A phenomenological model for pion photoproduction is constructed incorporating the dynamics of pions, nucleons, and 6 s. The importance of nonresonant background interactions for the elastic m. N scattering and pion photoproduction is emphasized. The photoproduction amplitudes calculated in our model satisfy two-body unitarity, so that the requirement imposed by Watson s theorem is automatically fulfilled. By fitting the amplitudes to data, M1 and E2 yN -+6 transition amplitudes are estimated, eliminating background contributions. The results are 2~~2(M 1)=( -84+5) )& 10 GeV ' and E2/M 1=(3.7+0.4) %. Our M1 amplitude disentangled from the mN rescattering term is in good agreement with the quark model predictions. The sign and magnitude of our E2 amplitude are, however, incompatible with the existing quark models.
A new, rigorous model for solving three-dimensional light-scattering problems in the optical lithography process of semiconductor manufacturing is introduced. The new model employs a hybrid approach to solve Maxwell's equations in the spatial frequency domain with the use of vector potentials. The model extends a successful two-dimensional lithography model and has been applied to the simulation of the patterning of light by three-dimensional (3-D) photomasks. The theory behind the new model is presented, and examples are given of the model's results and computational efficiency on an engineering workstation. The efficiency is highest for fully symmetric structures where the paraxial partial-coherence approximation is valid. The model can easily be extended to the efficient simulation of light scattering in 3-D optical alignment and photosensitive polymer problems.
Background: Thin mask model has been conventionally used in optical lithography simulation. In extreme ultraviolet (EUV) lithography thin mask model is not valid because the absorber thickness is comparable to the mask pattern size. Rigorous electromagnetic (EM) simulations have been used to calculate the thick mask amplitudes. However, these simulations are highly time consuming.Aim: Proposing a prototype of a convolutional neural network (CNN) which reduces the calculation time of rigorous EM simulations in a small mask area with specific mask patterns.Approach: We construct a CNN which reproduces the results of the EM simulation. We define mask 3D amplitude as the difference between the thick mask amplitude and the thin mask amplitude. The mask 3D amplitude of each diffraction order is approximated using three parameters which represent the on-axis and the off-axis mask 3D effects. The mask 3D parameters of all diffraction orders are trained by a CNN.
Results:The input and the targets of the CNN are a cut-mask pattern and mask 3D parameters calculated by the EM simulation, respectively. After the training with 199,900 random cut-mask patterns, the CNN successfully predicts the mask 3D parameters of new cut-mask patterns.Conclusions: We construct a CNN which predicts the diffraction amplitudes from 2D EUV mask patterns. After the training, the CNN successfully reproduces the mask 3D amplitude. CNN prediction is 5000 times faster than the rigorous EM simulation. Next challenge is to construct a practical CNN which covers a large area with general mask patterns.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.