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    jsp.display-item.identifier=請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/32575


    题名: 第一原理贗勢方法在處理光學躍遷矩陣上所需之修正方法的比較以及靜電場下分子和晶體之光電與介電性質研究
    其它题名: Comparison on corrections to optical transition matrix elements in first principles pseudopotential methods and the studies of optoelectronic as well as dielectric properties of molecules and crystals under static electric field
    作者: 鄭尊謙;Cheng, Tsun-chien
    贡献者: 淡江大學物理學系碩士班
    李明憲;Lee, Ming-hsien
    关键词: 密度泛函理論;贗勢;倍頻係數;核修補;密度泛函微擾理論;介電常數;超極化率;EFISH;DFT;Pseudopotential;SHG;Core-repair term;DFPT;Dielectric constant;Hyperpolarizability;EFISH
    日期: 2007
    上传时间: 2010-01-11 02:22:46 (UTC+8)
    摘要: 方法發展:對於固體的光學性質計算、其躍遷矩陣,必須用動量算符表示,而因為使用 Pseudopotential 的緣故動量算符也就必須做相關修正。修正動量算符的方法不只一種,常見的有 commutator 修正法與核修補方法兩種。在我們研究群使用的程式中前者已經存在,也給出了合理結果,而我們想要進一步把後者也作進去同一程式中,以便比較兩者的優劣異同

    應用計算:介電係數在現今半導體及光電材料裡是一個重要的物理量,很多新型元件需要針對材料的介電係數來加以調控設計,以便達到所需要的效果,材料中會影響到其介電常數之相關因素因此成為重要的研究議題。我們選擇了幾種 high k、low k 材料來進行第一原理計算,並建立新的分析方法,讓我們可以在三度空間中呈現出影響介電常數貢獻的部份來自何處,所選擇得材料包括了一系列不同結晶相的二氧化矽、常見的氧化物晶體、以及近年來受矚目的 HfO2。另外,固態材料受外在靜電場影響的物性變異,隨著奈米科技的發展材料尺寸及元件都大幅縮小,在相當之電位差之下,產生的電場強度就極為巨大,因而其引發的物性變易也就明顯重要。在這一部分的研究中,我們計算分子光電特性之一的超極化率並與實驗比較,也探討它是如何受到外場強大靜電場而有所改變。

    關鍵詞:密度泛函理論;贗勢;倍頻係數;核修補;密度泛函微擾理論;介電常數;超極化率;EFISH
    Methodology :

    To calculate the optical properties of solids, one has to use the expectation values of momentum between bands instead of that of position operator for the evaluation of transition matrix elements. Therefore, when pseudopotential is used, the expectation value needs to be corrected because for r < rc the wavefunction is very different from the true wavefunctions. There are more than one methods to realise such correction, two commonly seen are the so called commutator correction, which to suppress error at small-r pseudo core region, choose to use the position operator and express it in terms of momentum operator plus a commutator term between r and nonlocal (pseudo) potential; another is to subtract the effect of pseudo wavefunction to momentum matrix elements and add back the matrix elements calculated by using (approximate)
    atomic true wavefunction Before this work, the commutator term correction has already been implemented into the computational code used in our group, the main methodology development of my thesis is to implement the second method into the same computer code, so that their results can be compared.
    Applications :

    Dielectric constant is an important physical quantity of semiconductor and opto-electronic industry nowadays, many new devices relay on tuning dielectric constants of its constituent materials in order to achieved the desired properties. Therefore the factors that will affect dielectric properties of a material become an important subject of research. In this work we have used first principles methods to study several chosen high k and low k materials, we have also developed new analysis scheme which allow us to visualised spatial distribution of dielectric contribution in real-space. We have chosen several SiO2 crystals, some commonly seen oxide crystals, and HfO2 which received broad attention recently. On the other hand, we are interested in how physical properties change under the influence of static electric field. Extremely large electric field is possible today, thanks to the development of nanotechnologies which reduce the dimension of devices and cause a regular potential step to generate very large electric field, it is therefore important to study such electric field induced variation of physical properties. In the last part of this work, not only did we calculate hyperpolarisability of molecule and compare with experimental results, but also we investigated how this quantity is changed under large external static electric field.
    显示于类别:[物理學系暨研究所] 學位論文

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