Computational analysis and diagonal preconditioning for the discrete dipole approximation on surface

The construction of a matrix for the discrete dipole approximation (DDA) on surface and its relationship to an iterative solver is analyzed. It is shown that the spectral characteristics of the DDA for free space and surface correlates to different convergence characteristics. Compared with the free space DDA, when a surface is introduced, both the dipole polarizability matrix and the reflection–interaction matrix contributes to the diagonal/off-diagonal element, and solvability of the iterative method is related to several physical parameters such as incident angle, polarization, and refractive indices. Finally, we propose a diagonal preconditioning technique and show the effectiveness of the preconditioned to a semiconductor pattern with isolated contaminant which is assumed to be PSL, Si₃N₄, and Si. The result shows that when there is difference in the refractive index, the diagonal preconditioning reduces the total computation time up to 27% for low refractive index cases. However the result shows limitation for the higher refractive index cases.