Moving Mesh Method for Semiconductor Device Simulations

We propose a moving mesh method based on the harmonic mapping to numerically simulate the fundamental equations of two-dimensional semiconductors. The objective is to redistribute the mesh to the regions exhibiting large and sharp gradients in the numerical solution, thus achieving finer meshes in these areas. This approach leads to a reduction in the total number of meshes compared to traditional uniform meshes. In the case of multiple PN junctions, we divide the computational domain appropriately to ensure that each subdomain contains at most one PN junction. Furthermore, independent monitor functions can be employed in different subdomains. Numerical experiments demonstrate the efficacy of this method in automatically adjusting the mesh placement based on the gradient of physical quantities. Notably, this approach enables local refinement without altering the number of meshes.