本研究藉由研究矽奈米線，尋找提高其熱電優值方法，以取代目前熱電材料。目前熱電材料如鉍鍗化合物(Bi2Te3)轉換效率ZT可至約1.0；若以矽奈米線(Silicon nanowire, SiNW)取代，除了材料取得便利，與目前各種矽基電子技術也有理想相容介面，運用在商品上潛力無窮。
熱電材料其效能受到材料本身電子傳導率(electrical conductivity)、席貝克係數(Seebeck coefficient)及熱傳導係數(thermal conductivity)等傳輸性質影響；而這些性質會隨著材料的能帶結構(band structure)、能隙(band gap)以及態密度分布(density of state, DOS)等材料性質改變而影響。而以上描述之材料性質會隨著改變材料尺寸大小及成長截面方向的不同而有所改變。是故本研究第一階段以密度泛函理論(density functional theory, DFT)，建立矽奈米線原子團簇(Silicon cluster)，以改變長度、截面積大小及成長截面方向，其中主要探討矽在常壓下鑽石結構以及高壓(7.5~10.5GPa)下beta-phase結構的差異性，配合週期性邊界條件模擬計算矽奈米線之材料性質；另外以密度泛函微擾理論(density functional perturbation theory, DFPT)計算聲子頻散關係(phonon dispersion relation)、聲子態密度(phonon density of state)並後處理聲子群速度(group velocity)以及定容比熱(specific heat)與聲子供應之熱傳導係數。
第二部分研究以波茲曼傳輸方程式(Boltzmann transport equation)計算影響熱電材料轉換效率之電子傳導率、熱傳導係數、席貝克係數、熱電功率因子(power factor)以及熱電優值ZT (figure of merit)。本論文計算結果發現若以目前矽材料中擁有最好熱電轉換效率的[110]鑽石結構矽奈米線為比較基準，高壓beta-phase結構矽奈米線轉換效率最高可增加約5100倍，應用上將有極為龐大潛力。

The purpose of this research is to use a First Principles study in an effort to enhance the Figure of Merit of silicon nanowires. Nowadays, most of the constituents in thermoelectric materials are rare earth elements; however, those elements are usually too expensive for commercial applications. Silicon is the second most abundant element in the Earth’s crust that enables a relatively cost effective extraction and a sound availability, thus its low price. Moreover, silicon is an ideal material for compatibility with electronic technology. On the basis of the above, we focus on silicon nanowires and investigate its thermoelectric properties under different pressure conditions.
The efficiency of thermoelectric materials will mainly be affected by the electrical conductivity, Seebeck coefficient, and thermal conductivity, etc. All these parameters will be inevitably influenced by changing the basic material properties which include; the band structure, band gap, density of state, to name a few. Theoretically, these material properties will also vary with different sizes, orientations and crystal structures (e.g., diamond structure for 1 atm. and beta-phase for 7.5~10.5GPa). Therefore, silicon cluster models in these different conditions were built and their transport properties employing a Density Functional Theory (DFT) approach were evaluated. Additionally, these silicon cluster models will be approximated to real nanowires for the sake of periodic crystal structures using periodic boundary conditions. This research is also concerned on the thermodynamic properties including; the phonon dispersion relation and phonon density of states, as well as specific heat. All these calculations are determined on the basis of the Density Functional Perturbation Theory (DFPT).
Furthermore, using the Boltzmann transport equation will include a holistic sum of the previously calculated properties. As a result, key parameters concerning the figure of merit of thermoelectric materials of interest will be obtained. Finally, a comparison between the electric and thermal properties of both diamond and beta-phase Si NW structures will be conducted place in order to determine the structure with superior efficiency.

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