近年來，鈣鈦礦相關的研究蓬勃發展，無論是實驗的精確度或是理論計算的高度預測都使這類充滿吸引力的材料的性質更加被理解。在組成元素多元的複雜材料中，各種前所未見的物理機制正一步一步被科學解密，這不僅僅只是為了滿足學術的好奇心，也是次世代材料科學中必要的一環。

以熱門的綠能產業為例，第一代太陽能電池如矽晶電池雖能達到22.5%的轉換效率，但仍受限於地域日照與材料的物理性質。為提高轉換效率，學術界不斷尋找能更好的材料與技術，以突破矽晶電池的物理極限。第二代太陽能電池如銅銦硒(CIS)薄膜電池，將來有望大幅降低生產成本與提高穩定性，可見光吸收能力更是矽晶電池望塵莫及。而第三代便是鈣鈦礦電池，轉換效率已達25%，與矽晶電池相比，在弱光環境下仍保有良好的發電能力，而且可在大氣環境下生產。除此之外，鈣鈦礦電池的吸收波段不與矽晶電池競爭，因此可結合使用，還可製成透光建材，保有室內光照的同時進行發電。鈣鈦礦太陽能電池的另一個優點是以可撓材料作為基板，與不可撓的多矽晶基板相比有更多的安裝彈性。然而現階段鈣鈦礦電池的穩定性仍不及矽晶電池，以使用年限為例，僅有矽晶電池30年壽命的三分之一，未來研究的一大重點將會是如何提高材料的穩定性。

撇去轉換效率與泛用性，研發矽晶電池以外的太陽能電池仍有相當的必要性，矽晶電池生產過程中產生之強鹼廢液的後續處理以及目前超過70%的矽金屬來自中國。目前台灣位於鈣鈦礦太陽能電池研究與發展的第一線，在環保與能源議題不斷升溫的現代，持續發展高效綠能材料的重要性不言而喻，然而尋找新材料的過程耗工費時，若如無頭蒼蠅般盲目猜測，往往徒勞無功。隨著電腦算力的發展，計算物理成為理論物理與實驗物理之間的橋樑，在既有的實驗基礎上建立可靠的理論模型，又以數值方法驗證理論並提供實驗發展的方向。

能帶理論成功預測許多材料之物理性質，但凡事總有例外。YTiO_3(YTO)}在傳統能帶理論上應具有導體特性，但實驗卻顯示為絕緣體，具有此種特性之材料被稱作Mutt insulator，被認為是電子之間的強交互作用所致。對於YTO之研究已臻極致，但從YTO出發之各種材料仍有許多探討空間，如以La元素取代Y元素之Y_1-xLa_xTiO_3(YLTO)隨著取代率x上升，其基態從鐵磁相變為反鐵磁相之變化已被發現，而以Ca元素作為取代之Y_1-xCa_xTiO_3(YCTO)亦具有鐵磁相變為順磁相以及絕緣體變為導體之相變。

本研究以第一原理計算方法針對YCTO在x= 0.25, 0.5, 0.75等不同取代率下能保持穩定之不同磁相進行討論，並試圖解釋實驗中發生之相變發生之原因，以及預測在取代率高於0.5之情況下，是否能找出從導體變回絕緣體之相變可能範圍。

Recently, researches relating to Perovskite develop and flourish with highly realized properties of such material by precisely prediction of theoretical calculation and precision of experiment. Unprecedented physical mechanisms are revealing step by step for complex compound with various composition, not only to fulfill curiosity to science but also an necessary part for next generation material science development.

Taking popular renewable energy industry as example, the first generation solar cells, made of crystalline silicon, reach an efficiency of 22.5% but still confined by local sunshine duration and physical properties of material. Acedemia keeps looking for better material and technology to improve efficiency and to break physical limits of silicon cell. The second generation solar cells, thin-film solar cells, copper indium diselenide(CIS) cells for example, would reduce production costs and increase stability. Also, the absorption ability of visible light is 100 times of silicon cells. The third generation solar cells as known as perovskite solar cells have efficiency reach 25%. Compare with silicon cells, it remains good efficiency in a low light environment and can be produced in atmospheric environment. Furthermore, perovskite cells does not scramble absorption wave band with silicon cells such that these two can be used together. Also, perovskite cells can be used in light-transmitting material that can keep indoor light while generating electricity. Another advantage is perovskite cells can use flexible material as substrate that have more flexibility than silicon cells which use glass as substrate. However, stability of perovskite cells is still less than silicon cells. From a practicality point of view, service life of perovskite cells is one third of silicon cells. Therefore, the following research should focus on increasing material stability.

Efficiency and multiusability aside, research and development of non-silicon cells is still necessary. One reason is the treatment of waste liquid contains strong base produced during manufacturing of silicon cells. Another reason is that more than 70% of silicon supplied by China. At this point, Taiwan plays a role of bellwether in the region of research and development of perovskite solar cells. There is no doubt to continuously study green materials in such a age that eco and energy issues simmer. However, there are always protracted processes of looking for new material. If researchers tried baselessly, they usually cost a lot but in vain. As the computing power increasing, computation physics become the bridge connects theoretical physics and experimental physics. Theoretical models built on exact experiment evidence provide following direction to experiment while verifying theories.

Band theory successfully predict physical properties for many materials, but there are always an exception. YTiO_3(YTO)} is expected to conduct electricity by conventional band theory but turn out to be insulator according to experimental result. Materials with such property are called Mutt insulator, and strong electron-electron interaction is supposed to be the reason. For YTO, researches perfects but there is still lots of unknown to compound ideas started from YTO like Y_1-xLa_xTiO_3(YLTO)} which change ground state from Ferromagnetism to Antiferromagnetism while replacement rate x rise up. Another case is Y_1-xCa_xTiO_3(YCTO) which has a transition from ferromagnetism to paramagnetism and from insulator to metal.

This research is focus on different magnetic phase of YCTO under replacement rate x= 0.25, 0.5, 0.75 by First principle calculation and try to explain the reasons to phase transition happened in experiments. And we will try to make a prediction to figure out at which range will YCTO transit from metal to insulator at high replacement rate(x>0.5).

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