The rational development of organic electronic devices can greatly benefit from a molecular‐level description, where an accurate description of the Coulombic interactions among charge carriers holds paramount importance. However, the molecular‐level organic field‐effect transistor (OFET) simulations do not fully include the short‐range charge‐carrier Coulombic interactions, thus limiting their accuracy. Here, an efficient solution is demonstrated to the 3D Poisson's equation with mixed boundary conditions, optimized for integration into the simulations of organic electronic devices. It leverages the finite difference method for discretization, the Krylov subspace iterative methods for solving the linear system, the algebraic multigrid algorithm for preconditioning, and OpenMP and CUDA parallelization for acceleration. For the organic field‐effect transistors of micrometer sizes or smaller dimensions, obtaining the electric potential within the device takes less than 0.1 s, which is sufficiently efficient for molecular‐level modeling. As a result, both short‐ and long‐range electrostatic interactions are successfully incorporated in the molecular‐level modeling of OFET devices. This integration significantly enhances the robustness of OFET modeling for future applications.

中文翻译：

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通过具有混合边界条件的高效 3D 泊松方程求解器实现有机场效应晶体管中库仑相互作用的准确描述

有机电子器件的合理发展可以极大地受益于分子水平的描述，其中电荷载流子之间库仑相互作用的准确描述至关重要。然而，分子级有机场效应晶体管（OFET）模拟并未完全包含短程载流子库仑相互作用，从而限制了其准确性。在这里，演示了具有混合边界条件的 3D 泊松方程的有效解决方案，并针对集成到有机电子器件的模拟中进行了优化。它利用有限差分法进行离散化，利用 Krylov 子空间迭代法求解线性系统，利用代数多重网格算法进行预处理，并利用 OpenMP 和 CUDA 并行化进行加速。对于微米尺寸或更小尺寸的有机场效应晶体管，获得器件内的电势只需不到 0.1 秒，这对于分子级建模来说足够有效。因此，短程和长程静电相互作用都成功地纳入了 OFET 器件的分子级建模中。这种集成显着增强了 OFET 建模在未来应用中的稳健性。