離子植入矽標靶為例﹐與蒙地卡羅結果比
較下﹐投射距離的誤差由14%降為10%。 我們同時也發展了多次往復的
波茲曼傳輸方程式模擬程式﹐以運用於較輕的離子入射和回彈原子的模擬
問題。除了單元素標靶外﹐我們亦考慮到多元素標靶的問題﹐與實驗結果
比較發現﹐採用我們所發展的直接核子散射截面計算和不等分離子能量分
格的動量矩陣﹐對中低能量的重離子入射多元素標靶的模擬上﹐可得到較
準確的結果。以鉺離子植入碳化矽標靶為例﹐與實驗結果比較下﹐投射距
離的誤差由15%降為11%。 此外﹐我們也藉助具有多顆處理器的CONVEX
SPP-1000超級電腦以及平行虛擬機(PVM)的軟體環境﹐我們成功地發展出
平行處理的多元素標靶的波茲曼傳輸方程式離子植入模擬程式。以砷離子
植入五元素標靶AZ1350的問題為例﹐平行化程式的計算速度要比原先程式
快上3.3倍。
In this dissertation, we have developed some physical models
and numerical techniques for stepwise Boltzmann transport
equation (BTE) simulations. They are the rational function
fitting of the nuclear scattering cross-section function, the
exact nuclear scattering cross-section calculation and the non-
uniform energy grid momentum matrix which records the ion energy
and direction angle. They are successfully applied in ion
implantation simulations including ion and recoil distributions.
The stopping power is expressed in terms of the differential
scattering cross-section. The nuclear differential scattering
cross-section is examined in great detail in this work. In order
to simplify the scattering cross-section, Lindhard, Nielson and
Scharff (LNS) had proposed a nuclear scattering cross-section
function to reduce the nuclear cross-section into one-variable.
However, current existing cross-section function equations are
too tedious or not accurate enough. A more efficient and precise
rational function fitting is devised for the LNS nuclear
scattering cross-section function. In order to describe the
nuclear stopping effects correctly, a systematic evaluation of
the exact nuclear differential scattering cross-section is
presented. It is composed of a two-dimensional table
construction and a two-dimensional divided difference
interpolation. The two-dimensional table is synthesized of the
impact parameter as a function of ion energy and scattering
angle. It is obtained by the iterative reverse magic formula
method. The integrals involving the nuclear scattering cross-
section are carefully evaluated with our interpolation. After
comparing to conventional methods, we find our new scheme can
produce a better agreement with the experiment and Monte Carlo
(MC) simulations. For example, the relative errors of projected
ranges for B in Si are reduced to be lower than 10% compared to
MC. In addition, a non-uniform energy grid momentum
matrix is proposed to replace the conventional uniform grid
matrix for heavy ion implantations. The non-uniform grid can
consider the low energy part strictly and the number of stopped
particles is obtained exactly. As an example, the relative
errors of projected ranges for 100 keV Bi in Si are reduced from
14% to 10% compared to MC. Our program is also applied to
other implantation problems, a multi-pass BTE is developed for
the calculations of the light ion and recoil distributions.
Besides, the multi-component target implantations are
considered. It is proved that our program can give a more
correct outcome, for instance, the errors of projected ranges
for Er in SiC are reduced from 15% to 11% compared to the
experiment. A parallelized BTE program for the multi-component
target implantation simulation is developed on CONVEX SPP-1000
with PVM (Parallel Virtual Machine) environment. A speed-up
factor of 3.3 has been achieved for the simulation of AZ1350 of
five components.
Cover
Chinese Abstract
English Abstract
Acknowledgment
Table of Contents
Table Captions
Figure Captions
Chapter 1 Introduction
Chapter 2 Boltzmann Transport Equation Simulation and Nuclear Scattering Cross-Section
2.1 Introduction
2.2 Boltzmann Transport Equation
2.3 Discretelization of the Boltzmann Transport Equation
2.4 Multi-Pass Simulations
2.5 Nuclear Scattering and its Differential Scattering Cross-Section
2.6 One-Parameter Approximation of the Nuclear Scattering Cross-Section
Chapter 3 Rational Fitting of the Nuclear Scattering Cross-Section Function
3.1 Introduction
3.2 Accurate Calculation of the Nuclear Differential Scattering Cross-Section Function
3.3 Rational Function Approximation of the Cross-Section Function
3.4 Fitting Results and Discussion
Chapter 4 Direct Calculation with the Exact Nuclear Scattering Cross-Section
4.1 Introduction
4.2 Computing of the Impact Parameter from Ion Energy and Scattering Angle
4.3 Calculation of the Integrals Involving the Nuclera Cross-Section
4.4 Simulation Results and Discussion
Chapter 5 Improved Formation of the Momentum Distribution Matrix
5.1 Introduction
5.2 Non-Uniform Energy Grid for the Momentum Distribution Matrix
5.3 Angular Distribution after Scattering
Chapter 6 Other Applications
6.1 Introduction
6.2 Recoil Atom Distributions
6.3 Multi-Component Targer Simulations
6.4 Parallel Simulations for Multi-Component Targer
Chapter 7 Conclusion and Future Works
References
Vita
Publication List
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔