Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

Synergistic stabilization of CsPbI_(3) inorganic perovskite via 1D capping and secondary growth

Cesium lead iodide(CsPbI_(3)) perovskite has gained great attention in the photovoltaic(PV) community because of its unique optoelectronic properties, good chemical stability and appropriate bandgap for sunlight harvesting applications. However, compared to solar cells fabricated from organic-inorganic hybrid perovskites, the commercialization of devices based on all-inorganic CsPbI_(3) perovskites still faces many challenges regarding PV performance and long-term stability. In this work, we discovered that tetrabutylammonium bromide(TBABr) post-treatment to CsPbI_(3) perovskite films could achieve synergistic stabilization with both TBA+cation intercalation and Br-doping. Such TBA^(+) cation intercalation leads to onedimensional capping with TBAPb I3 perovskite formed in situ, while the Br-induced crystal secondary growth helps effectively passivate the defects of CsPbI_(3) perovskite, thus enhancing the stability. In addition, the incorporation of TBABr can improve energy-level alignment and reduce interfacial charge recombination loss for better device performance. Finally, the highly stable TBABr-treated CsPbI_(3)-based perovskite solar cells show reproducible photovoltaic performance with a champion efficiency up to 19.04%, while retaining 90% of the initial efficiency after 500 h storage without encapsulation.

功能型有机阳离子诱导实现CsPbI_(3)全无机钙钛矿三维至零维晶相转化与表面重构

铅卤钙钛矿太阳能电池兼具高效率和低成本的突出优势,近年来研究进展迅速、应用前景广阔,对于进一步推进光伏产业发展、实现碳中和目标具有重要意义.相比于有机无机杂化钙钛矿,CsPbI_(3)全无机钙钛矿具有更高的化学稳定性,但同时也面临着缺陷密度较高的挑战,制约了该组分电池器件效率的进一步提升.钙钛矿表面重构是一种降低缺陷密度的有效方法,但受限于全无机结构中铅碘八面体与铯离子之间较强的离子键作用,诱发无机钙钛矿表面二次生长的困难远高于杂化钙钛矿体系.本文通过选取辛基十二烷基二甲基铵这一特殊的季铵阳离子,成功实现了CsPbI_(3)钙钛矿薄膜的表面重构与三维至零维的原位晶相转化.在这种功能型季铵溴盐的诱导作用下,零维Cs_(4)bI_(6)在CsPbI_(3)薄膜的表面晶界处原位生成,有效钝化了缺陷,提高了结构稳定性.基于表面重构与缺陷钝化的无机钙钛矿太阳能电池获得了20.63%的高光电转换效率,实现了长期的高效稳定运行.

Solution chemistry quasi-epitaxial growth of atomic CaTiO_(3)perovskite layers to stabilize and passivate TiO_(2)photoelectrodes for efficient water splitting

Perovskite oxides with unique crystal structures and high defect tolerance are promising as atomic surface passivation layers for photoelectrodes for efficient and stable water splitting.However,controllably depositing and crystalizing perovskite-type metal oxides at the atomic level remains challenging,as they usually crystalize at higher temperatures than regular metal oxides.Here,we report a mild solution chemistry approach for the quasi-epitaxial growth of an atomic CaTiO_(3)perovskite layer on rutile TiO_(2)nanorod arrays.The high-temperature crystallization of CaTiO_(3)perovskite is overcome by a sequential hydrothermal conversion of the atomic amorphous TiOx layer to CaTiO_(3)perovskite.The atomic quasi-epitaxial CaTiO_(3)layer passivated TiO_(2)nanorod arrays exhibit more efficient interface charge transfer and high photoelectrochemical performance for water splitting.Such a mild solution-based approach for the quasi-epitaxial growth of atomic metal oxide perovskite layers could be a promising strategy for both fabricating atomic perovskite layers and improving their photoelectrochemical properties.

Organic salt mediated growth of phase pure and stable all-inorganic CsPbX3（X = I, Br） perovskites for efficient photovoltaics

All-inorganic CsPbX3(X = I, Br) perovskites without organic component are promising for long-term stability but face main challenges of facile fabrication and phase stability. Here we discover a general organic methylamine acetate salt mediated growth method to deposit high quality phase pure and stable CsPbX3(X = I, Br) perovskite films via a novel precursor consisting of stoichiometric cesium acetate(CsAc),methylamine halide(MAX) and lead halide(PbX2). Interestingly, these organic salts of CsAc and MAX could efficiently promote the crystallization process especially lower the crystallization temperature,but do not introduce the incorporation of organic MA cation into all-inorganic CsPbX3 perovskites.These phase pure and stable CsPbX3 perovskites with tunable band gaps can be fabricated into high efficiency photovoltaics. Our organic salt mediated growth of all-inorganic perovskite not only reveals the all-inorganic CsPbX3 perovskite’s unique crystal growth mechanism but also demonstrates their promising application for photovoltaics.

In situ growth of ultra-thin perovskitoid layer to stabilize and passivate MAPbI_(3)for efficient and stable photovoltaics

The efficiency and stability of typical three-dimensional(3D)MAPbI_(3)perovskite-based solar cells are highly restricted,due to the weak interaction between methylammonium(MA^(+))and[PbI 6]4-octahedra in the 3D structure,which can cause the ion migration and the related defects.Here,we found that the in situ-grown perovskitoid TEAPbI_(3)layer on 3D MAPbI_(3)can inhibit the MA^(+)migration in a polar solvent,thus enhancing the thermal and moisture stability of perovskite films.The crystal structure and orientation of TEAPbI_(3)are reported for the first time by single crystal and synchrotron radiation analysis.The ultra-thin perovskitoid layer can reduce the trap states and accelerate photo-carrier diffusion in perovskite solar cells,as confirmed by ultra-fast spectroscopy.The power conversion efficiency of TEAPbI_(3)-MAPbI_(3)based solar cells increases from 18.87%to 21.79%with enhanced stability.This work suggests that passivation and stabilization by in situ-grown perovskitoid can be a promising strategy for efficient and stable perovskite solar cells.

MA Cation-Induced Diffusional Growth of Low-Bandgap FA-Cs Perovskites Driven by Natural Gradient Annealing

Low-bandgap formamidinium-cesium(FA-Cs)perovskites of FA_(1-x)CsxPbI_(3)(x<0:1)are promising candidates for efficient and robust perovskite solar cells,but their black-phase crystallization is very sensitive to annealing temperature.Unfortunately,the low heat conductivity of the glass substrate builds up a temperature gradient within from bottom to top and makes the initial annealing temperature of the perovskite film lower than the black-phase crystallization point(~150℃).Herein,we take advantage of such temperature gradient for the diffusional growth of high-quality FA-Cs perovskites by introducing a thermally unstable MA^(+)cation,which would firstly formα-phase FA-MA-Cs mixed perovskites with low formation energy at the hot bottom of the perovskite films in the early annealing stage.The natural gradient annealing temperature and the thermally unstable MA^(+)cation then lead to the bottom-to-top diffusional growth of highly orientatedα-phase FA-Cs perovskite,which exhibits 10-fold of enhanced crystallinity and reduced trap density(~3:85×10^(15) cm^(−3)).Eventually,such FA-Cs perovskite films were fabricated into stable solar cell devices with champion efficiency up to 23.11%,among the highest efficiency of MA-free perovskite solar cells.