應用人工神經網路勢能場研究複雜鈣鈦礦材料微觀結構

Abstract

鈣鈦礦與鈦酸鈣(CaTiO3)的晶體結構相同，其特色為擁有一鹵素原子位於晶格之面心上，而一負離子位於立體晶格中心，陽離子則位於晶格立方體之頂點位置，鈣鈦礦是同時擁有無機元素以及有機離子的成分，在近年來短短的時間內發展迅速，光伏效應之轉換效率從3%增長到了20%以上，被視為跟能夠矽太陽能電池競爭的材料，因此在學術界、產業界為重點發掘項目。然而，鈣鈦礦太陽能電池性能的不斷提升也伴隨著材料本身的化學複雜度直線上升，現在的高性能鈣鈦礦太陽能電池已經混摻了多種有機/無機陽離子以及鹵素陰離子，使得微觀尺度的材料化學秩序(chemical order)對於鈣鈦礦的光電性能扮演了極為重要的角色。然而，由於量測技術的先天限制，這些重要的材料化學秩序幾乎無法由實驗中得到，因此實驗團隊在研究先進鈣鈦礦材料時往往深陷於重複試誤的無限迴圈中，不但造成資源的巨大浪費，也招致了 “the kitchen thing“的嘲諷。原子尺度模擬因為可以提供原子尺度的材料結構，表面上看似乎提供了解決方案，然而，由於鈣鈦礦材料的原子間作用力混合了共價、離子、凡德瓦乃至氫鍵，使得所有現有原子尺度模擬中僅有第一原理計算能滿足精確度的要求。由於第一原理計算的計算過於耗時且能處理的系統大小受到極大限制，以第一原理計算來研究複雜鈣鈦礦的微觀化學序基本上是一個無法達成的任務。本研究將使用人工神經網路，藉由大量小尺度的密度泛函計算訓練出擁有六種元素之鈣鈦礦神經網路勢能模型以及力場模型進一步以研究大系統鈣鈦礦結構性質。 使用訓練出來之神經網路模型可以進行約2,000顆原子系統之分子動力學模擬以及結構最佳化，由於神經網路模型的快速計算特性，我們可以利用窮舉方法進行離子的交換進行數以萬計的系統勢能計算以找出不同成分的鈣鈦礦之最穩定結構。本論文證實了神經網路可以快速並準確的描述擁有六種元素之鈣鈦礦結構能量，並且成功應用於研究複雜鈣鈦礦系統原子尺度化學秩序，從而提供鈣鈦礦材料結構與相應製程以及材料性質關聯的寶貴資訊，以協助實驗團隊能更快設計出更有效率的新穎鈣鈦礦材料。

Organic-inorganic halide perovskite materials are one of the promising materials for photovoltaic applications with conversion efficiencies advancing from merely 3% to over 20% in the recent years, making them a strong competitor against conventional silicon-based photovoltaic devices. Nevertheless, the soaring efficiencies of perovskite solar cells come with the increasing chemical complexities. Advanced perovskite materials today are comprised of a variety of mixed organic/inorganic cations as well as halogen ions, making microscale chemical ordering critical for material performance. However, the chemical ordering of complex perovskite materials is difficult to be extracted from current state-of-the-art characterization techniques. As a result, experimental teams often rely on the trial-and-error, and are often being nicknamed as “the kitchen thing”. On the other hand, atomistic simulations can provide atomistic scale insights into atomic arrangement of complex perovskite materials. Nonetheless, the first-principle calculations are by far the only accurate simulation method because of the complex interatomic interactions mixing covalent, ionic, van der Waals, and hydrogen bonding interactions in perovskite materials. Because the first-principle calculations are computationally intensive, it is literally impossible to explore the chemical ordering of complex perovskite materials using the first-principle calculations. In this study, we trained an artificial neural network (ANN) potential model of complex perovskite materials based on a large number of small-scale training images labelled with energies/atomic forces from density functional theory (DFT) calculations. The trained ANN model allows us to exhaustively sample tens of thousands of chemical configurations of complex perovskite materials using Monte Carlo simulations to isolate stable configurations and respective chemical orders. The present study demonstrates that ANN potential models can accurately describe atomic interactions in the complex perovskite materials, thereby providing valuable insights into microscale chemical ordering of complex perovskite materials to help experimental teams design novel perovskite materials with efficacy.