鑽石「氮原子─空缺」缺陷中心光譜性質之理論研究

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研究生：	林至闓 Chih-Kai Lin
論文名稱：	鑽石「氮原子─空缺」缺陷中心光譜性質之理論研究 Theoretical Studies on Spectroscopic Properties of Diamond Nitrogen-Vacancy Defect Centers
指導教授：	林聖賢 Sheng Hsien Lin 張煥正 Huan-Cheng Chang 倪其焜 Chi-Kun Ni
口試委員:
學位類別：	博士 Doctor
系所名稱：	理學院 - 化學系 Department of Chemistry
論文出版年：	2008
畢業學年度：	96
語文別：	英文
論文頁數：	135
中文關鍵詞：	鑽石缺陷中心、吸收光譜、螢光光譜、雙井位能面、全從始計算、垂直激發能量、吸收截面
外文關鍵詞：	Diamond Defect Center, Absorption Spectrum, Fluorescence Spectrum, Double-Well Potential, Ab initio, Vertical Excitation Energy, Absorption Cross Section
相關次數：	點閱：3 下載：0
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本論文敘述鑽石中帶負電荷的「氮原子─空缺」缺陷中心〔記為 (NV)-〕與相關缺陷中心的光譜性質理論研究，內容分為三大部分。第一部分以簡諧振子位能面加上 Gaussian 函數，建構對稱雙井位能面模型，用以描述氮原子在缺陷中心的可能振動模式，進而模擬 (NV)- 吸收光譜與螢光光譜的譜線。我們根據此位能面之 Schroedinger 方程式，以數值方法解出電子基態與激發態之各振動能階能量、波函數，並得到兩電子態間的 Franck-Condon 因子及波函數與振動座標的積分。本模型套用於氨分子的反轉振動模式以及鑽石 (NV)- 缺陷中心，可獲得與實驗光譜相符的模擬結果。

第二部分為鑽石 (NV)- 缺陷中心之全從始（ab initio）與密度泛函理論（DFT）量子化學計算結果。我們建構了數個尺寸的鑽石晶格分子模型，以 24 至 104 個碳原子包圍 1 個氮原子和 1 個空缺位置，仿造缺陷中心周圍的環境。各分子模型先以 Hartree-Fock（HF）或 DFT 進行幾何結構最佳化，再以時間相關方法如 TD-HF、TD-DFT，以及單激發組態交互作用（CIS）、完全活化空間自洽場（CASSCF）等方法求得垂直激發能量、單光子與雙光子吸收截面值等性質。比較各計算方法與所採用基函數可知，TD-DFT 使用 B3LYP 泛函與 6-31G(d) 基函數可獲得最準確的垂直激發能量，而 TD-HF、CIS、CASSCF 能預測較接近實驗值的吸收截面值。

最後一部分敘述兩個與 (NV)- 相關的鑽石缺陷中心：具有「氮原子─空缺─氮原子」結構的 H3 缺陷中心，與電中性的「氮原子─空缺」缺陷中心〔記為 (NV)0〕之量子化學計算結果。H3 缺陷中心的激發態性質可依循處理 (NV)- 的方式獲得，同樣由 TD-DFT 預測垂直激發能量，由 TD-HF 和 CIS 預測單光子吸收截面值。而 (NV)0 缺陷中心因多個激發態波函數具有多重 Slater 行列式性質，TD-DFT 只適用於其中第一激發態之計算，其餘皆需使用 CASSCF；所得激發態能量仍以 TD-DFT 結果較接近實驗值，CASSCF 受限於模型尺寸而過度高估，但甚小的單光子吸收截面值與實驗結果一致。

The theoretical studies on spectroscopic properties of the negatively charged diamond nitrogen-vacancy defect center, (NV)-, and related point defects presented in this report consists of three parts. The first part demonstrates the simulation of excitation and fluorescence spectra based on a symmetric double-well potential model constructed from a harmonic oscillator perturbed by a Gaussian-function barrier. Mathematical formulas were deduced to describe the vibronic transition involving the nitrogen-tunneling motion within this potential model, followed by numerical solutions to the Schroedinger equation that gave vibrational energy levels, wavefunctions, and Franck-Condon factors with consideration of overlap integrals. The model has been tested with the inversion vibrational mode of the ammonia molecule as well as the diamond (NV)- center, giving good agreements between experimental and simulated spectra.

The second part shows computational results of the diamond (NV)- center by ab initio and density functional theory calculations. Different-sized model clusters composed of 24 to 104 carbon atoms surrounding one nitrogen atom and one vacancy were constructed to imitate the local environment of the defect center. The structures were optimized using either HF or DFT algorithm, followed by TD-HF, TD-DFT, CIS, and CASSCF calculations to obtain excitation properties such as vertical excitation energies, one-photon and two-photon absorption cross sections corresponding to transitions from the ground to the first excited state. The dependences on computational methods and basis sets have been compared. While TD-DFT with the B3LYP functional and the 6-31G(d) basis set gave the most accurate prediction of the vertical excitation energy, TD-HF, CIS, and CASSCF provided suitable estimations on the absorption cross sections. The 6-31+G(d) basis set, however, always spoiled the results due to enhancements of electron density leakage from the defect center and interference from surface atoms. A large enough model is thus thought more important than a large basis set.

The last part concerns computational results of two other diamond defect centers related to nitrogen atoms and vacancy, the H3 (N-V-N) and the neutral (NV)0 centers. The excitation properties of the H3 center could be well reproduced analogously to the (NV)- case, giving satisfactory agreements to experimental values of vertical excitation energies by TD-DFT and one-photon absorption cross sections by TD-HF and CIS. For the (NV)0 center, on the other hand, TD-DFT could only characterize the first excited state while other states require CASSCF since they have the multiple-Slater-determinant character of electronic configurations. Again TD-DFT obtained agreement with the experimental vertical excitation energy; CASSCF overestimated it by size-limited models, but the very low one-photon absorption cross sections were predicted in consistent with experimental findings.

Introduction ............................................................................................. 1
Symmetric Double-Well Potential Model .................................................................... 5
1  Origination of Symmetric Double-Well Potential Model ................................................... 5
2  Mathematical Formulas of Harmonic Oscillator Potential with Gaussian-Function Barrier .................. 7
2.1  Energy levels and wavefunctions of symmetric double-well potential ................................... 7
2.2  Franck-Condon factors of distorted harmonic oscillators ............................................. 13
2.3  Absorption and photoluminescence spectra ............................................................ 17
3  Application on Ammonia Inversion Mode ................................................................. 19
4  Application on Diamond Nitrogen-Vacancy Defect Center ................................................. 27
5  Summary ............................................................................................... 32
One-Photon and Two-Photon Excitation Properties ......................................................... 35
1  Experimental One-Photon vs. Two-Photon Excitation-Fluorescence Spectra and Absorption Cross Sections .. 35
2  Mathematical Formulas of Excitation Transition Rates and Absorption Cross Sections .................... 37
2.1  Perturbation treatment .............................................................................. 37
2.2  One-photon excitation ............................................................................... 39
2.3  Two-photon excitation ............................................................................... 42
3  Computational Methods ................................................................................. 49
3.1  Model compounds ..................................................................................... 49
3.2  Computational details ............................................................................... 51
4  Computational Results of Ground and the First Excited States .......................................... 54
4.1  Optimized structures of ground states ............................................................... 54
4.2  Vertical excitation energies ........................................................................ 56
4.3  One-photon absorption cross sections ................................................................ 66
4.4  Two-photon absorption cross sections ................................................................ 70
5  Higher Excited States ................................................................................. 75
6  Summary ............................................................................................... 78
Other Defect Centers Related to Nitrogen Atoms and Vacancies in Diamond.................................. 81
1  Common Defect Centers Related to Nitrogen Atoms and Vacancies ......................................... 81
2  The H3 Defect Center .................................................................................. 84
3  The Neutral NV Defect Center .......................................................................... 93
4  Summary .............................................................................................. 104
Conclusions ............................................................................................ 107
Appendices ................................................................................................ 111
Appendix A: Gaussian-Function-Coupled Matrix Elements of Harmonic Oscillator Wavefunctions ................ 111
Appendix B: Variational Method and Calculation of Expansion Coefficients .................................. 115
Appendix C: Overlap integrals of distorted harmonic oscillator wavefunctions .............................. 122
Publication List .......................................................................................... 127
References ................................................................................................ 129

                                

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