Driven by Moore's Law, the dimensions of transistors have been pushed down to the nanometer scale. Advanced quantum transport (QT) solvers are required to accurately simulate such nano-devices. The non-equilibrium Green's function (NEGF) formalism lends itself optimally to these tasks, but it is computationally very intensive, involving the selected inversion (SI) of matrices and the selected solution of quadratic matrix (SQ) equations. Existing algorithms to tackle these numerical problems are ideally suited to GPU acceleration, e.g., the so-called recursive Green's function (RGF) technique, but they are typically sequential, require block-tridiagonal (BT) matrices as inputs, and their implementation has been so far restricted to shared memory parallelism, thus limiting the achievable device sizes. To address these shortcomings, we introduce distributed methods that build on RGF and enable parallel selected inversion and selected solution of the quadratic matrix equation. We further extend them to handle BT matrices with arrowhead, which allows for the investigation of multi-terminal transistor structures. We evaluate the performance of our approach on a real dataset from the QT simulation of a nano-ribbon transistor and compare it with the sparse direct package PARDISO. When scaling to 16 GPUs, our fused SI and SQ solver is 5.2x faster than the SI module of PARDISO applied to a device 16x shorter. These results highlight the potential of our method to accelerate NEGF-based nano-device simulations.

翻译：受摩尔定律驱动，晶体管的尺寸已缩小至纳米尺度。精确模拟此类纳米器件需要先进的量子输运（QT）求解器。非平衡格林函数（NEGF）形式体系非常适合这些任务，但其计算量极大，涉及矩阵的选择性求逆（SI）和二次矩阵方程的选择性求解（SQ）。解决这些数值问题的现有算法（例如所谓的递归格林函数（RGF）技术）非常适合GPU加速，但它们通常是顺序执行的，需要块三对角（BT）矩阵作为输入，并且迄今为止其实现仅限于共享内存并行，从而限制了可实现的器件尺寸。为了解决这些不足，我们引入了基于RGF的分布式方法，实现了并行选择性求逆和二次矩阵方程的选择性求解。我们进一步将其扩展以处理具有箭头结构的BT矩阵，从而能够研究多端晶体管结构。我们在纳米带晶体管QT模拟的真实数据集上评估了所提方法的性能，并与稀疏直接求解包PARDISO进行了比较。当扩展到16个GPU时，我们的融合SI和SQ求解器比应用于缩短16倍的器件的PARDISO的SI模块快5.2倍。这些结果凸显了我们的方法在加速基于NEGF的纳米器件模拟方面的潜力。