利用SNAP勢能和蒙地卡羅模擬二維R-P鈣鈦礦形貌與其對元件性能可能的影響

Morphology and possible effects on device performance of 2D R-P perovskites by using SNAP potential and Monte Carlo simulations

楊譯賢(Yi-Xian Yang)

指導教授 ： 張建成

國立臺灣大學/工學院/應用力學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202203004

摘要

近年來，二維R-P鈣鈦礦材料是光電和光伏應用領域中具有前途的替代品，無機層與有機層的交互擺列構成了量子阱，賦予了更多樣化的化學性質。而有機陽離子的引入有效地將無機八面體的離子晶格與周圍的水分子隔離開來，使得它在環境條件下相對於三維對應物，具有更出色的穩定性而引起了廣泛的研究。而二維R-P材料之激子結合能和帶隙與陰離子無機層的層數直接相關，其值皆會隨著鈣鈦礦層數的增加而減少。
二維R-P鈣鈦礦的化學式為(R-NH3)2A(n-1)BnX3n+1，近期實驗表明，對於選定的正丁基銨(n-Butylammonium,BA)與苯乙胺(Phenethylamine,PEA)與陽離子比率，合成物的鈣鈦礦層數分佈並不均勻，若將此材料應用於太陽能電池上，其分佈對於提高元件的效率來說至關重要，而不同的有機陽離子也會對鈣鈦礦造成不一樣的影響，於是吾人嘗試利用多尺度原子模擬來探討不同有機陽離子之層與層之間的分佈關係。
對於多尺度原子模擬而言，以量子力學為理論基礎的第一原理計算(Ab initio calculation)雖然可以算出最準確的原子間受力，但缺點是是需要耗費大量的時間以及計算資源，且計算的範圍僅限於幾百顆原子內。古典分子動力學可以考慮大範圍原子尺度的系統，能夠處理第一原理較難解決的問題，但需要一組能充分描述材料特性的勢能函數。於是本研究利用第一原理先獲得一些二維R-P鈣鈦礦以PEA及BA為有機陽離子的訓練資料，再搭配機器學習擬合出能夠精確描述大範圍系統的Spectral Neighbor Analysis Potential(SNAP)勢能函數，並用於進行分子動力學模擬。
之後將完成訓練的勢能函數與訓練集和驗證集進行比較，在能量與原子受力方面都與第一原理的計算結果相符，並且可以在正則系綜下的分子動力學模擬過程中穩定運作，這代表訓練出來的SNAP勢能函數與第一原理相比，除了擁有較高的計算效率，還可以準確的預估更高層數鈣鈦礦結構的化學環境及進行結構最佳化。最後利用Metropolis蒙地卡羅結合分子動力學進行大規模的層交換模擬，並在不同的溫度及初始結構下，分析PEA與BA為間隔物之鈣鈦礦層分佈及其對二維R-P鈣鈦礦光電效率的影響。

關鍵字

二維R-P鈣鈦礦 ； SNAP勢能 ； 第一原理 ； 機器學習 ； 密度泛函理論 ； Metropolis蒙地卡羅 ； 分子動力學

並列摘要

In recent years, 2D R-P perovskite materials are promising alternatives in optoelectronic and photovoltaic applications, where the alternating arrangement of inorganic and organic layers constitutes a quantum well structures, endowed with more diverse chemical properties. The introduction of organic cations effectively isolates the ionic lattice of the inorganic octahedron from the surrounding water molecules, making it more stable than 3D perovskites under ambient conditions, which has attracted extensive research. Besides, the binding energy and band gap of R-P perovskite materials are directly associate to the number of anionic inorganic perovskite layers, and their values both decrease with the increase of the number of perovskite layers.
The 2D R-P perovskite has the chemical formula (R-NH3)2A(n-1)BnX3n+1, and recent experiments have shown that for a selected ratio of phenethylamine (PEA) to n-butylammonium (BA) cations, the synthetic distribution of perovskite layers is not uniform. If this material is applied to solar cells, its distribution is decisive for increasing the efficiency of the element, and different organic cations will also have different effects on perovskite,so we try to use multi-scale atomic simulation to explore the distribution relationship between layers of different organic cations.
For multi-scale atomic simulation, although Ab initio calculation based on quantum mechanics can calculate the most accurate interatomic force, the fly in the ointment is that it can be time-consuming and computing resources, and calculations are limited to a few hundred atoms. Classical molecular dynamics can consider a wide range of atomic-scale systems and can deal with problems that are difficult to solve in Ab initio calculation, but requires a set of potential energy functions that can fully describe the properties of materials. Therefore, in our research uses the Ab initio calculation to obtain some training data of 2D R-P perovskite with PEA and BA as organic cations, and then uses machine learning to fit the Spectral Neighbor Analysis Potential (SNAP) potential energy function that can accurately describe the large-scale system, and used to perform molecular dynamics simulations.
The trained potential energy function is then compared with the validation set and training set, which are identical to ab initio calculations in terms of energies and atomic forces, and can operate stably during the molecular dynamics simulation process under the canonical ensemble, This means that compared with the Ab initio, the trained SNAP potential energy function not only has higher computational efficiency, but also can accurately predict the chemical environment and optimize the structure of higher-layer perovskite structures. Finally, Finally, a large-scale layer exchange simulation was performed using Metropolis Monte Carlo combined with molecular dynamics, and at different temperatures and initial structures, the distribution of perovskite layers with PEA and BA as spacers and their effect on the photoelectric efficiency of 2D R-P perovskites were analyzed.

並列關鍵字

2D R-P perovskites ； SNAP potential ； Ab initio calculation ； Machine learning ； Density functional theory ； Metropolis Monte Carlo ； Molecular dynamics

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