Finite element analysis on global and local estimation for thermo-mechanical response of EPL wafer heating

In this paper, an approach is presented for the computation of the in-plane pattern placement error (PPE) caused by the wafer heating during exposure of electron projection lithography (EPL) using the finite element method (FEM), which is one of candidates in the next-generation lithography (NGL) exposure tools. The PPE is the global and local distortion, and is the thermo-mechanical response due to the thermal deformation of the wafer in the lithography process. The prediction of PPE requires high accuracy for NGL exposure tools. The simultaneous estimation of the global and local PPE to the whole wafer of a full three-dimensional FE model using a solid element requires excessive computation time. A novel technique of numerical simulation is developed and proposed, which is the employment of a shell element combined with previously proposed the dynamic meshing technique (DMT), being possible to predict PPE in realistic computation time with high accuracy. Simulations are performed for the wafer heating of EPL effectively using three techniques, that is the equivalent average heating technique and two proposed techniques. The simulation results agree closely with the result of a full three-dimensional FE analysis, and the required computation time becomes 1/16 or much less of that.