Design and implementation of semiconductor multi-physical parallel computing program JEMS-CDS-Device
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摘要: 针对复杂电磁环境下器件多物理效应机理研究需求，研发了半导体多物理效应并行计算程序JEMS-CDS-Device。介绍了JEMS-CDS-Device的架构设计与实现技术。程序基于非结构网格并行框架JAUMIN实现，采用有限体积法（FVM）离散，使用牛顿法全耦合求解“电-载流子输运-热”问题。程序采用“内核＋算法库”形式架构，支持2维和3维非结构网格、千万自由度问题并行求解，支持物理方程、离散算法、材料物理模型等的扩展开发。Abstract: Aiming at the research requirements of multi-physical effects mechanism of devices in complex electromagnetic environment, a parallel computing program for semiconductor multi-physics effects, JEMS-CDS-Device, is developed. This paper introduces the architecture design and implementation technology of JEMS-CDS-Device. The program is based on the unstructured grid parallel framework—JAUMIN. It uses the finite volume method (FVM) to discretize and uses the Newton method to get fully coupled solution of the “electric-carrier transport-thermal” problem. The program which adopts the “kernel ＋ algorithm library” form architecture, supports 2D/3D unstructured mesh, and can solve problems of tens of millions of degrees of freedom parallelly. It supports extended development of physical effect equations, discrete algorithms, material physics models, etc.
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图 4 异质界面处的间断与算法区域处理
Figure 4. Discontinuity heterogeneous interface and algorithm region processing (right figure, there are two logical nodes M1 and M2 in node A)
图 8 3维PN净掺杂密度分布与二极管阳极V-I曲线
Figure 8. PN diode ’s density distribution of net doping and anode V-I curve
图 9 2维NMOS管平衡态电势分布结果对比（电势单位：V，参考零点为无穷远）
Figure 9. 2D NMOS equilibrium potential distribution comparison（potential unit: V, the potential reference zero is at infinity）
图 10 2维PN管的净掺杂分布与载流子分布（正向偏压0.5 V）
Figure 10. Net doping and carrier distribution of 2D PN device (positive deviation 0.5 V)
图 11 输入的波形与某时刻PIN的温度分布
Figure 11. Input waveform and temperature distribution of PIN (at 7.78 ns)
表 1 DDM1非线性迭代中线性解法器典型收敛情况）
Table 1. Typical convergence of linear solver in DDM1 nonlinear iteration
linear solver precondition time （iterations）/s mesh refinement 0;
DOF: 11 165mesh refinement 1;
DOF: 43 925mesh refinement 2;
DOF: 174 245mesh refinement 3;
DOF: 694 085LU − 0.209 6 (1) 1.065 2 (1) 7.018 4 (1) 50.442 3 (1) BiCGSTAB Jacobi 0.131 8 (106) 0.868 3 (226) 7.119 6 (455) 68.205 1 (1 011) BiCGSTAB ASM 0.126 5 (106) 0.919 0 (226) 7.666 1 (455) 72.558 4 (1 011) BiCGSTAB ILU 0.127 6 (106) 0.840 7 (226) 7.020 5 (455) 69.624 0 (1 011) GMRES BJacobi 0.263 5 (448) 2.358 7 (940) 26.995 4 (2 548) 427.814 (9 450) GMRES ASM 0.291 4 (448) 2.466 6 (940) 27.758 8 (2 548) 462.929 (9 450) GMRES ILU 0.283 8 (448) 2.311 4 (940) 27.126 1 (2 548) 425.375 450) 
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表 2 弱扩展并行测试（Basic Newton，ASM＋BiCGSTAB）
Table 2. Weak extension parallel test (Basic Newton，ASM＋BiCGSTAB)
cores unknowns average iterations time/s efficiency/% 4 1.74×105 154 83.32 100 16 6.94×105 353 151.70 54.9 64 2.77×106 757 285.78 29.1 256 1.11×107 1727 531.19 15.7
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表 3 强扩展并行测试（Basic Newton，ASM＋BiCGSTAB，2.771×106未知量）
Table 3. Strongly extended parallel test (Basic Newton，ASM＋BiCGSTAB，2.771×106 Unknowns)
cores total time/s linear solver time/s speedup efficiency/% 32 470.31 228.44 1.00 100.0 64 284.78 113.67 1.65 82.6 128 157.90 59.20 2.98 74.5 256 99.56 32.31 4.72 59.1
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